GRE Math Practice

Try a few of these tricky questions to gauge where you stand on the GRE Math section.

There will be more practice questions posted on this page so keep revisiting!


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.
10

 

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 s2

Given s1 = 20 d = 10

For s2 = 60 d2 : ?

Hence

Or d2 = d1

= 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

1st digit = 9

2nd digit = 8

Sum of first two digits = 17

Sum of four digits is  given as 23, hence

Sum of 3rd and 4th 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 1st 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

32 – 3 = k = 0 \k = - 6

The expression become x2- x – 6

For x = 2

Value is 22 – 2 – 6 = 4 – 2 – 6 = – 4  

Hence (A)