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15 Jan 2020, 02:21
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B
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Difficulty:
5%
(low)
Question Stats:
84% (00:49) correct
16%
(01:30)
wrong
based on 120
sessions
History
Date
Time
Result
Not Attempted Yet
Is 6x/13 an integer?
(1) x is a prime number
(2) 3x is divisible by 13
(1) x is a prime number
(2) 3x is divisible by 13
15 Jan 2020, 07:07
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Bunuel
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
Answer: B
Cheers,
Brent
Archit3110
Major Poster
15 Jan 2020, 07:43
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Bunuel
#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
