GMAT Changed on April 16th - Read about the latest changes here

It is currently 20 May 2018, 06:53

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

Events & Promotions in June
Open Detailed Calendar

The functions f and g are defined for all the positive

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

Hide Tags

3 KUDOS received
Intern
Intern
User avatar
Status: Learning
Joined: 07 Aug 2011
Posts: 37
Location: India
Schools: WBUT - Class of 2011
GMAT Date: 01-06-2014
GPA: 2.6
WE: Research (Education)
The functions f and g are defined for all the positive [#permalink]

Show Tags

New post 09 May 2014, 06:00
3
This post received
KUDOS
5
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

32% (01:45) correct 68% (01:40) wrong based on 126 sessions

HideShow timer Statistics

The functions f and g are defined for all the positive integers n by the following rule: f(n) is the number of perfect squares less than n and g(n) is the number of primes numbers less than n. If f(x) + g(x) = 16, then x is in the range:

A. 30 < x < 36

B. 30 < x < 37

C. 31 < x < 37

D. 31 < x < 38

E. 32 < x < 38
[Reveal] Spoiler: OA

_________________

If you like my post give me kudos.

Arindam Sur
Researcher, Academian

3 KUDOS received
Senior Manager
Senior Manager
avatar
Status: busyness school student
Joined: 09 Sep 2013
Posts: 419
Location: United States
Schools: Tepper '16 (M)
GMAT 1: 730 Q52 V37
Premium Member
Re: The functions f and g are defined for all the positive [#permalink]

Show Tags

New post 09 May 2014, 06:26
3
This post received
KUDOS
f(n) = number of perfect squares less than n
1,4,9,16,25,36

f(25) = 4
f(26)=f(27)=...=f(35)=f(36) = 5
f(37) = 6

g(n) = number of prime numbers less than n
2,3,5,7,11,13,17,19,23,29,31,37

g(31)=10
g(32)=g(33)=...=g(36)=g(37) = 11
g(38)=12


f(x)+g(x)=16 implies that f(x)=5 and g(x)=11.

So, x = 32,33,34,35,or36.

Answer C, 31 < x < 37.
_________________

My review of some of the CAT practice exams
You can usually find me on gmatclub's chat.

Senior Manager
Senior Manager
avatar
Joined: 08 Apr 2012
Posts: 405
Re: The functions f and g are defined for all the positive [#permalink]

Show Tags

New post 09 May 2014, 06:41
farful wrote:
f(n) = number of perfect squares less than n
1,4,9,16,25,36

f(25) = 4
f(26)=f(27)=...=f(35)=f(36) = 5
f(37) = 6

g(n) = number of prime numbers less than n
2,3,5,7,11,13,17,19,23,29,31,37

g(31)=10
g(32)=g(33)=...=g(36)=g(37) = 11
g(38)=12


f(x)+g(x)=16 implies that f(x)=5 and g(x)=11.

So, x = 32,33,34,35,or36.

Answer C, 31 < x < 37.



Than why not not f(x)=6 and g(x)=10?
Senior Manager
Senior Manager
avatar
Status: busyness school student
Joined: 09 Sep 2013
Posts: 419
Location: United States
Schools: Tepper '16 (M)
GMAT 1: 730 Q52 V37
Premium Member
Re: The functions f and g are defined for all the positive [#permalink]

Show Tags

New post 09 May 2014, 06:48
ronr34 wrote:
farful wrote:
f(n) = number of perfect squares less than n
1,4,9,16,25,36

f(25) = 4
f(26)=f(27)=...=f(35)=f(36) = 5
f(37) = 6

g(n) = number of prime numbers less than n
2,3,5,7,11,13,17,19,23,29,31,37

g(31)=10
g(32)=g(33)=...=g(36)=g(37) = 11
g(38)=12


f(x)+g(x)=16 implies that f(x)=5 and g(x)=11.

So, x = 32,33,34,35,or36.

Answer C, 31 < x < 37.



Than why not not f(x)=6 and g(x)=10?



f(x) >= 6 implies x > 36.
g(x) <= 10 implies x < 32.
_________________

My review of some of the CAT practice exams
You can usually find me on gmatclub's chat.

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 45180
Re: The functions f and g are defined for all the positive [#permalink]

Show Tags

New post 09 May 2014, 06:58
Expert's post
1
This post was
BOOKMARKED
The functions f and g are defined for all the positive integers n by the following rule: f(n) is the number of positive perfect squares less than n and g(n) is the number of primes numbers less than n. If f(x) + g(x) = 16, then x is in the range:

A. 30 < x < 36
B. 30 < x < 37
C. 31 < x < 37
D. 31 < x < 38
E. 32 < x < 38

Perfect squares: 1, 4, 9, 16, 25, 36, ..,
Prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, ...

If x = 31, then f(31) = 5 and g(31) = 10: f(x) + g(x) = 5 + 10 = 15.
If x = 32, then f(32) = 5 and g(32) = 11: f(x) + g(x) = 5 + 11 = 16.
...
If x = 36, then f(36) = 5 and g(36) = 11: f(x) + g(x) = 5 + 11 = 16.
If x = 37, then f(37) = 6 and g(37) = 11: f(x) + g(x) = 6 + 11 = 17.

Thus x could be 32, 33, 34, 35 or 36: 31<x<37.

Answer: C.

P.S. This is GMAT Club's question, not Grockit's.
_________________

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

Expert Post
EMPOWERgmat Instructor
User avatar
D
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11633
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Re: The functions f and g are defined for all the positive [#permalink]

Show Tags

New post 27 Jan 2018, 12:48
Hi All,

We can use the answer choices to our advantage on this question (by determining if number of possible or impossible, we can eliminate answer choices).

Let's start by TESTing X=31. According to the prompt...

f(31) = number of perfect squares less than 31 = {1, 4, 9, 16, 25] = 5
g(31) = number of primes less than 31 = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29} = 10

f(31) + g(31) = 15; we're told that it's SUPPOSED to be 16 though, so X CANNOT be 31. Eliminate Answers A and B.

Next, let's TEST X = 37. According to the prompt...

f(37) = number of perfect squares less than 31 = {1, 4, 9, 16, 25, 36] = 6
g(37) = number of primes less than 31 = {2, 3, 5, 7, 11, 13, 17, 23, 29, 31, 3} = 11

f(37) + g(37) = 17; we're told that it's SUPPOSED to be 16 though, so X CANNOT be 37. Eliminate Answers D and E.

Final Answer:
[Reveal] Spoiler:
C


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

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Intern
Intern
avatar
Joined: 08 Jul 2017
Posts: 5
Re: The functions f and g are defined for all the positive [#permalink]

Show Tags

New post 28 Jan 2018, 06:08
farful wrote:
f(n) = number of perfect squares less than n
1,4,9,16,25,36

f(25) = 4
f(26)=f(27)=...=f(35)=f(36) = 5
f(37) = 6

g(n) = number of prime numbers less than n
2,3,5,7,11,13,17,19,23,29,31,37

g(31)=10
g(32)=g(33)=...=g(36)=g(37) = 11
g(38)=12


f(x)+g(x)=16 implies that f(x)=5 and g(x)=11.

So, x = 32,33,34,35,or36.

Answer C, 31 < x < 37.


Why are we not considering 0 as a perfect square?
Intern
Intern
avatar
Joined: 08 Jul 2017
Posts: 5
Re: The functions f and g are defined for all the positive [#permalink]

Show Tags

New post 28 Jan 2018, 06:10
Bunuel wrote:
The functions f and g are defined for all the positive integers n by the following rule: f(n) is the number of positive perfect squares less than n and g(n) is the number of primes numbers less than n. If f(x) + g(x) = 16, then x is in the range:

A. 30 < x < 36
B. 30 < x < 37
C. 31 < x < 37
D. 31 < x < 38
E. 32 < x < 38

Perfect squares: 1, 4, 9, 16, 25, 36, ..,
Prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, ...

If x = 31, then f(31) = 5 and g(31) = 10: f(x) + g(x) = 5 + 10 = 15.
If x = 32, then f(32) = 5 and g(32) = 11: f(x) + g(x) = 5 + 11 = 16.
...
If x = 36, then f(36) = 5 and g(36) = 11: f(x) + g(x) = 5 + 11 = 16.
If x = 37, then f(37) = 6 and g(37) = 11: f(x) + g(x) = 6 + 11 = 17.

Thus x could be 32, 33, 34, 35 or 36: 31<x<37.

Answer: C.

P.S. This is GMAT Club's question, not Grockit's.


Why are we not considering 0 as a perfect square?
Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 45180
Re: The functions f and g are defined for all the positive [#permalink]

Show Tags

New post 28 Jan 2018, 07:43
1
This post received
KUDOS
Expert's post
shwetakoshija wrote:
Bunuel wrote:
The functions f and g are defined for all the positive integers n by the following rule: f(n) is the number of positive perfect squares less than n and g(n) is the number of primes numbers less than n. If f(x) + g(x) = 16, then x is in the range:

A. 30 < x < 36
B. 30 < x < 37
C. 31 < x < 37
D. 31 < x < 38
E. 32 < x < 38

Perfect squares: 1, 4, 9, 16, 25, 36, ..,
Prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, ...

If x = 31, then f(31) = 5 and g(31) = 10: f(x) + g(x) = 5 + 10 = 15.
If x = 32, then f(32) = 5 and g(32) = 11: f(x) + g(x) = 5 + 11 = 16.
...
If x = 36, then f(36) = 5 and g(36) = 11: f(x) + g(x) = 5 + 11 = 16.
If x = 37, then f(37) = 6 and g(37) = 11: f(x) + g(x) = 6 + 11 = 17.

Thus x could be 32, 33, 34, 35 or 36: 31<x<37.

Answer: C.

P.S. This is GMAT Club's question, not Grockit's.


Why are we not considering 0 as a perfect square?


Check the highlighted parts.
_________________

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

Re: The functions f and g are defined for all the positive   [#permalink] 28 Jan 2018, 07:43
Display posts from previous: Sort by

The functions f and g are defined for all the positive

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


GMAT Club MBA Forum Home| About| Terms and Conditions| 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®.