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An integer grater than 1 that is not prime is called

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by BTGmoderatorDC » Wed Oct 23, 2019 5:27 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

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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Wed Oct 23, 2019 9:25 pm
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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