Arithmetic

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Arithmetic

by swerve » Wed Apr 29, 2020 12:22 pm

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\(M\) is a positive two-digit number. When the digits are reversed, the number is \(N\). If \(K = M + N\), which of the following is true?

A. \(K\) must be even
B. \(K\) cannot be square
C. \(K\) cannot be divisible by \(13\)
D. \(K\) must be divisible by \(11\)
E. If \(M\) is even then \(K\) must be even

The OA is D

Source: Magoosh
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Re: Arithmetic

by Scott@TargetTestPrep » Fri May 01, 2020 3:11 pm
swerve wrote:
Wed Apr 29, 2020 12:22 pm
\(M\) is a positive two-digit number. When the digits are reversed, the number is \(N\). If \(K = M + N\), which of the following is true?

A. \(K\) must be even
B. \(K\) cannot be square
C. \(K\) cannot be divisible by \(13\)
D. \(K\) must be divisible by \(11\)
E. If \(M\) is even then \(K\) must be even

The OA is D

Source: Magoosh
We can let M = 10a + b (i.e., a is M’s tens digit and b is its units digit). So N = 10b + a and K = M + N = (10a + b) + (10b + a) = 11a + 11b = 11(a + b). We see that K must be divisible by 11.

Answer: D

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