# Problem Solving Select Many GRE Sample Questions 4

## GRE Problem Solving Select Many Sample Questions

1. Question:

Which of the following is true for the equations 11/u-7/v=1 and 9/u-4/v=6? Indicate all correct statements.

• A. The equations have a unique solutions
• B. The equations represent parallel lines
• C. u<v
• D. v<u
• E. u+v=5/6
Correct Answer: A, D and E

Explanation:

11/u-7/v=1 and 9/u-4/v=6

Put x = 1/u and y = 1/v

11x - 7y = 1 ...(1)

9x - 4y = 6 ...(2)

Multiply (1) by 4 and (2) by 7 and subtract one from the other

44x - 28y - 63x + 28y = 4 - 42

- 19x = -38

x = 38/19=2

Putting in (1), we get

11(2) - 7y = 1

7y = 22-1

y = 21/7 = 3

x = 2, y = 3

u = 1/x = 1/2 and v = 1/y = 1/3

The equations have a unique solution.

Option A is true and B is false.

v

u+v = 1/2+1/3 = (3+2)/6 = 5/6

Option E is true.

2. Question:

If x/a+y/b=2 and ax-by = a^2-b^2, then which of the following statements is true? Indicate all correct statements.

• A. ax+by=2
• B. bx-ay=0
• C. bx+ay = 2
• D. x/b+y/a = (a^2-b^2)
• E. x/b+y/a = (a^2+b^2)/ab

[a^2=a*a]

Explanation:

x/a+y/b=2 ...(1)

ax-by=a^2-b^2 ...(2)

Multiply (1) by a^2 and subtract (2) from it

ax+a^2y/b- ax + by = 2a^2 -a^2 + b^2

a^2y/b+by = a^2+b^2

(a^2+b^2)y/b = (a^2+b^2)

y = b

Put y = b in (1)

x/a+b/b=2

x/a = 2-1 = 1

x = a

x=a and y = b

bx-ay=ba-ab=0

x/b+y/a = a/b+ b/a

= (a^2+b^2)/ab

Options B and E are true and A, C and D are false.

3. Question:

The difference between two numbers is 5 and the difference between their squares is 65. Which of the following is true? Indicate all correct options.

• A. The sum of the numbers is 13
• B. The sum of their squares is 100
• C. The product of the numbers is 40
• D. The difference of their cubes is 665
• E. The product of their squares is 1296
Correct Answer: A, D and E

Explanation:

Let the two numbers be x and y, x>y

x-y = 5 ...(1)

x^2-y^2=65 ...(2)

Put x = y+5 in (2)

(y+5)^2-y^2=65

y^2+25+10y-y^2=65

10y = 65 - 25 = 40

y = 4

x = y+5 = 4+5 = 9

The sum of the numbers = x+y = 9+4= 13

The sum of their squares = x^2+y^2

= 9^2+4^2 = 81+16 = 97

The product of the numbers = xy=9*4=36

The difference of their cubes = x^3-y^3

= 9^3-4^3 = 729 - 64 = 665

The product of their squares = x^2*y^2

= 9^2*4^2 = 81*16 = 1296

Options A, D and E are true.

## GRE Problem Solving Select Many Sample Questions

### Terms and Conditions

Information published in TestPrepPractice.net is provided for informational and educational purpose alone for deserving students, researchers and academicians. Though our volunteers take great amount of pain and spend significant time in validating the veracity of the information or study material presented here, we cannot be held liable for any incidental mistakes. All rights reserved. No information or study material in this web site can be reproduced or transmitted in any form, without our prior consent. However the study materials and web pages can be linked from your web site or web page for

• Research

• Education

No permission is required to link any of the web page with educational information available in this web site from your web site or web page