• 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

Let f(x) denotes the sum of...

This topic has 1 expert reply and 0 member replies

Let f(x) denotes the sum of...

Post
Let f(x) denotes the sum of the digits of the positive integer x. For example, f(8) =8, f(123) = 1+2+3=6. For how many two-digit values of x is f(f(x))=3?

A) 3
B) 4
C) 6
D) 9
E) 10

The OA is E.

Can any expert help me with this PS question please? I don't have it clear. Thanks.

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
Hello LUANDATO.

It is a really interesting question.

The idea is that we must find the numbers of two digits such that the sum of their digits is:

- 3, that is to say, f(x)=3, so that f(f(x))=f(3)=3.
- 12, that is to say, f(x)=12, so that f(f(x))=f(12)=3.

The numbers that satisfy this property are: 12, 21, 30, 39, 48, 57, 66, 75, 84 and 93.

f(f(12))=f(3)=3
f(f(21))=f(3)=3
f(f(30))=f(3)=3
f(f(39))=f(12)=3
f(f(48))=f(12)=3
f(f(57))=f(12)=3
f(f(66))=f(12)=3
f(f(75))=f(12)=3
f(f(84))=f(12)=3
f(f(93))=f(12)=3

So, the answer is E.

Note that f(f(3))=3, but 3 is one-digit number, that is why it is not on the list above.

I hope this can help you to understand how to solve this kind of questions.

_________________
GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.

  • +1 Upvote Post
  • Quote
  • Flag
Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now.
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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

Top First Responders*

1 Ian Stewart 44 first replies
2 Brent@GMATPrepNow 34 first replies
3 Scott@TargetTestPrep 32 first replies
4 Jay@ManhattanReview 31 first replies
5 GMATGuruNY 18 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

139 posts
2 image description Max@Math Revolution

Math Revolution

90 posts
3 image description Ian Stewart

GMATiX Teacher

53 posts
4 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

51 posts
5 image description Jay@ManhattanReview

Manhattan Review

31 posts
See More Top Beat The GMAT Experts