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

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M7MBA: Moderator; Posts: 2058; Joined: Sun Oct 29, 2017 4:24 am; Thanked: 1 times; Followed by:5 members

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

by M7MBA » 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.

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Source: Beat The GMAT — Problem Solving | Mon Feb 26, 2018 2:04 am

EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pm; Thanked: 180 times; Followed by:12 members

by EconomistGMATTutor » 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 [spoiler]E=51[/spoiler].

I hope it helps you.

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

Regards.

GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8085; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » 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.

Answer: E

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