If a and b are positive integer,is ab−−√3ab3 an intege

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by GMATGuruNY » Sat Jul 30, 2016 2:41 am
AbdurRakib wrote:Image
Statement 1:
Case 1: a=1, b=1
In this case, ∛(ab) = ∛(1*1) = 1, so the answer to the question stem is YES.
Case 2: a=1, b=2
In this case, ∛(ab) = ∛(1*2) = ∛2, so the answer to the question stem is NO.
INSUFFICIENT.

Statement 2:
b = √a
b² = a.
Thus:
∛(ab) = ∛(b²b) = ∛b³ = b = integer, so the answer to the question stem is YES.
SUFFICIENT.

The correct answer is B.
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by Matt@VeritasPrep » Fri Aug 05, 2016 3:29 pm
Try numbers, I'd say.

S1:

If a = 1 and b = 1, we're set.

If a = 4 and b = 1, we're not.

NOT SUFFICIENT

S2:

If a = 1, then b = 1, we're set.

If a = 4, then b = 2, we're set.

If a = 9, then b = 3, we're set, etc.

So it seems apparent enough that we'll always get an integer; SUFFICIENT. (Of course, the algebra in Guru's solution shows you why, but in a pinch, trying valid values of a and b should help you discern that S2 is probably sufficient on its own.)