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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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New post 27 Dec 2014, 12:05
2
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

79% (00:39) correct 21% (00:40) wrong based on 166 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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S

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

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New post 27 Dec 2014, 12:09
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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New post 27 Dec 2014, 12:14
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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

Final Answer:

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

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New post 27 Dec 2014, 12:42
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


w=2k+1
x=2k+3
y=2k+5

here k can be 0,1,2,3,4----

now y-x-w = 2k+5-2k-3-2k-1
=1-2k

we know that odd-odd-odd will always be odd. hence answer choices a,b and d are out. Also, maximum value of 1-2k is 1, when k=0. hence option E is also out. thus answer must be 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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New post 27 Dec 2014, 17:26
1
Hi All,

I mentioned earlier that this question could be approached with "brute force" - that's a concept that I haven't seen used too often on this site, so here's how to use that approach to get to the correct answer. Essentially, "brute force" in this case will involve TESTing VALUES until we get a solution that matches one of the 5 answer choices.

Since W, X and Y are CONSECUTIVE ODD POSITIVE INTEGERS and W < X < Y, we can start with the easiest set of values that comes to mind:

W = 1
X = 3
Y = 5

The question asks for what COULD be the value of Y - X - W.
In this case, the value would be...
5 - 3 - 1 = 1
+1 is NOT among the answer choices, so we have to keep working...

The next easiest set of values would be...
W = 3
X = 5
Y = 7

Here, Y - X - W is....
7 - 5 - 3 = -1

-1 IS among the answer choices, so we're done.

Final Answer:

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

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New post 07 May 2016, 10:37
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

Answer will be -1 :P :-D

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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New post 17 Apr 2017, 04:17
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 &nbs [#permalink] 17 Apr 2017, 04:17
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