• 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 N is a positive two-digit integer, is N+1 prime?

This topic has 4 expert replies and 0 member replies

GMAT/MBA Expert

If N is a positive two-digit integer, is N+1 prime?

Post

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Difficult



GMATH practice exercise (Quant Class 16)

If N is a positive two-digit integer, is N+1 prime?

(1) The sum of the digits of N is equal to 11.
(2) N-1 is divisible by 7.

Answer: _____(A)__

_________________
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
fskilnik@GMATH wrote:
[size=17]GMATH practice exercise (Quant Class 16)

If N is a positive two-digit integer, is N+1 prime?

(1) The sum of the digits of N is equal to 11.
(2) N-1 is divisible by 7.
Statement 1:
Any integer whose digits sum to a multiple of 3 must itself be a multiple of 3.
Since N has a digit sum of 11, N+1 must have a digit sum of 12.
One exception: If N=29, then N+1 = 30, which has a digit sum of 3.
Since the digit sum of N+1 must be a multiple of 3 -- either 12 or 3 -- N+1 itself must be a 2-digit multiple of 3 and thus cannot be prime.
Since N+1 is not prime, the answer to the question stem is NO.
SUFFICIENT.

Statement 2:
N-1 = 14, 21, 28...
N = 15, 22, 29...
N+1 = 16, 23, 30...
If N+1 = 16, the answer to the question stem is NO.
If N+1 = 23, the answer to the question stem is YES.
INSUFFICIENT.

The correct answer is A.

_________________
Mitch Hunt
Private Tutor for the GMAT and GRE
GMATGuruNY@gmail.com

If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.

Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.
Student Review #1
Student Review #2
Student Review #3



Last edited by GMATGuruNY on Thu Mar 14, 2019 9:07 am; edited 2 times in total

  • +1 Upvote Post
  • Quote
  • Flag
Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.

GMAT/MBA Expert

Post
GMATGuruNY wrote:
Since N has a digit sum of 11, N+1 must have a digit sum of 12.
The logic of your answer is perfect, but this is not quite true - when you add 1 to a number, when that number ends in 9, the digit sum drops by 8 (the tens digit goes up by 1, the units digit falls by 8) rather than increases by 1. So here, when N = 29, after adding 1 we don't get a digit sum of 12, but instead of 3. That's still divisible by 3 of course.

_________________
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

GMAT/MBA Expert

Post
Ian Stewart wrote:
The logic of your answer is perfect, but this is not quite true - when you add 1 to a number, when that number ends in 9, the digit sum drops by 8 (the tens digit goes up by 1, the units digit falls by 8) rather than increases by 1. So here, when N = 29, after adding 1 we don't get a digit sum of 12, but instead of 3. That's still divisible by 3 of course.
Good catch.
In my solution, the lone exception (N=29) is now noted.

_________________
Mitch Hunt
Private Tutor for the GMAT and GRE
GMATGuruNY@gmail.com

If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.

Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.
Student Review #1
Student Review #2
Student Review #3

  • +1 Upvote Post
  • Quote
  • Flag
Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.

GMAT/MBA Expert

GMAT Instructor
Joined
09 Oct 2010
Posted:
1449 messages
Followed by:
32 members
Upvotes:
59
Post
fskilnik@GMATH wrote:
GMATH practice exercise (Quant Class 16)

If N is a positive two-digit integer, is N+1 prime?

(1) The sum of the digits of N is equal to 11.
(2) N-1 is divisible by 7.
Thank you both (Mitch and Ian) for your nice contributions!

$$N = \left\langle {AB} \right\rangle $$
$$N + 1\,\,\mathop = \limits^? \,\,{\rm{prime}}$$
$$\left( 1 \right)\,\,A + B = 11\,\,\,\,\left\{ \matrix{
\,B\,\,{\rm{odd}}\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\,\,\,\,\,\left[ {N + 1\,\,{\rm{even}}\,\, > 2\,\,} \right] \hfill \cr
\,B\,\,{\rm{even}}\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\,\,\,\,\,\left[ {N + 1\,\, \in \left\{ {92 + 1,74 + 1,56 + 1,38 + 1} \right\}\,\,\, \Rightarrow \,\,\,{\rm{multiple}}\,\,{\rm{of}}\,\,3\,\,\, > 3} \right]\,\, \hfill \cr} \right.$$
$$\left( 2 \right)\,\,{{N - 1} \over 7} = {\mathop{\rm int}} \,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,N = 15\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr
\,{\rm{Take}}\,\,N = 22\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr} \right.$$

The correct answer is (A).


We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.

P.S. (to the careful reader): there is at least one number N that satisfies the question stem (pre-statements) and both statements together (92). This is expected to avoid "internal contradictions".

_________________
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist 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
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • 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
  • 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

Top First Responders*

1 Brent@GMATPrepNow 43 first replies
2 Ian Stewart 35 first replies
3 Jay@ManhattanReview 32 first replies
4 GMATGuruNY 27 first replies
5 Scott@TargetTestPrep 13 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

189 posts
2 image description Max@Math Revolution

Math Revolution

90 posts
3 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

75 posts
4 image description GMATGuruNY

The Princeton Review Teacher

44 posts
5 image description Ian Stewart

GMATiX Teacher

42 posts
See More Top Beat The GMAT Experts