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If x is a positive even integer, and n and m...

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by swerve » Sun Jan 14, 2018 6:11 am
If x is a positive even integer, and n and m are cosecutive integers, then
$$\frac{\left(n-m\right)^x}{\left(m-n\right)^x}=?$$
A. -2
B. -1
C. 0
D. 1
E. 2

The OA is D.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.
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by DavidG@VeritasPrep » Sun Jan 14, 2018 11:31 am
swerve wrote:If x is a positive even integer, and n and m are cosecutive integers, then
$$\frac{\left(n-m\right)^x}{\left(m-n\right)^x}=?$$
A. -2
B. -1
C. 0
D. 1
E. 2

The OA is D.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.
Pick easy numbers. Say x = 2, n = 4 and m = 3.
We want (4-3)^2 /(3-4)^2 = 1^2 / (-1)^2 = 1/1 = 1. The answer is D
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by DavidG@VeritasPrep » Sun Jan 14, 2018 11:33 am
swerve wrote:If x is a positive even integer, and n and m are cosecutive integers, then
$$\frac{\left(n-m\right)^x}{\left(m-n\right)^x}=?$$
A. -2
B. -1
C. 0
D. 1
E. 2

The OA is D.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.
You can also use some simple number properties. Because we're raising both expressions to an even exponent, we know both numerator and denominator must be non-negative. We also know that the difference of two consecutive numbers will always be 1 or -1. If they can't be negative, we know both values must equal 1.
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by DrMaths » Mon Jan 15, 2018 4:46 am
The difference between consecutive integers is 1 or -1.
Raising to an even power will always produce 1 (because -1 x -1 = 1).
And 1/1 = 1
So answer = 1.
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by [email protected] » Mon Jan 15, 2018 11:39 am
Hi swerve,

We're told that X is a positive EVEN integer, and N and M are CONSECUTIVE integers. We're asked to find the value of [(N - M)^X] / ([M - N)^X]. This question can be solved by TESTing VALUES.

IF...
X = 2, N = 2 and M=3....
(2-3)^2 = (-1)^2 = +1
(3-2)^2 = (1)^2 = +1
+1/+1 = +1

Final Answer: D

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by Scott@TargetTestPrep » Thu Jan 18, 2018 1:35 pm
swerve wrote:If x is a positive even integer, and n and m are cosecutive integers, then
$$\frac{\left(n-m\right)^x}{\left(m-n\right)^x}=?$$
A. -2
B. -1
C. 0
D. 1
E. 2
Notice that (n - m)^x / (m - n)^x = [(n - m)/(m - n)]^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:

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

Answer: D

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