# GRE Problem Solving Select Many SAMPLE QUESTIONS-4

## GRE Problem Solving Select Many Sample Questions

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1. Question:

Which of the following is true? Indicate all such options.

A. 36 is the fourth proportional to the numbers 60, 48 and 30

B. 27:72::5:8

C. The third proportional to 0.8 and 0.2 is 0.05.

D. The numbers 0.2, 0.12, 0.3 and 0.18 are in proportion

E. 3:5::7:9

Explanation:

For 36 to be the fourth proportional 60/48 = 30/36

5/4 = 5/6, which is not true. Option A is false.

27/72=5/8

3/8 = 5/8 is not true. Option B is false.

Let x be the third proportional

0.8/0.2=0.2/x

x = 0.2*0.2/0.8 = 0.1/2 = 0.05

Option C is true.

For the numbers to be in proportion 0.2/0.12 = 0.3/0.18

1/0.6 = 1/0.6, which is true. Option D is true.

3/5 is not equal to 7/9. Option E is false.

2. Question:

A, B and C invested capital in the ratio 6:4:9 and their shares of profits were in ratio 3:2:5. Which of the following is true? Indicate all such options.

A. Their time of investment was in ratio 9:9:10

B. Their time of investment was in ratio 9:6:14

C. Their time of investment was in ratio 18:8:45

D. If the total profit was \$50000, A received \$15000

E. If the total profit was \$50000, B received \$15000

Explanation:

Ratio of investment = 6:4:9

Ratio of profit = 3:2:5

Ratio of time of investment = 3/6:2/4:5/9

= 1/2:1/2:5/9

= 9/2:9/2:5

= 9:9:10

Option A is true and B and C are false.

If the total profit was \$50000,

then the share of A is given by

Share = 3/(3+2+5)*50000

= 3/10*50000

= \$15000

Share of B = 2/(3+2+5)*50000

= 2/10*50000

= 10000

Option D is true and E is false.

3. Question:

Amit, Paul and Sam invest \$50000 in a business. Amit invests \$4000 more than Paul does and Paul invests \$5000 more than Sam does. If the total profit was \$70000, then which of the following is true? Indicate all correct statements.

A. The ratio of the investment of Amit, Paul and Sam is 21:17:12

B. The ratio of the investment of Amit, Paul and Sam is 12:17:21

C. The ratio of the investment of Amit, Paul and Sam is 12:5:4

D. The profit of Paul was \$23800

E. The profit of Sam was \$16800

Correct Answer: A, D and E

Explanation:

Let the investment of Sam be \$x

Investment of Paul = \$(x+5000)

Investment of Amit = \$(x+5000+4000) = \$(x+9000)

50000 = x+(x+5000)+(x+9000)

50000 = 3x + 14000

3x = 50000-14000

x = 36000/3 = 12000

Sam invested \$12000

Paul invested \$12000+5000 = \$17000

Amit invested \$17000+4000 = \$21000

The ratio of the investment of Amit, Paul and Sam is 21:17:12

Option A is true and B and C are false.

Total profit = 70000

Total profit of Sam = 12/(21+17+12)*70000

= 12/50*70000 = 16800

Total profit of Paul = 17/50*70000

= 23800

Options D and E are true.

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