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

It is currently 22 Feb 2019, 06:28

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 February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
  • Free GMAT RC Webinar

     February 23, 2019

     February 23, 2019

     07:00 AM PST

     09:00 AM PST

    Learn reading strategies that can help even non-voracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT
  • FREE Quant Workshop by e-GMAT!

     February 24, 2019

     February 24, 2019

     07:00 AM PST

     09:00 AM PST

    Get personalized insights on how to achieve your Target Quant Score.

If n and m are positive integers, is m a factor of n?

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

Hide Tags

 
SVP
SVP
User avatar
D
Joined: 26 Mar 2013
Posts: 2068
Reviews Badge CAT Tests
If n and m are positive integers, is m a factor of n?  [#permalink]

Show Tags

New post 14 Jan 2017, 10:22
1
2
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

88% (01:17) correct 12% (01:36) wrong based on 132 sessions

HideShow timer Statistics

If n and m are positive integers, is m a factor of n?

(1) n = 5(3^k), for any positive integer k
(2) m = 3^(k-1), for any positive integer k
Magoosh GMAT Instructor
User avatar
G
Joined: 28 Dec 2011
Posts: 4486
Re: If n and m are positive integers, is m a factor of n?  [#permalink]

Show Tags

New post 16 Jan 2017, 16:25
3
1
Mo2men wrote:
If n and m are positive integers, is m a factor of n?

(1) n = 5(3^k), for any positive integer k
(2) m = 3^(k-1), for any positive integer k

Dear Mo2men,

I'm happy to respond. :-) This problem is not very challenging: it would be among the easier questions the GMAT would ask.

Either statement by itself is obviously insufficient, because with each statement we get information about only one variable and know nothing about the other, so we can't say anything meaningful about their relation.

If we consider both statements together, we note that any power of an integer is divisible by all the powers below it of that same integer. Thus, 3^(k-1) has to be a factor of 3^k, and therefore also has to be a factor of any multiple of (3^k). Thus, we get a definitive "yes" answer, and the answer to the DS question is (C).

Here's a more GMAT-like problem:
k is mult of 1440

Mike :-)
_________________

Mike McGarry
Magoosh Test Prep


Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 53069
Re: If n and m are positive integers, is m a factor of n?  [#permalink]

Show Tags

New post 17 Jan 2017, 00:14
1
mikemcgarry wrote:
Mo2men wrote:
If n and m are positive integers, is m a factor of n?

(1) n = 5(3^k), for any positive integer k
(2) m = 3^(k-1), for any positive integer k

Dear Mo2men,

I'm happy to respond. :-) This problem is not very challenging: it would be among the easier questions the GMAT would ask.

Either statement by itself is obviously insufficient, because with each statement we get information about only one variable and know nothing about the other, so we can't say anything meaningful about their relation.

If we consider both statements together, we note that any power of an integer is divisible by all the powers below it of that same integer. Thus, 3^(k-1) has to be a factor of 3^k, and therefore also has to be a factor of any multiple of (3^k). Thus, we get a definitive "yes" answer, and the answer to the DS question is (C).

Here's a more GMAT-like problem:
k is mult of 1440

Mike :-)


Thank you Mike.

If interested, here is the problem Mike is referring to: n-is-a-positive-integer-and-k-is-the-product-of-all-integer-104272.html
_________________

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

Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2827
Re: If n and m are positive integers, is m a factor of n?  [#permalink]

Show Tags

New post 11 Dec 2017, 11:01
Mo2men wrote:
If n and m are positive integers, is m a factor of n?

(1) n = 5(3^k), for any positive integer k
(2) m = 3^(k-1), for any positive integer k


We are given that n and m are positive integers and need to determine whether m is a factor of n, i.e., whether n/m = integer.

Statement One Alone:

n = 5(3^k), for any positive integer k

Since we do not have any information regarding m, statement one alone is not sufficient to answer the question.

Statement Two Alone:

m = 3^(k-1), for any positive integer k

Since we do not have any information regarding n, statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Using statements one and two, we can create the following equation:

n/m = 5(3^k)/3^(k-1)

n/m = 5(3^k)/(3^k)(3^-1)

n/m = 5/(3^-1)

n/m = 5 x 3 = 15

Thus, n/m IS an integer.

Answer: C
_________________

Jeffery Miller
Head of GMAT Instruction

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

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 9890
Premium Member
Re: If n and m are positive integers, is m a factor of n?  [#permalink]

Show Tags

New post 18 Jan 2019, 10:46
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: If n and m are positive integers, is m a factor of n?   [#permalink] 18 Jan 2019, 10:46
Display posts from previous: Sort by

If n and m are positive integers, is m a factor of n?

  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®.