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# A number n has the prime factors a, b, and c, and only these

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Manager
Joined: 25 Jun 2012
Posts: 65
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Kudos [?]: 55 [0], given: 21

A number n has the prime factors a, b, and c, and only these [#permalink]

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06 Nov 2012, 22:59
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Difficulty:

55% (hard)

Question Stats:

43% (02:05) correct 57% (01:12) wrong based on 30 sessions

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A number n has the prime factors a, b, and c, and only these prime factors. Can n be factored as ab^2c^2?

(1) n is a multiple of ab

(2) n contains exactly 5 factors.
[Reveal] Spoiler: OA
Manager
Joined: 27 Feb 2012
Posts: 136
Followers: 1

Kudos [?]: 54 [0], given: 22

Re: A number n has the prime factors a, b, and c, and only these [#permalink]

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06 Nov 2012, 23:13
A number n has the prime factors a, b, and c, and only these prime factors. Can n be factored as ab^2c^2?

(1) n is a multiple of ab

(2) n contains exactly 5 factors.

(A) Statement (1) ALONE is sufficient, but statement (2) is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.

Can you clarify the question stem?
n be factored as ab^2c^2
is it ab*2c*2 ?
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Manager
Joined: 25 Jun 2012
Posts: 65
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Kudos [?]: 55 [0], given: 21

Re: A number n has the prime factors a, b, and c, and only these [#permalink]

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07 Nov 2012, 13:11
BangOn wrote:
A number n has the prime factors a, b, and c, and only these prime factors. Can n be factored as ab^2c^2?

(1) n is a multiple of ab

(2) n contains exactly 5 factors.

(A) Statement (1) ALONE is sufficient, but statement (2) is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.

Can you clarify the question stem?
n be factored as ab^2c^2
is it ab*2c*2 ?

Hi, sorry for question posted not quite understandably.
$$ab^2c^2$$
Director
Affiliations: GMATQuantum
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Posts: 597
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Kudos [?]: 443 [1] , given: 16

Re: A number n has the prime factors a, b, and c, and only these [#permalink]

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07 Nov 2012, 14:37
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This is a poorly written question, and there are several mistakes.

If a, b, and c are the prime factors of n, then we know that at the very least n must have 8 factors, inclusive of 1 and n. This is because if n = abc, then the number of factors is equal to (1+1)(1+1)(1+1) = 8, essentially add 1 to the powers of all the primes in the factorization and multiply them. I won't go over why that is the case, but that is an important concept to understand. Here statement 2 contradicts this condition and says n has 5 factors.

Also, in a real GMAT question the writers will always clarify and say that n has five factors, inclusive of 1 and n.

Here are few examples of similar questions that are actual GMAT questions, and I would say your valuable time is better spent on these.
I know there are so many problems here and sorting through what is useful and what is not is indeed a daunting task.

1) how-many-different-prime-numbers-are-factors-of-the-positive-126744.html
2) in-n-is-a-positive-integer-less-than-200-and-14n-60-is-an-81459.html
3) if-the-prime-numbers-p-and-t-are-the-only-prime-factors-of-85836.html
4) how-many-different-factors-does-the-integer-n-have-1-n-47115.html
5) if-p-s-and-t-are-positive-prime-numbers-what-is-the-value-78410.html

Cheers,
Dabral
Re: A number n has the prime factors a, b, and c, and only these   [#permalink] 07 Nov 2012, 14:37
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