## GRE Problem Solving Select Many Sample Questions

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1. Question:

Raman bought an article after a 20% discount. Had he bought the
article after a 25% discount, he would have saved \$500. Which of the
following
is true? Indicate all such options.

A. The marked price of the article was \$25000

B. The marked price of the article cannot be determined

C. The marked price of the article was \$10000

D. If he sells the article for \$10000, he gains 20%

E. If he sells the article for \$10000, he gains 25%

C and E

Explanation:

Let MP be the marked price and SP be the selling price.

SP=(100-discount%)MP/100

Price after 20% discount – Price after 25% discount=\$500

MP(100-20)/100 – MP(100-25)/100=500

MP*5/100=500

MP=50000/5=10000

The article was marked at \$10000

He bought the article for MP(100-discount)/100

=10000(100-20)/100

=10000*80/100

=\$8000

Let CP be the cost price and SP be the selling price.

Profit%=(SP-CP)/CP*100

=(10000-8000)/8000*100

=25%

Option C is true and A and B are false.

Option D is false and E is true.

2. Question:

Five men and 2 boys can together work four times as much as a man
and a boy working together can. Which of the following is true?
Indicate all correct statements.

A. Each man is twice as fast as a boy

B. Each boy is half as efficient as a man

C. Each boy is twice as fast as a man

D. Ten men complete the task in one hour that five boys do in two hours

E. Five boys and ten men are equally efficient as 13 men together are

A and B

Explanation:

Let the work done by one man in one hour be x and that done by a boy be y.

According to the conditions, we have

5x+2y=4(x+y)

5x + 2y=4x + 4y

5x – 4x=4y – 2y

x=2y

Hence, each man is twice as fast as a boy or each boy is half as efficient as a man.

Options A and B are true.

Each man is twice as fast as a boy. Option C is false.

x/y=2/1

Let work done by a boy in one hour be 1

Work done by one man in one hour will be 2

Work done by 10 men in one hour=10*2=20

Work done by 5 boys in two hours=5*1+5*1=5+5=10

Option D is false

Work done by 5 boys and 10 men in one hour=5*1+10*2

=5+20=25

Work done by 13 men in one hour=13*2=26

Option E is false.

3. Question:

Pipe A can fill a tank in 12 minutes and pipe B can fill it in 15 minutes. Pipe C can empty the tank in 5 minutes.
Which of the following is true? Indicate all correct options.

A. When all the pipes are open, the tank cannot be filled at all

B. When pipes A and B are open, the tank fills in 20 minutes

C. When pipes A and B are open, the tank fills in 20/3 minutes

D. When all the pipes are open, the tank fills in 25 minutes

E. When all the pipes are open, the tank fills in 45 minutes

[x^2=x*x]

A and C

Explanation:

Tank filled by pipe A in one minute=1/12

Tank filled by pipe B in one minute=1/15

Tank emptied by pipe C in one minute=1/5

Tank filled by pipe A and B together in one minute=1/12+1/15

=(5+4)/(2*2*3*5)

=9/60=3/20

Time taken by pipes A and B to fill the tank=20/3 minutes.

Option C is true and B is false.

Tank filled in one minute when all pipes are open=1/12+1/15-1/5

=(5+4-12)/(2*2*3*5)

=-3/60

=-1/20

Option A is true and D and E are false.

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