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# Even numbers

Author Message
Director
Joined: 23 Apr 2010
Posts: 573

Kudos [?]: 100 [0], given: 7

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04 Dec 2011, 06:52
00:00

Difficulty:

(N/A)

Question Stats:

50% (00:00) correct 50% (01:41) wrong based on 4 sessions

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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.
[Reveal] Spoiler: OA

Last edited by nonameee on 04 Dec 2011, 07:51, edited 1 time in total.

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Director
Joined: 23 Apr 2010
Posts: 573

Kudos [?]: 100 [0], given: 7

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04 Dec 2011, 06:56
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

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Senior Manager
Joined: 23 Mar 2011
Posts: 461

Kudos [?]: 283 [0], given: 59

Location: India
GPA: 2.5
WE: Operations (Hospitality and Tourism)

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04 Dec 2011, 07:44
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
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Director
Joined: 23 Apr 2010
Posts: 573

Kudos [?]: 100 [0], given: 7

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04 Dec 2011, 07:51

I'll correct the OA.

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Director
Joined: 23 Apr 2010
Posts: 573

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04 Dec 2011, 07:55
Quote:
(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

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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Re: Even numbers   [#permalink] 04 Dec 2011, 07:55
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