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

It is currently 12 Dec 2018, 13:12

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
  • The winning strategy for 700+ on the GMAT

     December 13, 2018

     December 13, 2018

     08:00 AM PST

     09:00 AM PST

    What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.
  • GMATbuster's Weekly GMAT Quant Quiz, Tomorrow, Saturday at 9 AM PST

     December 14, 2018

     December 14, 2018

     09:00 AM PST

     10:00 AM PST

    10 Questions will be posted on the forum and we will post a reply in this Topic with a link to each question. There are prizes for the winners.

T is the set of all positive integers x such that x^2 is a multiple of

  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: 51121
T is the set of all positive integers x such that x^2 is a multiple of  [#permalink]

Show Tags

New post 12 May 2015, 03:45
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

54% (02:07) correct 46% (02:16) wrong based on 250 sessions

HideShow timer Statistics

T is the set of all positive integers x such that x^2 is a multiple of both 27 and 375. Which of the following integers must be a divisor of every integer x in T?

I. 9
II. 15
III. 27

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III


Kudos for a correct solution.

_________________

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

Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51121
Re: T is the set of all positive integers x such that x^2 is a multiple of  [#permalink]

Show Tags

New post 18 May 2015, 05:02
1
4
Bunuel wrote:
T is the set of all positive integers x such that x^2 is a multiple of both 27 and 375. Which of the following integers must be a divisor of every integer x in T?

I. 9
II. 15
III. 27

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III


Kudos for a correct solution.


OFFICIAL SOLUTION:

The least common multiple of 27 = 3^3 and 375 = 3*5^3 is 3^3*5^3.

For an integer x, the least value of x^2 which is a multiple of 3^3*5^3 is 3^4*5^4, so the least value of x is 3^2*5^2. Therefore, T = {3^2*5^2; 2*(3^2*5^2); 3*(3^2*5^2); 4*(3^2*5^2); ...}.

The question asks which of the options must be a divisor of every integer x in T. So, the answer is I and II only (27 = 3^3 is NOT a divisor of 3^2*5^2).

Answer: C.
_________________

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

General Discussion
Intern
Intern
avatar
Joined: 01 Jan 2015
Posts: 17
Re: T is the set of all positive integers x such that x^2 is a multiple of  [#permalink]

Show Tags

New post 12 May 2015, 08:40
1
x = sq rt 27*375 = 3^2*5*sqrt5

I 3^2 - yes, its a factor
II 3*5 - yes, its a factor
III 3^3 - not a factor

Hence C
Senior Manager
Senior Manager
User avatar
S
Joined: 21 Jan 2015
Posts: 355
Location: India
Concentration: Strategy, Marketing
GMAT 1: 620 Q48 V28
GMAT 2: 690 Q49 V35
WE: Sales (Consumer Products)
GMAT ToolKit User CAT Tests
T is the set of all positive integers x such that x^2 is a multiple of  [#permalink]

Show Tags

New post 12 May 2015, 20:08
2
Bunuel wrote:
T is the set of all positive integers x such that x^2 is a multiple of both 27 and 375. Which of the following integers must be a divisor of every integer x in T?

I. 9
II. 15
III. 27

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III

Ans: C
Solution:
T->{x} where x^2 is a multiple of both 27 and 375 means 3^3 and (5^3)*3
means x must contain 3^2 and 5^2
so with these conditions we know that 9=3^2 and 15=3*5 both have required factors for the divisibility of lowest int for x which is 9*25
but 27 is not a divisor because it can't divide 9*25 fully.

so Ans : C
_________________

--------------------------------------------------------------------
The Mind is Everything, What we Think we Become.

Director
Director
User avatar
S
Status: Come! Fall in Love with Learning!
Joined: 05 Jan 2017
Posts: 508
Location: India
Premium Member
Re: T is the set of all positive integers x such that x^2 is a multiple of  [#permalink]

Show Tags

New post 08 Mar 2017, 01:54
1
27 = 3^3
375 = 3 x 5^3
LCM = 3^3 x 5^3

if x^2 is divisible by LCM, then x^2 should have 3^4 x 5^4
therefore x should have 3^2 x 5^2 = 225. therefore every integer in T will be divisible by 225 or factors of 225 which is 1, 3,5,9,15, 25,45, 75, 225.

looking at the option we can see that Option C is correct
_________________

GMAT Mentors
Image

Target Test Prep Representative
User avatar
P
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4294
Location: United States (CA)
Re: T is the set of all positive integers x such that x^2 is a multiple of  [#permalink]

Show Tags

New post 10 Mar 2017, 09:35
1
Bunuel wrote:
T is the set of all positive integers x such that x^2 is a multiple of both 27 and 375. Which of the following integers must be a divisor of every integer x in T?

I. 9
II. 15
III. 27

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III


Since x^2 is a multiple of both 27 and 375, x^2 is a multiple of the LCM of 27 and 375.

27 = 3^3

375 = 25 x 15 = 5^3 x 3^1

Thus, the LCM of 27 and 375 is 3^3 x 5^3 = 15^3 and x^2 must be a multiple of 15^3. Since x^2 is a perfect square and a multiple of 15^3, the minimum value of x^2 must be be 15 * 15^3 = 15^4. Since x is the square root of x^2, taking the square root of 15^4, the minimum value of x must be 15^2 = 225. We see that both 9 and 15 are factors of 225, but 27 is not.

Answer: C
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 9139
Premium Member
Re: T is the set of all positive integers x such that x^2 is a multiple of  [#permalink]

Show Tags

New post 16 Apr 2018, 09:54
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: T is the set of all positive integers x such that x^2 is a multiple of &nbs [#permalink] 16 Apr 2018, 09:54
Display posts from previous: Sort by

T is the set of all positive integers x such that x^2 is a multiple of

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


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®.