Last visit was: 12 Jul 2024, 17:34 It is currently 12 Jul 2024, 17:34
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
SORT BY:
Date
Tags:
Show Tags
Hide Tags
User avatar
Manager
Manager
Joined: 03 Jul 2013
Posts: 76
Own Kudos [?]: 728 [28]
Given Kudos: 14
GMAT 1: 660 Q48 V32
Send PM
Most Helpful Reply
Tutor
Joined: 16 Oct 2010
Posts: 15105
Own Kudos [?]: 66592 [16]
Given Kudos: 436
Location: Pune, India
Send PM
avatar
Manager
Manager
Joined: 07 Dec 2009
Posts: 69
Own Kudos [?]: 102 [11]
Given Kudos: 375
GMAT Date: 12-03-2014
Send PM
General Discussion
avatar
SVP
SVP
Joined: 27 Dec 2012
Status:The Best Or Nothing
Posts: 1558
Own Kudos [?]: 7290 [2]
Given Kudos: 193
Location: India
Concentration: General Management, Technology
WE:Information Technology (Computer Software)
Send PM
Re: All factors of a positive integer A are multiplied and the product [#permalink]
2
Kudos
Answer = D = 6

Number ................ Factors ........................ Product

2 ............................. 1, 2 ................................. 2

3 ............................... 1, 3 ............................... 3

4 ................................ 1, 2, 4 ............................... 8

5 ............................... 1, 5 .................................. 5

6 ............................... 1, 2, 3, 6 ......................... 36

7 ................................ 1, 7 ................................. 7

8 ................................. 1, 2, 4, 8 ........................... 64

9 ............................... 1, 3, 9 ............................ 27

10 ................................ 1, 2, 5 ............................ 10

11.................................... 1, 11 ........................... 11

12 ................................... 1, 2, 3, 4, 6, 12 ................. 12 * 12 * 12

Number which we are looking for = 12

Answer = D
avatar
Intern
Intern
Joined: 26 May 2014
Posts: 6
Own Kudos [?]: 5 [0]
Given Kudos: 1
Location: India
Send PM
Re: All factors of a positive integer A are multiplied and the product [#permalink]
Thanks Paresh for the solution. But this approach is basically a hit and trial. Can anyone suggest a generic approach?
GMAT Club Legend
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21835
Own Kudos [?]: 11773 [3]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Send PM
Re: All factors of a positive integer A are multiplied and the product [#permalink]
1
Kudos
2
Bookmarks
Expert Reply
Hi All,

This question is more about Number Properties and how math "works" than anything else.

Since the question tells us to multiply the factors of a number A and end up with A^3, you have to first thing about what A^3 "means."

A^3 = (A)(A)(A)

So each of these individual "A's" has to be the same number

When you're dealing with factors, this means that each "A" should be a PAIR of factors that are multiplied. Since there are 3 PAIRS of factors, then the total number of factors MUST be 3(2) = 6

The proof can be seen if we use A = 12

The factors of 12 are: (1 and 12), (2 and 6), (3 and 4).

A= 12
A^2 = 12^3
(1x12)(2x6)(3x4) = A^3

Final Answer:

GMAT assassins aren't born, they're made,
Rich
Tutor
Joined: 07 Nov 2016
Posts: 41
Own Kudos [?]: 61 [0]
Given Kudos: 12
GMAT 1: 760 Q51 V42
Send PM
Re: All factors of a positive integer A are multiplied and the product [#permalink]
Expert Reply
aadikamagic wrote:
All factors of a positive integer A are multiplied and the product obtained is A^3. If A is greater than 1, how many factors does A have?

A. 2
B. 3
C. 5
D. 6
E. 8


One way to solve this problem is as follows :

The three pairs of factors can be

A * 1

A/2 * 2

A/3 * 3

Note : Product of each Pair is A and the product of all the factors is \(A^3\)

Each factor should be distinct. The minimum value for A ( which should be a multiple of both 2 and 3 ) will be 12.

There are six distinct factors (12,1), (6,2), and (4,3)

Choice D
Tutor
Joined: 11 May 2022
Posts: 1085
Own Kudos [?]: 730 [0]
Given Kudos: 81
Send PM
Re: All factors of a positive integer A are multiplied and the product [#permalink]
Expert Reply
aadikamagic wrote:
All factors of a positive integer A are multiplied and the product obtained is A^3. If A is greater than 1, how many factors does A have?

A. 2
B. 3
C. 5
D. 6
E. 8


We only have five answer choices. Let's use that to our advantage.

A) What's a number with 2 factors? How about 2? 1*2 = 2. Is that 2^3? Nope. Eliminate.

B) What's a number with 3 factors? How about 4? 1*2*4 = 8. Is that 4^3? Nope. Eliminate.

C) What's a number with 5 factors? Maybe you see that 16 does. Or maybe you don't and you skip C.

D) What's a number with 6 factors? How about 12? 1*2*3*4*6*12 = (1*12)*(2*6)*(3*4). Heeyyyyy, that's 12^3!

Answer choice D.
User avatar
Non-Human User
Joined: 09 Sep 2013
Posts: 33952
Own Kudos [?]: 851 [0]
Given Kudos: 0
Send PM
Re: All factors of a positive integer A are multiplied and the product [#permalink]
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 Club Bot
Re: All factors of a positive integer A are multiplied and the product [#permalink]
Moderator:
Math Expert
94302 posts