• NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    Hundreds of Questions Highly Detailed Reporting Expert Explanations TAKE A FREE GMAT QUIZ
  • 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

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

This topic has 4 expert replies and 1 member reply

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

Post
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.

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Elite Legendary Member
Joined
23 Jun 2013
Posted:
10197 messages
Followed by:
496 members
Upvotes:
2867
GMAT Score:
800
Most Active Expert
Top Reply
Post
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

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

_________________
Contact Rich at Rich.C@empowergmat.com

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Legendary Member
Joined
14 Jan 2015
Posted:
2667 messages
Followed by:
122 members
Upvotes:
1153
GMAT Score:
770
Top Reply
Post
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.

_________________
Veritas Prep | GMAT Instructor

Veritas Prep Reviews
Save $100 off any live Veritas Prep GMAT Course

  • +1 Upvote Post
  • Quote
  • Flag
Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!

GMAT/MBA Expert

Legendary Member
Joined
14 Jan 2015
Posted:
2667 messages
Followed by:
122 members
Upvotes:
1153
GMAT Score:
770
Post
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

_________________
Veritas Prep | GMAT Instructor

Veritas Prep Reviews
Save $100 off any live Veritas Prep GMAT Course

  • +1 Upvote Post
  • Quote
  • Flag
Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!
Senior | Next Rank: 100 Posts Default Avatar
Joined
15 Jan 2018
Posted:
83 messages
Post
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.

  • +1 Upvote Post
  • Quote
  • Flag
Post
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

_________________

Scott Woodbury-Stewart
Founder and CEO
scott@targettestprep.com



See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

  • +1 Upvote Post
  • Quote
  • Flag
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review

Top First Responders*

1 Ian Stewart 57 first replies
2 Brent@GMATPrepNow 31 first replies
3 Jay@ManhattanReview 29 first replies
4 GMATGuruNY 20 first replies
5 ceilidh.erickson 15 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description Scott@TargetTestPrep

Target Test Prep

211 posts
2 image description Max@Math Revolution

Math Revolution

88 posts
3 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

70 posts
4 image description Ian Stewart

GMATiX Teacher

65 posts
5 image description GMATGuruNY

The Princeton Review Teacher

39 posts
See More Top Beat The GMAT Experts