BTGmoderatorDC wrote: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 the two-digit integer n is greater than 20 is xy. Thus, the required integer n = 10x + y.
Let's take each statement one by one.
(1) The tens digit of n is a factor of the units digit of n.
=> y = px
Thus, n = 10x + px = x(10 + p). We see that n is a multiple of x. Since n > 20, we have x > 1. Thus, n is a multiple of an integer greater than 1; thus n is a composite number. The answer is no. Sufficient.
(2) The tens digit of n is 2.
If n = 21/22/24/25/26/27/28, n is a composite number; however, if n = 23/29, n is not a composite number. No unique answer. Insufficient.
The correct answer:
A
Hope this helps!
-Jay
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