Problem Solving

BTGmoderatorDC wrote:If w, x, and y are consecutive odd positive integers and w < x < y, which of the following could be equal to y - x - w ?

(A) -4
(B) -2
(C) -1
(D) 0
(E) 3

OA C

Source: GMAT Prep

An odd positive integer can be represented as 2x + 1, where x is a non-negative integer

Thus, we have

w = 2x + 1; x = 2x + 3; and y = 2x + 5

Thus, y - x - w = 2x + 5 - 2x - 3 - 2x - 1 = 1 - 2x

y - x - w = 1 - 2x

We may plug-in x = 0, 1, 2, 3, etc. in 1 - 2x to see which option value fits.

@x = 0, we have y - x - w = 1 - 2x = 1 (there is no option)
@x = 1, we have y - x - w = 1 - 2x = -1 (the correct answer is C)

The correct answer: C

Hope this helps!

-Jay
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BTGmoderatorDC wrote:If w, x, and y are consecutive odd positive integers and w < x < y, which of the following could be equal to y - x - w ?

(A) -4
(B) -2
(C) -1
(D) 0
(E) 3

OA C

Source: GMAT Prep

Here's a 3rd approach:

GIVEN: w, x, and y are consecutive odd positive integers and w < x < y
Since consecutive odd integers go up by 2, we can write: x = w + 2, and y = w + 2 + 2 = w + 4

So, y - x - w = (w + 4) - (w + 2) - w
= w + 4 - w - 2 - w
= 2 - w
Since w is an ODD integer, (2 - w) will be ODD, so eliminate A, B, and D
Also, since w is POSITIVE, (2 - w) will be less than 2. So, eliminate E
By the process of elimination, the correct answer is C

Alternatively, if w = 3(a positive odd integer) than 2-w = -1 (answer C)

Cheers,
Brent