Even numbers

Question

If A, B, and C are integers, is A + B + C even?

(1) A - C - B is even
(2) (A-C)/B is even

This is a similar question to m22 #22 except that the original question didn't pose any restrictions on numbers.

nonameee · Answer

Here's my solution and I would like to double check it:

(1) A-C-B is EVEN

In terms of even/odd the signs before the numbers don't matter. So A-C-B is the same as A+B+C or -A-B-C

Sufficient

(2) (A-C)/B is ODD

There are two options:

I. (A-C) is ODD & B is ODD
II. (A-C) is EVEN & B is EVEN

Using the same logic as in (1), we can conclude that (2) is sufficient since ODD+ODD = EVEN and EVEN+EVEN = EVEN

Hence D

sdas · Answer

statement 1 is (A-C-B) is even, rephrased as -(A+B+C) is even. Thus sufficient

Statement 2
(A-C)/B is even
two options

1. (A-C) is even, B is even thus (A-C)/B is even
2. (A-C) is even, B is odd thus (A-C)/B is odd

Thus, (A-C) is even always, which is possible under 2 options
1. both A and C are even, even+/- even = even
2. both A and C are odd, odd+/- odd = odd

Thus, as per statement 2 A,B or C can either be odd or even.
So statement 2 is insufficient.

Ans:A

nonameee · Answer

Sdas, thanks for your reply. I figured out the mistake I made.

I'll correct the OA.

nonameee · Answer

Correction

(2) (A-C)/B is EVEN

The expression above can be EVEN only if (A-C) is EVEN (ODD/ODD is always ODD, ODD/EVEN is not an integer).

B can be either EVEN or ODD (48/3 = 16, 48/4 = 12)

Insufficient.

A

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