If x is a positive even integer, and n and m are consecutive integers,

Question

If x is a positive even integer, and n and m are consecutive integers, then (n - m)^x/(m - n)^x =
 
A. -2
B. -1
C. 0
D. 1
E. 2

Skywalker18 · Answer

x= +ve even integer
Since,n and m are consecutive integers , their difference will be 1

((n-m)^x)/((m-n)^x)= ((n-m)/(m-n))^x = (-1)^x
Since we are raising the difference of n and m to power x , which is even , the answer will be 1 .

Answer D

GMATinsight · Answer

Let,
x = 2 (Positive EVEN Integer)
m = 3 and n = 2

Now,
(n - m)^x/(m - n)^x = (2-3)^2 / (3-2)^2 = 1

Answer: option D

Key : When the question gives open ended information like Positive Even Integer etc. then it's best to assume values and solve the expression. The answer will remain constant for any value assumed as per information unless there is an option like 'Can NOT be determined'

MaticSkok · Answer

Since n and m are consecutive integers, the difference will always be either 1 or -1. 
E.g.: n=5, m=6

\frac{(5-6)^x}{(6-5)^x} =  \frac{(-1)^x}{(1)^x}

And since we have the even exponent the resolved exponent will always be 1. Thus result 1.

Abhishek009 · Answer

Lets plug in some values -

x = 2
m = 4 ; n = 5
 
 \frac{(n - m)^x}{(m - n)^x}  =  \frac{(5 - 4)^2}{(4 - 5)^2}  = \frac{1^2}{-1^2}  = 1

Hence among the given options IMHO answer is D. 1

nipunjain14 · Answer

X is even 
N and M are consecutive, thus their difference will always be -1 or 1.
 Anything raised to even power is positive and 1 to power anything is 1 
Thus OME : D

ScottTargetTestPrep · Answer

Notice that (n - m)^x / (m - n)^x =  ^x = (-1)^x

Since x is a positive even integer, (-1)^x will always be equal to 1.

Alternate solution:

Let’s use some strategic numbers for n, m, and x.

n = 4, m = 3, and x = 2, thus:

/(3 - 4)^2 = 1^2/(-1)^2 = 1

Answer: D

AkshdeepS · Answer

If power is even, then base can never be negative. Therefore, A & B are out.

Try n = 1, m = 2, x = 2

\frac{(1 - 2)^2}{(2 - 1)^2}

\frac{(-1)^2}{(1)^2}

1

(D)

If x is a positive even integer, and n and m are consecutive integers,

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GMAT Problem Solving (PS) Questions

If x is a positive even integer, and n and m are consecutive integers,

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