GRE Problem Solving Select Many Sample Questions

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1. Question :

Two shopkeepers mark items at the same marked price. The first
allows two successive discounts of 15% and 20%. The second shopkeeper
allows two discounts of 20% and 10%. Which of the following is true?
Indicate all correct options.

A. The first sold the items at a lower price

B. The second sold the items at a lower price

C. Both of them sold the items for the same price

D. Total discount given by the first shopkeeper was 22%

E. Total discount given by the second shopkeeper was 28%

Correct Answer:

A and E

Explanation:

Let the marked price be MP

SP=(100-discount)*MP/100

SP of the first shopkeeper

SP after 15% off=(100-15)MP/100

=85MP/100

SP after 20% off=(100-20)(85MP/100)/100

=80*85MP/10000

=68MP/100

Total discount=100-68=32%

SP of the second shopkeeper

SP after 20% off=(100-20)MP/100

=80MP/100

SP after 10% off=(100-10)(80MP/100)/100

=90*80MP/10000

=72MP/100

Total discount=100-72=28%

Option A is true and B and C are false.

Option D is false and E is true.

2. Question:

Which of the following numbers are co-primes? Indicate all correct options.

A. 7 and 47

B. 6 and 36

C. 8 and 81

D. 10 and 109

E. 3 and 39

Correct Answer:

A, C and D

Explanation:

7 and 47 are co-primes since both 7 and 47 are primes.

6 and 36 are not co-primes since they have 6 as their common factor.

8 and 81 are coprimes.

10 and 109 are co-primes.

3 and 39 have 3 as their common factor and hence they are not co-primes.

Options A, C and D are true.

3. Question:

Which of the following numbers are divisible by 125? Indicate all such options.

A. 55120

B. 50512

C. 50125

D. 51250

E. 52105

Correct Answer:

C and D

Explanation:

Those numbers that end in three zeros or its last three digits are divisible by 125 are divisible by 125

55120, 50512 and 52105 are not divisible by 125.

50125 and 51250 are divisible by 125.

GRE Problem Solving Select Many Sample Questions

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