(k â€“ w) + (k â€“ x) + (k â€“ y)?

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Thu Feb 24, 2011 4:24 am

What is the value of (k - w) + (k - x) + (k - y)?

(1) w, x, and y are three consecutive odd numbers.

(2) The mean of w, x, and y is k.

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Source: Beat The GMAT — Data Sufficiency | Thu Feb 24, 2011 4:24 am

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Thu Feb 24, 2011 4:36 am

(1) w, x, and y are three consecutive odd numbers does not give any info about k.
So, (1) is NOT SUFFICIENT.

(2) (w + x + y)/3 = k implies w + x + y = 3k
3k - w - x - y = 0 or (k - w) + (k - x) + (k - y) = 0
So, (2) is SUFFICIENT.

The correct answer is B.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Thu Feb 24, 2011 5:55 am

sanju09 wrote:What is the value of (k - w) + (k - x) + (k - y)?

(1) w, x, and y are three consecutive odd numbers.

(2) The mean of w, x, and y is k.

Source: https://readyforgmat.com

Since (k - w) + (k - x) + (k - y) = 3k - (w+x+y), the question can be rephrased:

What is the value of 3k - (w+x+y)?

Statement 1: w, x, and y are consecutive odd numbers
No information about k.
Insufficient.

Statement 2: The mean of w, x, and y is k
k = (w+x+y)/3
3k = w+x+y
Thus, 3k - (w+y+z) = 3k - 3k = 0.
Sufficient.

The correct answer is B.

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