Entries Tagged 'Prep Material' ↓

How many number of times will the digit ‘7′ be written when listing the integers from 1 to 1000?

Sol:
7 does not occur in 1000. So we have to count the number of times it appears between 1 and 999. Any number between 1 and 999 can be expressed in the form of xyz where 0 < x, y, z < 9.

1. The numbers in which 7 occurs only once. e.g 7, 17, 78, 217, 743 etc. This means that 7 is one of the digits and the remaining two digits will be any of the other 9 digits (i.e 0 to 9 with the exception of 7). You have 1*9*9 = 81 such numbers. However, 7 could appear as the first or the second or the third digit. Therefore, there will be 3*81 = 243 numbers (1-digit, 2-digits and 3- digits) in which 7 will appear only once. In each of these numbers, 7 is written once. Therefore, 243 times.

2. The numbers in which 7 will appear twice. e.g 772 or 377 or 747 or 77 In these numbers, one of the digits is not 7 and it can be any of the 9 digits ( 0 to 9 with the exception of 7). There will be 9 such numbers. However, this digit which is not 7 can appear in the first or second or the third place. So there are 3 * 9 = 27 such numbers. In each of these 27 numbers, the digit 7 is written twice. Therefore, 7 is written 54 times.

3. The number in which 7 appears thrice - 777 - 1 number. 7 is written thrice in it. Therefore, the total number of times the digit 7 is written between 1 and 999 is 243 + 54 + 3 = 300
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A three digit number consists of 9,5 and one more number . When these digits are reversed and then subtracted from the original number the answer yielded will be consisting of the same digits arranged yet in a different order. What is the other digit?

Ans : 4

Sol. Let the digit unknown be n.

The given number is then 900+50+n=950+n.
When reversed the new number is 100n+50+9=59+100n.
Subtracting these two numbers we get 891-99n.
The digit can be arranged in 3 ways or 6 ways.
We have already investigated 2 of these ways.
We can now try one of the remaining 4 ways. One of these is n 95

100n+90+5=891-99n
or 199n =796
so, n=4
the unknown digit is 4.
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On sports day,if 30 children were made to stand in a column,16 columns could be formed. If 24 children were made to stand in a column, how many columns could be formed?

Ans. 20

Sol:

Total number of children=30*16=480
Number of columns of 24 children each =480/24=20.
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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
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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

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)
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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)

1. Neeru is Sohan’s mother’s daughter’s daughter. What is the relationship with Sohan ?
(a) niece
(b) aunt
(c) friend
(d) nephew.

2. The average age of a committee of five members is the same as it was five years ago, a young man having been substituted for one of them. The new man, compared to the replaced man, is younger in age by :
(a) 5 yrs.
(b) 25 yrs.
(c) 18 yrs.
(d) 12 yrs.

3. Suman is older than Manju but Manju is not older than Geeta. If Geeta is older than Manju but not older than Suman, then which one of the following is the correct relationship ?
(a) Geeta is older than Suman
(b) Geeta is the younger of them all
(c) Geeta is the oldest among all three
(d) Suman is older than Geeta.

4. If Sita is a faster sprinter than Gita and Meera, Gita is faster than Lucy, but slower than Riya, then who is the slowest ?
(a) Lucy
(b) Sita
(c) Meera
(d) Riya.

5. In a class, there are two sections A and B. If 10 students of section B shift over to section A, the strength of A becomes three times the strength of B. But if 10 students shift over from A to B, both A and B become equal in strength. How many students are there in sections A and B
(a) 50 and 30
(b) 45 and 15
(c) 90 and 40
(d) 80 and 40.

Answers
1. a
2. b
3. d
4. a
5. a

Practice Problems.

Q. A tank is fitted with 8 pipes, some of them that fill the tank and others that are waste pipe meant to empty the tank. Each of the pipes that fill the tank can fill it in 8 hours, while each of those that empty the tank can empty it in 6 hours. If all the pipes are kept open when the tank is full, it will take exactly 6 hours for the tank to empty. How many of these are fill pipes?
(1) 2 (2) 4 (3) 6 (4) 5

Correct Answer - (2)

Solution:
Let the number of fill pipes be ‘n’. Therefore, there will be 8-n, waste pipes.
Each of the fill pipes can fill the tank in 8 hours. Therefore, each of the fill pipes will fill 1/8th of the tank in an hour.
Hence, n fill pipes will fill n/8th of the tank in an hour.

Similarly, each of the waste pipes will drain the full tank in 6 hours. That is, each of the waste pipes will drain 1/6th of the tank in an hour.
Therefore, (8-n) waste pipes will drain ((8-n)/6)th of the tank in an hour.

Between the fill pipes and the waste pipes, they drain the tank in 6 hours. That is, when all 8 of them are opened, 1/6th of the tank gets drained in an hour.

(Amount of water filled by fill pipes in 1 hour - Amount of water drained by waste pipes 1 hour)
= 1/6th capacity of the tank drained in 1 hour.

Note: In problems pertaining to Pipes and Cisterns, as a general rule find out the amount of the tank that gets filled or drained by each of the pipes in unit time (say in 1 minute or 1 hour).

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Q. Pipe A fills a tank of 700 litres capacity at the rate of 40 litres a minute. Another pipe B fills the same tank at the rate of 30 litres a minute. A pipe at the bottom of the tank drains the tank at the rate of 20 litres a minute. If pipe A is kept open for a minute and then closed and pipe B is kept open for a minute and then closed and then pipe C is kept open for a minute and then closed and the cycle repeated, how long will it take for the empty tank to overflow?
(1) 42 minutes (2) 14 minutes (3) 39 minutes (4) None of these

Correct Answer - (4)

Solution:
Pipe A fills the tank at the rate of 40 litres a minute. Pipe B at the rate of 30 litres a minute and Pipe C drains the tank at the rate of 20 litres a minute.

If each of them is kept open for a minute in the order A-B-C, the tank will have 50 litres of water at the end of 3 minutes.

After 13 such cycles, the tank will have 13 * 50 = 650 litres of water.
It will take 13 * 3 = 39 minutes for the 13 cycles to be over.

At the end of the 39th minute, Pipe C will be closed and Pipe A will be opened. It will add 40 litres to the tank.

Therefore, at the end of the 40th minute, the tank will have 650 + 40 = 690 litres of water.
At the end of the 40th minute, Pipe A will be closed and Pipe B will be opened. It will add 30 litres of water in a minute.

Therefore, at the end of the 41st minute, the tank will have 690 + 30 = 720 litres of water.
But then at 700 litres, the tank will overflow. Therefore, Pipe B need not be kept open for a full minute at the end of 40 minutes.

Pipe B needs to add 10 more litres of water at the end of 40 minutes. It will take 1/3rd of a minute to fill 10 litres of water.

Therefore, the total time taken for the tank to overflow = 40 minutes + 1/3 of a minute
or 40 minutes 20 seconds.
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Q. There are 12 pipes that are connected to a tank. Some of them are fill pipes and the others are drain pipes. Each of the fill pipes can fill the tank in 8 hours and each of the drain pipes can drain the tank completely in 6 hours. If all the fill pipes and drain pipes are kept open, an empty tank gets filled in 24 hours. How many of the 12 pipes are fill pipes?
(1) 6 (2) 8 (3) 7 (4) 5

Correct Answer - (3)

Solution:
Let there be ‘n’ fill pipes attached to the tank.
Therefore, there will be 12 - n drain pipes attached to the tank

Each fill pipe fills the tank in 8 hours. Therefore, each of the fill pipes will fill 1/8 of the tank in an hour.
Hence, n fill pipes will fill n/8 of the tank in an hour.
Each drain pipe will drain the tank in 6 hours. Therefore, each of the drain pipes will drain 1/6 of the tank in an hour.
Hence, 12 - n drain pipes will drain (12-n)/6 th of the tank in an hour.
When all these 12 pipes are kept open, it takes 24 hours for an empty tank to overflow. Therefore, in an hour 1/24th of the tank gets filled.
Hence, .
i.e. or 7n - 48 = 1 => 7n = 49 or n = 7.
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Q. Pipe A usually fills a tank in 2 hours. On account of a leak at the bottom of the tank, it takes pipe A 30 more minutes to fill the tank. How long will the leak take to empty a full tank if pipe A is shut?
(1) 2 hours 30 minutes (2) 5 hours (3) 4 hours (4) 10 hours

Correct Answer - (4)

Solution:
The problem can also be mentally done as follows.

Pipe A takes 2 hours to fill the tank. Therefore, it fills half the tank in an hour or 50% of the tank in an hour.
When there is a leak it takes 2 hours 30 minutes for the tank to fill. i.e hours to fill the tank or or 40% of the tank gets filled.

On account of the leak, (50 - 40)% = 10% of the water gets wasted every hour. Therefore, the leak will take 10 hours to drain a full tank.

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Q. There are 12 pipes attached to a tank. Some of them are fill pipes and some are drain pipes. Each of the fill pipes can fill the tank in 12 hours, while each of the drain pipes will take 24 hours to drain a full tank completely. If all the pipes are kept open when the tank was empty, it takes 2 hours for the tank to overflow. How many of these pipes are drain pipes?
(1) 6 (2) 11 (3) 4 (4) 7

Correct Answer - (3)

Solution:
There are 12 pipes attached to the tank. Let ‘n’ of them be fill pipes. Therefore, there will be 12-n drain pipes.

Each fill pipe, fills the tank in 12 hours. Therefore, 1/12n th of the tank gets filled every hour by one fill pipe.
‘n’ fill pipes will, therefore, fill 1/12th of the tank in an hour.

Each drain pipe drains the tank in 24 hours. That is, 1/(12-n)24 th of the tank gets drained by one drain pipe every hour.
12-n drain pipes, will therefore, drain 1/24th of the tank in an hour.
When all the pipes are open when the tank is empty, it takes 2 hours for the tank to overflow. i.e. ½ the tank gets filled every hour.

Equating the information, we get
3n - 12 = 12 or 3n = 24 or n = 8.

Therefore, there are 8 fill pipes and (12 - 8) = 4 drain pipes.

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Q. A pump can be used either to fill or to empty a tank. The capacity of the tank is 3600 m3. The emptying capacity of the pump is 10 m3/min higher than its filling capacity. What is the emptying capacity of the pump if the pump needs 12 more minutes to fill the tank than to empty it?
(1) 50 m3 / min (2) 60 m3 / min (3) 45 m3 / min (4) 90 m3 /min

Correct Answer - (2)

Solution:
Let ‘f’ m3/min be the filling capacity of the pump. Therefore, the emptying capacity of the pump will be = (f + 10 ) m3 / min.
We know that it takes 12 more minutes to fill the tank than to empty it
i.e => 3600 f + 36000 - 3600 f = 12 (f2 + 10 f)
=> 36000 = 12 (f2 + 10 f) => 3000 = f2 + 10 f => f2 + 10 f - 3000 = 0.
Solving for positive value of ‘f’ we get, f = 50.
Therefore, the emptying capacity of the pump = 50 + 10 = 60 m3 / min

Directions :
All questions are based on a passage or a set of conditions. While answering a few of the questions, you would find it useful to draw a rough diagram. To answer any question, choose the answer you think is most appropriate among the given options.

Questions 1- 6

Nine individuals - Z, Y, X, W, V, U, T, S and R - are the only candidates, who can serve on three committees– A, B and C, and each candidate should serve on exactly one of the committees.
Committee A should consist of exactly one member more than committee B.
It is possible that there are no members of committee C.
Among Z, Y and X none can serve on committee A.
Among W, V and U none can serve on committee G.
Among T, S and R none can serve on committee C.

1. In case T and Z are the individuals serving on committee B, how many of the nine individuals should serve on committee C?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7

Ans : B
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2. Of the nine individuals, the largest number that can serve together on committee C is
(A) 9
(B) 8
(C) 7
(D) 6
(E) 5

Ans : D
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3. In case R is the only individual serving on committee B, which among the following should serve on committee A?
(A) W and S
(B) V and U
(C) V and T
(D) U and S
(E) T and S

Ans : E
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4. In case any of the nine individuals serves on committee C, which among the following should be the candidate to serve on committee A?
(A) Z
(B) Y
(C) W
(D) T
(E) S

Ans : C
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5. In case T, S and X are the only individuals serving on committee B, the total membership of committee C should be:
(A) Z and Y
(B) Z and W
(C) Y and V
(D) Y and U
(E) X and V

Ans : A
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6. Among the following combinations which could constitute the membership of committee C?
(A) Y and T
(B) X and U
(C) Y, X and W
(D) W, V and U
(E) Z, X, U and R

Ans : B
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Questions 7- 9

(M, N, O and P are all different individuals)
I. M is the daughter of N.
II. N is the son of O
III. O is the father of P.

7. Among the following statements, which is true ?
(A) O is the uncle of M.
(B) P and N are brothers
(C) M is the daughter of P.
(D) If B is the daughter of N, then M and B are sisters.
(E) If C is the granddaughter of O, then C and M are sisters.

Ans : D
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8. Which among the following statements is contradictory to the above premises?
(A) P is the father of M.
(B) O has three children.
(C) M has one brother.
(D) M is the granddaughter of O.
(E) Another party C, could be the mother of M.

Ans : A
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9. If B is the son of N and B has one brother, D, then
I. M is the sister of D.
II. D and N are brothers.
III. O is the grandfather of D.
(A) I only
(B) II only
(C) III only
(D) I and III only
(E) I and II only

Ans : D

Directions :
All questions are based on a passage or a set of conditions. While answering a few of the questions, you would find it useful to draw a rough diagram. To answer any question, choose the answer you think is most appropriate among the given options.

Questions 1- 7

The only people to attend a conference were four ship captains and the first mates of three of those captains. The captains were L, M, N and O; the first mates were A, D and G. Each person in turn delivered a report to the assembly as follows:

Each of the first mates delivered their report exactly after his or her captain.
The first captain to speak was M, and captain N spoke after him.

1. Among the following which is not an appropriate order of delivered reports?
(A) M, A, N, G, O, L, D
(B) M, D, N, G, L, O, A
(C) M, N, A, L, D, O, G
(D) M, N, A, O, D, L, G
(E) M, N, G, D, O, L, A

Ans : E
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2. In case L speaks after A, and A is the third of the first mates to speak, then among the following statements which would be untrue?
(A) O spoke immediately after G.
(B) The order of the first four speakers was M, G, N, D.
(C) O’s first mate was present.
(D) A was the fourth speaker after M.
(E) The captains spoke in the order M, N, O, L.

Ans : D
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3. Among the following statements which statement must be true?
(A) In case the second speaker was a captain, the seventh speaker was a first mate.
(B) In case the second speaker was a first mate, the seventh speaker was a captain.
(C) In case the third speaker was a first mate, the seventh speaker was a captain.
(D) In case the third speaker was a captain, the seventh speaker was a first mate.
(E) In case the seventh speaker was a first mate, the first and third speakers were captains.

Ans : A
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4. In case A spoke immediately after L and immediately before O, and O was not the last speaker, L spoke
(A) second
(B) third
(C) fourth
(D) fifth
(E) sixth

Ans : C
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5. In case G is M’s first mate, D could be the person who spoke immediately
(A) prior to T
(B) prior to L
(C) prior to V
(D) after T
(E) after V

Ans : D
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6.. In case A is the third of the first mates to speak, and L is the captain whose first mate is not present, which among the following statements must be true?
(A) A spoke sometime before L.
(B) D spoke sometime before O.
(C) L spoke sometime before O.
(D) O spoke sometime before L.
(E) O spoke sometime before N.

Ans : B
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7. Among the following statements, which would make M, D, N, G, L, O, A the only possible sequence of speakers?
(A) D is M’s first mate; G is N’s first mate; A is O’s first mate.
(B) D is M’s first mate; G is N’s first mate; A was the second to speak after L.
(C) The order of the first four speakers was M, D, N, G.
(D) The order of the last three speakers was L, O, A.
(E) The order in which the captains spoke was M, N, L, O.
Ans : B
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Directions :
All questions are based on a passage or a set of conditions. While answering a few of the questions, you would find it useful to draw a rough diagram. To answer any question, choose the answer you think is most appropriate among the given options.

Questions 1-4

(1) The microbe A causes the contagious disease A.
(2) The first symptoms appear after a period of two days since the microbe A enters the body.
(3) The microbe A is found in some flies and bees.
(4) A fly bit Jack on Monday, February 6.
(5) Nick worked with Jack the next day, Tuesday, February 7.
There were no other possibilities of exposure to Disease A.

1. In case Jack showed symptoms of Disease A, which of the following statements would be true?
I. Jack contracted the Disease A from Nick.
II. Jack first noticed symptoms of Disease A on February 8.
III. The fly that Jack was bitten by was not a carrier of the microbe A.
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only

Ans : B
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2. In case Nick displayed symptoms of the disease A, which among the following would be true?
(A) I only
(B) II only
(C) III only
(D) II and III only
(E) I, II and III

Ans : D
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3. In case Jack displayed symptoms of Disease A, which would be true?
I. Jack was also bitten by a fly on February 5.
II. Jack was bitten by a mosquito which carried the microbe A.
III. Nick contracted Disease A from Jack.
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) II and III only

Ans : D
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4. In case Nick displayed the symptoms of Disease A which would be true?
I. Nick was bitten by a bee on February 6.
II. Nick ate food which contained the microbe A.
III. Nick also worked with Jack on February 6.
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II and III

Ans : A
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Questions 5 - 6
The principal evil in today’s society is selfishness. Everywhere we see people, who are concerned only with themselves. Personal advancement is the only motivating force in the world today. This does not mean that individuals are not willing to help one another; on the contrary, _________. But, these are only short-term occurrences which ultimately serve our long-term goal of personal gain.

5. To fill in the blank in the above passage, select one of the options from the below mentioned options:
(A) we are always trying to undermine others’ endeavors.
(B) my uncle Jeremy used to help me with my homework.
(C) no one can be trusted, not even close friends.
(D) our yearning for power prevents us from understanding our existential purpose.
(E) there are many occasions when we graciously offer our assistance.

Ans : E
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6. Which among the following options would most strongly contradict the author’s attitude towards society?
(A) The greatest strength of society is altruism.
(B) The forces of good will ultimately triumph over evil.
(C) Our short-term actions may ostensibly contradict our long-term goals.
(D) We must all learn the art of selfishness.
(E) Morality is the bedrock of a growing community.

Ans : A
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7. It can be proved by an example that our words are devoid of meaning as they cannot be distinguished from their opposites. People think that they are aware of the difference between the meanings of ‘bald’ and ‘having hair’ Let us suppose that an average twenty-one year old has X strands of hair on his or her head. We say that such a person is not bald but has hair. But surely one hair less would make no difference, and a person with X - 1 hairs on his or her head would be said to have hair. Suppose we go on like this, decreasing one hair at a time, the result would be the same. Then what difference would there be between someone who has one hair and someone who has none? We call them both bald. Thus, we cannot make a distinction between the terms ‘bald’ and ‘having hair.’

Among the following statements, which statement best counters the argument above?

(A) The word ‘bald’ can be translated into other languages.
(B) A word can have more than one meaning.
(C) A word such as ‘monkey’ can be applied to several animals that differ in some respects.
(D) Words can lack precision without being meaningless.
(E) People cannot think clearly without using words.

Ans : D
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8. Virus M helps in controlling the population of gnats; they manage to do this by killing the moth’s larvae. Though the virus is always present in the larvae, it is only every six or seven years that the virus seriously decimates the numbers of larvae, greatly reducing the population of the gnats. Scientists are of the opinion that the gnats, usually latent, are activated only when the larvae experience biological stress.
In case the above mentioned scientists are correct, it can be inferred that the decimation of gnat populations by the virus M could be most probably activated by the following conditions?
(A) A shift by the gnats from drought areas to a normal area occupied by them
(B) The resultant stress from defoliation of trees attacked by the gnats for the second consecutive year.
(C) Attacks on the larvae by all kinds by parasitic wasps and flies.
(D) Starvation of the gnat larvae due to over population.
(E) Spraying of gnat infested areas with laboratory - raised Virus M.

Ans : D
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9. In a particular code, the digits from 0 to 9 inclusive are each represented by a different letter of the alphabet, the letter always representing the same digit. In case the following sum
B O P B
+ S K B
———–
C V B Q
————
holds true when it is expressed in digits, which of the following cannot be properly inferred:
(A) B cannot be 0.
(B) B must be less than 5.
(C) Q must be even.
(D) O + S must be greater than 8.
(E) C must be greater than B by 1.
Ans : B

Each question consists of six statements followed by four sets of combinations of three statements. Choose the set in which the statement are most logically related.

1. A. cooks spoil the broth.
B. all cooks are chefs.
C. chefs are professionals.
D. broth is unspoilt by cooks.
E. some professionals are cooks.
F. some chefs cannot make broth.

a. BCE b. DCE c. CDE d. ADF

2. A. P is suffering from anoxeria.
B. anoxeria is when a women is obsessed with her weight.
C. Q must have anoxeria.
D. Best friend often know each others secret.
E. P and Q are best friends.
F. P is obessed with her weight.

a. AED b. AEF c. BAF d. DEC

3. A. Bill Clinton is the most powerful person in the world.
B. Bill will induce India to sign CTBT.
C. The US president is more powerful than anyone else in the world.
D. Bill Clinton is the president of the US.
E. Bill is in India on an official visit.
F. talks include signing the CTBT, removal of trade tariff.

a. BEF b. CED c. CDA d. ACE

4. A. brands are priceless
B. Kissan is a developed brand.
C. Fair & Lovely is a brand.
D. Kissan has leading share in Mumbai.
E. Fair&Lovely is priceless.
F. Mumbai is a big market for developed brands.

a. ACE b. ABF c. ABD d. CDE

5. A. infosys is a leading company.
B. wipro thus has a high market cap.
C. ll leading companies have high market cap.
D. Azim Premji is the second richest man in the world.
E. Wipro has a zooming share price.
F. Infosys has a high market cap.

a. ABD b. BDE c. AEF d. ACF

6. A. all birds are wings.
B. Feathers keep the birds warm.
C. wings are made of feathers.
D. birds are fly.
E. wings are fly.
F. feathers have small holes in them.

a. DBC b. ABC c. CDE d. AED

7. A. economists are very well-read.
B. Keynes is a noted economist.
C. Amartya Sen is also an economist.
D. the Nobel price was won by Amartya Sen.
E. Economists are not philosophers.
F. Keynes is not a philosopher.

a. DEF b. ABD c. BEF d. DCB

8. A. some fishes are whales.
B. Solomon is a fish.
C. All whales live in water.
D. fish have nostrils.
E. all whales have nostrils.
F. some fishes live in water.

a. ACF b. ADE c. FBC d. EDB

9. A. Coca Cola has a market share of 70% in cola market.
B. Frooti is a soft drink.
C. Frooti is an adulterated drink.
D. coca cola contains 1% preservative.
E. Frooti contains preservative.
F. some soft drinks contains preservative.

a. BEF b. CDE c. ABE d. BDA

10. A. Only economists read The Economic Times.
B. B also must be liking The Economic Times.
C. A is an Economist.
D. A reads The Economic Times.
E. A was B’s classmate in graduation.
F. A must have done a PhD in economics.

a. BCD b. ACF c. ADC d. ACE

ANSWERS:
1. a
2. c
3. c
4. a
5. d
6. d
7. c
8. a
9. a
10. c

1. A 5 cubic centimeter cube is painted on all its side. If it is sliced into 1 cubic centimer cubes, how many 1 cubic centimeter cubes will have exactly one of their sides painted?
1. 9
2. 61
3. 98
4. 54

Correct Answer - 54. Choice (4)

Explanation:
When a 5 cc cube is sliced into 1 cc cubes, we will get 5*5*5 = 125 1 cc cubes.

In each side of the larger cube, the smaller cubes on the edges will have more than one of their sides painted.
Therefore, the cubes which are not on the edge of the larger cube and that lie on the facing sides of the larger cube will have exactly one side painted.

In each face of the larger cube, there will be 5*5 = 25 cubes. Of these, there will be 16 cubes on the edge and 3*3 = 9 cubes which are not on the edge.
Therefore, there will be 9 1-cc cubes per face that will have exactly one of their sides painted.
In total, there will be 9*6 = 54 such cubes.

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2. The area of a square field is 24200 sq m. How long will a lady take to cross the field diagonally at the rate of 6.6 km/hr?
(1) 3 minutes (2) 2 minutes
(3) 2.4 minutes (4) 2 minutes 40 seconds

Correct choice - (2) Correct Answer -(2 minutes)

Explanation:
Let ‘a’ meters be the length of a side of the square field.
Therefore, its area = a2 square meters. — (1)
We know that the length of the diagonal ‘d’ of a square whose side is ‘a’ meters = a –– (2)
From (1) and (2), we can deduce that the square of the diagonal = d2 = 2a2

Or d = meters.

The time taken to cross a length of 220 meters while traveling at 6.6 kmph is given by
(converting 1 km = 1000 meters and 1 hour = 60 minutes).

= 2 minutes

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3. The circumference of the front wheel of a cart is 30 ft long and that of the back wheel is 36 ft long. What is the distance travelled by the cart, when the front wheel has done five more revolutions than the rear wheel?
(1) 20 ft (2) 25 ft
(3) 750 ft (4) 900 ft
Correct Answer - (4)

Explanation:
The circumference of the front wheel is 30 ft and that of the rear wheel is 36 feet.
Let the rear wheel make n revolutions. At this time, the front wheel should have made n+5 revolutions.
As both the wheels would have covered the same distance, n*36 = (n+5)*30
36n = 30n + 150
6n = 150
n = 25.
Distance covered = 25*36 = 900 ft.

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4. If the sides of a triangle measure 72, 75 and 21, what is the measure of its in radius?
(1) 37.5 (2) 24
(3) 9 (4) 15
Correct Answer - (3)

Explanation:
The sides of the triangle happen to be a Pythagorean triplet. Hence, the triangle is a right angled triangle.
For a right angled triangle,
The measure of in radius = (product of perpendicular sides) / (perimeter of triangle)
= (72 * 21) / (72 + 21 +75) = 1512 / 168 = 9

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5. A 5 cm cube is cut into as many 1 cm cubes as possible. What is the ratio of the surface area of the larger cube to that of the sum of the surface areas of the smaller cubes?
(1) 1 : 6 (2) 1 : 5
(3) 1 : 25 (4) 1 : 125
Correct Answer - (2)

Explanation:
The volume of the larger cube = 53 = 125 cm3.
The volume of each of the smaller cubes = 13 = 1 cm3. Therefore, one would get 125 smaller cubes.
The surface area of the larger cube = 6a2 = 6(52) = 6 * 25 = 150
The surface area of each of the smaller cubes = 6 (12) = 6.
Therefore, surface area of all of the 125, 1 cm3 cubes = 125 * 6 = 750.
Therefore, the required ratio = 150 : 750 = 1 : 5

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6. If each interior angle of a regular polygon is 150 degrees, then it is
(1) Octagon (2) Decagon
(3) Dodecagon (4) Tetrahedron
Correct Answer - (3)

Explanation:
The sum of the exterior angle and interior angle of a regular polygon is 3600.
As the measure of each interior angle is 1500, the measure of each exterior angle will be 300.
The number of sides of a regular polygon is given by the following relationship n = 360/exterior angle
As the value of each exterior angle is 300, the number of sides = 12.

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7. Four horses are tethered at 4 corners of a square field of side 70 metres so that they just cannot reach one another. The area left ungrazed by the horses is:
(1) 1050 sq.m (2) 3850 sq.m
(3) 950 sq.m (4) 1075 sq.m
Correct Answer - (1)

Explanation:
The length of the rope in which the horses tied should be equal to half of the side of the square plot so that they just cannot reach one another.
Therefore, the length of the rope is 35m (70/2).
The area covered by each horse should be equal to the area of sector with radius of 70/2 = 35m(length of the rope).
Total area covered by the four horses = 4* area of sector of radius 35 metres = Area of circle of radius 35m.
Area left ungrazed by the horses = Area of square field - Area covered by four horses.

= 702 - (22/7)*35*35 = 4900 - 3850 = 1050 sq.m.

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8. The surface area of the three coterminous faces of a cuboid are 6, 15, 10 sq.cm respectively. Find the volume of the cuboid.
(1) 30
(2) 20
(3) 40
(4) 35

Correct Answer - (1)

Explanation:
If l, b, h be the dimensions of the cuboid, then volume of the cuboid = l X b X h
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9. If the diagonal and the area of a rectangle are 25 m and 168 m2, what is the length of the rectangle?
(1) 17 m
(2) 31 m
(3) 12 m
(4) 24 m

Correct Answer - (4)

Explanation:

The diagonal d = 25m. and area A = 168 m2.
Let ‘l’ be the length and ‘b’ be the width of the rectangle.
Therefore, l2 + b2 = d2. and lb = A
We can therefore write (l + b)2 = d2 + 2A and (l - b)2 = d2 - 2A.
Substituting and solving we get, l + b = 31 and l - b = 17. Hence l = 24 and b = 7

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10. A 4 cm cube is cut into 1 cm cubes. What is the percentage increase in the surface area after such cutting?
(1) 4%
(2) 300%
(3) 75%
(4) 400%
Correct Answer - (2)

Solution:

Volume of 4 cm cube = 64 cc. When it is cut into 1 cm cube, the volume of each of the cubes = 1cc
Hence, there will be 64 such cubes. Surface area of small cubes = 6 (12) = 6 sqcm.
Therefore, the surface area of 64 such cubes = 64 * 6 = 384 sqcm.
The surface area of the large cube = 6(42) = 6*16 = 96.
% increase = = 300%
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