GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 10 Dec 2018, 07:24

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • Free lesson on number properties

     December 10, 2018

     December 10, 2018

     10:00 PM PST

     11:00 PM PST

    Practice the one most important Quant section - Integer properties, and rapidly improve your skills.
  • Free GMAT Prep Hour

     December 11, 2018

     December 11, 2018

     09:00 PM EST

     10:00 PM EST

    Strategies and techniques for approaching featured GMAT topics. December 11 at 9 PM EST.

Let f(x) denotes the sum of the digits of the positive integer x. For

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51070
Let f(x) denotes the sum of the digits of the positive integer x. For  [#permalink]

Show Tags

New post 03 Aug 2018, 02:58
2
1
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

36% (01:40) correct 64% (01:37) wrong based on 80 sessions

HideShow timer Statistics

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

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
User avatar
S
Joined: 13 Feb 2018
Posts: 135
CAT Tests
Re: Let f(x) denotes the sum of the digits of the positive integer x. For  [#permalink]

Show Tags

New post 03 Aug 2018, 03:16
We need two digit integers with the sum of digits equal to 3
here they are
12, 21
30,
49, 94
58, 85
67, 76

IMO
Ans: D
Intern
Intern
User avatar
B
Joined: 25 Feb 2017
Posts: 25
Re: Let f(x) denotes the sum of the digits of the positive integer x. For  [#permalink]

Show Tags

New post 03 Aug 2018, 03:21
12,21,30
39,48,57,66,75,84,93

Total 10 possibilities.

So E

Posted from my mobile device
Director
Director
User avatar
P
Status: Learning stage
Joined: 01 Oct 2017
Posts: 931
WE: Supply Chain Management (Energy and Utilities)
Premium Member
Re: Let f(x) denotes the sum of the digits of the positive integer x. For  [#permalink]

Show Tags

New post 03 Aug 2018, 03:28
Bunuel wrote:
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


f(12)=1+2=3; so, f(f(12))=f(3)=3
f(21)=2+1=3; so, f(f(21))=f(3)=3
f(30)=3+0=3; so, f(f(30))=f(3)=3

Now we have to check any pair of integers those sum to 12, 12, and 31 as f(12) yields 3 and f(f(3))=3.

4+8=8+4=12
5+7=7+5=12
6+6=12
3+9=9+3=12
hence, we have 3+7=10 nos. of two-digit values. (12,21,30,48,84,57,75,66,39,93)

Ans. (E)
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

Manager
Manager
User avatar
B
Joined: 01 Feb 2018
Posts: 77
Location: India
Concentration: Entrepreneurship, Marketing
GPA: 4
WE: Consulting (Consulting)
Re: Let f(x) denotes the sum of the digits of the positive integer x. For  [#permalink]

Show Tags

New post 24 Oct 2018, 21:36
LevanKhukhunashvili wrote:
We need two digit integers with the sum of digits equal to 3
here they are
12, 21
30,
49, 94
58, 85
67, 76

IMO
Ans: D



it will be
12,21,
30,
39, 93
48,84
57, 75
66
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8656
Location: Pune, India
Re: Let f(x) denotes the sum of the digits of the positive integer x. For  [#permalink]

Show Tags

New post 24 Oct 2018, 23:34
Bunuel wrote:
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



Here is how I will think about it:

x needs to be a 2 digit number. It can be anything from 10 to 99 (minimum sum of digits 1 and maximum sum of digits is 18)
So f(x) will vary from 1 to 18.

f(f(x) = 3 when f(x) = 3 or 12 (note that f(x) cannot be 21 or 30 since f(x) cannot take these values)

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

In all, we have 10 values for x.
_________________

[b]Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT Club Bot
Re: Let f(x) denotes the sum of the digits of the positive integer x. For &nbs [#permalink] 24 Oct 2018, 23:34
Display posts from previous: Sort by

Let f(x) denotes the sum of the digits of the positive integer x. For

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


cron
Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.