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Is the integer x divisible by 24 ?

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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Thu Sep 14, 2017 10:34 pm
Vincen wrote:Is the integer x divisible by 24 ?

(1) x is divisible by 8
(2) x is divisible 6

OA is C.

How can I make this DS question? Is the statement (1) sufficient?
Statement 1: x is divisible by 8

For x to be divisible by 24, it must be divisible by 8 as well as 3. However, we do not know if x is also divisible by 3 too. Insufficient.

Statement 2: x is divisible by 6

For x to be divisible by 24, it must be divisible by 6 as well as 4. However, we do not know if x is also divisible by 4 too. Insufficient.

Statement 1 & 2:

The LCM of 8 and 6 is 24, thus x is divisible by 24. Sufficient.

The correct answer: C

Hope this helps!

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-Jay
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