1.If 2x-y=4 then 6x-3y=?

(a)15

(b)12

(c)18

(d)10

Ans. (b)

2.If x=y=2z and xyz=256 then what is the value of x?

(a)12

(b)8

(c)16

(d)6

Ans. (b)

3. (1/10)18 - (1/10)20 = ?

(a) 99/1020

(b) 99/10

(c) 0.9

(d) none of these

Ans. (a)

4.Pipe A can fill in 20 minutes and Pipe B in 30 mins

and Pipe C can

empty the same in 40 mins.If all of them work

together, find the time

taken to fill the tank

(a) 17 1/7 mins

(b) 20 mins

(c) 8 mins

(d) none of these

Ans. (a)

5. Thirty men take 20 days to complete a job working 9

hours a day.How

many hour a day should 40 men work to complete the

job?

(a) 8 hrs

(b) 7 1/2 hrs

(c) 7 hrs

(d) 9 hrs

Ans. (b)

6. Find the smallest number in a GP whose sum is 38

and product 1728

(a) 12

(b) 20

(c) 8

(d) none of these

Ans. (c)

7. A boat travels 20 kms upstream in 6 hrs and 18 kms

downstream in 4

hrs.Find the speed of the boat in still water and the

speed of the

water current?

(a) 1/2 kmph

(b) 7/12 kmph

(c) 5 kmph

(d) none of these

Ans. (b)

8. A goat is tied to one corner of a square plot of

side 12m by a rope

7m long.Find the area it can graze?

(a) 38.5 sq.m

(b) 155 sq.m

(c) 144 sq.m

(d) 19.25 sq.m

Ans. (a)

9. Mr. Shah decided to walk down the escalator of a

tube station. He

found that if he walks down 26 steps, he requires 30

seconds to

reach the bottom. However, if he steps down 34 stairs

he would only

require 18 seconds to get to the bottom. If the time

is measured from

the moment the top step begins to descend to the

time he steps off

the last step at the bottom, find out the height of

the stair way in

steps?

Ans.46 steps.

10. The average age of 10 members of a committee is

the same as it was

4 years ago, because an old member has been replaced

by a young

member. Find how much younger is the new member ?

Ans.40 years.

11. Three containers A, B and C have volumes a, b, and

c respectively;

and container A is full of water while the other two

are empty. If

from container A water is poured into container B

which becomes 1/3

full, and into container C which becomes 1/2 full, how

much water is

left in container A?

12. ABCE is an isosceles trapezoid and ACDE is a

rectangle. AB = 10

and EC = 20. What is the length of AE?

Ans. AE = 10.

13. In the given figure, PA and PB are tangents to the

circle at A and

B respectively and the chord BC is parallel to

tangent PA. If AC = 6

cm, and length of the tangent AP is 9 cm, then what

is the length of

the chord BC?

Ans. BC = 4 cm.

15 Three cards are drawn at random from an ordinary

pack of cards.

Find the probability that they will consist of a king,

a queen and an ace.

Ans. 64/2210.

16. A number of cats got together and decided to kill

between them

999919 mice. Every cat killed an equal number of

mice. Each cat

killed more mice than there were cats. How many cats

do you think

there were ?

Ans. 991.

17. If Log2 x - 5 Log x + 6 = 0, then what would the

value / values of

x be?

Ans. x = e2 or e3.

18. The square of a two digit number is divided by

half the number.

After 36 is added to the quotient, this sum is then

divided by 2.

The digits of the resulting number are the same as

those in the

original number, but they are in reverse order. The

ten's place of

the original number is equal to twice the difference

between its

digits. What is the number?

Ans. 46

19.Can you tender a one rupee note in such a manner

that there shall

be total 50 coins but none of them would be 2 paise

coins.?

Ans. 45 one paisa coins, 2 five paise coins, 2 ten

paise coins, and 1

twenty-five paise coins.

20.A monkey starts climbing up a tree 20ft. tall. Each

hour, it hops

3ft. and slips back 2ft. How much time would it take

the monkey to

reach the top?

Ans.18 hours.

21. What is the missing number in this series? 8 2

14 6 11 ? 14 6 18 12

Ans. 9

22. A certain type of mixture is prepared by mixing

brand A at Rs.9 a

kg. with brand B at Rs.4 a kg. If the mixture is worth

Rs.7 a kg., how

many kgs. of brand A are needed to make 40kgs. of

the mixture?

Ans. Brand A needed is 24kgs.

23. A wizard named Nepo says "I am only three times my

son's age. My

father is 40 years more than twice my age. Together

the three of us

are a mere 1240 years old." How old is Nepo?

Ans. 360 years old.

24. One dog tells the other that there are two dogs in

front of me.

The other one also shouts that he too had two behind

him. How many are

they?

Ans. Three.

25. A man ate 100 bananas in five days, each day

eating 6 more than

the previous day. How many bananas did he eat on the

first day?

Ans. Eight.

26. If it takes five minutes to boil one egg, how long

will it take to

boil four eggs?

Ans. Five minutes.

27. The minute hand of a clock overtakes the hour hand

at intervals of

64 minutes of correct time. How much a day does the

clock gain or lose?

Ans. 32 8/11 minutes.

28. Solve for x and y: 1/x - 1/y = 1/3, 1/x2 + 1/y2

= 5/9.

Ans. x = 3/2 or -3 and y = 3 or -3/2.

29. Daal is now being sold at Rs. 20 a kg. During last

month its rate

was Rs. 16 per kg. By how much percent should a family

reduce its

consumption so as to keep the expenditure fixed?

Ans. 20 %.

30. Find the least value of 3x + 4y if x2y3 = 6.

Ans. 10.

31. Can you find out what day of the week was January

12, 1979?

Ans. Friday.

32. A garrison of 3300 men has provisions for 32 days,

when given at a

rate of 850 grams per head. At the end of 7 days a

reinforcement

arrives and it was found that now the provisions will

last 8 days

less, when given at the rate of 825 grams per head.

How, many more men

can it feed?

Ans. 1700 men.

33. From 5 different green balls, four different blue

balls and three

different red balls, how many combinations of balls

can be chosen

taking at least one green and one blue ball?

Ans. 3720.

34. Three pipes, A, B, & C are attached to a tank. A &

B can fill it

in 20 & 30 minutes respectively while C can empty it

in 15 minutes.

If A, B & C are kept open successively for 1 minute

each, how soon

will the tank be filled?

Ans. 167 minutes.

35. A person walking 5/6 of his usual rate is 40

minutes late. What is

his usual time? Ans. 3 hours 20 minutes.

36.For a motorist there are three ways going from City

A to City C. By

way of bridge the distance is 20 miles and toll is

$0.75. A tunnel

between the two cities is a distance of 10 miles and

toll is $1.00 for

the vehicle and driver and $0.10 for each passenger. A

two-lane

highway without toll goes east for 30 miles to city B

and then 20

miles in a northwest direction to City C.

1. Which is the shortest route from B to C

(a) Directly on toll free highway to City C

(b) The bridge

(c) The Tunnel

(d) The bridge or the tunnel

(e) The bridge only if traffic is heavy on the toll

free highway

Ans. (a)

2. The most economical way of going from City A to

City B, in terms of

toll and distance is to use the

(a) tunnel

(b) bridge

(c) bridge or tunnel

(d) toll free highway

(e) bridge and highway

Ans. (a)

3. Jim usually drives alone from City C to City A

every working day.

His firm deducts a percentage of employee pay for

lateness. Which

factor would most influence his choice of the bridge

or the tunnel ?

(a) Whether his wife goes with him

(b) scenic beauty on the route

(c) Traffic conditions on the road, bridge and tunnel

(d) saving $0.25 in tolls

(e) price of gasoline consumed in covering additional

10 miles on the

bridge

Ans. (a)

4. In choosing between the use of the bridge and the

tunnel the chief

factor(s) would be:

I. Traffic and road conditions

II. Number of passengers in the car

III. Location of one's homes in the center or

outskirts of one of the

cities

IV. Desire to save $0.25

(a) I only

(b) II only

(c) II and III only

(d) III and IV only

(e) I and II only

Ans. (a)

37.The letters A, B, C, D, E, F and G, not necessarily

in that order,

stand for seven consecutive integers from 1 to 10

D is 3 less than A

B is the middle term

F is as much less than B as C is greater than D

G is greater than F

1. The fifth integer is

(a) A

(b) C

(c) D

(d) E

(e) F

Ans. (a)

2. A is as much greater than F as which integer is

less than G

(a) A

(b) B

(c) C

(d) D

(e) E

Ans. (a)

3. If A = 7, the sum of E and G is

(a) 8

(b) 10

(c) 12

(d) 14

(e) 16

Ans. (a)

4. A - F = ?

(a) 1

(b) 2

(c) 3

(d) 4

(e) Cannot be determined

Ans. (a)

5. An integer T is as much greater than C as C is

greater than E. T

can be written as A + E. What is D?

(a) 2

(b) 3

(c) 4

(d) 5

(e) Cannot be determined

Ans. (a)

6. The greatest possible value of C is how much

greater than the

smallest possible value of D?

(a) 2

(b) 3

(c) 4

(d) 5

(e) 6

Ans. (a)

38.

1. All G's are H's

2. All G's are J's or K's

3. All J's and K's are G's

4. All L's are K's

5. All N's are M's

6. No M's are G's

1. If no P's are K's, which of the following must be

true?

(a) All P's are J's

(b) No P is a G

(c) No P is an H

(d) If any P is an H it is a G

(e) If any P is a G it is a J

Ans. (a)

2. Which of the following can be logically deduced

from the conditions

stated?

(a) No M's are H's

(b) No M's that are not N's are H's

(c) No H's are M's

(d) Some M's are H's

(e) All M's are H's

Ans. (a)

3. Which of the following is inconsistent with one or

more of the

conditions?

(a) All H's are G's

(b) All H's that are not G's are M's

(c) Some H's are both M's and G's

(d) No M's are H's

(e) All M's are H's

Ans. (a)

4. The statement "No L's are J's" is

I. Logically deducible from the conditions stated

II. Consistent with but not deducible from the

conditions stated

III. Deducible from the stated conditions together

with the additional

statement "No J's are K's"

(a) I only

(b) II only

(c) III only

(d) II and III only

(e) Neither I, II nor III

Ans. (a)

39.In country X, democratic, conservative and justice

parties have

fought three civil wars in twenty years. TO restore

stability an

agreement is reached to rotate the top offices

President, Prime

Minister and Army Chief among the parties so that each

party controls

one and only one office at all times. The three top

office holders

must each have two deputies, one from each of the

other parties. Each

deputy must choose a staff composed of equally members

of his or her

chiefs party and member of the third party.

1. When Justice party holds one of the top offices,

which of the

following cannot be true

(a) Some of the staff members within that office are

justice party members

(b) Some of the staff members within that office are

democratic party

members

(c) Two of the deputies within the other offices are

justice party members

(d) Two of the deputies within the other offices are

conservative

party members

(e) Some of the staff members within the other offices

are justice

party members.

Ans. (a)

2. When the democratic party holds presidency, the

staff of the prime

minister's deputies are composed

I. One-fourth of democratic party members

II. One-half of justice party members and one-fourth

of conservative

party members

III. One-half of conservative party members and

one-fourth of justice

party members.

(a) I only

(b) I and II only

(c) II or III but not both

(d) I and II or I and III

(e) None of these

Ans. (a)

3. Which of the following is allowable under the rules

as stated:

(a) More than half of the staff within a given office

belonging to a

single party

(b) Half of the staff within a given office belonging

to a single party

(c) Any person having a member of the same party as

his or her

immediate superior

(d) Half the total number of staff members in all

three offices

belonging to a single party

(e) Half the staff members in a given office belonging

to parties

different from the party of the top office holder in

that office.

Ans. (a)

4. The office of the Army Chief passes from

Conservative to Justice

party. Which of the following must be fired.

(a) The democratic deputy and all staff members

belonging to Justice party

(b) Justice party deputy and all his or hers staff

members

(c) Justice party deputy and half of his Conservative

staff members in

the chief of staff office

(d) The Conservative deputy and all of his or her

staff members

belonging to Conservative party

(e) No deputies and all staff members belonging to

conservative parties.

Ans. (a)

40.In recommendations to the board of trustees a

tuition increase of

$500 per year, the president of the university said

"There were no

student demonstrations over the previous increases of

$300 last year

and $200 the year before". If the president's

statement is accurate

then which of the following can be validly inferred

from the

information given:

I. Most students in previous years felt that the

increases were

justified because of increased operating costs.

II. Student apathy was responsible for the failure of

students to

protest the previous tuition increases.

III. Students are not likely to demonstrate over new

tuition increases.

(a) I only

(b) II only

(c) I or II but not both

(d) I, II and III

(e) None

Ans. (a)

41. The office staff of XYZ corporation presently

consists of three

bookeepers--A, B, C and 5 secretaries D, E, F, G, H.

The management is

planning to open a new office in another city using 2

bookeepers and 3

secretaries of the present staff . To do so they plan

to seperate

certain individuals who don't function well together.

The following

guidelines were established to set up the new office

I. Bookeepers A and C are constantly finding fault

with one another

and should not be sent together to the new office as a

team

II. C and E function well alone but not as a team ,

they should be

seperated

III. D and G have not been on speaking terms and

shouldn't go together

IV Since D and F have been competing for promotion

they shouldn't be a

team

1.If A is to be moved as one of the bookeepers,which

of the following

cannot be a possible working unit.

A.ABDEH

B.ABDGH

C.ABEFH

D.ABEGH

Ans.B

2.If C and F are moved to the new office,how many

combinations are

possible

A.1

B.2

C.3

D.4

Ans.A

3.If C is sent to the new office,which member of the

staff cannot go

with C

A.B

B.D

C.F

D.G

Ans.B

4.Under the guidelines developed,which of the

following must go to the

new office

A.B

B.D

C.E

D.G

Ans.A

5.If D goes to the new office,which of the following

is/are true

I.C cannot go

II.A cannot go

III.H must also go

A.I only

B.II only

C.I and II only

D.I and III only

Ans.D

42.After months of talent searching for an

administrative assistant to

the president of the college the field of applicants

has been narrowed

down to 5--A, B, C, D, E .It was announced that the

finalist would be

chosen after a series of all-day group personal

interviews were

held.The examining committee agreed upon the following

procedure

I.The interviews will be held once a week

II.3 candidates will appear at any all-day interview

session

III.Each candidate will appear at least once

IV.If it becomes necessary to call applicants for

additonal

interviews, no more 1 such applicant should be asked

to appear the

next week

V.Because of a detail in the written applications,it

was agreed that

whenever candidate B appears, A should also be

present.

VI.Because of travel difficulties it was agreed that C

will appear for

only 1 interview.

1.At the first interview the following candidates

appear A,B,D.Which

of the follwing combinations can be called for the

interview to be

held next week.

A.BCD

B.CDE

C.ABE

D.ABC

Ans.B

2.Which of the following is a possible sequence of

combinations for

interviews in 2 successive weeks

A.ABC;BDE

B.ABD;ABE

C.ADE;ABC

D.BDE;ACD

Ans.C

3.If A ,B and D appear for the interview and D is

called for

additional interview the following week,which 2

candidates may be

asked to appear with D?

I. A

II B

III.C

IV.E

A.I and II

B.I and III only

C.II and III only

D.III and IV only

Ans.D

4.Which of the following correctly state(s) the

procedure followed by

the search committee

I.After the second interview all applicants have

appeared at least once

II.The committee sees each applicant a second time

III.If a third session,it is possible for all

applicants to appear at

least twice

A.I only

B.II only

C.III only

D.Both I and II

Ans.A

43. A certain city is served by subway lines A,B and C

and numbers 1 2

and 3

When it snows , morning service on B is delayed

When it rains or snows , service on A, 2 and 3 are

delayed both in the

morning and afternoon

When temp. falls below 30 degrees farenheit afternoon

service is

cancelled in either the A line or the 3 line,

but not both.

When the temperature rises over 90 degrees farenheit,

the afternoon

service is cancelled in either the line C or the

3 line but not both.

When the service on the A line is delayed or

cancelled, service on the

C line which connects the A line, is delayed.

When service on the 3 line is cancelled, service on

the B line which

connects the 3 line is delayed.

Q1. On Jan 10th, with the temperature at 15 degree

farenheit, it

snows all day. On how many lines will service be

affected, including both morning and afternoon.

(A) 2

(B) 3

(C) 4

(D) 5

Ans. D

Q2. On Aug 15th with the temperature at 97 degrees

farenheit it begins

to rain at 1 PM. What is the minimum number

of lines on which service will be affected?

(A) 2

(B) 3

(C) 4

(D) 5

Ans. C

Q3. On which of the following occasions would service

be on the

greatest number of lines disrupted.

(A) A snowy afternoon with the temperature at 45

degree farenheit

(B) A snowy morning with the temperature at 45 degree

farenheit

(C) A rainy afternoon with the temperature at 45

degree farenheit

(D) A rainy afternoon with the temperature at 95

degree farenheit

Ans. B

44. In a certain society, there are two marriage

groups, red and

brown. No marriage is permitted within a group. On

marriage, males

become part of their wives groups; women remain in

their own group.

Children belong to the same group as their parents.

Widowers and

divorced males revert to the group of their birth.

Marriage to more

than one person at the same time and marriage to a

direct descendant

are forbidden

Q1. A brown female could have had

I. A grandfather born Red

II. A grandmother born Red

III Two grandfathers born Brown

(A) I only

(B) III only

(C) I, II and III

(D) I and II only

Ans. D

Q2. A male born into the brown group may have

(A) An uncle in either group

(B) A brown daughter

(C) A brown son

(D) A son-in-law born into red group

Ans. A

Q3. Which of the following is not permitted under the

rules as stated.

(A) A brown male marrying his father's sister

(B) A red female marrying her mother's brother

(C) A widower marrying his wife's sister

(D) A widow marrying her divorced daughter's

ex-husband

Ans. B

Q4. If widowers and divorced males retained their

group they had upon

marrying which of the following would be permissible (

Assume that no

previous marriage occurred)

(A) A woman marrying her dead sister's husband

(B) A woman marrying her divorced daughter's

ex-husband

(C) A widower marrying his brother's daughter

(D) A woman marrying her mother's brother who is a

widower.

Ans. D

Q5. I. All G's are H's

II. All G's are J's or K's

III All J's and K's are G's

IV All L's are K's

V All N's are M's

VI No M's are G's

45. There are six steps that lead from the first to

the second floor.

No two people can be on the same step

Mr. A is two steps below Mr. C

Mr. B is a step next to Mr. D

Only one step is vacant ( No one standing on that step

)

Denote the first step by step 1 and second step by

step 2 etc.

1. If Mr. A is on the first step, Which of the

following is true?

(a) Mr. B is on the second step

(b) Mr. C is on the fourth step.

(c) A person Mr. E, could be on the third step

(d) Mr. D is on higher step than Mr. C.

Ans: (d)

2. If Mr. E was on the third step & Mr. B was on a

higher step than

Mr. E which step must be vacant

(a) step 1

(b) step 2

(c) step 4

(d) step 5

(e) step 6

Ans: (a)

3. If Mr. B was on step 1, which step could A be on?

(a) 2&e only

(b) 3&5 only

(c) 3&4 only

(d) 4&5 only

(e) 2&4 only

Ans: (c)

4. If there were two steps between the step that A was

standing and

the step that B was standing on, and A was on a higher

step than D , A

must be on step

(a) 2

(b) 3

(c) 4

(d) 5

(e) 6

Ans: (c)

5. Which of the following is false

i. B&D can be both on odd-numbered steps in one

configuration

ii. In a particular configuration A and C must either

both an odd

numbered steps or both an even-numbered steps

iii. A person E can be on a step next to the vacant

step.

(a) i only

(b) ii only

(c) iii only

(d) both i and iii

Ans: (c)

46. Six swimmers A, B, C, D, E, F compete in a race.

The outcome is as

follows.

i. B does not win.

ii. Only two swimmers separate E & D

iii. A is behind D & E

iv. B is ahead of E , with one swimmer intervening

v. F is a head of D

1. Who stood fifth in the race ?

(a) A

(b) B

(c) C

(d) D

(e) E

Ans: (e)

2. How many swimmers seperate A and F ?

(a) 1

(b) 2

(c) 3

(d) 4

(e) cannot be determined

Ans: (d)

3. The swimmer between C & E is

(a) none

(b) F

(c) D

(d) B

(e) A

Ans: (a)

4. If the end of the race, swimmer D is disqualified

by the Judges

then swimmer B finishes in which place

(a) 1

(b) 2

(c) 3

(d) 4

(e) 5

Ans: (b)

47. Five houses lettered A,B,C,D, & E are built in a

row next to each

other. The houses are lined up in the order A,B,C,D, &

E. Each of the

five houses has a colored chimney. The roof and

chimney of each

housemust be painted as follows.

i. The roof must be painted either green,red ,or

yellow.

ii. The chimney must be painted either white, black,

or red.

iii. No house may have the same color chimney as the

color of roof.

iv. No house may use any of the same colors that the

every next house

uses.

v. House E has a green roof.

vi. House B has a red roof and a black chimney

1. Which of the following is true ?

(a) At least two houses have black chimney.

(b) At least two houses have red roofs.

(c) At least two houses have white chimneys

(d) At least two houses have green roofs

(e) At least two houses have yellow roofs

Ans: (c)

2. Which must be false ?

(a) House A has a yellow roof

(b) House A & C have different color chimney

(c) House D has a black chimney

(d) House E has a white chimney

(e) House B&D have the same color roof.

Ans: (b)

3. If house C has a yellow roof. Which must be true.

(a) House E has a white chimney

(b) House E has a black chimney

(c) House E has a red chimney

(d) House D has a red chimney

(e) House C has a black chimney

Ans: (a)

4. Which possible combinations of roof & chimney can

house

I. A red roof 7 a black chimney

II. A yellow roof & a red chimney

III. A yellow roof & a black chimney

(a) I only

(b) II only

(c) III only

(d) I & II only

(e) I&II&III

Ans: (e)

48. Find x+2y

(i). x+y=10

(ii). 2x+4y=20

Ans: (b)

49. Is angle BAC is a right angle

(i) AB=2BC

(2) BC=1.5AC

Ans: (e)

50. Is x greater than y

(i) x=2k

(ii) k=2y

Ans: (e)

(a)15

(b)12

(c)18

(d)10

Ans. (b)

2.If x=y=2z and xyz=256 then what is the value of x?

(a)12

(b)8

(c)16

(d)6

Ans. (b)

3. (1/10)18 - (1/10)20 = ?

(a) 99/1020

(b) 99/10

(c) 0.9

(d) none of these

Ans. (a)

4.Pipe A can fill in 20 minutes and Pipe B in 30 mins

and Pipe C can

empty the same in 40 mins.If all of them work

together, find the time

taken to fill the tank

(a) 17 1/7 mins

(b) 20 mins

(c) 8 mins

(d) none of these

Ans. (a)

5. Thirty men take 20 days to complete a job working 9

hours a day.How

many hour a day should 40 men work to complete the

job?

(a) 8 hrs

(b) 7 1/2 hrs

(c) 7 hrs

(d) 9 hrs

Ans. (b)

6. Find the smallest number in a GP whose sum is 38

and product 1728

(a) 12

(b) 20

(c) 8

(d) none of these

Ans. (c)

7. A boat travels 20 kms upstream in 6 hrs and 18 kms

downstream in 4

hrs.Find the speed of the boat in still water and the

speed of the

water current?

(a) 1/2 kmph

(b) 7/12 kmph

(c) 5 kmph

(d) none of these

Ans. (b)

8. A goat is tied to one corner of a square plot of

side 12m by a rope

7m long.Find the area it can graze?

(a) 38.5 sq.m

(b) 155 sq.m

(c) 144 sq.m

(d) 19.25 sq.m

Ans. (a)

9. Mr. Shah decided to walk down the escalator of a

tube station. He

found that if he walks down 26 steps, he requires 30

seconds to

reach the bottom. However, if he steps down 34 stairs

he would only

require 18 seconds to get to the bottom. If the time

is measured from

the moment the top step begins to descend to the

time he steps off

the last step at the bottom, find out the height of

the stair way in

steps?

Ans.46 steps.

10. The average age of 10 members of a committee is

the same as it was

4 years ago, because an old member has been replaced

by a young

member. Find how much younger is the new member ?

Ans.40 years.

11. Three containers A, B and C have volumes a, b, and

c respectively;

and container A is full of water while the other two

are empty. If

from container A water is poured into container B

which becomes 1/3

full, and into container C which becomes 1/2 full, how

much water is

left in container A?

12. ABCE is an isosceles trapezoid and ACDE is a

rectangle. AB = 10

and EC = 20. What is the length of AE?

Ans. AE = 10.

13. In the given figure, PA and PB are tangents to the

circle at A and

B respectively and the chord BC is parallel to

tangent PA. If AC = 6

cm, and length of the tangent AP is 9 cm, then what

is the length of

the chord BC?

Ans. BC = 4 cm.

15 Three cards are drawn at random from an ordinary

pack of cards.

Find the probability that they will consist of a king,

a queen and an ace.

Ans. 64/2210.

16. A number of cats got together and decided to kill

between them

999919 mice. Every cat killed an equal number of

mice. Each cat

killed more mice than there were cats. How many cats

do you think

there were ?

Ans. 991.

17. If Log2 x - 5 Log x + 6 = 0, then what would the

value / values of

x be?

Ans. x = e2 or e3.

18. The square of a two digit number is divided by

half the number.

After 36 is added to the quotient, this sum is then

divided by 2.

The digits of the resulting number are the same as

those in the

original number, but they are in reverse order. The

ten's place of

the original number is equal to twice the difference

between its

digits. What is the number?

Ans. 46

19.Can you tender a one rupee note in such a manner

that there shall

be total 50 coins but none of them would be 2 paise

coins.?

Ans. 45 one paisa coins, 2 five paise coins, 2 ten

paise coins, and 1

twenty-five paise coins.

20.A monkey starts climbing up a tree 20ft. tall. Each

hour, it hops

3ft. and slips back 2ft. How much time would it take

the monkey to

reach the top?

Ans.18 hours.

21. What is the missing number in this series? 8 2

14 6 11 ? 14 6 18 12

Ans. 9

22. A certain type of mixture is prepared by mixing

brand A at Rs.9 a

kg. with brand B at Rs.4 a kg. If the mixture is worth

Rs.7 a kg., how

many kgs. of brand A are needed to make 40kgs. of

the mixture?

Ans. Brand A needed is 24kgs.

23. A wizard named Nepo says "I am only three times my

son's age. My

father is 40 years more than twice my age. Together

the three of us

are a mere 1240 years old." How old is Nepo?

Ans. 360 years old.

24. One dog tells the other that there are two dogs in

front of me.

The other one also shouts that he too had two behind

him. How many are

they?

Ans. Three.

25. A man ate 100 bananas in five days, each day

eating 6 more than

the previous day. How many bananas did he eat on the

first day?

Ans. Eight.

26. If it takes five minutes to boil one egg, how long

will it take to

boil four eggs?

Ans. Five minutes.

27. The minute hand of a clock overtakes the hour hand

at intervals of

64 minutes of correct time. How much a day does the

clock gain or lose?

Ans. 32 8/11 minutes.

28. Solve for x and y: 1/x - 1/y = 1/3, 1/x2 + 1/y2

= 5/9.

Ans. x = 3/2 or -3 and y = 3 or -3/2.

29. Daal is now being sold at Rs. 20 a kg. During last

month its rate

was Rs. 16 per kg. By how much percent should a family

reduce its

consumption so as to keep the expenditure fixed?

Ans. 20 %.

30. Find the least value of 3x + 4y if x2y3 = 6.

Ans. 10.

31. Can you find out what day of the week was January

12, 1979?

Ans. Friday.

32. A garrison of 3300 men has provisions for 32 days,

when given at a

rate of 850 grams per head. At the end of 7 days a

reinforcement

arrives and it was found that now the provisions will

last 8 days

less, when given at the rate of 825 grams per head.

How, many more men

can it feed?

Ans. 1700 men.

33. From 5 different green balls, four different blue

balls and three

different red balls, how many combinations of balls

can be chosen

taking at least one green and one blue ball?

Ans. 3720.

34. Three pipes, A, B, & C are attached to a tank. A &

B can fill it

in 20 & 30 minutes respectively while C can empty it

in 15 minutes.

If A, B & C are kept open successively for 1 minute

each, how soon

will the tank be filled?

Ans. 167 minutes.

35. A person walking 5/6 of his usual rate is 40

minutes late. What is

his usual time? Ans. 3 hours 20 minutes.

36.For a motorist there are three ways going from City

A to City C. By

way of bridge the distance is 20 miles and toll is

$0.75. A tunnel

between the two cities is a distance of 10 miles and

toll is $1.00 for

the vehicle and driver and $0.10 for each passenger. A

two-lane

highway without toll goes east for 30 miles to city B

and then 20

miles in a northwest direction to City C.

1. Which is the shortest route from B to C

(a) Directly on toll free highway to City C

(b) The bridge

(c) The Tunnel

(d) The bridge or the tunnel

(e) The bridge only if traffic is heavy on the toll

free highway

Ans. (a)

2. The most economical way of going from City A to

City B, in terms of

toll and distance is to use the

(a) tunnel

(b) bridge

(c) bridge or tunnel

(d) toll free highway

(e) bridge and highway

Ans. (a)

3. Jim usually drives alone from City C to City A

every working day.

His firm deducts a percentage of employee pay for

lateness. Which

factor would most influence his choice of the bridge

or the tunnel ?

(a) Whether his wife goes with him

(b) scenic beauty on the route

(c) Traffic conditions on the road, bridge and tunnel

(d) saving $0.25 in tolls

(e) price of gasoline consumed in covering additional

10 miles on the

bridge

Ans. (a)

4. In choosing between the use of the bridge and the

tunnel the chief

factor(s) would be:

I. Traffic and road conditions

II. Number of passengers in the car

III. Location of one's homes in the center or

outskirts of one of the

cities

IV. Desire to save $0.25

(a) I only

(b) II only

(c) II and III only

(d) III and IV only

(e) I and II only

Ans. (a)

37.The letters A, B, C, D, E, F and G, not necessarily

in that order,

stand for seven consecutive integers from 1 to 10

D is 3 less than A

B is the middle term

F is as much less than B as C is greater than D

G is greater than F

1. The fifth integer is

(a) A

(b) C

(c) D

(d) E

(e) F

Ans. (a)

2. A is as much greater than F as which integer is

less than G

(a) A

(b) B

(c) C

(d) D

(e) E

Ans. (a)

3. If A = 7, the sum of E and G is

(a) 8

(b) 10

(c) 12

(d) 14

(e) 16

Ans. (a)

4. A - F = ?

(a) 1

(b) 2

(c) 3

(d) 4

(e) Cannot be determined

Ans. (a)

5. An integer T is as much greater than C as C is

greater than E. T

can be written as A + E. What is D?

(a) 2

(b) 3

(c) 4

(d) 5

(e) Cannot be determined

Ans. (a)

6. The greatest possible value of C is how much

greater than the

smallest possible value of D?

(a) 2

(b) 3

(c) 4

(d) 5

(e) 6

Ans. (a)

38.

1. All G's are H's

2. All G's are J's or K's

3. All J's and K's are G's

4. All L's are K's

5. All N's are M's

6. No M's are G's

1. If no P's are K's, which of the following must be

true?

(a) All P's are J's

(b) No P is a G

(c) No P is an H

(d) If any P is an H it is a G

(e) If any P is a G it is a J

Ans. (a)

2. Which of the following can be logically deduced

from the conditions

stated?

(a) No M's are H's

(b) No M's that are not N's are H's

(c) No H's are M's

(d) Some M's are H's

(e) All M's are H's

Ans. (a)

3. Which of the following is inconsistent with one or

more of the

conditions?

(a) All H's are G's

(b) All H's that are not G's are M's

(c) Some H's are both M's and G's

(d) No M's are H's

(e) All M's are H's

Ans. (a)

4. The statement "No L's are J's" is

I. Logically deducible from the conditions stated

II. Consistent with but not deducible from the

conditions stated

III. Deducible from the stated conditions together

with the additional

statement "No J's are K's"

(a) I only

(b) II only

(c) III only

(d) II and III only

(e) Neither I, II nor III

Ans. (a)

39.In country X, democratic, conservative and justice

parties have

fought three civil wars in twenty years. TO restore

stability an

agreement is reached to rotate the top offices

President, Prime

Minister and Army Chief among the parties so that each

party controls

one and only one office at all times. The three top

office holders

must each have two deputies, one from each of the

other parties. Each

deputy must choose a staff composed of equally members

of his or her

chiefs party and member of the third party.

1. When Justice party holds one of the top offices,

which of the

following cannot be true

(a) Some of the staff members within that office are

justice party members

(b) Some of the staff members within that office are

democratic party

members

(c) Two of the deputies within the other offices are

justice party members

(d) Two of the deputies within the other offices are

conservative

party members

(e) Some of the staff members within the other offices

are justice

party members.

Ans. (a)

2. When the democratic party holds presidency, the

staff of the prime

minister's deputies are composed

I. One-fourth of democratic party members

II. One-half of justice party members and one-fourth

of conservative

party members

III. One-half of conservative party members and

one-fourth of justice

party members.

(a) I only

(b) I and II only

(c) II or III but not both

(d) I and II or I and III

(e) None of these

Ans. (a)

3. Which of the following is allowable under the rules

as stated:

(a) More than half of the staff within a given office

belonging to a

single party

(b) Half of the staff within a given office belonging

to a single party

(c) Any person having a member of the same party as

his or her

immediate superior

(d) Half the total number of staff members in all

three offices

belonging to a single party

(e) Half the staff members in a given office belonging

to parties

different from the party of the top office holder in

that office.

Ans. (a)

4. The office of the Army Chief passes from

Conservative to Justice

party. Which of the following must be fired.

(a) The democratic deputy and all staff members

belonging to Justice party

(b) Justice party deputy and all his or hers staff

members

(c) Justice party deputy and half of his Conservative

staff members in

the chief of staff office

(d) The Conservative deputy and all of his or her

staff members

belonging to Conservative party

(e) No deputies and all staff members belonging to

conservative parties.

Ans. (a)

40.In recommendations to the board of trustees a

tuition increase of

$500 per year, the president of the university said

"There were no

student demonstrations over the previous increases of

$300 last year

and $200 the year before". If the president's

statement is accurate

then which of the following can be validly inferred

from the

information given:

I. Most students in previous years felt that the

increases were

justified because of increased operating costs.

II. Student apathy was responsible for the failure of

students to

protest the previous tuition increases.

III. Students are not likely to demonstrate over new

tuition increases.

(a) I only

(b) II only

(c) I or II but not both

(d) I, II and III

(e) None

Ans. (a)

41. The office staff of XYZ corporation presently

consists of three

bookeepers--A, B, C and 5 secretaries D, E, F, G, H.

The management is

planning to open a new office in another city using 2

bookeepers and 3

secretaries of the present staff . To do so they plan

to seperate

certain individuals who don't function well together.

The following

guidelines were established to set up the new office

I. Bookeepers A and C are constantly finding fault

with one another

and should not be sent together to the new office as a

team

II. C and E function well alone but not as a team ,

they should be

seperated

III. D and G have not been on speaking terms and

shouldn't go together

IV Since D and F have been competing for promotion

they shouldn't be a

team

1.If A is to be moved as one of the bookeepers,which

of the following

cannot be a possible working unit.

A.ABDEH

B.ABDGH

C.ABEFH

D.ABEGH

Ans.B

2.If C and F are moved to the new office,how many

combinations are

possible

A.1

B.2

C.3

D.4

Ans.A

3.If C is sent to the new office,which member of the

staff cannot go

with C

A.B

B.D

C.F

D.G

Ans.B

4.Under the guidelines developed,which of the

following must go to the

new office

A.B

B.D

C.E

D.G

Ans.A

5.If D goes to the new office,which of the following

is/are true

I.C cannot go

II.A cannot go

III.H must also go

A.I only

B.II only

C.I and II only

D.I and III only

Ans.D

42.After months of talent searching for an

administrative assistant to

the president of the college the field of applicants

has been narrowed

down to 5--A, B, C, D, E .It was announced that the

finalist would be

chosen after a series of all-day group personal

interviews were

held.The examining committee agreed upon the following

procedure

I.The interviews will be held once a week

II.3 candidates will appear at any all-day interview

session

III.Each candidate will appear at least once

IV.If it becomes necessary to call applicants for

additonal

interviews, no more 1 such applicant should be asked

to appear the

next week

V.Because of a detail in the written applications,it

was agreed that

whenever candidate B appears, A should also be

present.

VI.Because of travel difficulties it was agreed that C

will appear for

only 1 interview.

1.At the first interview the following candidates

appear A,B,D.Which

of the follwing combinations can be called for the

interview to be

held next week.

A.BCD

B.CDE

C.ABE

D.ABC

Ans.B

2.Which of the following is a possible sequence of

combinations for

interviews in 2 successive weeks

A.ABC;BDE

B.ABD;ABE

C.ADE;ABC

D.BDE;ACD

Ans.C

3.If A ,B and D appear for the interview and D is

called for

additional interview the following week,which 2

candidates may be

asked to appear with D?

I. A

II B

III.C

IV.E

A.I and II

B.I and III only

C.II and III only

D.III and IV only

Ans.D

4.Which of the following correctly state(s) the

procedure followed by

the search committee

I.After the second interview all applicants have

appeared at least once

II.The committee sees each applicant a second time

III.If a third session,it is possible for all

applicants to appear at

least twice

A.I only

B.II only

C.III only

D.Both I and II

Ans.A

43. A certain city is served by subway lines A,B and C

and numbers 1 2

and 3

When it snows , morning service on B is delayed

When it rains or snows , service on A, 2 and 3 are

delayed both in the

morning and afternoon

When temp. falls below 30 degrees farenheit afternoon

service is

cancelled in either the A line or the 3 line,

but not both.

When the temperature rises over 90 degrees farenheit,

the afternoon

service is cancelled in either the line C or the

3 line but not both.

When the service on the A line is delayed or

cancelled, service on the

C line which connects the A line, is delayed.

When service on the 3 line is cancelled, service on

the B line which

connects the 3 line is delayed.

Q1. On Jan 10th, with the temperature at 15 degree

farenheit, it

snows all day. On how many lines will service be

affected, including both morning and afternoon.

(A) 2

(B) 3

(C) 4

(D) 5

Ans. D

Q2. On Aug 15th with the temperature at 97 degrees

farenheit it begins

to rain at 1 PM. What is the minimum number

of lines on which service will be affected?

(A) 2

(B) 3

(C) 4

(D) 5

Ans. C

Q3. On which of the following occasions would service

be on the

greatest number of lines disrupted.

(A) A snowy afternoon with the temperature at 45

degree farenheit

(B) A snowy morning with the temperature at 45 degree

farenheit

(C) A rainy afternoon with the temperature at 45

degree farenheit

(D) A rainy afternoon with the temperature at 95

degree farenheit

Ans. B

44. In a certain society, there are two marriage

groups, red and

brown. No marriage is permitted within a group. On

marriage, males

become part of their wives groups; women remain in

their own group.

Children belong to the same group as their parents.

Widowers and

divorced males revert to the group of their birth.

Marriage to more

than one person at the same time and marriage to a

direct descendant

are forbidden

Q1. A brown female could have had

I. A grandfather born Red

II. A grandmother born Red

III Two grandfathers born Brown

(A) I only

(B) III only

(C) I, II and III

(D) I and II only

Ans. D

Q2. A male born into the brown group may have

(A) An uncle in either group

(B) A brown daughter

(C) A brown son

(D) A son-in-law born into red group

Ans. A

Q3. Which of the following is not permitted under the

rules as stated.

(A) A brown male marrying his father's sister

(B) A red female marrying her mother's brother

(C) A widower marrying his wife's sister

(D) A widow marrying her divorced daughter's

ex-husband

Ans. B

Q4. If widowers and divorced males retained their

group they had upon

marrying which of the following would be permissible (

Assume that no

previous marriage occurred)

(A) A woman marrying her dead sister's husband

(B) A woman marrying her divorced daughter's

ex-husband

(C) A widower marrying his brother's daughter

(D) A woman marrying her mother's brother who is a

widower.

Ans. D

Q5. I. All G's are H's

II. All G's are J's or K's

III All J's and K's are G's

IV All L's are K's

V All N's are M's

VI No M's are G's

45. There are six steps that lead from the first to

the second floor.

No two people can be on the same step

Mr. A is two steps below Mr. C

Mr. B is a step next to Mr. D

Only one step is vacant ( No one standing on that step

)

Denote the first step by step 1 and second step by

step 2 etc.

1. If Mr. A is on the first step, Which of the

following is true?

(a) Mr. B is on the second step

(b) Mr. C is on the fourth step.

(c) A person Mr. E, could be on the third step

(d) Mr. D is on higher step than Mr. C.

Ans: (d)

2. If Mr. E was on the third step & Mr. B was on a

higher step than

Mr. E which step must be vacant

(a) step 1

(b) step 2

(c) step 4

(d) step 5

(e) step 6

Ans: (a)

3. If Mr. B was on step 1, which step could A be on?

(a) 2&e only

(b) 3&5 only

(c) 3&4 only

(d) 4&5 only

(e) 2&4 only

Ans: (c)

4. If there were two steps between the step that A was

standing and

the step that B was standing on, and A was on a higher

step than D , A

must be on step

(a) 2

(b) 3

(c) 4

(d) 5

(e) 6

Ans: (c)

5. Which of the following is false

i. B&D can be both on odd-numbered steps in one

configuration

ii. In a particular configuration A and C must either

both an odd

numbered steps or both an even-numbered steps

iii. A person E can be on a step next to the vacant

step.

(a) i only

(b) ii only

(c) iii only

(d) both i and iii

Ans: (c)

46. Six swimmers A, B, C, D, E, F compete in a race.

The outcome is as

follows.

i. B does not win.

ii. Only two swimmers separate E & D

iii. A is behind D & E

iv. B is ahead of E , with one swimmer intervening

v. F is a head of D

1. Who stood fifth in the race ?

(a) A

(b) B

(c) C

(d) D

(e) E

Ans: (e)

2. How many swimmers seperate A and F ?

(a) 1

(b) 2

(c) 3

(d) 4

(e) cannot be determined

Ans: (d)

3. The swimmer between C & E is

(a) none

(b) F

(c) D

(d) B

(e) A

Ans: (a)

4. If the end of the race, swimmer D is disqualified

by the Judges

then swimmer B finishes in which place

(a) 1

(b) 2

(c) 3

(d) 4

(e) 5

Ans: (b)

47. Five houses lettered A,B,C,D, & E are built in a

row next to each

other. The houses are lined up in the order A,B,C,D, &

E. Each of the

five houses has a colored chimney. The roof and

chimney of each

housemust be painted as follows.

i. The roof must be painted either green,red ,or

yellow.

ii. The chimney must be painted either white, black,

or red.

iii. No house may have the same color chimney as the

color of roof.

iv. No house may use any of the same colors that the

every next house

uses.

v. House E has a green roof.

vi. House B has a red roof and a black chimney

1. Which of the following is true ?

(a) At least two houses have black chimney.

(b) At least two houses have red roofs.

(c) At least two houses have white chimneys

(d) At least two houses have green roofs

(e) At least two houses have yellow roofs

Ans: (c)

2. Which must be false ?

(a) House A has a yellow roof

(b) House A & C have different color chimney

(c) House D has a black chimney

(d) House E has a white chimney

(e) House B&D have the same color roof.

Ans: (b)

3. If house C has a yellow roof. Which must be true.

(a) House E has a white chimney

(b) House E has a black chimney

(c) House E has a red chimney

(d) House D has a red chimney

(e) House C has a black chimney

Ans: (a)

4. Which possible combinations of roof & chimney can

house

I. A red roof 7 a black chimney

II. A yellow roof & a red chimney

III. A yellow roof & a black chimney

(a) I only

(b) II only

(c) III only

(d) I & II only

(e) I&II&III

Ans: (e)

48. Find x+2y

(i). x+y=10

(ii). 2x+4y=20

Ans: (b)

49. Is angle BAC is a right angle

(i) AB=2BC

(2) BC=1.5AC

Ans: (e)

50. Is x greater than y

(i) x=2k

(ii) k=2y

Ans: (e)