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

It is currently 13 Nov 2018, 10:17

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 November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • Essential GMAT Time-Management Hacks

     November 14, 2018

     November 14, 2018

     07:00 PM PST

     08:00 PM PST

    Join the webinar and learn time-management tactics that will guarantee you answer all questions, in all sections, on time. Save your spot today! Nov. 14th at 7 PM PST
  • $450 Tuition Credit & Official CAT Packs FREE

     November 15, 2018

     November 15, 2018

     10:00 PM MST

     11:00 PM MST

    EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299)

If a, b, c and n are positive integers and m=a4b3cn, how many factors

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

Hide Tags

Senior SC Moderator
User avatar
V
Joined: 14 Nov 2016
Posts: 1316
Location: Malaysia
GMAT ToolKit User Premium Member CAT Tests
If a, b, c and n are positive integers and m=a4b3cn, how many factors  [#permalink]

Show Tags

New post 22 Mar 2017, 23:15
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

33% (00:41) correct 67% (01:08) wrong based on 30 sessions

HideShow timer Statistics

If a, b, c and n are positive integers and \(m=a^4*b^3*c^n\), how many factors does m have?

1) a, b, and c are prime numbers

2) n=2

_________________

"Be challenged at EVERY MOMENT."

“Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.”

"Each stage of the journey is crucial to attaining new heights of knowledge."

Rules for posting in verbal forum | Please DO NOT post short answer in your post!

Advanced Search : https://gmatclub.com/forum/advanced-search/

Senior Manager
Senior Manager
avatar
B
Joined: 13 Oct 2016
Posts: 367
GPA: 3.98
Re: If a, b, c and n are positive integers and m=a4b3cn, how many factors  [#permalink]

Show Tags

New post 23 Mar 2017, 02:02
ziyuen wrote:
If a, b, c and n are positive integers and \(m=a^4*b^3*c^n\), how many factors does m have?

1) a, b, and c are prime numbers

2) n=2


Hi

1) a, b, and c are prime numbers

There is no information about "n" and we are not directly told that they are distinct primes. Insufficient.

2) n=2

a, b, c can be primes or composite. Insufficient.

(1)&(2) We know that a, b and c are primes, we know the power of c, but we still don't know wheather a,b,c are distinct primes or not:

Say: \(2^4*b^3*5*2\) -----> \(5*4*3 = 60\) factors.

or \(2^4*3^3*3^2 = 2^4*3^5\) -------> \(5*6 = 30\) factors. Still insufficient.

Answer E.
CEO
CEO
User avatar
D
Joined: 11 Sep 2015
Posts: 3112
Location: Canada
Re: If a, b, c and n are positive integers and m=a4b3cn, how many factors  [#permalink]

Show Tags

New post 23 Mar 2017, 13:32
1
Top Contributor
ziyuen wrote:
If a, b, c and n are positive integers and \(m=a^4*b^3*c^n\), how many factors does m have?

1) a, b, and c are prime numbers

2) n=2


Target question: How many factors does m have?

Given: m = (a^4)(b^3)(c^n)

The two statements seem to provide a lot of information, so I'm going to jump straight to..

Statements 1 and 2 combined
There are several values of a, b, c, and n that satisfy BOTH statements. Here are two:
Case a: a = 2, b = 2, c = 2 and n = 2, in which case m = (2^4)(2^3)(2^2) = 2^9. In this case, m has 10 factors.
Case b: a = 3, b = 3, c = 2 and n = 2, in which case m = (3^4)(3^3)(2^2) = (3^7)(2^2). In this case, m has 24 factors.
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer:

---------ASIDE---------------
To determine the number of factors of m, I used the following rule:

If N = (p^a)(q^b)(r^c)..., where p, q, r,...(etc.) are prime numbers, then the total number of positive divisors of N is equal to (a+1)(b+1)(c+1)...

Example: 14000 = (2^4)(5^3)(7^1)
So, the number of positive divisors of 14000 = (4+1)(3+1)(1+1) = (5)(4)(2) = 40
_________________

Brent Hanneson – GMATPrepNow.com
Image

GMAT Club Bot
Re: If a, b, c and n are positive integers and m=a4b3cn, how many factors &nbs [#permalink] 23 Mar 2017, 13:32
Display posts from previous: Sort by

If a, b, c and n are positive integers and m=a4b3cn, how many factors

  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®.