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21 Mar 2019, 22:22
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
38% (01:53) correct
62%
(01:54)
wrong
based on 133
sessions
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A positive integer N has exactly 6 unique positive factors. What is the highest prime factor of N?
(1) 6 is a factor of N.
(2) 9 is a factor of N.
(1) 6 is a factor of N.
(2) 9 is a factor of N.
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
29 Mar 2019, 08:28
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amanvermagmat
Question involving 'number of factors = x' are almost always solved via basic number properties.
We'll look for such a solution, a Logical approach.
(1) if 6 is a positive factor of N then so are 1,2, and 3 so we have at least 4 factors (1,2,3,6). If a different prime number p were a factor, then we would also have 2p,3p and 6p, too many. So all factors of N must be powers of 2 or 3 and the highest prime factor of N is 3.
Sufficient.
(2) then (1,3,9) are factors of N. If we also have p other than 3, then we would have (1,3,9,p,3p,9p) which is fine. So we can have p = 2 like before or p > 3. Then we cannot answer the question.
Insufficient.
(A) is our answer.
29 Mar 2019, 18:04
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amanvermagmat
Since N has exactly 6 unique positive factors. It can be expressed as either \(z^5\) or \(x^1*y^2\) because number of factor is (p+1)(q+1).... where \(x=y^p*z^q*....\)
Statement 1:
6 is a factor of N. So, both 2 and 3 are factors of N. Which means N can be expressed as either \(2^1*3^2\) or\(2^2*3^1\). In both case highest prime factor is 3. Sufficient.
Statement 2:
9 is a factor of N. Now N can be either written as \(3^5\) or \(3^2*x^1\), where x is the other prime factor. x can be greater than 3 or not. So, we can't say for sure which is greatest prime factor. Insufficient.
IMO, Option A.
