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

Question

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.

BangOn · Answer

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

actleader · Answer

Hi, sorry for question posted not quite understandably.
 ab^2c^2

dabral · Answer

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

This Question is Locked Due to Poor Quality

Hi there,

The question you've reached has been archived due to not meeting our community quality standards. No more replies are possible here.

Looking for better-quality questions? Check out the 'Similar Questions' block below for a list of similar but high-quality questions.

Want to join other relevant Problem Solving discussions? Visit our Data Sufficiency (DS) Forum for the most recent and top-quality discussions.

Thank you for understanding, and happy exploring!

Prep Toolkit