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## The product P of two prime numbers is between 9 and 55.

tagged by: M7MBA

This topic has 2 expert replies and 0 member replies

### Top Member

M7MBA Moderator
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#### The product P of two prime numbers is between 9 and 55.

Mon Feb 26, 2018 2:04 am
The product P of two prime numbers is between 9 and 55. If one of the prime numbers is greater than 2 but less than 6 and the other is greater than 13 but less than 25, then P =

A. 15
B. 33
C. 34
D. 46
E. 51

The OA is the option E.

Experts, how can I determine that the answer is the option E? May you give me an explanation here? Please.

### GMAT/MBA Expert

EconomistGMATTutor GMAT Instructor
Joined
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Mon Feb 26, 2018 3:20 am
Hello M7MBA.

Let's take a look at your question.

We have one prime number "a" that is greater than 2 and less than 6. Hence a=3, 5.

The other primer number "b" is greater than 13 and less than 25. Hence b=17, 19, 23.

Hence, the possible products are:

If a=3 then

if b=17-------------------a*b=51.
if b=19-------------------a*b=57.
if b=23-------------------a*b=69.

If a=5 then

if b=17------------------a*b=85.
if b=19------------------a*b=95.
if b=23------------------a*b=115.

Therefore the correct answer is the option E=51.

I hope it helps you.

I'm available if you'd like a follow-up.

Regards.

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### GMAT/MBA Expert

Scott@TargetTestPrep GMAT Instructor
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Tue Feb 27, 2018 10:54 am
M7MBA wrote:
The product P of two prime numbers is between 9 and 55. If one of the prime numbers is greater than 2 but less than 6 and the other is greater than 13 but less than 25, then P =

A. 15
B. 33
C. 34
D. 46
E. 51
The primes greater than 2 but less than 6 are 3 and 5.

The primes greater than 13 but less than 25 are 17, 19, and 23.

Thus, we see that P could only be 3 x 17 = 51. Increasing either factor in this product would result in a number that is greater than 55.

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Scott Woodbury-Stewart Founder and CEO

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