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If x = abc, is x/3 an integer?

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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Wed Oct 25, 2017 1:49 am
LUANDATO wrote:If x = abc, is x/3 an integer?

(1) a, b, and c are consecutive integers.
(2) a < b < c

The OA is A.

Can any expert explain this DS question please? I don't understand it.
(1) a, b, and c are consecutive integers.

The product of three consecutive integers is divisible by 3. Sufficient.

See how.

Say the three consecutive integers are n, (n + 1), and (n + 2). Since an integer divisible by 3 will leave a reminder either 0, 1, or 2, we see that one among n, (n + 1), and (n + 2) will leave a reminder 0 upon being divided by 3. Thus abc is divisible by 3.

You may test with few examples. Sufficient.

(2) a < b < c

Case 1: a < b < c => 1 < 2 < 3. abc = 1*2*3 is divisible by 3.
Case 2: a < b < c => 1 < 2 < 4. abc = 1*2*4 is not divisible by 3.

Insufficient.

The correct answer: A

Hope this helps!

-Jay

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