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# Q1 | Prime Numbers

Author Message
Intern
Joined: 31 Jan 2017
Posts: 5

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20 Mar 2017, 05:02
For any positive integer n, the length of n is defined as the number of prime factors whose product is n. For example, the length of 75 is 3, since 75 = 3 x 5 x 5. How many two-digit positive integers have length 6?

(A) None
(B) One
(C) Two
(D) Three
(E) Four

The correct answer is (C). Can anyone explain how to get to this answer?

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Intern
Joined: 31 Jan 2017
Posts: 5
Re: Q1 | Prime Numbers  [#permalink]

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20 Mar 2017, 05:25
Okay, I solved it. I started with the smallest prime number:
2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 64
Then I changed the last number with the next prime number 3:
2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 = 96
Every other combination with 6 prime numbers exceeds 99/ last two-digit positive integer. Therefore the answer must be two.

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Math Expert
Joined: 02 Sep 2009
Posts: 55804
Re: Q1 | Prime Numbers  [#permalink]

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22 Mar 2017, 06:53
thtran wrote:
For any positive integer n, the length of n is defined as the number of prime factors whose product is n. For example, the length of 75 is 3, since 75 = 3 x 5 x 5. How many two-digit positive integers have length 6?

(A) None
(B) One
(C) Two
(D) Three
(E) Four

The correct answer is (C). Can anyone explain how to get to this answer?

Sent from my iPhone using GMAT Club Forum mobile app

This question is discussed here: for-any-positive-integer-n-the-length-of-n-is-defined-as-126740.html

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

_________________
Re: Q1 | Prime Numbers   [#permalink] 22 Mar 2017, 06:53
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