BTGmoderatorDC wrote: ↑Tue Mar 03, 2020 7:53 pm
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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