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20 Jun 2018, 06:06
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
62% (01:44) correct
38%
(01:49)
wrong
based on 193
sessions
History
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Time
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Not Attempted Yet
If \(\frac{x}{6}\) is a positive integer, does \(x\) have more than two different positive prime factors?
(1) \(\frac{x}{4}\) is a positive integer.
(2) \(\frac{x}{9}\) is a positive integer.
(1) \(\frac{x}{4}\) is a positive integer.
(2) \(\frac{x}{9}\) is a positive integer.
20 Jun 2018, 06:49
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gmatbusters
From the question stem, we know that \frac{x}{6} is a positive integer. So, the possible values of x = 6, 12, 18, 24, 30, ...
The question stem asks whether x have more than two different positive prime factors. From the previous analysis, we know that the least possible prime factors are 2 and 3 (since the possible values of x are the multiple of 6)
(1) \(\frac{x}{4}\) is a positive integer.
When we consider this statement, it means that x is divisible by 4 and 6. The possible values of x are 12, 24, 36, 48, 60, ...
Let's take a look at some possible values;
x = 12 = \(2^2*3\) --> 2 prime factors
x = 60 = \(2^2*3*5\) --> 3 prime factors
(1) insufficient
(2) \(\frac{x}{9}\) is a positive integer.
When we consider this statement, it means that x is divisible by 6 and 9. The possible values of x are 18, 36, 54, 72, 90 ...
Let's take a look at some possible values;
x = 18 = \(2*3^2\) --> 2 prime factors
x = 90 = \(2*3^2*5\) --> 3 prime factors
(2) insufficient
Consider (1) and (2) together, x must be divisible by 4,6,9. The possible values of x are 36, 72, 108 ... (multiple of 36)
applying the same concept, we will know that both statements is still insufficient e.g. 36 --> 2 prime factors, \(36*5\) --> 3 prime factors
So my answer is "E"
20 Jun 2018, 08:06
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gmatbusters
Hi Folks!
Since x/6 is a positive integer : x is 6 or positive multiples of 6.
For x to have more than two different positive prime factors the prime factorization of x should give us a minimum of 3 different primes. ( as 2 & 3 are already present no matter what)
(1) x/4 is a positive integer - tells us 2^2 is present in prime factorization of x. No new prime is added. Hence insuff
(2) x/9 is a positive integer - tells us 3^2 is present in prime fac of x. Again no new prime is added. Hence insuff
(1) + (2) combined - No new info is added. Again insuff
Hence Option (E) is correct. As 2 or more than 2 prime factors may be present in x.
Best,
Gladi
