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If w, x, and y are consecutive odd positive integers and w &

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by BTGmoderatorDC » Tue Dec 04, 2018 10:52 pm

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Answers

A

B

C

D

E

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Difficulty—

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
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by Jay@ManhattanReview » Wed Dec 05, 2018 12:50 am
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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by GMATGuruNY » Wed Dec 05, 2018 4:07 am
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
Test easy cases:
5-3-1 = 1
7-5-3 = -1
The case in green indicates that -1 is a possible value of y-x-w.

The correct answer is C.
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by Brent@GMATPrepNow » Wed Dec 05, 2018 6:58 am
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
Brent Hanneson - Creator of GMATPrepNow.com
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by fskilnik@GMATH » Wed Dec 05, 2018 6:41 pm
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
Source: GMAT Prep
$$\left\{ \matrix{
w = 2M - 1 \hfill \cr
x = 2M + 1 \hfill \cr
y = 2M + 3 \hfill \cr} \right.\,\,\,\,\,\,\,\left( {M \ge 1\,\,{\mathop{\rm int}} } \right)$$
$$? = y - x - w = - 2M + 3\,\,\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{{\rm{alternatives!}}} \,\,\,\, - 1\,\,\,\,\,\,\,\left( {{\rm{when}}\,\,M = 2} \right)$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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Portuguese-speakers :: https://www.gmath.com.br
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by Scott@TargetTestPrep » Fri Mar 22, 2019 8:22 am
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
We see that x = w + 2, and y = w + 4; thus, y - x - w is:

w + 4 - (w + 2) - w = 2 - w

Since w is odd and positive, then (2 - w) must be odd and no greater than 1. The only answer choice that works is -1.

Answer: C

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