• 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 the two digit integers M and N are positive and have the

This topic has 3 expert replies and 0 member replies

If the two digit integers M and N are positive and have the

Post

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Difficult



Official Guide

If the two digit integers M and N are positive and have the same digits, but in reverse order, which of the following cannot be the sum of M and N?

A. 181
B. 165
C. 121
D. 99
E. 44

OA A

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
If we have a two digit number AB, where A is the tens digit and B the units digit, then the number is equal to 10A + B.

So here, if A and B represent digits, our numbers are AB and BA. These are equal to 10A + B and 10B + A, and their sum is equal to 11A + 11B. This sum is clearly divisible by 11. So if an answer choice is not divisible by 11, it cannot be our sum, and A, 181, is correct.

_________________
If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

  • +1 Upvote Post
  • Quote
  • Flag
Post
AAPL wrote:
Official Guide

If the two digit integers M and N are positive and have the same digits, but in reverse order, which of the following cannot be the sum of M and N?

A. 181
B. 165
C. 121
D. 99
E. 44

OA A
Since 98 + 89 = 187 and 97 + 79 = 176, we see that there is no way for the sum to be 181.

Alternate solution:

We can let M = 10t + u where t is the tens digit of M and u is the units digit of M. Thus N = 10u + t and M + N = (10t + u) + (10u + t) = 11t + 11u = 11(t + u). We see that the sum of M and N must be a multiple of 11 and all the given choices are multiples of 11 except choice A. So 181 can’t be the sum of M and N.

Answer: A

_________________

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

GMAT/MBA Expert

Post
AAPL wrote:
Official Guide

If the two digit integers M and N are positive and have the same digits, but in reverse order, which of the following cannot be the sum of M and N?

A. 181
B. 165
C. 121
D. 99
E. 44

OA A
This question relies on our ability to determine the VALUE of any 2-digit number.
For example, what is the VALUE of 83?
For many of us, it has been a very long time since we examined this (we learned this when we were 5 or 6). Most of us just say that 83 has a value of 83, but 83 is really just a "recipe" for determining value.
83 is equal to 8 tens plus 3 ones.
Similarly, 76 is equal to 7 tens plus 6 ones.

In general, if tu represents a 2-digit number (where the t stands for the digit in the tens position, and the u stands for the digit in the units position), then the value of tu is 10t + u

So, if M = tu, then N = ut
The VALUE of M is 10t + u, and the VALUE of N us 10u + t
So, the VALUE of M+N = (10t + u) + (10u + t) = 11t + 11u = 11(t + u)

So, we can see that M+N must be a MULTIPLE OF 11

Answer choices B, C, D and E are all multiples of 11.
Since 181 is not a multiple of 11, M+N cannot equal 181

Answer: A

Cheers,
Brent

_________________
Brent Hanneson – Creator of GMATPrepNow.com
Use my video course along with Beat The GMAT's free 60-Day Study Guide

Sign up for free Question of the Day emails
And check out all of these free resources

  • +1 Upvote Post
  • Quote
  • Flag
GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!
  • 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
  • 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
  • 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
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test 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
  • 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 59 first replies
2 Brent@GMATPrepNow 59 first replies
3 Jay@ManhattanReview 53 first replies
4 GMATGuruNY 30 first replies
5 ceilidh.erickson 20 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

188 posts
2 image description Max@Math Revolution

Math Revolution

90 posts
3 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

88 posts
4 image description Ian Stewart

GMATiX Teacher

68 posts
5 image description Jay@ManhattanReview

Manhattan Review

61 posts
See More Top Beat The GMAT Experts