Short Cut Methods for solving the questions of Percentages

When any value increases by

10%, it becomes 1.1 times of itself. (since 100+10 = 110% = 1.1)

20%, it becomes 1.2 times of itself.

36%, it becomes 1.36 times of itself.

4%, it becomes 1.04 times of itself.

Thus we can see the effects on the values due to various percentage increases.

When any value decreases by

10%, it becomes 0.9 times of itself. (Since 100-10 = 90% = 0.9)

20%, it becomes 0.8 times of itself

36%, it becomes 0.64 times of itself

4%, it becomes 0.96 times of itself.

Thus we can see the effects on a value due to various percentage decreases.

1. When a value is multiplied by a decimal more than 1 it will be increased and when multiplied by less than 1 it will be decreased.

2. The percentage increase or decrease depends on the decimal multiplied.

PUZZLE TEST SHORT CUT METHODS IN REASONING ABILITY

i) Five friends , P, Q, R, S AND T travelled to five different cities of Chennai, Kolkata, Delhi, Banglore and Hyderabad by different modes of transport of Bus, Train , Aeroplane , Car and Boat from Mumbai.

ii) The person who travelled to Delhi did not travel by boat.

iii) R went to Bangalore by car and Q went to Kolkata by aeroplane

iv) S travelled by boat whereas T travelled by train .

v) Mumbai is not connected by bus to Delhi and Chennai.

1. Which of the following combinations of person and mode is not correct?

a. P- Bus b. Q-Aero plane c.R- Car d. S- Boat e. T- Aero plane.

2. Which of the following combinations is true for S?

a. Delhi-Bus b. Chennai-Bus c.Chennai- Boat

d. Data inadequate e. None of these

3. Which of the following combinations of place and mode is not correct?

a. Delhi-Bus b.Kolkata- Aero plane c.Bangalore- Car

d.Chennai-boat e. hyderabad- bus

4. The person traveling to delhi went by which of the following modes?

a. bus b. train c. aero plane d. car e. boat

5. Who among the following traveled to delhi

a. R b. S c. T d. data inadequate e. none of these.

Soln. the given information can be analysed as follows:

a) mode of transport : RTravels by car, Q by aeroplane , S by boat and T by train . Now , only P remains . S o, P travels by Bus.

b) place of travel: R goes to bangalore , Q to kolkata. N ow , bus transport is not available for delhi or chennai. so , p who travels by bus goes to hyderabad. S travels by boat and hence by (ii) , did not go to delhi. So, S goes to chennai. Now, only T remains. So, T goes to delhi

Person

P

Q

R

S

T

Place

Hyderabad

Kolkata

Bangalore

Chennai

Delhi

Mode

Bus

Aero plane

Car

Boat

Train

1. clearly , the incorrect combination is T-aeroplane . So , the answer is (e)

2. clearly, the correct combination for S is chennai- boat. So, the answer is (c).

3. clearly , the incorrect combination is delhi-bus. So the answer is (a).

4. clearly, T travel to delhi by train . So the answer is (b).

5. clearly , T travel to delhi. So , the answer is (c).

Ex.2-

i) B and E are good in dramatics and computer science

ii) A and B are good in computer science and physics.

iii) A, D and C are good in physics and mathematics .

iv) C and A are good in physics and mathematics .

v) D and E are good in history and dramatics.

1. Who is good in physics , history and dramatics ?

a. A b. B c. D d. E

2. Who is good in physics, history and mathematics but not in computer science ?

a. A b. B c. C d. D

3. Who is good in computer science , history and dramatics?

a. A b. B c. C d. E

4. Who is good in history , physics , and computer science and mathematics?

a. A b. B c. C d. D

5. Who is good in physics , dramatics and computer science ?

a. A b. B c. D d. E

Soln. The given information can be analysed as under :

dramatics

com. sc.

Phy

His

Math

A

X

√

√

√

√

B

√

√

√

X

X

C

X

X

√

√

√

D

√

X

√

√

X

E

√

√

X

√

X

1. D is good in physics , history and dramatics . so the answer is ( c).

2. Both A and C are good in physics , History and mathematics . But A is good in computer science , while C is not . So , the answer is (c).

3. E is good in computer science , history and dramatics. Hence , the answer is (d).

4. A is good in history , physics , computer science and mathematics . Hence , the answer is (a).

5. B is good in physics, dramatics and computer science. Hence , the answer is (b).

Ex.-3

Study the following information carefully to answer the given question .

Madan and Rohit are in same team of hockey . Parth defeated Rohit in badminton but lost to sachin in tennis . nitin teams with sagar in football . and with sachin in hockey . rohit defeated sachin in chess. Those who play cricket donot play badminton , volleyball or tennis . madan and parth are in opposite team of basketball. nitin represent his state in cricket while sagar does so at the district level. Boys who play chess donot play football , basketball or volleyball. Madan and parth are together in volleyball team . Boys who play football also play hockey.

1. Name the boy who donot play football ?

a. Sachin , Nitin b. Rohit , Sagar c. Rohit , Sachin d. Rohit , Nitin

2. Who play both hockey and tennis?

a. Sachin b. Rohit c. Nitin d. Parth

3. Which is the most popular game with this group?

a. cricket b. hockey c. football d. badminton

4. Who play the largest number of games ?

a. Sagar b. Rohit c. Parth d. Nitin

5. Which boy play both badminton and hockey?

a. Sachin b. Rohit c. Nitin d. Parth

Soln.

Madan

Rohit

Parth

Sachin

Nitin

Sagar

Hockey

√

√

√

√

√

Badminton

√

√

X

X

Tennis

√

√

X

X

Chess

√

√

Football

X

X

√

√

Basketball

√

X

√

X

Volleyball

√

X

√

X

X

X

Cricket

√

√

1. (c) Rohit and Sachin donot play football

2. (a) Sachin play both hockey and tennis .

3. (b) Since hockey is played by the maximum nos. of student in the group so, hockey is the most popular game.

4. (c) Parth , play the largest nos. of game i.e. four.

5. (b) Rohit play both badminton and hockey

EX.

Study the following information carefully to answer the given question

1. A, B, C, D, E ,F and G are sitting around a circle and are facing the centre.

2. G is second to the left of C, who is to the immediate left of F.

3. A is third to the left of E.

4. B is between D and E.

i)which of the following is false ?

a. A is the fourth to the right of E. b. G is to the immediate right of D . c. F is the third to the right of D . d. B is the immediate left of D . e. None of these

ii) Which of the following is true?

a. C is fourth to left of B . b. A is to the immediate right of G. c. D is second to the left of E. d. B is second to the right of G.

e. None of these

iii) Which of the following pair has the first person sitting to the immediate left of the second person?

a. BE b. CA c . GD d. DG e. None of these

iv) Which of the following is the positions of F?

a. Fourth to the right of D. b. To the immediate left of C. c. Between A and C. d. To the immediate right of A e. None of these.

Solutions.

We first of all marki the seven balank polsitions around a circle . Now , G is second to the left of C and C is to the immediate left of F . We mark their positons as shown . also , B is between D and E. tHUS , D , B, E sit together and occupy the three consecutive blank positions . Now , only one position remains blank betwen G and C, and this must be occupied by A. now , D, B, E may sit in any of the postions ( D,B,E) or ( E,B,D). But A is third to the left of E only when they sit in the order ( D, B, E). Thus we mark their postions as shown.

1. Clearly , F is fourth to the right of D . So , (c) is false . hence , the answer is (c)

2. C is third to the left of B. So, (a) is false

A is to the immediate right of G. So , (b) is true.

D is second to the right of E. So, (c) is false .

B is second to the left of G. So, ( d) is false .

Hence , the answer is (b)

3. Clearly , only in the pair DG , the first person D sits to the immediate left to the second person G . Hence the answer is (d).

4. C sits between A and F ; F sits between E and C ;E sits between B and F: D sits between G and B. So, none of the given groups satisfies the given condition.

5. Clearly, F's postion is . fourth to the right of D.

. to the immediate right of C.

. between C and E

.Second to the right of A.

Hence, the answer is (a).

Number, Ranking and Time Sequence SHORT CUT METHODS FOR REASONING

type1- Number test :- In this type of questions, generally a set , group or series of numerals is given and the candidate is asked to trace out numerals following certain given conditions or lying at specific mentioned positions after shuffling according to a certain given pattern.

1. How many 5s are there in the following number sequence, which are immediately preceded by 7 and immediately followed by 6?

7 5 5 9 4 5 7 6 4 5 9 8 7 5 6 7 6 4 3 2 5 6 7 8

a. One b. two c. three d. four

2. How many 6's are there in the following number series , each of which is immediately preceded by 1 or 5 and immediately followed by 3 or 9?

2 6 3 7 5 6 4 2 9 6 1 3 4 1 6 3 9 1 5 6 9 2 3 1 6 5 4 3 2 1 9 6 7 1 6 3

a. none b. one c.two d.three e.none of these

3. How many 7's immediately preceded by 6 but not immediately followed by 4 are there in the following series ?

7 4 2 7 6 4 3 6 7 5 3 5 7 8 4 3 7 6 7 2 4 0 6 7 4 3

a.one b. two c.four d.six

4. In the series given below , count the number of 9's , each of which is not immediately preceded by 5 but is immediately followed by either 2 or 3. How many such 9's are there ?

1 9 3 2 1 7 4 2 6 9 7 4 6 1 3 2 8 7 4 1 3 8 3 2 5 6 7 4 3 9 5 8 2 0 1 8 7 4 6 3

a. one b. three c. five d. six

5. How many 4's are there preceded by 7 but not followed by 3?

5 9 3 2 1 7 4 2 6 9 7 4 6 1 3 2 8 7 4 1 3 8 3 2 5 6 7 4 3 9 5 8 2 0 1 8 7 4 6 3

a. three b. four c. five d.six.

soln. 1(a ) , 2(d ) , 3 ( b ) , 4 ( b ) , 5 ( b )

TYPE- RANKING TEST

EX.1 Rohan ranks 7th from the top and 26th from the bottom in the class. How many students are there in the class?

a.31 b.32 c.33 b.34

Soln. Clearly , the whole class consist of

i) 6 students who have ranked higher than Rohan

ii) Rohan, and

iii) 25 students who have ranks lower than Rohan i.e. 6+1+25 = 32 students

EX.2 Manik is 14 th from the right end in the row of 40 students . What is his position from the left end ?

i) 24 ii) 25 iii)26 iv)27

Soln. Clearly, The number of students towards the left of the Manik = 40-14= 26

so Manik is coming 27th from the left end . Hence the answer is (d)

EX.3 In a row of boys facing the north , A is 16th from the left end and C is 16 th from the right end . B , who is 4th to the right of A , is 5th to the left of C, in a row. How many boys are there in a row?

a. 39 b. 40 c.41 d. 42 e. 43

Soln. Clearly , according to given conditions , there are 15 boys to the left of A , as well as to the right of C . Also , B lies between A and C such that there are three boys between A and B, and 4 boys between B and C.

N

A B C

15 3 4 15

so, number of boys in a row = ( 15+1+3+1+4+1+15)= 40. Hence our answer is (b).

Data sufficiency SHORT CUTS FOR REASONING ABILIT

Direction: Each of the questions below consist of a question and statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question.

a. If the data in statement I alone are sufficient to answer the question, while the data in

Statement II alone are not sufficient to answer the question

b. If the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question

c. If the data either in statement I alone or in statement II alone are sufficient to answer the question.

d. If the data both in statement I and statement II together are not sufficient to answer the question.

e. If the data both in statement I and statement II together are necessary to answer the question.

1. What is the colour of the fresh grass?

i) Blue is called green , red is called orange, orange is called yellow.

ii) Yellow is called white , white is called black, green is called brown and brown is called purple .

2. What does nip stands for in a code language ?

i) In the code language ,that is very beautiful is written as , " nip sto sre tip "

ii) In the same code language , " my house is beautiful is written as " nip sto sre tip .

3. In a certain code , nop al ed means they like flower . Which code word means flowers?

i) Id nim nop means they are innocent .

ii) gob ots al means we like roses .

4. What is the code for sky in the code language ?

i) In the code language , sky is clear is written as de ga jo

ii) In the same code language , make is clear is written as de ra fa.

5. How J related to p?

i) M is the brother of P and T is the sister of P.

ii) P's mother is married to J's husband, who has one son and two daughter .

6 .How is T related to K?

I) R's sister J has married T's brother L, who is the only son of his parent.

ii) K is the only daughter of L and J.

7.B is the brother of A . How is A related to B?

iii) A is the sister of C.

iv) E is the husband of A .

8. How is M related to N ?

I) P, who has only two kids , M and N is the mother -in-law of Q , who is sister -in-law of N.

II) R, the sister-in-law of M, is the daughter -in -law of S, who has only two kids , M and N.

9. P, Q, R,and S are sitting around a circle facing at the center. Who is to the immediate right of Q?

i) R is between P and S

ii) S is to the immediate right of R.

10. What is Sumit's position from the right in a row of children?

i) There are ten children between sumit and ranjan

ii) Ranjan is the twentieth from the left end of the row of the children

11. What is the Nitin's rank from the top in a class of 40 students?

i) There are ten student between Nitin and Deepak

ii) Deepak is the twentieth from the top

12. On which date of the month was Anjali born in february , 2004 ?

i) Anjali was born on an even date of the month.

ii) Anjali's birthdate was a prime number.

13. Which train did Aman catch to go to office?

i) Aman missed his usual train of 10:25 a.m..A train comes in every five minutes .

ii) Aman did not catch the train 10:40 a.m, train or any train after that time

Soln .

1. (b). The colour of fresh grass is green and as given in II , green is called brown . So the color of fresh grass is brown

2. (d). In I and II , the common codes are nip and sre and the common words are is and beautiful . So nip and sre are the codes for is and beautiful . But the exact word for nip; cannot be found out

3. (e). In the given statement, and I , the common word is they and the common code word is nop . So , nop is the code for They . In the given statement and II , the common word is like and the common code word is al . So , al is the code for like . Thus , in the given statement, ed is the code for flowers.

4. (d). The only word common to I and II is clear and as such , only the code for clear can be ascertained from the given information .

5. (b). From II, we know that P's mother is married to J's husband , which means that J is P's mother .

6. (e). From I, we know that L is T's brother and J's husband . Since L is the only son of his parents , T is L's sister .

From II, we know that K is L's daughter .

Thus , from I and II, we conclude that T is the sister of K's father i.e.T is K's aunt.

7.(c) . B is A's brother means A is either brother or sister of

B. Now , each one of I and II individually indicates

that A is female , which means that A is B's sister .

8.(a). From I, we conclude that P is the mother of M and N , while Q is the daughter -in-law of P and sister -in-law of N. Thus , Q is M's wife and hence , M is N's brother . From II, we conclude that M and N are the children of S. Also, R is the daughter -in-las of S . Hence , M is either brother or sister of N.

Answer is (d).. Clearly, neither the number of children in the row is given nor the position of Sumit relative to Ranjan is mentioned in any one of I or II.

11. Answer is (d). Since there are ten students between Nitin and Deepak , so Nitin may be eleven ranks above or below Deepak . Thus Nitin may be 9th, or 31st from the top.

12. Answer is (e). From I and II , We conclude that Anjali was born in February, 2004 on a date which is an even prime number . Since the only even prime number is 2 , so Anjali was born on 2nd February, 2004.

13. Answer is (d). From I and II , we conclude that Aman went to office by either 10:30 a.m. or 10:35 a.m train.

SYLLOLOGISM SHORT CUTS FOR REASONING ABILITY

Step 1: How to align

1) Changing the order of statement (Up & Down).
2) Converting anyone statement through It IEA" rule.
A -I, E-E, I-I, 0 - Not Converted (SUBJECT as PREDICATE, PREDICATE as SUBJECT).

COMBINATION: only six types combination's possible . Other combination has no conclusion

1)A+A=A

2)A+E=E

3)A+I=no conclusion

4)E+A=O*

5)E+I =O*

6)I +E=O

7)I +A=I

explanations :1)A+A=A

All M are N (A type)

All N are P (A type)

We can combine this two types only if predicate of first sentence :N and subject of second sentence :N are same .in other words the same words must come diagonally. conclusion is .

All M are P

2) A+E=E

All M are N(A type)

No N are P(E type)

conclusion :No M are P

3) A+I = no conclusion

4) I +I = no conclusion

5)I +E=O

Some M are N ( I type)

No N are P (E type)

conclusion : Some M are not P ( O type)

6) I +A = I

Some M are N ( I type)

All N are P (A type )

conclusion :Some M are P (I type)

7) E +A =O*

No M are N (E type )

All N are P (A type)

conclusion: Some P are not M ( O* type)

Note: In O* we use some not but the subject is the predicate of 2nd sentence

8)E +I =O*

No M are N (E type)

Some N are P(I type)

conclusion: Some P are not M (O* type)

Rest combination are not possible E + E = No conclusion

Complementary pair: If the options given in conclusion part is not our conclusion then we check for complementary. There are mainly three pairs coming under complementary pair. They are

1)A-O

2)I-O

3)I-E

But the condition is subject and predicate of both the sentences should be same.

1)A-O pair: All M are N (A type)

Some M are not N (O type)

2)I-O pair : Some M are N (I type)

Some m are not N (O type)

3)I-E pair: Some M are N (I type)

No M are N (E type)

Coded inequality SHORTCUTS FOR REASONING ABILITY

Few points to remember

A) Similar points between two variable and common variable in middle .Conclusion is similar signs .

1)A>=B, B>= C

conclusion: A>=C

2)A<=B,B<=C conclusion: A<=C 3) A>B, B>C

conclusion: A>C

4)A=and > and <=and < prevails then conclusion is >and < 6) A>=B , B>C

conclusion : A> C

7) A<=B, B< C C) If the conclusion we get >= or <= signs and in option we have two choices >and

= signs or < and = between two variables then conclusion will be either choice follow Ex- A>=B , B>= C A<=B, B<=C 1)AC, 2) A=C Our answer is either 1 or 2 D) We can't combine two variables with common variable in middle having sign >= and <=or > and < for example 1)A>=B, B<=C no conclusion between A and C 2) A>B , B < C no conclusion between A and C E) At least if we don't get any conclusions yhen we check for complementary pair. So there are two complementary pair 1) >= and < 2) <=and >

Ex: 1)A>=B, B <=C conclusion: a) A >= C

b) A <=C d) A >C

Ans: Either a or b

Either c or d

E) If any new alphabet is compared in the conclusion part ,and if it is not used in the question part then it can't have a definite conclusion .It will have complementary pair

Ex- A >=B, B>=C

option 1) T > C

2)T<=C 3) T>= C

4) T

conclusion : either 1 or 2 and either 3 or 4

P @Q means P is either greater than or equal to Q

P+ Q means P is either smaller than or equal to Q

P%Q means P is greater than Q

PX Q means P is smaller than Q

P$ Q means P is neither greater than nor smaller than Q

Now in each of the following questions assuming the given statement to be true ,find which of the two conditions I and II given below them is /are definately true ? Give answer.

a) If only conclusion I is true

b) If only conclusion II is true

c) If either I or II is true

d) If neither I or II is true

e) If both I and II is true

1) Statements : M @R , R%T , T$ K

Conclusion : I) KXM, II) TXM

2) Statements : H%J, B+J, B@F

Conclusion: I)F$J, II) J%F

3) Statements : D$M, M%W, W@R

Conclusion : I) RXD, II) W+D

4) Statements : A+N , NXV, V$J

Conclusion: I) J@N, II) A +V

5) Statements : KXT , T@B , B+M

Conclusion : I)M%T II) K+B

6) Statements : B@H, HXM , M$N

Conclusion : I) B@N, Ii) N%H

Answers: 1)- e 2)C 3)a 4)d) 5)d 6)b

RELATION

Mother or father's son ----------------------------------------------Brother

Mother's of father's daughter ----------------------------------------Sister

Mother or father's brother ------------------------------------------Uncle

Mothers or fathers sister --------------------------------------------Aunt

Mothers or fathers father--------------------------------------------Grandfather

Mothers or fathers mother-------------------------------------------Grandmother

Son's wife-----------------------------------------------------------Daughter-in-law

Daughters husband--------------------------------------------------Son -in -law

Husbands or wifes sister---------------------------------------------Sister-in-law

Husbands or wifes brother-------------------------------------------Brother-in-law

Brother's son--------------------------------------------------------Nephew

Brother's daughter --------------------------------------------------Niece

Uncle or aunts son or daughter--------------------------------------Cousin

Sisters husband-----------------------------------------------------Brother-in-law

Brothers wife-------------------------------------------------------Sister-in-law

Grandsons or geand daughter --------------------------------------Great grand daughter

Ex-- A man pointing to a photographer says "the lady in the photograph is my nephew's maternal grandmother" .How is the lady in the photograph related to the man's sister who has no other sister ?

a)Cousin b) Sister-in -law c)Mother d)Mother-in-law

Solution: Clearly the lady is the grandmother of man's sister's son that is the mother of the mother of man's sister's son that is the mother of man's sister.Hence the answer is c

Ex: A woman going with a boy is asked by another woman about the relationship between them .The womwn replied ,"My maternal uncle and the uncle of his maternal uncle is the same". How is the lady related with that boy?

a)grandmother and Grandson b)Mother and son

c)Aunt and nephew d)None of these

Solution:Clearly the brother of woman's mother is the same as the brother of the father of boys maternal uncle .So, the womans mother's brother is the boy's maternal uncle's father ,Thus the woman's mother's brother's son is boy's maternal uncle that is ,woman's mother's brother's daughter is boy's mother .So the woman and boy's mother are cousins. Thus the woman is boys aunt .Hence the answer is c

Ex: Pointing out to a lady ,Rajan said ,"she is the daughter of the woman who is the mother of the husband of my mother ."Who is the lady to Rajan ?

a)Aunt b)Grand daughter c) Daughter d)Sister e) Sister-in-law

Sol:The relation may be analysed as follows

Mother's husband --Father ;Father's mother --Grandmother ; Grandmother's daughter -- Father's sister,Father's sister --Aunt

Hence, the answer is a

Ex: 1. Pointing towards a person a man said to a woman "His mother is the only daughter of your father . How is the woman related to that person?

a)Daughter b) Sister c)Mother d) wife

sol: The only daughter of woman's father is she herself ,so the person is woman's son that is the woman is the person's mother .Hence the answer is c

Ex: 2) Pointing to a lady in a photograph ,Shaloo said , "Her sons father is the son-in-law of my mother ," How is shaloo related to the lady ?

a)Aunt b) Sister c)Mother d) Cousin e) nono of these

sol:Lady's son's father is lady's husband .So the lady's husband is the son -in law of shaloo's mother that is the lady is the daughter of shaloo's mother .Thus Shaloo is the lady's sister . Hence the answer is b

Ex- 3: Anil introduces Rohit as the son of the only brother of his father's wife. How is Rohit related to Anil

a)Cousin b) Son c) Uncle d) Son-in-law e) Brother

sol: The relation may be analysed as follow

Father's wife --Mother ,Mother's brother --Uncle ,Uncle's son --Cousin

So ,Rohit is Anils Cousin .Hence answer is a

Ex-4:Pointing towards a person in the photograph Anjali said "He is the only son of the father of my sister's brother " . How is that person related to Anjali ?

a) Mother b) Father c) Maternal uncle d)Cousin e)none of these

sol:Relation may be analysed as follow

Sisters brother -- Brother ,Brother's father -Father , Father's son -Brother

So the person in the photograph is Anjali's brother .Hence the answer is e

Ex-5: Rita told Mani,"The girl i met yesterday at the beach was the youngest daughter of the brother-in-law of my freind's mother " How is the girl related to Rita's freind ?

a) Cousin b) Daughter c) Nice d) Freind e)Aunt

sol: The relation may be analysed as follow

Daughter of brother -in-law --Niece : Mother niece --Cousin : so the girl is the cousin of Rita's freind . Hence the answer is a

TYPE-2 BLOOD RELATIONS

Direction : Read the following information and answer the question given below it .

A is the father of a C .But C is not his son .

E is the daughter of C .F is the spouse of A.

B is the brother of C. D is the son of B.

G is the spouse of B. H is the father of G.

Q.:- Who is the grandmother of D?

a) A b) C c) F d) H

Solutions:- ( answer is c.) D is the son of B, B is the brother of C and A is the father of C. Thus means that B is the father of D and A is the father of B . So , A is the grandfather of D. Since F is the spouse of A, So F is the grandmother of D.

Q.) Who is the son of F?

a) B b) C c) D d) E

Solutions:- ( Answer is a.) As explained above , B is the son of A and F is the spouse of A. So , B is the son of F.

EX
i) In a family of six persons A, B, C, D, E, and F, There are two married couples .

ii). D is grandmother of A and mother of F.

iii). C is wife of B and mother of F.

iv) F is the granddaughter of E.

Q:- What is C to A?

a) Daughter b) grandmother c) mother d) cannot be determined e) none of these

Solutions:- ( answer is c.) Cis the wife of B and D is the mother of B. Also , D is grandmother of A. So , C is the mother of A.

Q.:- How many male members are there in the family?

a) two b) three c) four d) cannot be determined e) none of these

Solutions:- Clearly the sex of A cannot be determined so answer is (d).

Q:- Which of the following is true?

a) A is brother of F.

b) A is the sister of F.

c) D has two grandsons .

d) B has two daughters

e) None of these.

Solutions:-The sex of A is not known , so, neither (a) nor (b) is definitely true. Clearly , D is the grandmother of A and F. So, the answer is (e).

Q.) Who among the following is one of the couples .

a) CD b) DE c) EB d) Cannot be determined e) None of these

Solutions:- C is the wife of B, so , one couple is BC. Now , D is grandmother of A. B is the son of D and his wife C is the mother of F . So , D is also grandmother of F. But F is the granddaughter of E . So , E is the grandfather of F and the husband of D . Thus , DE is another couple. Therefore , our answer is (b).

Ex. Read the following information and answer the questions given below :

A is the son of B. C, B's sister has a son D and a daughter E. F is the maternal uncle of D.

Q. How is A related to D?

a) cousin b) nephew c) uncle d)brother

Q. How is E related to F?

a) sister b) Daughter c) Niece d) Wife

Q. How many nephews does F have ?

a) nil b) one c) two d) three

Solutions:- First answer is (a) . A is the son of B and D is the son of the sister of B. So , A is the cousin of D.

Second answer is (c). E is the daughter of C and D is the son of C. So, F, who is the maternal uncle of D, is also the maternal uncle of E. Thus , E is the niece of F.

Third answer is (c). Clearly , F is the maternal uncle of D means F is the brother of D's mother i.e. F is the brother of C. C is the sister of B. So , F is the brother of B who is A's mother . Thus F is the maternal uncle of A . So , A and D are the nephews of F i.e.F has two nephews.

DIRECTION TEST SHORT CUT METHODS IN REASONING ABILITY

Tips for Question based on Sense of Direction

1. Always try to use the direction planes as the reference for all the questions.

2. Now , as the statement of the question progresses, you should also proceed over this reference plane only.

3. always mark the starting point and end point different from the other points.

4. mark be attentive while taking right and/or left turns.

5. mark distance with a scale ( if your rough diagram confuse you)

6. To solve this type of questions you should remember the following diagram.

7. One should aware of the basic geometric rule, such as Pythagoras Theorem.

Pythagoras Theorem  AC2= Ab2+BC2

Ex. 1. Abinav walked 2 km west of his of house and then turn south covering 4 km. Finally he moved 3 km towards the east and then again 1 km west. How far is he from his initial position?

a. 2 km b. 4 km c. 9 km d. 10 km

Soln. Abhinav start from his house at A, Moves 2 Km west upto B, then 4 km to the south upto C 3 km east upto D and finally 1 km west upto E. thus his distance from the initial position A = AE = BC = 4 Km. hence ans is (b)

CODING DECODING IN REASONING ABILITY

Type I: Letter coding

Case- I To from the code for another word (coding)

Ex-1) In a certain code, TEACHER is written as VGCEJGT .How is children written in that code?

a) EJKNEGTP b) EGKNFITP C) EJKNFGTO d)EJKNFTGP

Solution : Each letter in the word "TEACHER " is moved two steps forward to obtain the corresponding letter of the code.

T E A C H E R : Ans : V G C E J G T

(Each letter is increasing by 2)

Similarly we have

C H I L D R E N Ans: E J K N F T G D

( Each letter is increasing by 2 )

Ex-2) In a certain code language , RUSTICATE is written as QTTUIDBSD ,How would ( Each letter is increasing by 2 )

STATISTIC be written in thqt code?

a) RSBUJTUHB b) RSBUITUHB c) RSBUIRSJD d)TUBUITUMB

Solution: Clearly , the middle letter of the word remains the same in the code. Each of the first two and the last two letters of the word is moved one step backward ,while each of the remaining letters is moved one step forward to obtain the corresponding letters of the code.

R U S T I C A T E

Ans: QTTUIDBSD

Similarly we have

S T A T I S T I C

Ans: RSBUITUHB

So the required code is RSBUITUHB. Hence the answer is b

Ex- 3) If ROAST is coded s PQYUR in a certain language, then how will SLOPPY be coded in coded in that language?

a) MRNAQN b) NRMNQA c) QNMRNA d) RANNMQ

Sol: Clearly the letters in the word ROAST are moved alternately two-step backward and two steps forward to obtain the letters of the code. Thus we have:

R O A S T Ans: (PQYUR). S L O P P Y Ans: (QNMRNA)

So required answer is c

Ques:5) If HEALTH is written as GSKZDG , then how will NORTH be weitten in that Code?

a) OPSUI b) GSQNM C) FRPML d) IUSPO

Sol: Clearly the letters of the given word are written in a reverse order and then each letter is moved one step backward to obtain the code.

Reversing the order of the letter in NORTH, we get HTRON, thus we have

H T R O N Ans: ( G S Q N M ) Hence the answer is b

Ques:6) In a certain code , BREAKTHROUGH is written as EAOUHRBRGHKT. How is

DISTRIBUTION written that code?

a) TISTBUONDIRI B) STTIBUONRIDI c)STTIBUDIONRI d)RISTTIBUDION

e) None of these

Sol: Let us divide the letters of the given word into pair and label there pairs from 1 to 6.

BR EA KT HR OV GH

1 2 3 4 5 6

Clearly ,the code contains there pairs arranged in the order 2 ,5 ,4 . 1 ,6 ,3

Dividing the letters of the word DISTRIBUTION in pairs we have :

DI ST RI BU TI ON

1 2 3 4 5 6

Arranging there in the order 2 ,5 ,4 ,1 ,6 ,3.

we get the requires code that is STTIBUDIONRI Hence the answer is c

Ques-7: In a certain code language ,BEAT is written as a certain code language , BEAT is written as YVZG,then what will be code of MILD?

a) B,E,A,T, are respectively the 2nd ,5th, 1st ,20th letter from the begining

of the English alphabet. Similarly M, I, L, D are respectively the

13th,9th,12th, 4th letters from the begining of the English alphabet ,and the 13th,9th,12th, 4th letters from the begining of the English alphabet are NROW, hence the answer is d

Ques-8:In a certain system of coding ,the word STATEMENT is written as

TNEMETATS.In the same system of coding .what should be the code for the word POLITICAL

a) LACITILOP b) LCATILTOP c)POILITCAL d)none of these

Sol: Clearly the letters of the given word are written in a reverse order to obtain the code. Reversing the order of letters in POLITICAL, we gwt LACITILOP, which is required code ,hence the answer is a

CASE -II: To find the word by analysing the given code(decoding ) .

Ex:On a certain code ,the word ROAD is written as WTFI. Following

the same rule of coding ,what should be the word for the code GJFY?

a)REAP b) TAKE c) BEAT D) LATE

sol: Each letter of the word is five steps behind the corresponding letter of

the code we have

W T F I Ans: R O A D

G J F Y Ans :B E A T

So BEAT is coded as GJFY. Hence the answer is c

Ex:If NARGRUED is the code for GRANDEUR , which word is coded as

SERPEVRE?

Sol:Clearly ,the code has been obtained by writting the first four and the last

four letters of SERPEVRE

SERP/EVRE PRES/ERVE Hence answer is e

Q. if in a certain language , ITNIETAM is the code for INTIMATE, which word has the code TREVNIETARBI?

a. INVRETIBRATE b. INVERTIBARTE c. INVERTIBRETA d. INVERTIBRATE e. INVERITBARTE

Soln. our ans (d) . The letters in the first half and the latter half of the code are separately reversed to obtain the word.

Q. If QOSCFLBJO is the code for PORCELAIN , which word is coded as BKMOUSPP?

a).ALTOLROPY b.ALLOTROPY c.ALOTROLPY d. ATLOROPLY e. None of these

Soln. In the code , we have alternately one letter one step ahead of and the other the same as the corresponding letter in the word.

Q.If in a certain language , MACHINE is coded as LBBIHOD, which word would be coded as SLTMFNB?

a. RKSLEMA b.TKULGMC c.RMSNEOA d.TMUNGMC

Soln. In the code , we have alternately one letter one step behind and the other one step ahead of the corresponding letter in the word..

Q.Study the following information carefully and answer the questions given below.

The consonants of English alphabet have been coded by using digits 1 to 8 and the vowels have been coded by using different symbols.

Letters	G	B	K	H	Z	M	F
	R	V	C	S	D	Q	X
	J	N	T	L	W	Y	P
Digit	5	4	1	3	2	8	7

If any vowel is not in the beginning or last , it is coded as 6. If any vowel is at the beginning or in the last , it is coded as 9. However , if the same vowel is placed at both beginning and in the last , it is coded as $ at both the places . Now, choose the correct coded forms of each of the following letter groups.

Q1. AFDQENI

a. 6728949 b.$72864$ c.9728649 d.9728949 e. None of these

Q2.ENIANGE

a.6499456 b.$466453$ c.$4$$45$ d.9466456 e. None of these

Q3. PKDEJHI

a.7126539 b.712653$ c.7129539 d.712$53$ e. none of these

Q4. OPTIONAL

a.67199493 b.97166463 c.$7199493 e. none of these

Q5. EGTARLQE

a.65195386 b.$51$538$ c.95165389 d.$519538$ e. none of these

Soln. 1-(c), 2 (b), 3(a), 4(b), 5(e)

Ex. In each of the questions below, a group of numerals is given, followed by four groups of symbols/letter combination labeled (a), (b), (c), (d). Numerals are to be coded as per the codes and conditions given below. You have to find out which of the combination (a), (b), (c), (d) is correct and indicate your answer accordingly. If none of the four combination represents the correct code, mark ( e) as your answer.

Numerals	3	5	7	4	2	6	8	1	0	9
Letter/ Symbol code	*	B	E	A	@	F	K	%	R	M

Following condition apply:

1. If the first digit as well as the last digit is odd, both are to be coded as X.

2. If the first digit as well as the last digit is even, both are to be coded as $.

3. If the last digit is 0, it is to be coded as #.

1. 546839

a. XAFK*M b. BAFK*M c. XAFK*X d.BAFK*X e. None of the these

2. 713540

a.E%*BA# b. X%*BA# c. X%*BAR d.E%*BAR e. None of the these

3. 765082

a.XFBRK@ b. EFB#K@ c. EFBR#K d.EFBRK@ e. None of the these

4. 487692

a.AKEFM@ b. $KEFM@ c. AKEFM$ d. $KEFM$ e. None of the these

5. 364819

a.XFAK@M b. *FAK%X c. *FAK%M d. *EAK%X e. None of the these

Sol. 1. Clearly, in the given number- group, both the first and last digits are odd no. So, each of them is to be coded as X. The remaining numerals are to be coded with their respective codes from the given table. So, the required code XAFK*X. hence, answer is (C).

2. The last digits in the given number group is 0, which shall thus be coded as #. Choosing the individual Codes for the remaining digits from the given table, we obtain the code for 713540 as E%*BA#. Hence, answer is (a)

4. Each digit of the given number group is to coded by individual letter/symbol code

So, required code is EFBRK@. Hence, the answer is (d)

5. the first and the last digits, both being odd numbers, each of the them is to be coded as X. hence answer is (c).

Type: Substitution

1.If sky is star, star is cloud, cloud is earth, earth is tree, and tree is book, than where do the birds fly ?

a. Cloud b. Sky c. Star d. data inadequate e. None of these

Sol. answer is (c). Birds fly in the sky and as given, sky is star . So birds fly in the star .

2. If orange is called butter, butter is called soap, soap is called ink, ink is called honey and honey is called orange , which of the following is used for washing clothes?

a. honey b. butter c. orange d. soap e. ink

Soln. answer is (e). Clearly , soap is used for washing the clothes. But , soap is called called ink. So, ink is used for washing the clothes.

3. If light is called morning , morning is called dark , dark is called night , night is called sunshine and sunshine is called dusk, when do we sleep?

a. night b. sunshine c. dusk d. dark

Soln. Answer is (b). We sleep in the night . But night is called sunshine . So we sleep in the sunshine.

4. I f blue means green , green means white , white means yellow , yellow means black, black means red and red means brown , then what is the color of milk?

a. black b. brown c. blue d. yellow e. green

Soln. Answer is (e). The colour of milk is white . But as given green means white . So the color of milk is green .

5.If in a language , finger is called toe, toe is called foot , foot is called thumb , thumb is called ankle , ankle is called palm and palm is called knee, then in that languaghe , what will an illiterate man put to mark his signatures?

a.toe b. knee c. Thumb d. ankle

Soln. Anwer is (d). Clearly, an illiterate man puts his thumb to mark his signatures . But as given , thumb is called ankle . So an illiterate man will put his ankle to mark his signatures.

Type- DECIPHERING MESSAGE WORD CODES

EX.1 In a certain language, sun shines brightly is written as ba lo sul, houses are grightly lit as kado ula ari ba and light comes from sun as dopi kup lo nro. What code words are written for sun and brightly?

a. ba, sul b. sul, lo c. lo, ba d.ba, lo

Soln . In the first and third statements , the common word is sun and the common code-word is lo . So , lo is the code for sun . In the first and second statements, the common word is brightly and the common code word is ba . So , ba is the code for brightly. Hence, the answer is (c).

Ex.2. If in a certain language, oka peru means fine cloth , meta lisa means clear water and dona lisa peru means fine clear weather , which word in that language means weather?

Soln . In the first and third statements , the common code word is peru and the common word is fine . S o , peru means fine . In the second and third statements, the common code word is lisa and the common word is clear. so lisa means clear. Thus , in the third statement, lisa means clear and peru means fine . So, dona means weather. Hence the answer is (d).

EX.3 Read the information given below to answer the questions that follow :

In a certain code language ,

i) pit na sa means you are welcome ;

ii) na ho pa la means they are very good ;

iii) ka da la means who is good ;

iv) od ho pit la means they welcome good people .

1. Which of the following means people in that code language ?

a. od b. la c.ho d. pit e. data inadequate

2. Which of the following means very in that code language ?

a. pa b.na c.da d. data inadequate e. none of these

3. Which of the following statements is / are redundant to answer the above two questions?

a. none b. (i) and (ii) c.(ii) or (iv) d. (i) or (iv) e. none of these

Soln .

1. In statements (i) and (iv) , the common code word is pit and the code word is welcome , so , pit means welcome .

In statements (ii) and (iv) the common code words are ho and la and the common words are they and good . So , ho and la mean they and good . Thus , in (iv) , the remaining code word i.e. od means people .

Hence the answer is (a).

2. From 1, we know that ho and la are codes for they and good

Now , in statements (i) and (ii), the common code word is na and the common word is are . So , na means are. Thus , in (ii), the remaining code word i.e. pa means very .

Hence the answer is (a).

3.Clearly , to answer the above two questions, we used statements (i) , (ii), and (iv) and didnot require (iii). So , (iii) is redundant . Hence , the answer is (e).

TYPES ALPHABET SERIES COMPLETION IN REASONING ABILITY

TYPE-1 :- Alphabet series

a) Increasing by a definite number
e.g i) IJKL? ( each letter increases by 1)
ii) AGMSY? ( each letter increases by 6 place to its right position)

b) Decreasing by a definite number
e.g. i) ZXVTRP ? ( each letter decreases by 2 places to its left )

c) Increasing successively
e.g. DEGJNS? ( +1,+2,+3,+4,+5)

d) Decreasing successively
e.g.
i) ZYWTP ( -1,-2,-3,-4 ..)
ii) ZTOKHFE ( -6,-5,-4,-3,-2,-1)

e) Decreasing and Increasing by a constant value.
e.g. i) DFCEBDACZ (+2,-3,+2,-3,...)

TYPE-II :- ALPHANUMERIC SERIES

EX-1: Z1A, X2D,V6G,T21J,R88M, P445P,?

First letter: ZXVTRP (-2,-2,-2,.....)
Second letter: ADGJMP ( +3, +3,+3,...)
Series of numerals: 1,2,6,21,88,445 ( x1+1, x2+2, x3+3...)
So next term is N2676S.

EX.2:- 2Z5,7Y7,14X9,23W11,34V13,?

First numeral- 2,7,14,23,34 (+5,+7,+9,+11..)
Second letter- ZYXWV ( decreases by 1 each time)
Third numeral- 5,7,9,11,13 ( increases by 2 each time)

EX-3 :- W-144 , U-121, S-100, Q-81,?
First letter- decreases by 2 each time
Second numeral- square of 12,11,10,9,8..

Type-III :- Continuous patterns series

Ex-1 : ab_ _ baa_ _ ab_
options i) aaaaa ii) aabaa iii) caabab iv) baabb

solution: our answer is ii) . Here series aba is repeated

Ex-2 :ab_aa_bbb_aaa_bbba
options i) abba ii) baab iii) aabb iv) abab

Solution- our answer is ii) . The series is abb/aaabbb/aaaabbbb/a. Thus the letter are repeated twice , then thrice , then four times and so on .

Ex.3 - _bc_ca_aba_c_ca
Options i)abcbb ii)bbbcc iii)bacba iv)abbcc
Solutions- our answer is i) . The series is abc/bca/cab/abc/bca. Thus the letter change in cyclic order .

Ex.4- _c_bd_cbcda_a_db_a
Options i) adabcd ii) bdbcba iii) cdbbca iv)daabbc
Solutions- our answer is i). The series is acdb/dacb/cdab/acdb/da. Each group of four letters contains the letters of the previous group in the order - third , first , second and fourth.

Ex.5:- a_bb_baa_bbb_aa_

Options i) aabba ii) bbaab iii)abaaa iv)baabb
Solutions:- our answer is iii). The series is aabbbb/aaabbb/aaaa. At each step , the number of a's increases by one while the number of b's decrease by one.

Ex.6- _aba_cabc_dcba_bab _a

Options i) abdca ii) bcadc iii) abcdb iv) cbdaa
Solutions- Our answer is i) . The series is aababcabcd/dcbacbabaa. The letters equidistant from the beginning and the end of the series is same .

Ex.7- mnonopqopqrs_ _ _ _ _
Options- i) mnopq ii)oqrst iii)pqrst iv) qrstu
Solutions- our answer is iii) . The series is mno/nopq/opqrs

ALBHABETS SERIES IN REASONING ABILITY

1 11 21

A K U OPPOSITE LETTERS

B L V ( SUM IS 27 )

C M W UF BY LOVE

D N X SHIRT GAZ

E O Y PK MN JQ

F P Z CX DW

G Q

H R

I S

J T

E	J	O	T	Y
5	10	15	20	25

Although such question are very simple, yet by doing them in a systematic manner you can save some extra seconds. We suggest that you perform recalculation .In this method,

1) Subtract the numbers if both the direction are same

2) Add the numbers if the directions are opposite

For example: 1) ABCDEFGHIJKLMNOPQRSTUVWXYZ

Which letter would be the seventh to the right of the eleventh letter from?

The right end 1)K 2) W 3) J 4) U 5) none of these

Since both directions are same (right, right) we request we subtract 7

From 11.Hence the answer would be the 4th from the right that is, W

Some more examples are given below.

3) Which letter is seventh to the right of the thirteen letters from the left?

a) S b) T c) U d) V e) none of these

sol: Since we want the seventh letter to the right of the thirteen letter from the left -directions are opposite -hence we add 7+13=20 .Hence the answer is 20th from the left . Now 20th from the left means 26-20+1=7th from right (note this step). Hence answer is T.

You must have understood the method of pre-calculation by now .The trick is to calculate the actual position of the required letter before going to search for it .Now there may be some variations to the above type of problem. Some variations are presented below. See how we precalculate the position of the required letter.

Ex: 3If the above alphabet is written in reverse order, which will be the eighth letter to the right of O?

a) F b) G c) V d) W e) none of these

Sol: The letter which is eighth to the right of O when the alphabet is , reversed must be presently eighth to the left of O. Hence it is G .

Ex:4 If the first half of the alphabet is written in reverse order which letter would be the nineteenth letter from the right ?

a)F b) G c) E d) H e) none of these

sol: Since the second half is not reversed the first 13 letters would be the same when counting is done from right .But next letters after 13th will be actually from the left end( the 14th letter would be A) Hence the

Some more rules on English alphabet series

a)Question based on dropping or deleting of letters in the english alphabet at regular intervals

Ex- every third letter from left to right of the English alphabet is dropped. Find the 7th letter from the left of the new series obtained.

sol: In the English alphabet ,every third letter is dropped from the left (given) ,Hence the new series will be like ,

AB C DE F GH I JK L MN O PQ R ST U VW X YZ

That is ; A B D E G H J K M N P Q S T V W Y Z

Clearly, 7th letter from the left in the new series is J

Quicker method:

Above discussed method is lengthy and time consuming. Therefore you need a quicker method to solve such kind of problems.

Question says that every 3rd letter is dropped in the original series that is we are left with two letters after every dropping of letters. Here 2 is the key figure .We have to seek a digit which is just les than 7 but divisible by 2. In this case the required digit is 6. Now we do the following operations to get the required answer.

7th letter from the left in the new series = 7+6/2=10th letter from the left in the original series=J

Similarly, you can find any letter at a particular position in the new series.

Question based on reversed English alphabet series.

The English alphabet series can be reversed in many ways. Some of them are discussed below

1) The whole English Alphabet is reversed

2) First half of the series is reversed

3) Second half of the series is reversed

4) Many sections of the English alphabet series are reversed

To solve the questions of the Reversed English alphabet series, you should

Remember the basic rule, that is:

Mth element counting from left to right of a series of N characters is equal to the (N +1-M)th element counting from right to left of that series.

let us take a example :

Let us take the english alphabet series as given below:

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

Suppose we have to find the position of L in the above series counting from right to left.

We know that the English alphabet has 26 characters.

Hence N =26

Position of L in English alphabet starting from A (left to right) is 12. Hence M=12

Hence Position of L in the above series is from right to left is (26+1-12)=15

Let us take a typical example: Suppose first five letters, then next six letters, then next 7 letters and then after last 8 letters of the following English alphabet series are reversed.

ABCDEFGHIJKLMNOPQRSTUVWXYZ

Then you are asked to find I) 4th II) 20th elements from the left of the new series .How will you proceed to get the answer? Let us see.

According the question, first 5, then next 6,7,8 letters of the English alphabet are reversed.

Hence we obtain a new series as given below

EDCBA / KJIHGF / RQPONML / ZYXWVUTS

1 2 3 4

We have to find i) 4th letter from the new series, 4th letter falls into group 1

Hence fourth letter in group 1= (5+1-4)=2nd letter from the left in the

Original series.(refer to the basic rule )

II) 20th letter from the left of the new series falls into the group 4.There are

8 characters in-group 4.We have to find second letter of the group 4

(Since 5 letters of group 1, 6 letters of group 2 and 7 letters of group 3

Does not effect the position of letter that falls into the group 4 that is

20=5+6+7+2) 2nd letter in the group 4 =18+(8+1-2)=25th letter from the

Left in the original series=Ys

Remember: - If we want to go back 3 places back from c then answer will be z. similarly if we want to go back 5 places back from the alphabet e then answer will be z.

C-3 = Z

E-5 = Z

C- 5 = X (26+3-5=24 which is the position of x)

ANALOGY

Individual and Dwelling Place

Ex. Dog: Kennel

Bee: hive
Bird: Nest
Cow: Byre/Pen

Eagle: Eyrie
Hare: Burrow
Horse: Stable

Lion: Den
Mouse: Hole
Owl: Barn

Pig: Sty S
pider: Web C
onvict: Prison

Eskimo: Igloo
Gypsy: Carvan
King: Palace

Knight: Mansion
Lunatic: Asylum
Monk: Monastery

Nun: Convent
Peasant: Cottage
Soldier: Barracks

Animal/ thing And Keeping Place

Ex. Car: Garage

Aeroplane: Hanger
Bees: Apiary
Birds: Aviary

Animal: Zoo
Cloths: Wardobe
Fish: Aquarium

Grains: Granery
Guns: Armoury
Curios: Museum

Medicine: Dispensary
Patient: Hospital
Wine: Cellar

Workers and Tool

Ex. Blacksmith: Anvil

Carpenter: Saw
Chef: Knife
Woodcutter: Axe

Auther: Pen
Soldier: Gun
Warrior: Sword

Docter: Stethoscope
Farmer: Plough
Surgeon: Scalpel

Gardener: Harrow
Mason: Plumbline
Sculptor: Chinsel

Labourer: Spade
Tailor: Needle

Tool and Action

Ex. Needle and Sew

Knife: Cut
Gun: Shoot
Spoon: Feed

Binocular: View
Sword: Slaughter
Shovel: Scoop

Chisel: Carve
Oar: Row
Axe: Grind

Auger: Bore
Spade:Dig
Shield: Guard

Mattock: Dig
Pen: Write
Spanner: Grip

Tongs: Hold
Microscope: Magnify
Loudspeaker: Amplify

Workers and Working Place

Ex. Chef: Kitchen

Farmer: Field
Teacher: School
Clerk: Office

Sailor: Ship
Engineer: Site
Warrior: Battlefield

Doctor: Hospital
Servant: House
Grocer: Shop

Painter: Gallery
Waiter: Restaurant
Worker: Factory

Umpire: Pitch
Gambler: Casino
Beautician: Parlor

Artist: Theatre
Actor: Stage
Mechanic: Garage

Lawyer: Court
Scientist: Laboratory
Astronomer:Obsevatory

Workers and Product

Ex. Manson: Wall

Choreographer: Ballet
Dramatist: Play
Cobbler: Shoe

Editor: Newspaper
Producer: Film
Chef: Food

Architect: Design
Tailor: Clothes
Poet: Poem

Farmer: Crop
Auther: Book
Goldsmith: Ornament

Carpenter: Furniture
Butcher: Meat
Teacher: Education

Product and raw Material

Ex. Prism: Glass

Butter: Milk
Cloth: Fibre
Paper: pulp

Wine: Grapes
Fabric: Yarn
Wall: Brick

Road: Asphalt
Furniture: Wood
Book: Paper

Shoes: Leather
Pullover: Wool
Sack: Jute

Omelette: Egg
Metal: Ore
Jewellery: Gold

Rubber: Latex
Linen: Flax
Jaggery: Sugarcane

Oil: Seed

Part and Whole Relationship

Ex. Pen: Nib

Pencil: Lead
Class: Student
Clock: needle

Circle: Arc
House: Room
Car: Steering

Aeroplane: Cockpit
Book: Chapter
Fan: Blade

Cart: Wheel

Pair Relationship

Ex. Shoes: Socks

Shirt: Trouser
Chair: Table
Lock: key

Saree: Blouse
Pencil: Eraser
Door: Window

Cup: Saucer
Horse: Carriage
Question: Answer

Study Topic

Ex. Ornithology: Birds

Anthropology: Man
Entomology: Insect
Botany: Plant

Seismology: Man
Cadilogy: Heart
Mycology: Fungi

Pathology: Disease
Physiology: Body
Haematology: Kidney

Palaeontology: Fossils
Ichthyology: Fishes
Herpeology:Ambhibian

Phycology: Algae
Pedology: Soil
Nephrology: Kidney

Taxonomy:Classification
Selenography: Moon
Eccrinology: Secretion

Word and Intensity

Ex. Anger: Rage

Wish: Desire
Touch: Push
Kindle: Burn

Sink: Drown
Qurrel: War
Error: Blunder

Famous: Renowned
Unhappy: Sad
Refuse: Deny

Crime: Sin
Moisten: Drench
Speak: Shout

Word and Synonym

Ex. Abode: Dweling

Blend: Mix
Solicit: Request
Ban: Prohibition

Flaw: Defect
Fierce: Voiolent
Fallacy: Illusion

Substitute: Replace
Mend: Repair
Alight: Descend

Pesume: Assume
Brim: Edge
House: Home

Sedate: Calm
Dissipate: Squander
Dearth: Scarsity

Abduct: Kidnap
Vacant: Empty
Prsage: Predict

Word and Antonym

Ex. Attack: Defend

Advance: Retreat
Sink: Float
Crual: Kind

Robust: Weak
Best: Worst
Gentle: Harsh

Deep: Shallow
Fresh: Stale
Ignore: Notice

Cordial: Hostile
Initial: Final
Lethargy: Alertness

Affirm: Deny
Mourn: Rejoice
Kindle: Extinguish

Lend: Borrow
Condense: Expand
Create: Destroy

Gradual: Abrubt
Chaos: Peace

Different Types Completing The Analogy pair

Type -1: Direct/Simple Analogy

1.Apparel is related to cloth in the same way as footwear is related to...?

a. Material b. leather c. cobbler d. shoes e. sandal

Sol first is made by other

2. Which of the following is related to Melody in the same way as Delicious is related to Taste?

a. Voice b. Speak c. Tongue d. Highness

Sol Delicious represents good taste. Similarly, Melody describe pleasant Voice

3. Wave is the related to air in the same way as Ripples is related to......?

a. Wind b. Water c.Strom d. Smoke

Sol Wave travel in air,ripples traval in water

4.Paddy is related to Field in the same way as Steel is related to ......?

a.mine b. factory c.Iron D.Ore

Sol

5. Tree is related to sapling in the same way as horse is related to......?

a.pony b. mule c. cub d. foal e. puppy

Sol second is the place where the first is grown/produce

*********************************************************

Type 2: Completing The Analogus pair

1. Giant: Dwarf:: Genious : ?

a. Wicked b. gentle c. Idiot d. tiny

Sol. Dwarf is the antonym Of Giant. Similarly, the antonym of Genius Is Idiot

2.Cattle: Herd :: Sheep : ?

a. Flock b. swarn c. shoal d. mob

Sol. herd is a group of cattle similarly; flock is a collection of sheep

3. Meningitis: Brain :: Cirrhois : ?

a. Lungs b. brain c. liver d. heart

Sol. First is a disease which effect the second

4. Horse: Jockey :: Car: ?

a. Mechanic b. Chauffeur c. Steering d. Brake

Sol first is driven by the second

5 Fruit: Banana :: mammal : ?

a. cow b. snake c.fish d. sparrow

Sol. first denote the class to which the second belongs

6. Rat: cat :: Worm : ?

a. Fishing b. earth c. bird d.silk

Sol.second feed the first

7 Walking: Running:: Smiling : ?

a. Feeling b.Laughing c. face d. Weeping

Sol second is the more intense form of the first

8. Eye : Wink :: Heart : ?

a. Move b. Throb c. Pump d. Quiver

Sol second denote the activity of the first

9 house : garbage :: ore : ?

a. Rubbish b. gangue c. sand d. dregs

Sol. the waste of the house is called garbage. simillarly, the impurities in the ore are called ganuge

10. fire : extinguish :: thirst : ?

a.quench b. satiate c mitigate d.drink

sol second is the name given to the act of doing away with the first

11. wizard : witch :: monk : ?

a. madam b. widow c. nun d. virgin

sol. second is feminine gender of the first

12. connoisseur : art :: gourmet : ?

a. food b. money c drink d.flesh

sol first has good tatse for the second

*********************************************************

Type 3- Choosing The Analogus Pair

1. Darekness: Lamp

a. Fatigue : Exercise b.Thirst : Water c.Medicine : Illness d. Study:Classroom

Soln. Just as a lamp eliminates daerkness, so also water eliminates thirest.

2. Fish: Shoal

a. Audience: Theatre b. Shark: School c.Elephant:Flock d.Whale:Herd

Soln. A group of fish is called shoal. Similarly, a group of elephants is called flock.

So, the answer is (c).

3. Energy: Joule

a.Axe:Grind b.Ammeter:Current c. Power : Ampere d.Resistance : Ohm

Soln. Joule is the unit of measuring energy.Similarly ohm is the unit of measuring resistance . So the answer is (d).

*********************************************************

TYPE 4 - Choosing a similar word

1. Iron :copper:zinc

a.ceramic b.carbon c.silver d.coke

Soln. answer is (c). All are metals.

2. Jute :cotton:wool

a.terylene b.silk c.rayon d.nylon

Soln. answer is (b). All are natural fibres.

3. Calf:Kid :Pup

a.infant b.young c.larva d.animal

Soln. anwer is (c). All are young one of animals.

4. Potato:Carrot:Raddish

a.Tomato b.Spinach c.Sesame d.Groundnut

Soln. answer is (d). All grows underground.

5.Marble: Slate: Gneiss

a.Quartzite b.Limestone c.Coal d.Sandstone

Soln. anwer is (a). All are metamorphic rocks.

*********************************************************

TYPE - NUMBER BASED

1. 14 : 9 :: 26 : ?

a. 12 b.13 c.15 d.31

Soln . answer is (c). The relationship is (2x-4): x

2. 8 : 28 :: 27 : ?

a.55 b.63 c.64 d.65

Soln. answer is (d). The relationship is x*3: ( x+1)*3 +1

3. 42 : 56 :: 72 : ?

a. 81 b.90 c.92 d.100

Soln. answer is (b). 42=6x7, 56=7x8, 72=8x9 so missing fig is 90 = 9x10 .

4. 49 : 81 :: 100 : ?

a.64 b.144 c.169 d.none of these

Soln. answer is (b).The relationship is x*2 : ( x+2)*2

CLASSIFICATION REASONING ABILITY FOR ALL EXAMS

type 1 : choosing the odd word

ex: 1 a. zebra b. lion c. tiger d.horse e.giraffe

Soln. here all except, horse are wild animals

ex: 2. a. parrot b.bat c.crow d . sparrow e.pigeon

Soln. here all except bat belongs to class of birds while bat is a mammal.

ex.3 a. copper b. zinc c.brass d.aluminium e.iron

Soln . here all except brass are metals while brass is an alloy.

ex.4 a. apple b. marigold c. rose d. lily e. lotus

Soln. here all except apple are flower while apple is a fruit .

ex.5 a. january b . may c. july d. august e.November

Soln here all except november are months having 31 day .

ex6. a. amethyst b. ruby c.marble d. sapphire e. diamond

Soln . here all except marble are precious stone .

ex.7 a. ginger b.onion c. beetroot d. coriander e. potato

Soln . her all except coriander are modified stem

ex.8 a. bake b. peel c. fry d. boil e.roast

Soln . here all except peel are different form of cooking .

ex.9 a. pistol b.sword c.gun d. rifle e. cannon

Soln . here all except sword are fire arms and can be used from a distance

ex.10 a. cathedral b. mosque c.church d. monastery e.temple

Soln . here all except monastery are place of worship while monastery is the place where monks stay.

TYPE: CHOOSING THE ODD PAIR

Ex.1 a. blacksmith: anvil b. Carpenter: saw c. barber: scissor d. Goldsmith: ornament e. sculptor: chisel

Soln. the answer is (d). In all other pairs, second is the tool used by the first.

Ex.2 a. painter: gallery b. actor: stage c. mason: wall d farmer: field e. worker: factory

Soln. the answer is (c). In all other pairs second is the working place of the first.

Ex.3 a. cow : calf b. dog : bitch c. lion : cub d. tortoise : turtle e. insect : larva

Soln . Clearly , the answer is b. In all other pairs second is the young one of other.

Ex.4 a. volume: litre b. time: second c. length: metre d. resistance: ohm e. pressure : barometer

Soln . Answer is (e). In all other pairs, second is the unit to measure the first.

Ex. 5. a. White: dirty b. easy: difficult c. brave: coward d . end : beginning

Soln . Answer is (a). In all other pairs, the two words are antonyms

TYPE- CHOOSING THE ODD NUMERALS

Ex.1. a. 13 b.17 c.23 d.63 e.71

Soln. Each of the number except 63 is the prime nos. hence answer is (d).

Ex. 2 a. 12 b.25 c.37 d. 49 e.57

Soln. 37 is the only prime nos in the group. Hence answer is (c).

Ex.3 a. 25 b.36 c. 78 d. 144 e.196

Soln. Each of the number except 78 is a perfect square . Hence answer is (c).

Ex.4 a. 131 b. 151 c. 161 d. 171 e.191

Soln. The sum of the digits of each of the number except 161 is an odd number. Hence answer is (c).

Ex. 5 a. 751 b. 734 c. 981 d.853 e.532

Soln. In each number except 751, the difference of the first and the third digit is equal to the middle digit.

Hence answer is (a)

TYPE - CHOOSING THE ODD LETTER GROUP

Ex.1 a. BD b. IK c. PN d.SU e. WY

Soln . The anwer is (c). All other group consist of two alternate letters in order while in this group, they are in reverse order.

Ex.2 a. BCD b. KMN c. QRS d. GHI e. WXY

Soln . The anwer is (b). All other group consist of three consecutive letters while this one doesnot.

ex.3 a. POCG b. KLIZ c. BUDX d. FQMV e. ARTG

Soln . the answer is (d) . All other group consist of one vowel each but this group doesnot .

ex.4 a. CZHK b. MLAG c. XUBU d. SENO e.YDFB

Soln . The answer is (c). This is the only group in which one letter has been repeated.

Example 1

The age of a father 3 years ago was 7 times the age of his son. At present the age of son is five times the age of son. What are the present age of father and son ?

Solution:

Let the present age of son = x years

the present age of father = 5x years

3 years ago

sons age = x-3

Fathers age = 5x-3

7(x-3) = 5x-3

7x-21=5x-3

2x=18

x=9

So, Present age of son is 9 years and father is 5*9=45.

Shortcut

Sons Age = T1(x-1)/x-y= 3*(7-1)/(7-5) = 9

Example 2

A sum of money doubles itself in 10years at S.I . What is the rate of Interest.

Solution:

Let the sum be x

After 10 years it becomes 2x

Interest= Rs.2x- Rs.x =Rs.x

Rate = 100*l/P*T =100*x/x*10 = 10%

Shortcut :

Time*Rate = 100(Multiple Number of Principal Amount -1)

Rate= 100 (Multiple Number of Principal Amount-1 ) /Time

Example

A sum of money doubles itself in 7 years.In how many years will it become four fold?

shortcut :

Double in 7 years

Triple in 14 years

4 times in 21 years

5 times in 28 years

Example

When a person covers a distance between his house and office at 50 km/hr . He is late by 20 min. But when he travels at 60km/hr. He reaches 10 min early.What is the difference between his house and office ?

Solution:

Let the distance be x km
Time taken to cover x km at 50km/hr is = x/50 hrs
Time taken to cover x km at 60km/hr is = x/60 hrs

Difference between time taken = 30 min
∴x/50-x/60 = 30/60

=> 6x-5x/300 = 1/2

=> x = 150 km

Shortcut:

Required Distance = Product of two speeds / Difference of two speeds * Difference between arrival time.

Finding number of Factors

To find the number of factors of a given number, express the number as a product of powers of prime numbers.
In this case, 48 can be written as 16 * 3 = (24 * 3)

Now, increment the power of each of the prime numbers by 1 and multiply the result.

In this case it will be (4 + 1)*(1 + 1) = 5 * 2 = 10 (the power of 2 is 4 and the power of 3 is 1)

Therefore, there will 10 factors including 1 and 48. Excluding, these two numbers, you will have 10 – 2 = 8 factors.

Sum of n natural numbers

The sum of first n natural numbers = n (n+1)/2
The sum of squares of first n natural numbers is n (n+1)(2n+1)/6
The sum of first n even numbers= n (n+1)
The sum of first n odd numbers= n^2

Finding Squares of numbers

To find the squares of numbers near numbers of which squares are known

To find 41^2 , Add 40+41 to 1600 =1681

To find 59^2 , Subtract 60^2-(60+59) =3481

Finding number of Positive Roots

If an equation (i:e f(x)=0 ) contains all positive co-efficient of any powers of x , it has no positive roots then.

Eg: x^4+3x^2+2x+6=0 has no positive roots .

Finding number of Imaginary Roots

For an equation f(x)=0 , the maximum number of positive roots it can have is the number of sign changes in f(x) ; and the maximum number of negative roots it can have is the number of sign changes in f(-x) .
Hence the remaining are the minimum number of imaginary roots of the equation(Since we also know that the index of the maximum power of x is the number of roots of an equation.)

Reciprocal Roots

The equation whose roots are the reciprocal of the roots of the equation ax^2+bx+c is cx^2+bx+a

Roots

Roots of x^2+x+1=0 are 1,w,w^2 where 1+w+w^2=0 and w^3=1

Finding Sum of the roots

For a cubic equation ax^3+bx^2+cx+d=o sum of the roots = – b/a sum of the product of the roots taken two at a time = c/a product of the roots = -d/a

For a biquadratic equation ax^4+bx^3+cx^2+dx+e = 0 sum of the roots = – b/a sum of the product of the roots taken three at a time = c/a sum of the product of the roots taken two at a time = -d/a product of the roots = e/a

Maximum/Minimum

If for two numbers x+y=k(=constant), then their PRODUCT is MAXIMUM if x=y(=k/2). The maximum product is then (k^2)/4
If for two numbers x*y=k(=constant), then their SUM is MINIMUM if x=y(=root(k)). The minimum sum is then 2*root(k) .

In Equalties

x + y >= x+y ( stands for absolute value or modulus ) (Useful in solving some inequations)
a+b=a+b if a*b>=0 else a+b >= a+b
2<= (1+1/n)^n <=3 -> (1+x)^n ~ (1+nx) if x<<<1> When you multiply each side of the inequality by -1, you have to reverse the direction of the inequality.

Product Vs HCF-LCM

Product of any two numbers = Product of their HCF and LCM . Hence product of two numbers = LCM of the numbers if they are prime to each other

AM GM HM

For any 2 numbers a>b a>AM>GM>HM>b (where AM, GM ,HM stand for arithmetic, geometric , harmonic menasa respectively) (GM)^2 = AM * HM

Sum of Exterior Angles

For any regular polygon , the sum of the exterior angles is equal to 360 degrees hence measure of any external angle is equal to 360/n. ( where n is the number of sides). For any regular polygon , the sum of interior angles =(n-2)180 degrees. So measure of one angle in

Square—–=90
Pentagon–=108
Hexagon—=120
Heptagon–=128.5
Octagon—=135
Nonagon–=140
Decagon–=144

Problems on clocks

Problems on clocks can be tackled as assuming two runners going round a circle , one 12 times as fast as the other . That is , the minute hand describes 6 degrees /minute the hour hand describes 1/2 degrees /minute . Thus the minute hand describes 5(1/2) degrees more than the hour hand per minute . The hour and the minute hand meet each other after every 65(5/11) minutes after being together at midnight. (This can be derived from the above) .

Co-ordinates

Given the coordinates (a,b) (c,d) (e,f) (g,h) of a parallelogram , the coordinates of the meeting point of the diagonals can be found out by solving for [(a+e)/2,(b+f)/2] =[ (c+g)/2 , (d+h)/2]

Ratio

If a1/b1 = a2/b2 = a3/b3 = ………….. , then each ratio is equal to (k1*a1+ k2*a2+k3*a3+…………..) / (k1*b1+ k2*b2+k3*b3+…………..) , which is also equal to (a1+a2+a3+…………./b1+b2+b3+……….)

Finding multiples

x^n -a^n = (x-a)(x^(n-1) + x^(n-2) + …….+ a^(n-1) ) ……Very useful for finding multiples .For example (17-14=3 will be a multiple of 17^3 – 14^3)

Exponents

e^x = 1 + (x)/1! + (x^2)/2! + (x^3)/3! + ……..to infinity 2 <>GP

In a GP the product of any two terms equidistant from a term is always constant .
The sum of an infinite GP = a/(1-r) , where a and r are resp. the first term and common ratio of the GP .

Mixtures

If Q be the volume of a vessel q qty of a mixture of water and wine be removed each time from a mixture n be the number of times this operation be done and A be the final qty of wine in the mixture then ,

A/Q = (1-q/Q)^n

Some Pythagorean triplets:

3,4,5———-(3^2=4+5)
5,12,13——–(5^2=12+13)
7,24,25——–(7^2=24+25)
8,15,17——–(8^2 / 2 = 15+17 )
9,40,41——–(9^2=40+41)
11,60,61——-(11^2=60+61)
12,35,37——-(12^2 / 2 = 35+37)
16,63,65——-(16^2 /2 = 63+65)
20,21,29——-(EXCEPTION)

Appolonius theorem

Appolonius theorem could be applied to the 4 triangles formed in a parallelogram.

Function

Any function of the type y=f(x)=(ax-b)/(bx-a) is always of the form x=f(y) .

Finding Squares

To find the squares of numbers from 50 to 59

For 5X^2 , use the formulae

(5X)^2 = 5^2 +X / X^2

Eg ; (55^2) = 25+5 /25
=3025
(56)^2 = 25+6/36
=3136
(59)^2 = 25+9/81
=3481

Successive Discounts

Formula for successive discounts
a+b+(ab/100)
This is used for succesive discounts types of sums.like 1999 population increses by 10% and then in 2000 by 5% so the population in 2000 now is 10+5+(50/100)=+15.5% more that was in 1999 and if there is a decrease then it will be preceeded by a -ve sign and likewise.

Rules of Logarithms:

loga(M)=y if and only if M=ay
loga(MN)=loga(M)+loga(N)
loga(M/N)=loga(M)-loga(N)
loga(Mp)=p*loga(M)
loga(1)=0-> loga(ap)=p
log(1+x) = x – (x^2)/2 + (x^3)/3 – (x^4)/4 ………to infinity [ Note the alternating sign . .Also note that the ogarithm is with respect to base e ]

Quantitative Aptitude – POINTS TO REMEMBER

If an equation (i.e. f(x) = 0) contains all positive co-efficients of any powers of x, it has no positive roots. Eg: x3+3×2+2x+6=0 has no positive roots
For an equation, if all the even powers of x have same sign coefficients and all the odd powers of x have the opposite sign coefficients, then it has no negative roots.
For an equation f(x)=0 , the maximum number of positive roots it can have is the number of sign changes in f(x) ; and the maximum number of negative roots it can have is the number of sign changes in f(-x)
Complex roots occur in pairs, hence if one of the roots of an equation is 2+3i, another has to be 2-3i and if there are three possible roots of the equation, we can conclude that the last root is real. This real root could be found out by finding the sum of the roots of the equation and subtracting (2+3i)+(2-3i)=4 from that sum. For a cubic equation ax3+bx2+cx+d=o

Sum of the roots = – b/a
Sum of the product of the roots taken two at a time = c/a
Product of the roots = -d/a

For a bi-quadratic equation ax4+bx3+cx2+dx+e = 0

Sum of the roots = – b/a
Sum of the product of the roots taken three at a time = c/a
Sum of the product of the roots taken two at a time = -d/a
Product of the roots = e/a

If an equation f(x)= 0 has only odd powers of x and all these have the same sign coefficients or if f(x) = 0 has only odd powers of x and all these have the same sign coefficients, then the equation has no real roots in each case (except for x=0 in the second case)

Consider the two equations, a1x+b1y=c1 and a2x+b2y=c2 Then,

If a1/a2 = b1/b2 = c1/c2, then we have infinite solutions for these equations.
If a1/a2 = b1/b2 <> c1/c2, then we have no solution.
If a1/a2 <> b1/b2, then we have a unique solution.

Roots of x2 + x + 1=0 are 1, w, w2 where 1 + w + w2=0 and w3=1

|a| + |b| = |a + b| if a*b>=0 else, |a| + |b| >= |a + b|

The equation ax2+bx+c=0 will have max. value when a<0 and min. value when a>0. The max. or min. value is given by (4ac-b2)/4a and will occur at x = -b/2a

If for two numbers x + y=k (a constant), then their PRODUCT is MAXIMUM if x=y (=k/2). The maximum product is then (k2)/4.

If for two numbers x*y=k (a constant), then their SUM is MINIMUM if
x=y (=root(k)). The minimum sum is then 2*root (k).

Product of any two numbers = Product of their HCF and LCM. Hence product of two numbers = LCM of the numbers if they are prime to each other.

For any 2 numbers a, b where a>b

a>AM>GM>HM>b (where AM, GM ,HM stand for arithmetic, geometric , harmonic means respectively)

(GM)^2 = AM * HM

For three positive numbers a, b, c

(a + b + c) * (1/a + 1/b + 1/c)>=9

For any positive integer n

2<= (1 + 1/n)^n <=3

a2 + b2 + c2 >= ab + bc + ca

If a=b=c, then the case of equality holds good.

a4 + b4 + c4 + d4 >= 4abcd (Equality arises when a=b=c=d=1)

(n!)2 > nn

If a + b + c + d=constant, then the product a^p * b^q * c^r * d^s will be maximum if a/p = b/q = c/r = d/s

If n is even, n(n+1)(n+2) is divisible by 24

x^n -a^n = (x-a)(x^(n-1) + x^(n-2) + …….+ a^(n-1) ) ……Very useful for finding multiples. For example (17-14=3 will be a multiple of 17^3 – 14^3)

e^x = 1 + (x)/1! + (x^2)/2! + (x^3)/3! + ……..to infinity

Note: 2 < e < 3

log(1+x) = x – (x^2)/2 + (x^3)/3 – (x^4)/4 ………to infinity [Note the alternating sign . .Also note that the logarithm is with respect to base e]

(m + n)! is divisible by m! * n!

When a three digit number is reversed and the difference of these two numbers is taken, the middle number is always 9 and the sum of the other two numbers is always 9.

Any function of the type y=f(x)=(ax-b)/(bx-a) is always of the form x=f(y)

To Find Square of a 3-Digit Number

Let the number be XYZ

Step No.	Operation to be Performed
1	Last digit = Last digit of Sq(Z)
2	Second last digit = 2YZ + any carryover from STEP 1
3	Third last digit 2XZ+ Sq(Y) + any carryover from STEP 2
4	Fourth last digit is 2XY + any carryover from STEP 3
5	Beginning of result will be Sq(X) + any carryover from Step 4

Eg) Let us find the square of 431

Step No.	Operation to be Performed
1	Last digit = Last digit of Sq(1) = 1
2	Second last digit = 231 + any carryover from STEP 1=6+0=6
3	Third last digit 241+ Sq(3) + any carryover from STEP 2 = 8+9+0 = 17 i.e. 7 with carry over of 1
4	Fourth last digit is 243 + any carryover from STEP 3 = 24+1 = 25 i.e. 5 with carry over of 2
5	Beginning of result will be Sq(4) + any carryover from Step 4 = 16+2 = 18
THUS SQ(431) = 185761

If the answer choices provided are such that the last two digits are different, then, we need to carry out only the first two steps only.

The sum of first n natural numbers = n(n+1)/2

The sum of squares of first n natural numbers is n(n+1)(2n+1)/6

The sum of cubes of first n natural numbers is (n(n+1)/2)2/4

The sum of first n even numbers= n (n+1)

The sum of first n odd numbers= n2

If a number ‘N’ is represented as a^x * b^y * c^z… where {a, b, c, …} are prime numbers, then

the total number of factors is (x+1)(y+1)(z+1) ….

the total number of relatively prime numbers less than the number is
N * (1-1/a) * (1-1/b) * (1-1/c)….

the sum of relatively prime numbers less than the number is
N/2 * N * (1-1/a) * (1-1/b) * (1-1/c)….

the sum of factors of the number is {a^(x+1)} * {b^(y+1)} * …../(x * y *…)

Total no. of prime numbers between 1 and 50 is 15

Total no. of prime numbers between 51 and 100 is 10

Total no. of prime numbers between 101 and 200 is 21

The number of squares in n*m board is given by m*(m+1)*(3n-m+1)/6

The number of rectangles in n*m board is given by n+1C2 * m+1C2

If ‘r’ is a rational no. lying between 0 and 1, then, r^r can never be rational.

Certain nos. to be remembered

210 = 45 = 322 = 1024

38 = 94 = 812 = 6561

7 * 11 * 13 = 1001

11 * 13 * 17 = 2431

13 * 17 * 19 = 4199

19 * 21 * 23 = 9177

19 * 23 * 29 = 12673

Where the digits of a no. are added and the resultant figure is 1 or 4 or 7 or 9, then, the no. could be a perfect square.

If a no. ‘N’ has got k factors and a^l is one of the factors such that l>=k/2, then, a is the only prime factor for that no.

To find out the sum of 3-digit nos. formed with a set of given digits

This is given by (sum of digits) * (no. of digits-1)! * 1111…1 (i.e. based on the no. of digits)

Eg) Find the sum of all 3-digit nos. formed using the digits 2, 3, 5, 7 & 8.

Sum = (2+3+5+7+8) * (5-1)! * 11111 (since 5 digits are there)

= 25 * 24 * 11111

=6666600

Consider the equation x^n + y^n = z^n

As per Fermat’s Last Theorem, the above equation will not have any solution whenever n>=3.

Further as per Fermat, where ‘p’ is a prime no. and ‘N’ is co-prime to p, then,
N^(p-1) – 1 is always divisible by p.

145 is the 3-digit no. expressed as sum of factorials of the individual digits i.e.

145 = 1! + 4! + 5!

Where a no. is of the form a^n – b^n, then,

The no. is always divisible by a – b
Further, the no. is divisible by a + b when n is even and not divisible by
a + b when n is odd

Where a no. is of the form a^n + b^n, then,

The no. is usually not divisible by a – b
However, the no. is divisible by a + b when n is odd and not divisible by
a + b when n is even

The relationship between base 10 and base ‘e’ in log is given by
log10N = 0.434 logeN

WINE and WATER formula

Let Q – volume of a vessel, q – qty of a mixture of water and wine be removed each time from a mixture, n – number of times this operation is done and A – final qty of wine in the mixture, then,

A/Q = (1-q / Q)^n

Pascal’s Triangle for computing Compound Interest (CI)

The traditional formula for computing CI is

CI = P*(1+R/100)^N – P

Using Pascal’s Triangle,

Number of Years (N)

——————-

1 1

2 1 2 1

3 1 3 3 1

4 1 4 6 4 1

… 1 …. …. … … ..1

Eg: P = 1000, R=10 %, and N=3 years. What is CI & Amount?

Step 1:

Amount after 3 years = 1 * 1000 + 3 * 100 + 3 * 10 + 1 * 1 = Rs.1331

The coefficients – 1,3,3,1 are lifted from the Pascal’s triangle above.

Step 2:

CI after 3 years = 3*100 + 3*10 + 3*1 = Rs.331 (leaving out first term in step 1)

If N =2, we would have had,

Amt = 1 * 1000 + 2 * 100 + 1 * 10 = Rs.1210

CI = 2 * 100 + 1* 10 = Rs.210

Suppose the price of a product is first increased by X% and then decreased by Y% , then, the final change % in the price is given by:

Final Difference% = X – Y – XY/100

Eg) The price of a T.V set is increased by 40 % of the cost price and then is decreased by 25% of the new price. On selling, the profit made by the dealer was Rs.1000. At what price was the T.V sold?

Applying the formula,

Final difference% = 40 – 25 – (40*25/100) = 5 %.

So if 5 % = 1,000

Then, 100 % = 20,000.

Hence, C.P = 20,000

& S.P = 20,000+ 1000= 21,000

Where the cost price of 2 articles is same and the mark up % is same, then, marked price and NOT cost price should be assumed as 100.

Where ‘P’ represents principal and ‘R’ represents the rate of interest, then, the difference between 2 years’ simple interest and compound interest is given by P * (R/100)2

The difference between 3 years’ simple interest and compound interest is given by (P * R2 *(300+R))/1003

If A can finish a work in X time and B can finish the same work in Y time then both of them together can finish that work in (X*Y)/ (X+Y) time.

If A can finish a work in X time and A & B together can finish the same work in S time then B can finish that work in (XS)/(X-S) time.

If A can finish a work in X time and B in Y time and C in Z time then all of them working together will finish the work in (XYZ)/ (XY +YZ +XZ) time

If A can finish a work in X time and B in Y time and A, B & C together in S time then

C can finish that work alone in (XYS)/ (XY-SX-SY)
B+C can finish in (SX)/(X-S); and
A+C can finish in (SY)/(Y-S)

In case ‘n’ faced die is thrown k times, then, probability of getting atleast one more than the previous throw = nC5/n5

When an unbiased coin is tossed odd no. (n) of times, then, the no. of heads can never be equal to the no. of tails i.e. P (no. of heads=no. of tails) = 0

When an unbiased coin is tossed even no. (2n) of times, then,
P (no. of heads=no. of tails) = 1-(2nCn/22n)

Where there are ‘n’ items and ‘m’ out of such items should follow a pattern, then, the probability is given by 1/m!

Eg)1. Suppose there are 10 girls dancing one after the other. What is the probability of A dancing before B dancing before C?

Here n=10, m=3 (i.e. A, B, C)

Hence, P (A>B>C) = 1/3! = 1/6

Eg)2. Consider the word ‘METHODS’. What is the probability that the letter ‘M’ comes before ‘S’ when all the letters of the given word are used for forming words, with or without meaning?

P (M>S) = 1/2! = 1/2

CALENDAR

Calendar repeats after every 400 years.

Leap year- it is always divisible by 4, but century years are not leap years unless they are divisible by 400.

Century has 5 odd days and leap century has 6 odd days.

In a normal year 1st January and 2nd July and 1st October fall on the same day. In a leap year 1st January 1st July and 30th September fall on the same day.

January 1, 1901 was a Tuesday.

For any regular polygon, the sum of the exterior angles is equal to 360 degrees, hence measure of any external angle is equal to 360/n (where n is the number of sides)

For any regular polygon, the sum of interior angles =(n-2)*180 degrees

So measure of one angle is (n-2)/n *180

If any parallelogram can be inscribed in a circle, it must be a rectangle.

If a trapezium can be inscribed in a circle it must be an isosceles trapezium (i.e. oblique sides equal).

For an isosceles trapezium, sum of a pair of opposite sides is equal in length to the sum of the other pair of opposite sides (i.e. AB+CD = AD+BC, taken in order)

For any quadrilateral whose diagonals intersect at right angles, the area of the quadrilateral is

0.5*d1*d2, where d1, d2 are the length of the diagonals.

For a cyclic quadrilateral, area = root((s-a) * (s-b) * (s-c) * (s-d)), where
s=(a + b + c + d)/2

Further, for a cyclic quadrilateral, the measure of an external angle is equal to the measure of the interior opposite angle.

Area of a Rhombus = Product of Diagonals/2

Given the coordinates (a, b); (c, d); (e, f); (g, h) of a parallelogram , the coordinates of the meeting point of the diagonals can be found out by solving for

[(a + e)/2, (b + f)/2] = [(c + g)/2, (d + h)/2]

Area of a triangle

1/2*base*altitude
1/2*a*b*sin C (or) 1/2*b*c*sin A (or) 1/2*c*a*sin B
root(s*(s-a)*(s-b)*(s-c)) where s=(a+b+c)/2
a*b*c/(4*R) where R is the circumradius of the triangle
r*s ,where r is the inradius of the triangle

In any triangle

a=b*cos C + c*cos B
b=c*cos A + a*cos C
c=a*cos B + b*cos A
a/sin A=b/sin B=c/sin C=2R, where R is the circumradius
cos C = (a^2 + b^2 – c^2)/2ab
sin 2A = 2 sin A * cos A
cos 2A = cos^2 (A) – sin^2 (A)

The ratio of the radii of the circumcircle and incircle of an equilateral triangle is 2:1

Appollonius Theorem

In a triangle ABC, if AD is the median to side BC, then

AB2 + AC2 = 2(AD2 + BD2) or 2(AD2 + DC2)

In an isosceles triangle, the perpendicular from the vertex to the base or the angular bisector from vertex to base bisects the base.
In any triangle the angular bisector of an angle bisects the base in the ratio of the other two sides.

The quadrilateral formed by joining the angular bisectors of another quadrilateral is always a rectangle.

Let W be any point inside a rectangle ABCD, then,

WD2 + WB2 = WC2 + WA2

Let a be the side of an equilateral triangle, then, if three circles are drawn inside this triangle such that they touch each other, then each circle’s radius is given by a/(2*(root(3)+1))

Distance between a point (x1, y1) and a line represented by the equation
ax + by + c=0 is given by |ax1+by1+c|/Sq(a2+b2)
Distance between 2 points (x1, y1) and (x2, y2) is given by
Sq((x1-x2)2+ (y1-y2)2)

Where a rectangle is inscribed in an isosceles right angled triangle, then, the length of the rectangle is twice its breadth and the ratio of area of rectangle to area of triangle is 1:2

Quantitative Aptitude Short cut Methods

Almost every competitive exam today is including quantitative aptitude and reasoning as the part of their entrance exam. Any one can solve aptitude problems but it takes lots of time which is not available at the time of exam. Therefore, the main concern is solve in time. If the solving method for particular problem is known , then problems can be analyzed in seconds, then you can answer the test easily. If you have such solving skills and if you know shortcut methods, then you can are good in aptitude. In aptitude for every problem or question we have short cut methods.

Short cut methods are necessary to be applied at

In bank exams like IBPS PO, IBPS Clerical , IBPS RRB etc.,\
Written test for an IT job/Software job for freshers
CAT,MAT,GRE,GATE ,railways exams,lic,all national level exams

Is Formula and Trick Same

Here you are not going to solve the problems in formula. If you hate mathematics and formulas, you can now try to solve in logical methods,which are not related to any formula. Thus, here you can find suggestions to apply tricks,which improves your logical thinking and solving

How to Learn Tricks to Solve Aptitude problems

These methods/tricks will not available in any books or any other websites,no any website providing the short cut tricks to solve the problems in less time.In this site you can learn aptitude short cut methods

IBPS EXAM SPECIAL

Learn short cut methods in aptitude to get your dream job,so for every day,apply new methods to solve the problems by using our short cut methods.Start from here,the lessons for aptitude tricks from all topics.Today we are explaining you,short cut methods in percentage topic ,which related to aptitude.

SHORT CUT METHODS/TRICKS IN PERCENTAGES

CONCEPT:

Important Points to Note:

When any value increases by
10%, it becomes 1.1 times of itself. (since 100+10 = 110% = 1.1)
20%, it becomes 1.2 times of itself.
36%, it becomes 1.36 times of itself.
4%, it becomes 1.04 times of itself.
Thus we can see the effects on the values due to various percentage increases.

When any value decreases by
10%, it becomes 0.9 times of itself. (Since 100-10 = 90% = 0.9)
20%, it becomes 0.8 times of itself
36%, it becomes 0.64 times of itself
4%, it becomes 0.96 times of itself.
Thus we can see the effects on a value due to various percentage decreases.

Note:

1. When a value is multiplied by a decimal more than 1 it will be increased and when multiplied by less than 1 it will be decreased.

2. The percentage increase or decrease depends on the decimal multiplied.

Eg: 0.7 => 30% decrease, 0.67 => 33% decrease, 0. 956 => 4.4% decrease and so on.

Eg: When the actual value is x, find the value when it is 30% decreased.

Soln: 30% decrease => 0.7 x.

Eg: A value after an increase of 20% became 600. What is the value?

Soln: 1.2x = 600 (since 20% increase)

ð x = 500.

Eg: If 600 is decrease by 20%, what is the new value?

Soln: new value = 0.8 X 600 = 480. (Since 20% decrease)

Thus depending on the decimal we can decide the % change and vice versa.

Eg: When a value is increased by 20%, by what percent should it be reduced to get the actual value?

Soln: (It is equivalent to 1.2 reduced to 1 and we can use % decrease formula)

% decrease = (1.2 – 1)/1.2 X 100 = 16.66%.

When a value is subjected multiple changes, the overall effect of all the changes can be obtained by multiplying all the individual factors of the changes.
Eg: The population of a town increased by 10%, 20% and then decreased by 30%. The new population is what % of the original?

Soln: The overall effect = 1.1 X 1.2 X 0.7 (Since 10%, 20% increase and 30% decrease)

= 0.924 = 92.4%.

Eg: Two successive discounts of 10% and 20% are equal to a single discount of ___

Soln: Discount is same as decrease of price.

So, decrease = 0.9 X 0.8 = 0.72 => 28% decrease (Since only 72% is remaining).

practice problems:

If 20% of 40% of a = 25% of a% of b, then what is b?
a. 8/5 b. 16/25 c. 8/25 d. None

2. By what % is 200 more than 50?

a. 100 b. 200 c. 300 d. None

3. A value changes from 30 to 80. What is the percentage change?

a. 125 b. 166.66 c. 156 d. None

4. The population of a city is increased by 30% and thus became 78000. What is the original population?

a. 76000 b. 64200 c. 60000 d. None

5. In a theatre, the number of seats is increased by 20% and the price per ticket is increased by 10% but the public response decreased by 30%. What is the net effect on the economy of the theatre?

a.10% rise b. 7% fall c. 7% rise d. None

6. A saves 20% of his income. His income is increased by 20% and so he increased his expenditure by 30%. What is the percentage change in his savings?

a. 20% fall b. 4% fall c. 20% rise d. 4% rise

7. The price of petrol is increased by 25%. By what percent the consumption be reduced to make the expenditure remain the same?

a. 25% b. 33.33% c. 20% d. None

8. The side of a square is increased by 20%. The percentage change in its area is ___

a. 20% b. 44% c. 36% d. None

9. If the length of a rectangle is increased by 33.33%, by what percentage should the breadth be reduced to make the area same?

a. 20% b. 33.33% c. 25% d. None

10. In an election between two candidates, A and B, A secured 56% of the votes and won by 48000 votes. Find the total number of votes polled if 20% of the votes were declared invalid.

a. 500000 b. 400000 c. 600000 d. None

Explanation for above problems:

1/5 X 2/5 X a = ¼ X a X b => b = 8/25
% difference = (200-50)/50 X 100 = 300 %
% increase = (80-30)/30 X 100 = 166.66 %
1.3 x = 78000 => x = 60000.
Net effect = 1.2 X 1.1 X 0.7
= 0.924 => 7.6% decrease.

Let I be the income.
Expenditure = 0.8I Savings = 0.2I => 20%

New income = 1.2I (since 20% rise)

New expenditure = (0.8I) X 1.3 (Since 30% rise)

= 1.04I

So, new savings = 1.2I – 1.04I = 0.16I => 16%

(So income decreased form 20% to 16%)

% decrease = (20-16)/20 X 100 = 20%.

It is equivalent to 1.25 decreased to 1.
% decrease = (1.25-1)/1.25 X 100 = 20%

8. % change in area = 1.2 X 1.2 (since area = side X side)

= 1.44 => 44%.

It is equivalent to 1.25 decreased to 1. So 20% decrease.
Valid Votes:
A got 56% => B got 44%

Difference = 12% = 48000

So, 100% = 400000. These are valid votes.

But valid votes are only 80% of total votes.

So, 80% of total votes = 400000 => total votes = 500000

SOURCE -
GOT THESE FROM VARIOUS SITES

Person	P	Q	R	S	T
Place	Hyderabad	Kolkata	Bangalore	Chennai	Delhi
Mode	Bus	Aero plane	Car	Boat	Train

	dramatics	com. sc.	Phy	His	Math
A	X	√	√	√	√
B	√	√	√	X	X
C	X	X	√	√	√
D	√	X	√	√	X
E	√	√	X	√	X

	Madan	Rohit	Parth	Sachin	Nitin	Sagar
Hockey	√	√		√	√	√
Badminton		√	√		X	X
Tennis			√	√	X	X
Chess		√		√
Football		X		X	√	√
Basketball	√	X	√	X
Volleyball	√	X	√	X	X	X
Cricket					√	√

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Saturday, 15 March 2014

ALL SHORTCUT METHODS TO SOLVE REASONING

Short Cut Methods for solving the questions of Percentages

Data sufficiency SHORT CUTS FOR REASONING ABILIT

Ans: RSBUITUHB

BR EA KT HR OV GH

Type: Substitution

Some more rules on English alphabet series

EDCBA / KJIHGF / RQPONML / ZYXWVUTS

Finding Squares of numbers

Finding number of Positive Roots

Finding number of Imaginary Roots

Reciprocal Roots

Roots

Finding Sum of the roots

In Equalties

Product Vs HCF-LCM

AM GM HM

Sum of Exterior Angles

Problems on clocks

Co-ordinates

Ratio

Finding multiples

Exponents

Mixtures

A/Q = (1-q/Q)^n

Quantitative Aptitude Short cut Methods

Short cut methods are necessary to be applied at

Is Formula and Trick Same

How to Learn Tricks to Solve Aptitude problems

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