An integer grater than 1 that is not prime is called composite. If the two-digit integer n is greater than 20, is n

[BTGmoderatorDC]

An integer grater than 1 that is not prime is called composite. If the two-digit integer n is greater than 20, is n composite?

(1) The tens digit of n is a factor of the units digit of n.
(2) The tens digit of n is 2


OA A

Source: GMAT Prep

[Jay@ManhattanReview]

An integer grater than 1 that is not prime is called composite. If the two-digit integer n is greater than 20, is n composite?

(1) The tens digit of n is a factor of the units digit of n.
(2) The tens digit of n is 2

OA A

Source: GMAT Prep

Say n = [xy], where x = tens digit ≥ 2, and y = units digit ≥ 1

Thus, n = 10x + y

Since n > 20, to ascertain whether n is composite, we must ensure wether n is non-prime.

Let's take each statement one by one.

(1) The tens digit of n is a factor of the units digit of n.

Given that n = 10x + y, from Statement (1), we have y = px, whether x = a psotive integer

Thus, n = 10x + px = x(10 + p)

Since x ≥ 2, we see that n is a multiple of two integers; thus, n is non-prime or a composite no. The answer is yes. Sufficient.

(2) The tens digit of n is 2.

If n = 22, the answer is yes; however, if n = 23, the answer is no. Insufficient.

The correct answer: A

Hope this helps!

-Jay
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