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

Correct Answer:

C and D

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

Correct Answer:

A and D

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.

GRE Problem Solving Select Many Sample Questions

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