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21 Jan 2020, 04:20
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D
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Difficulty:
15%
(low)
Question Stats:
77% (01:19) correct
23%
(01:42)
wrong
based on 289
sessions
History
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Time
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Not Attempted Yet
If x, n, and m are positive integers and x/ n = m, is x divisible by 3?
(1) m is divisible by 6.
(2) n is divisible by 15.
(1) m is divisible by 6.
(2) n is divisible by 15.
21 Jan 2020, 06:21
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Bunuel
Given: x/ n = m i.e. x = m*n and x, m and n are integers
Question: Is x divisible by 3?
Statement 1: m is divisible by 6 = 2*3.
and x is a multiple of m i.e. x is also divisible by 3 as well hence
SUFFICIENT
Statement 2: n is divisible by 15 = 3*5
and x is a multiple of n i.e. x is also divisible by 3 as well hence
SUFFICIENT
Answer: Option D
21 Jan 2020, 07:31
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Bunuel
Given: x, n, and m are positive integers and x/n = m
Take: x/n = m
Multiply both sides by n to get: x = nm
Target question: Is x divisible by 3
Statement 1: m is divisible by 6
In other words, m is a multiple of 6
So, we can write: m = 6k (for some integer k)
Since we already know that x = nm, we can now replace m to write: x = (n)(6k)
Rewrite as: x = (n)(3)(2)(k)
At this point we can clearly see that x is divisible by 3
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: n is divisible by 15
In other words, n is a multiple of 15
So, we can write: n = 15k (for some integer k)
Since we already know that x = nm, we can now replace n to write: x = (15k)(m)
Rewrite as: x = (n)(3)(5)(k)(m)
At this point we can clearly see that x is divisible by 3
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer: D
Cheers,
Brent
