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

Question

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

WaterFlowsUp · Answer

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.

EMPOWERgmatRichC · Answer

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:  C

GMAT assassins aren't born, they're made,
Rich

manpreetsingh86 · Answer

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.

EMPOWERgmatRichC · Answer

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:  C

GMAT assassins aren't born, they're made,
Rich

Abhishek009 · Answer

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

PS : This problem can be solved in less than 10 seconds if you plug in some values for this problem..

RR88 · Answer

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 , . . .

gmatkillerdude · Answer

Thankyou.. Great explanation

manisha12345 · Answer

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

Manisha

Posted from my mobile device

manisha12345 · Answer

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

Posted from my mobile device

ScottTargetTestPrep · Answer

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.

Answer: C

fskilnik · Answer

\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.

LaveenaPanchal · Answer

We can work out trial and error method.. 3 numbers in seq from 1,3,5,7,9,11

5-3-1 = 1
7-5-3= -1
9-7-5=-3
11-9-7=-5

The answer is -1..

ishaanmishra · Answer

try plugging in 9,7,5 consecutive integers.

ishaanmishra · Answer

try plugging in 9,7,5 consecutive integers.

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

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