Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 26 May 2015, 22:53

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If y^4 is divisible by 60, what is the minimum number of dis

Author Message
TAGS:
Manager
Status: Never ever give up on yourself.Period.
Joined: 23 Aug 2012
Posts: 147
Location: India
Concentration: Finance, Human Resources
Schools: MBS '17 (A)
GMAT 1: 570 Q47 V21
GMAT 2: 690 Q50 V33
GPA: 3.5
WE: Information Technology (Investment Banking)
Followers: 8

Kudos [?]: 152 [0], given: 35

If y^4 is divisible by 60, what is the minimum number of dis [#permalink]  06 Jan 2013, 06:50
5
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

52% (02:26) correct 48% (01:12) wrong based on 106 sessions
If y^4 is divisible by 60, what is the minimum number of distinct factors that y must have?

(A) 2
(B) 6
(C) 8
(D) 10
(E) 12
[Reveal] Spoiler: OA

_________________

Don't give up on yourself ever. Period.
Beat it, no one wants to be defeated (My journey from 570 to 690) : beat-it-no-one-wants-to-be-defeated-journey-570-to-149968.html

Last edited by Bunuel on 07 Jan 2013, 02:05, edited 1 time in total.
Edited the question.
Manager
Status: Never ever give up on yourself.Period.
Joined: 23 Aug 2012
Posts: 147
Location: India
Concentration: Finance, Human Resources
Schools: MBS '17 (A)
GMAT 1: 570 Q47 V21
GMAT 2: 690 Q50 V33
GPA: 3.5
WE: Information Technology (Investment Banking)
Followers: 8

Kudos [?]: 152 [1] , given: 35

Re: If y^4 is divisible by 60, what is the minimum number of dis [#permalink]  06 Jan 2013, 08:38
1
KUDOS
2,3,5 are dinstinct PRIME factors...we'r asked for distinct factors... we get minimun value of y as 2*3*5=30...and 30 has 8 following distinct factors....1,2,3,5,6,10,15 and 30...hope the answer is clear now...:)

Posted from my mobile device
_________________

Don't give up on yourself ever. Period.
Beat it, no one wants to be defeated (My journey from 570 to 690) : beat-it-no-one-wants-to-be-defeated-journey-570-to-149968.html

Verbal Forum Moderator
Status: Preparing for the another shot...!
Joined: 03 Feb 2011
Posts: 1422
Location: India
Concentration: Finance, Marketing
GPA: 3.75
Followers: 145

Kudos [?]: 790 [1] , given: 62

Re: If y^4 is divisible by 60, what is the minimum number of dis [#permalink]  06 Jan 2013, 10:41
1
KUDOS
Expert's post
1
This post was
BOOKMARKED
I feel that here it must be given that y is an integer.
Anyways, an alternative approach is:
To find the number of distinct factors of a number, first prime factorize it.
In this case, since its given that $$y^4$$ is a multiple of 60, hence $$y^4$$ must contain 2*2*3*5. But here taking the fourth root will yield y in decimal form. Henceforth, to make y an integer, $$y^4$$ must be atleast $$2^4 * 3^4 * 5^4$$.
Now since y is an integer and has 2,3 and 5 as its prime factors, so total number of prime factors will be
2*2*2=8.
Since the number of prime factors is the product of the (power+1) of the individual prime factor. Here the individual powers are 1, 1 and 1. Hence the number of prime factors will be (1+1)*(1+1)*(1+1) or 8. Answer.
_________________
Verbal Forum Moderator
Status: Preparing for the another shot...!
Joined: 03 Feb 2011
Posts: 1422
Location: India
Concentration: Finance, Marketing
GPA: 3.75
Followers: 145

Kudos [?]: 790 [1] , given: 62

Re: If y^4 is divisible by 60, what is the minimum number of dis [#permalink]  06 Jan 2013, 10:43
1
KUDOS
Expert's post
ConnectTheDots wrote:
daviesj wrote:
If $$y^4$$ is divisible by 60, what is the minimum number of distinct factors that y must have?
(A) 2
(B) 6
(C) 8
(D) 10
(E) 12

60= $$2^2*3^1*5^1$$

Number of distinct factors = (2+1)(1+1)(1+1) = 3*2*2 = 12
1,2,3,4
5,6,10,12,
15,20,30,60

Formula:
If N = $$a^p*b^q*c^r...$$, where a,b,c are prime numbers
then Number of distinct factors = (p+1)(q+1)(r+1)

Why the answer is 8 ?
What am I missing here ?

Here you are finding the distinct factors of $$y^4$$ and not y.
Rest of the method is correct.
Moreover, I feel that it should be mentioned that y is an integer.
_________________
Intern
Joined: 23 Nov 2012
Posts: 35
Location: France
Concentration: Finance, Economics
Schools: Said (D)
GMAT 1: 710 Q49 V38
WE: Sales (Investment Banking)
Followers: 0

Kudos [?]: 12 [0], given: 19

Re: If y^4 is divisible by 60, what is the minimum number of dis [#permalink]  06 Jan 2013, 07:14
I get 3, since 60^4 is divisable through 60 and 60 has only 3 distinct factors which are 2, 3 and 5...
_________________

Hodor?

Kudo!

Senior Manager
Joined: 28 Apr 2012
Posts: 308
Location: India
Concentration: Technology, General Management
GMAT 1: 650 Q48 V31
GMAT 2: 770 Q50 V47
WE: Information Technology (Computer Software)
Followers: 16

Kudos [?]: 247 [0], given: 142

Re: If y^4 is divisible by 60, what is the minimum number of dis [#permalink]  06 Jan 2013, 10:30
daviesj wrote:
If $$y^4$$ is divisible by 60, what is the minimum number of distinct factors that y must have?
(A) 2
(B) 6
(C) 8
(D) 10
(E) 12

60= $$2^2*3^1*5^1$$

Number of distinct factors = (2+1)(1+1)(1+1) = 3*2*2 = 12
1,2,3,4
5,6,10,12,
15,20,30,60

Formula:
If N = $$a^p*b^q*c^r...$$, where a,b,c are prime numbers
then Number of distinct factors = (p+1)(q+1)(r+1)

Why the answer is 8 ?
What am I missing here ?
_________________

"Appreciation is a wonderful thing. It makes what is excellent in others belong to us as well."
― Voltaire

Press Kudos, if I have helped.
Thanks!

shit-happens-my-journey-to-172475.html#p1372807

Math Expert
Joined: 02 Sep 2009
Posts: 27505
Followers: 4318

Kudos [?]: 42390 [0], given: 6024

Re: If y^4 is divisible by 60, what is the minimum number of dis [#permalink]  07 Jan 2013, 02:22
Expert's post
Marcab wrote:
ConnectTheDots wrote:
daviesj wrote:
If $$y^4$$ is divisible by 60, what is the minimum number of distinct factors that y must have?
(A) 2
(B) 6
(C) 8
(D) 10
(E) 12

60= $$2^2*3^1*5^1$$

Number of distinct factors = (2+1)(1+1)(1+1) = 3*2*2 = 12
1,2,3,4
5,6,10,12,
15,20,30,60

Formula:
If N = $$a^p*b^q*c^r...$$, where a,b,c are prime numbers
then Number of distinct factors = (p+1)(q+1)(r+1)

Why the answer is 8 ?
What am I missing here ?

Here you are finding the distinct factors of $$y^4$$ and not y.
Rest of the method is correct.
Moreover, I feel that it should be mentioned that y is an integer.

That's correct. More precisely, it must be mentioned that y is a positive integer.
_________________
Intern
Joined: 18 Nov 2011
Posts: 37
Concentration: Strategy, Marketing
GMAT Date: 06-18-2013
GPA: 3.98
Followers: 0

Kudos [?]: 9 [0], given: 0

Re: If y^4 is divisible by 60, what is the minimum number of dis [#permalink]  08 Jan 2013, 17:59
I think I am understanding this correctly, but a little confused.

Maybe if we change things up a little bit, I can see how this works:
If instead of 60, Y was 210, what would the answer be? How would you arrive to the conclusion?
Verbal Forum Moderator
Status: Preparing for the another shot...!
Joined: 03 Feb 2011
Posts: 1422
Location: India
Concentration: Finance, Marketing
GPA: 3.75
Followers: 145

Kudos [?]: 790 [0], given: 62

Re: If y^4 is divisible by 60, what is the minimum number of dis [#permalink]  08 Jan 2013, 18:24
Expert's post
hitman5532 wrote:
I think I am understanding this correctly, but a little confused.

Maybe if we change things up a little bit, I can see how this works:
If instead of 60, Y was 210, what would the answer be? How would you arrive to the conclusion?

If Y were 210,
then first step would have been finding the prime factors.
210=2*5*3*7

The total number of disntict factors would be 2*2*2*2=16.
_________________
Manager
Joined: 25 Jun 2012
Posts: 71
Location: India
WE: General Management (Energy and Utilities)
Followers: 2

Kudos [?]: 55 [0], given: 15

Re: If y^4 is divisible by 60, what is the minimum number of dis [#permalink]  09 Jan 2013, 02:12
Marcab wrote:
I feel that here it must be given that y is an integer.
Anyways, an alternative approach is:
To find the number of distinct factors of a number, first prime factorize it.
In this case, since its given that $$y^4$$ is a multiple of 60, hence $$y^4$$ must contain 2*2*3*5. But here taking the fourth root will yield y in decimal form. Henceforth, to make y an integer, $$y^4$$ must be atleast $$2^4 * 3^4 * 5^4$$.
Now since y is an integer and has 2,3 and 5 as its prime factors, so total number of prime factors will be
2*2*2=8.
Since the number of prime factors is the product of the (power+1) of the individual prime factor. Here the individual powers are 1, 1 and 1. Hence the number of prime factors will be (1+1)*(1+1)*(1+1) or 8. Answer.

Hey, Marcab,I still dont get the quoted part in ur statement...

Verbal Forum Moderator
Status: Preparing for the another shot...!
Joined: 03 Feb 2011
Posts: 1422
Location: India
Concentration: Finance, Marketing
GPA: 3.75
Followers: 145

Kudos [?]: 790 [0], given: 62

Re: If y^4 is divisible by 60, what is the minimum number of dis [#permalink]  09 Jan 2013, 02:50
Expert's post
bhavinshah5685 wrote:
Marcab wrote:
I feel that here it must be given that y is an integer.
Anyways, an alternative approach is:
To find the number of distinct factors of a number, first prime factorize it.
In this case, since its given that $$y^4$$ is a multiple of 60, hence $$y^4$$ must contain 2*2*3*5. But here taking the fourth root will yield y in decimal form. Henceforth, to make y an integer, $$y^4$$ must be atleast $$2^4 * 3^4 * 5^4$$.
Now since y is an integer and has 2,3 and 5 as its prime factors, so total number of prime factors will be
2*2*2=8.
Since the number of prime factors is the product of the (power+1) of the individual prime factor. Here the individual powers are 1, 1 and 1. Hence the number of prime factors will be (1+1)*(1+1)*(1+1) or 8. Answer.

Hey, Marcab,I still dont get the quoted part in ur statement...

Hii Bhavin.
Its given that $$y^4$$ is a multiple of 60. So $$y^4$$ must be atleast 60 or $$2^2 * 3 * 4$$.
Taking the fourth root will result:
$$2^{1/2} * 3^{1/4} * 5^{1/4}$$. Since neither of $$2^{1/2}$$ ,$$3^{1/4}$$ and $$5^{1/4}$$ is an integer, therefore fourth root will yield decimal number. To get y as an integer, the powers of 2,3 and 5 must be a multiple of 4, so that the fourth root yields an integer.
hope that helps.
_________________
Verbal Forum Moderator
Status: Preparing for the another shot...!
Joined: 03 Feb 2011
Posts: 1422
Location: India
Concentration: Finance, Marketing
GPA: 3.75
Followers: 145

Kudos [?]: 790 [0], given: 62

Re: If y^4 is divisible by 60, what is the minimum number of dis [#permalink]  09 Jan 2013, 03:03
Expert's post
First make prime factorization of an integer n=$$a^p * b^q * c^r$$, where a, b, and c are prime factors of $$n$$ and $$p$$, $$q$$, and $$r$$ are their powers.

The number of factors of will be expressed by the formula $$(p+1)*(q+1)*(r+1)$$. NOTE: this will include 1 and n itself.

For more on number theory, do visit:
math-number-theory-88376.html
_________________
Manager
Joined: 04 Oct 2011
Posts: 224
Location: India
GMAT 1: 440 Q33 V13
GMAT 2: 0 Q0 V0
GPA: 3
Followers: 0

Kudos [?]: 31 [0], given: 44

Re: If y^4 is divisible by 60, what is the minimum number of dis [#permalink]  09 Jan 2013, 19:22
Marcab wrote:
I feel that here it must be given that y is an integer.
Anyways, an alternative approach is:
To find the number of distinct factors of a number, first prime factorize it.
In this case, since its given that $$y^4$$ is a multiple of 60, hence $$y^4$$ must contain 2*2*3*5. But here taking the fourth root will yield y in decimal form. Henceforth, to make y an integer, $$y^4$$ must be atleast $$2^4 * 3^4 * 5^4$$.
Now since y is an integer and has 2,3 and 5 as its prime factors, so total number of prime factors will be
2*2*2=8.
Since the number of prime factors is the product of the (power+1) of the individual prime factor. Here the individual powers are 1, 1 and 1. Hence the number of prime factors will be (1+1)*(1+1)*(1+1) or 8. Answer.

Marcab,
Shouldn't this be $$2^8 * 3^4 * 5^4$$ since in y there are $$2^2 * 3^1 * 5^1$$ ?
Please explain where im going wrong
_________________

GMAT - Practice, Patience, Persistence
Kudos if u like

Current Student
Joined: 27 Jun 2012
Posts: 418
Concentration: Strategy, Finance
Followers: 56

Kudos [?]: 455 [0], given: 182

Re: If y^4 is divisible by 60, what is the minimum number of dis [#permalink]  09 Jan 2013, 19:50
1
This post was
BOOKMARKED
We need to find y with minimum possible value as the problem needs minimum distinct factors.

Prime factorization of $$60=2^2*3^1*5^1$$

As $$y^4$$ is divisible by 60, it will include above prime factors of 60 (i.e. 2, 3 & 5) and we need to raise each prime factor to the power of 4 to get minimum $$y^4$$
Minimum possible value of $$y^4 = (2^2*3^1*5^1) * (2^2*3^3*5^3) = (2^4*3^4*5^4)$$ --This one must be divisible by 60.

Hence$$y = 2^1*3^1*5^1$$

Distinct factors of y = $$(1+1)*(1+1)*(1+1) = 8$$
--multiply (power of each prime factor +1)

_________________

Thanks,
PraPon

Tough 700+ Level RCs: Passage1 | Passage2 | Passage3 | Passage4 | Passage5 | Passage6 | Passage7
VOTE: vote-best-gmat-practice-tests-excluding-gmatprep-144859.html
PowerScore CR Bible - Official Guide 13 Questions Set Mapped: Click here

Verbal Forum Moderator
Status: Preparing for the another shot...!
Joined: 03 Feb 2011
Posts: 1422
Location: India
Concentration: Finance, Marketing
GPA: 3.75
Followers: 145

Kudos [?]: 790 [0], given: 62

Re: If y^4 is divisible by 60, what is the minimum number of dis [#permalink]  09 Jan 2013, 20:48
Expert's post
shanmugamgsn wrote:
Marcab wrote:
I feel that here it must be given that y is an integer.
Anyways, an alternative approach is:
To find the number of distinct factors of a number, first prime factorize it.
In this case, since its given that $$y^4$$ is a multiple of 60, hence $$y^4$$ must contain 2*2*3*5. But here taking the fourth root will yield y in decimal form. Henceforth, to make y an integer, $$y^4$$ must be atleast $$2^4 * 3^4 * 5^4$$.
Now since y is an integer and has 2,3 and 5 as its prime factors, so total number of prime factors will be
2*2*2=8.
Since the number of prime factors is the product of the (power+1) of the individual prime factor. Here the individual powers are 1, 1 and 1. Hence the number of prime factors will be (1+1)*(1+1)*(1+1) or 8. Answer.

Marcab,
Shouldn't this be $$2^8 * 3^4 * 5^4$$ since in y there are $$2^2 * 3^1 * 5^1$$ ?
Please explain where im going wrong

See shan,
We don't have to multiply the respective powers of each prime number by 4. We just have to multiply the powers with the smallest number so that together the product becomes the multiple of 4. Thats why I multiplied $$2^2$$ with $$2^2$$, $$3^1$$ with $$3^3$$ and $$5^1$$ with $$5^3$$. The resulting product became the multiple of 60 and when one takes fourth root, it become $$y=2*3*5$$.

In the case $$2^8 * 3^4 * 5^4$$, if we take the fourth root, the result will be $$2^2 * 3 *5$$ and hence the number of prime factors will be $$3*2*2$$ or 12. This is not the smallest. Hence incorrect.

Hope that helps.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 4943
Followers: 299

Kudos [?]: 55 [0], given: 0

Re: If y^4 is divisible by 60, what is the minimum number of dis [#permalink]  12 Nov 2014, 09:27
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.
_________________
Re: If y^4 is divisible by 60, what is the minimum number of dis   [#permalink] 12 Nov 2014, 09:27
Similar topics Replies Last post
Similar
Topics:
2 What is the minimum number of RECTANGULAR shipping boxes 5 17 Apr 2013, 00:18
If a number (N) is divisible by 33, what will be the minimum 7 08 Jun 2012, 08:20
What is the minimum number of shipping boxes Company L will 14 19 Oct 2006, 18:34
What is the minimum number of shipping boxes Company L 5 23 May 2006, 21:44
There are 5 locks and 5 keys. What is the minimum number of 5 24 Nov 2005, 04:41
Display posts from previous: Sort by