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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # Is 6x/13 an integer? (1) x is a prime number (2) 3x is divisible by 13

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Math Expert V
Joined: 02 Sep 2009
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Is 6x/13 an integer? (1) x is a prime number (2) 3x is divisible by 13  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 84% (00:56) correct 16% (01:09) wrong based on 31 sessions

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Is 6x/13 an integer?

(1) x is a prime number
(2) 3x is divisible by 13

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GMAT Club Legend  V
Joined: 11 Sep 2015
Posts: 4342
Re: Is 6x/13 an integer? (1) x is a prime number (2) 3x is divisible by 13  [#permalink]

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Bunuel wrote:
Is 6x/13 an integer?

(1) x is a prime number
(2) 3x is divisible by 13

Target question: Is 6x/13 an integer?
ASIDE: In order for 6x/13 to be an integer, 6x must be divisible by 13.

Statement 1: x is a prime number
Let's TEST some values.
There are several values of x that satisfy statement 1. Here are two:
Case a: x = 13. In this case, 6x/13 = 6(13)/13 = 6. So, the answer to the target question is YES, 6x/13 IS an integer
Case b: x = 2. In this case, 6x/13 = 6(2)/13 = 12/13. So, the answer to the target question is NO, 6x/13 is NOT an integer
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 3x is divisible by 13
If 3x is divisible by 13, then we can say that 3x = 13k for some integer k.
Notice that: 6x/13 = (2)(3x)/13
Replace values to get: 6x/13 = (2)(3x)/13 = (2)(13k)/13 = 2k = some integer [if k is an integer, then 2k must also be an integer]
So, the answer to the target question is YES, 6x/13 IS an integer
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Cheers,
Brent
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Re: Is 6x/13 an integer? (1) x is a prime number (2) 3x is divisible by 13  [#permalink]

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Bunuel wrote:
Is 6x/13 an integer?

(1) x is a prime number
(2) 3x is divisible by 13

#1
x is prime no
x= 2,3,5,.. 13
we get 6x/13 as yes & no to be an integer value
insufficient
#2
3x is divisible by 13
x has to be 13
so 6x/13 would be 6 hence an integer ; sufficient
IMO B Re: Is 6x/13 an integer? (1) x is a prime number (2) 3x is divisible by 13   [#permalink] 15 Jan 2020, 06:43
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