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1. A rectangular airport runway is x feet long and y feet wide. If its

length is to be made 100 feet longer, by how many square feet will its area

be increased?

(A) xy + 100y (B) xy + 100 (C) 100 ly (D) 100l (E) 100 y

2. The probability of A’s winning a hockey match is 3/2 times the

probability of B’s winning a cricket match. The probability of C’s winning a

race is twice the probability of B’s winning the cricket match. What is the

maximum probability of A’s winning the hockey match?

(A) ¼ (B) ½ (C) 2/3 (D)¾ (E) 1

3. In a certain city, the number of commuters decreased 15 per cent

from June to July and decreased 10 per cent from July to August. By

approximately what per cent would the number of commuters have to

increase from August to September for the number of commuters in

September to be equal to the number of commuters in June?

(A) 80% (B) 77% (C) 75% (D) 31% (E) 24%

4. If the distance required for an automobile to stop varies directly as

the square of its speed, what is the distance required for an automobile

driven at 60 km/hr to stop if it takes 10 meters to stop the automobile

moving at 20 km/hr.

(A) 30m (B) 36m (C) 60m (D) 90m (E) 120m

5. Technological advances in manufacturing radios reduced the

manufacturing cost of parts by 50 per cent and the cost of labour by 60 per

cent. If labour originally accounted for 3 times as much of the

manufacturing cost as parts and it is assumed that total cost consisted only

of labour and parts, what was the per cent decrease in the total cost,

resulting from these advances?

(A) 30% (B) 42.5% (C) 55% (D) 57.5% (E) 70%

6. Of the following, which is the closest to 1?

(A) 1 + 0.04 (B) (1 – 0.04)2 (C) 1- (0.04)½ (D) 1 + 0.042

(E) 1- 0.043

7. Of the following, whish is the greatest amount of money that a

person can borrow at an annual interest rate of 6.5 per cent if the loan and

interest are to be paid off at the end of one year with the money from a

check of Rs. 1,600?

(A) Rs. 2,460 (B) Rs. 1,704 (C) Rs. 1,520 (D) Rs. 1,500

(E) Rs. 1,040

8. An 8 gram object is attached to a balance beam at a point 22 cm.

from the centre of the beam. If the beam is to remain horizontally balanced

how many grams must be attached to the other end of the beam 10 cms

away from the centre?

(A) 27.5 (B) 17.6 (C) 3.6 (D) 1.8 (E) 0.06

9. X can clean the garage in half the time it takes B. If they cleaned it

together in 3 hours, how many hours would it take form A to clean the

garage all by himself?

(A) 6 (B) 5.5 (C) 5 (D) 4.5 (E) 4

10. An office has two copying machines> Machine X can reduce the

size of a page and produces copies, in either the reduced or original size,

at the rate of 1 page per second. Machine Y cannot reduce pages and

produces copies at the rate of 1 page every 2 seconds. What is the least

amount of time required for the two machines together to make 60 copies of

a 120 page if exactly half of the pages of each copy of the report must be

reduced?

(A) 1 hour (B) 1 hour 20 minutes (C) 1 ½ hour (D) 2

hours (E) 3 hours

11. If 13 + x3 + 83 = 93, then x = ?

(A) -1 (B) 0 (C) 1 (D) 6 (E) 9

12. At a certain firm 81 per cent of the investments will mature in more

than 1 year and 27 per cent of the investments will mature in more than 2

years. What per cent of the investments of the firm will mature in more than

1 year but nor in not more than 2 years?

(A) 19% (B) 22% (C) 33% (D) 54% (E) 73%

13. If x is the greatest four- digit number such that the sum of the digits

is 23 and no two digit are the same, which of the following is NOT a digit of

x?

(A) 9 (B) 8 (C) 7 (D) 6 (E) 0

14. On a 200 question test the total score is the number of questions

correctly minus 1/5th of the total number of questions answered incorrectly

or left unanswered. What is the minimum number of questions that must be

answered correctly to receive a total score of at least 100?

(A) 75 (B) 116 (C) 117 (D) 125 (E) 175

15. The averages speed of an automobile for the first half of a 100 km.

trip was 60 km/hr and from the second half was 90 km/hr. What was the

average speed in km/hr for the entire distance?

(A) 68 (B) 72 (C) 75 (D) 78 (E) 80

16. On a certain day, an employee worked from 8:02 a.m. until 4:27 p.

m. and took off ¾ hour for lunch. If the employee did not take any other

breaks, how many hours did the employee work for?

(A) 4.4 (B) 7.15 (C) 7.25 (D) 7.65 (E) 8.4

17. In stack A, invoices are assigned consecutive numbers, beginning

with 1. In stack B, invoices are assigned consecutive odd numbers,

beginning with 1. In stack C, invoices are assigned consecutive multiples of

3. If there are 25 invoices in each of these stacks, how many assigned

numbers are common to all three stacks?

(A) 1 (B) 4 (C) 8 (D) 12 (E) 25

18. If the sum of all the positive divisors of an integer n is equal to 2n,

then n is called a perfect number. Which of the following is a perfect

number?

(A) 4 (B) 8 (C) 12 (D) 24 (E) 28

19. The average of a list of positive numbers is 20 per cent of the sum

of the numbers. How many numbers are there in the list?

(A) 5 (B) 20 (C) 80 (D) 100 (E) Cannot be

said.

20. If k is the constant in the expression x2 – x + k and the expression

has a value of 0 when 3 is substituted for x, what is the value of the

expression when 2 is substituted for x?

(A) -4 (B) -2 (C) 6 (D) 8 (E) Cannot

be found.

ANSWERS

**1.
Area = xy**

New lengths = (x + 100)

New area = (x + 100) y

Increase = xy + 100y xy = 100y

Hence (E)

**2.
P(A) = (P(B)**

** **

P(C) = 2(P(B)

Hence P(A) : P(B) : P(C) :: : 1 : 2

Or 3 : 2 : 4

P(A) is maximum

When P(C) is maximum

Maximum value of P(C) = 1

For P(C) = 1, P(A) =

Hence (D)

**3.
Let the initial number of commuters be x**

No. of commuters at

End of July = x(1 - .15)

= .85K

At end of August = .85 x (1 - .1)

= .85 (.9) x

= .765 x

Now, Let the reqd. Percentage be P

\

or

or p = 30.7%

Hence (D)

**4**
d a s^{2}

Given s_{1} =
20 d = 10

For s_{2} =
60 d_{2} : ?

Hence

Or d_{2} = d_{1}

= 10

= 90 m

Hence (D)

**5.
Let the original manufacturing cost of parts p and labour cost being 3p. Hence **total
cost = p + 3p = 4p

Net Cost

Manufacturing cost of parts =

Labour =

New total cost = 1.2p + .5 p = 1.7 p

Decrease = 4p 1.7p = 2.3p

% decrease = = 57.5%

Hence (D)

**6.
(A) = 1 + .04 = 1.04**

(B) = (1 - .04)2 = 1 + .0016 - .08

(C) = 1 - .2 = .8

(D) = 1 + (.04)2 = 1 +.0016 = 1.0016

(E) = 1 - .000064 = .999936

Hence (E)

**7.
Let the amount be x**

Int = .065 x

Total amount to be repayed = 1 + .065 x

= 1.065x

Given 1.065x = 1600

π x = 1502

Hence Answer is D

**8.
Formula to be used is **

Load x Load arm = effort x effort arm

Here load = 8 gm

Load arm = 22 cm

Effort arm = 10 cm

Effort = ?

Effort = load x load arm/effort arm

=

Hence (B)

**9.
Let two have taken by B be x hrs**

hence, have taken by A is hrs

± 1 hr B class of the room

A class of the room

Working together, in 1 hr pay

Class of the room

So 3

Or, x = 9

Hence, A alone with take or 4.5 hrs.

Hence (D)

**10.
Total number of copies to be made = 120 x 60 = 7200**

3600 pages have to be reduced.

3600 pages will take 3600 sec as Machine

Mean while machine y will have made = 1800 pages

In 1 hr

3600 + 1800 = 5400 pages have been done

Balance 7200 5400 = 1800

Together both machines copy 3/2 pages in sec.

Hence 1800 pages will take sec or 20 minutes.

Hence total hrs is 1 hr 20 minutes

Hence (B)

**11.
13 + x3 + 83 = 93**

or 1, + x3 + 512 = 729

or x3 = 729 512 1 = 216

or x = 6

Hence (D)

**12.
% of investments that nature in more than 1 yr but less than 2 yrs. **Percent
of investment that will nature in more than 1 yr percent of investment that
will where is more than 2 hrs = 81 27 = 54%

Hence (D)

13. **For greatest 4
digit number **

1^{st} digit
= 9

2^{nd} digit
= 8

Sum of first two digits = 17

Sum of four digits is given as 23, hence

Sum of 3^{rd}
and 4^{th} digit has to he 23 17 = 6

So, third digit can be 6 & the fourth digit O.

Hence (C)

**14.
Let the number of questions answered correctly be x.**

Hence Score : x (200 x)

According to condition

x (200 x) ³ 100

or, 5x 200 + x ³ 500

or, 6x ³ 700

x ³ 116.6

or x ³ 117

Hence (C)

**15.
Time taken in correcting 1 ^{st} half = **

Increasing second half =

Total time =

Speed =

= = 72

Hence (B)

**16.
Total time = 8hrs 24 minutes**

Break = 45 minutes

Hence working time = 7 hrs 39 minutes

Correcting into decimals : 7 +

= 7.65

Hence (D)

**17.
A = 1,2,3
.. 25**

B = 1,3,5 .. 50

C = 3,6,9,12, 75

Common values =

Odd multiples of 3

= 3,9,15,21

Hence (B)

**18.
Sum of positive divisors of a = 1+2+4=7**

Sum of the divisors of 8

= 1 + 2 + 4 + 8 = 15

of 12 = 1 + 2 + 3 + 4 + 6 +12 = 28

of 24 = 1 + 2 + 3 + 4 + 6 + 8 + 12 + 24 = 60

of 28 = 1+2+4+7+14+28 = 56 = 2 x 28 = 56 = 2 x 28

Hence (E)

**19.
Let there be n number and their sum be s **

According to condition

Hence n = 5

Hence (A)

**20.
For x = 3**

3^{2} 3 = k
= 0 \k = - 6

The expression become x2- x 6

For x = 2

Value is 2^{2}
2 6 = 4 2 6 = 4

Hence (A)