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# If w, x, and y are consecutive odd positive integers and w < x < y

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If w, x, and y are consecutive odd positive integers and w < x < y  [#permalink]

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27 Dec 2014, 11:05
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Difficulty:

5% (low)

Question Stats:

85% (00:40) correct 15% (00:36) wrong based on 248 sessions

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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
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Re: If w, x, and y are consecutive odd positive integers and w < x < y  [#permalink]

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27 Dec 2014, 11:09
1
I will also post the solution, should someone require at any point..
Given:w, x, and y are consecutive odd positive integers and w < x < y
Let take value of X as a ; value of y=x+2(consecutive odd integer) ; and w=x-2
So;
y-x-w = x+2 - x - (X+2)
therefore , y-x-w = 4-x
Now,
X is odd and x>= 3
so x can assume values= 3,5,7 ...
therefore when x=5
4-5= -1
As the question asks which could be possible a value we can say that C fits in.
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Re: If w, x, and y are consecutive odd positive integers and w < x < y  [#permalink]

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27 Dec 2014, 11:14
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Hi WaterFlowsUp,

This question can be solved in a couple of different ways: algebraically, with Number Properties, or with "brute force"

Here is an approach that combines Algebra with Number Properties.

We're told that W, X and Y are CONSECUTIVE ODD INTEGERS and W < X < Y. We're asked for a POSSIBLE value of Y - X - W

Since all 3 values are CONSECUTIVE ODD INTEGERS, we can write these terms as...

W = A
X = A+2
Y = A+4

So...
Y - X - W = (A+4) - (A+2) - A = -A +2

Since we know that A is an ODD integer, adding 2 to it will give us ANOTHER ODD integer. Since -A is a NEGATIVE INTEGER, adding 2 CANNOT get us to +3, so there's only one answer that fits: -1

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If w, x, and y are consecutive odd positive integers and w < x < y  [#permalink]

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07 May 2016, 09:37
WaterFlowsUp 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

Plug in some values for w < x < y

So, w < x < y = 3 < 5 < 7

Hence , y - x - w = 7 - 5 - 3 => -1

PS : This problem can be solved in less than 10 seconds if you plug in some values for this problem..
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Re: If w, x, and y are consecutive odd positive integers and w < x < y  [#permalink]

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17 Apr 2017, 03:17
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Option C

w, x & y are consecutive Positive Odd integers, such that w < x < y. Y - X - W = ?

Assume w = 2k + 1, then x = 2k + 3 & Y = 2k + 5. For k>=0.
Hence, Y - X - W = 2k + 5 - (2k + 3) - (2k + 1) = -2k + 1 = -1, -3, -5 , . . .
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Re: If w, x, and y are consecutive odd positive integers and w < x < y  [#permalink]

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16 Oct 2018, 07:51
RR88 wrote:
Option C

w, x & y are consecutive Positive Odd integers, such that w < x < y. Y - X - W = ?

Assume w = 2k + 1, then x = 2k + 3 & Y = 2k + 5. For k>=0.
Hence, Y - X - W = 2k + 5 - (2k + 3) - (2k + 1) = -2k + 1 = -1, -3, -5 , . . .

Thankyou.. Great explanation
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If w, x, and y are consecutive odd positive integers and w < x < y  [#permalink]

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Updated on: 16 Oct 2018, 08:23
1) Plug in any easy values satisfying the condition in the question:w,X,y are consecutive positive odd Integers and w<X<y

w=3,X=5,y=7

2) y-x-w=7-5-3=-1

3) option c

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Originally posted by manisha12345 on 16 Oct 2018, 08:14.
Last edited by manisha12345 on 16 Oct 2018, 08:23, edited 1 time in total.
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Re: If w, x, and y are consecutive odd positive integers and w < x < y  [#permalink]

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16 Oct 2018, 08:15
1) Plug in any easy values satisfying the condition in the question:w,X,y are consecutive positive odd Integers and w<X<y

w=3,X=5,y=7

2) y-x-w=7-5-3=-1

3) option c

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Re: If w, x, and y are consecutive odd positive integers and w < x < y  [#permalink]

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17 Oct 2018, 18:04
WaterFlowsUp 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

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

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Re: If w, x, and y are consecutive odd positive integers and w < x < y  [#permalink]

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05 Dec 2018, 18:51
WaterFlowsUp 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

$$\left\{ \matrix{ w = 2M - 1 \hfill \cr x = 2M + 1 \hfill \cr y = 2M + 3 \hfill \cr} \right.\,\,\,\,\,\,\,\left( {M \ge 1\,\,{\mathop{\rm int}} } \right)$$

$$? = y - x - w = - 2M + 3\,\,\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{{\rm{alternatives!}}} \,\,\,\, - 1\,\,\,\,\,\,\,\left( {{\rm{when}}\,\,M = 2} \right)$$

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

Regards,
Fabio.
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Re: If w, x, and y are consecutive odd positive integers and w < x < y &nbs [#permalink] 05 Dec 2018, 18:51
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