GRE Problem Solving Select Many SAMPLE QUESTIONS-4
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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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