Last visit was: 23 Jun 2025, 04:58 It is currently 23 Jun 2025, 04:58
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
User avatar
daviesj
Joined: 23 Aug 2012
Last visit: 09 May 2025
Posts: 115
Own Kudos:
1,376
 [56]
Given Kudos: 35
Status:Never ever give up on yourself.Period.
Location: India
Concentration: Finance, Human Resources
GMAT 1: 570 Q47 V21
GMAT 2: 690 Q50 V33
GPA: 3.5
WE:Information Technology (Finance: Investment Banking)
GMAT 2: 690 Q50 V33
Posts: 115
Kudos: 1,376
 [56]
10
Kudos
Add Kudos
46
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
PrashantPonde
Joined: 27 Jun 2012
Last visit: 29 Jan 2025
Posts: 322
Own Kudos:
2,667
 [15]
Given Kudos: 185
Concentration: Strategy, Finance
Posts: 322
Kudos: 2,667
 [15]
7
Kudos
Add Kudos
8
Bookmarks
Bookmark this Post
User avatar
daviesj
Joined: 23 Aug 2012
Last visit: 09 May 2025
Posts: 115
Own Kudos:
1,376
 [7]
Given Kudos: 35
Status:Never ever give up on yourself.Period.
Location: India
Concentration: Finance, Human Resources
GMAT 1: 570 Q47 V21
GMAT 2: 690 Q50 V33
GPA: 3.5
WE:Information Technology (Finance: Investment Banking)
GMAT 2: 690 Q50 V33
Posts: 115
Kudos: 1,376
 [7]
4
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
General Discussion
User avatar
Triforce
Joined: 23 Nov 2012
Last visit: 10 Sep 2013
Posts: 26
Own Kudos:
17
 [1]
Given Kudos: 19
Location: France
Concentration: Finance, Economics
Schools: Said (D)
GMAT 1: 710 Q49 V38
WE:Sales (Finance: Investment Banking)
Schools: Said (D)
GMAT 1: 710 Q49 V38
Posts: 26
Kudos: 17
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I get 3, since 60^4 is divisable through 60 and 60 has only 3 distinct factors which are 2, 3 and 5...
User avatar
ConnectTheDots
Joined: 28 Apr 2012
Last visit: 06 May 2020
Posts: 239
Own Kudos:
1,000
 [1]
Given Kudos: 142
Location: India
Concentration: Finance, Technology
GMAT 1: 650 Q48 V31
GMAT 2: 770 Q50 V47
WE:Information Technology (Computer Software)
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
daviesj
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 ?
User avatar
Marcab
Joined: 03 Feb 2011
Last visit: 22 Jan 2021
Posts: 852
Own Kudos:
4,767
 [4]
Given Kudos: 221
Status:Retaking after 7 years
Location: United States (NY)
Concentration: Finance, Economics
GMAT 1: 720 Q49 V39
GPA: 3.75
GMAT 1: 720 Q49 V39
Posts: 852
Kudos: 4,767
 [4]
3
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
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.
User avatar
Marcab
Joined: 03 Feb 2011
Last visit: 22 Jan 2021
Posts: 852
Own Kudos:
4,767
 [1]
Given Kudos: 221
Status:Retaking after 7 years
Location: United States (NY)
Concentration: Finance, Economics
GMAT 1: 720 Q49 V39
GPA: 3.75
GMAT 1: 720 Q49 V39
Posts: 852
Kudos: 4,767
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ConnectTheDots
daviesj
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.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 23 June 2025
Posts: 102,253
Own Kudos:
Given Kudos: 93,991
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,253
Kudos: 734,748
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Marcab
ConnectTheDots
daviesj
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.
User avatar
hitman5532
Joined: 18 Nov 2011
Last visit: 14 May 2013
Posts: 23
Own Kudos:
Concentration: Strategy, Marketing
GMAT Date: 06-18-2013
GPA: 3.98
Posts: 23
Kudos: 26
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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?
User avatar
Marcab
Joined: 03 Feb 2011
Last visit: 22 Jan 2021
Posts: 852
Own Kudos:
Given Kudos: 221
Status:Retaking after 7 years
Location: United States (NY)
Concentration: Finance, Economics
GMAT 1: 720 Q49 V39
GPA: 3.75
GMAT 1: 720 Q49 V39
Posts: 852
Kudos: 4,767
Kudos
Add Kudos
Bookmarks
Bookmark this Post
hitman5532
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.
avatar
bhavinshah5685
Joined: 25 Jun 2012
Last visit: 19 Jun 2017
Posts: 49
Own Kudos:
298
 [1]
Given Kudos: 21
Location: India
WE:General Management (Energy)
Posts: 49
Kudos: 298
 [1]
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Marcab
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...

I got answer 12.
User avatar
Marcab
Joined: 03 Feb 2011
Last visit: 22 Jan 2021
Posts: 852
Own Kudos:
Given Kudos: 221
Status:Retaking after 7 years
Location: United States (NY)
Concentration: Finance, Economics
GMAT 1: 720 Q49 V39
GPA: 3.75
GMAT 1: 720 Q49 V39
Posts: 852
Kudos: 4,767
Kudos
Add Kudos
Bookmarks
Bookmark this Post
bhavinshah5685
Marcab
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...

I got answer 12.

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.
User avatar
Marcab
Joined: 03 Feb 2011
Last visit: 22 Jan 2021
Posts: 852
Own Kudos:
Given Kudos: 221
Status:Retaking after 7 years
Location: United States (NY)
Concentration: Finance, Economics
GMAT 1: 720 Q49 V39
GPA: 3.75
GMAT 1: 720 Q49 V39
Posts: 852
Kudos: 4,767
Kudos
Add Kudos
Bookmarks
Bookmark this Post
12 can't be the answer. Correct answer is 8.
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
User avatar
shanmugamgsn
Joined: 04 Oct 2011
Last visit: 31 Dec 2014
Posts: 141
Own Kudos:
Given Kudos: 44
Location: India
Concentration: Entrepreneurship, International Business
GMAT 1: 440 Q33 V13
GPA: 3
GMAT 1: 440 Q33 V13
Posts: 141
Kudos: 152
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Marcab
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
User avatar
Marcab
Joined: 03 Feb 2011
Last visit: 22 Jan 2021
Posts: 852
Own Kudos:
4,767
 [2]
Given Kudos: 221
Status:Retaking after 7 years
Location: United States (NY)
Concentration: Finance, Economics
GMAT 1: 720 Q49 V39
GPA: 3.75
GMAT 1: 720 Q49 V39
Posts: 852
Kudos: 4,767
 [2]
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
shanmugamgsn
Marcab
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.
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 21 Jun 2025
Posts: 20,985
Own Kudos:
26,039
 [3]
Given Kudos: 293
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 20,985
Kudos: 26,039
 [3]
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
daviesj
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

We are given y^4/60 = integer. In other words:

y^4/(2^2 x 3^1 x 5^1) = integer

Since y must have at least one 2, one 3 and one 5 in order for y^4/60 = integer, the minimum value of y must be (2^1 x 3^1 x 5^1), or 30.

Now, to determine the number of distinct factors, we can use the following shortcut:

The total number of factors of a number can be obtained by multiplying the numbers resulting from adding 1 to the exponents in the prime factorization. Thus, the total number of factors of y is:

(1 + 1) x (1 + 1) x (1 + 1) = 2 x 2 x 2 = 8

Alternately, we could list all factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

Thus, y has 8 distinct factors.

Answer: C
avatar
mbah191
Joined: 01 Apr 2015
Last visit: 15 Oct 2019
Posts: 19
Own Kudos:
Given Kudos: 11
Location: United States
Posts: 19
Kudos: 5
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi all,

I read through all responses but I'm still having some trouble understanding this. Going by the formula... Number of distinct factors = (p+1)(q+1)(r+1)... I have 2^2, 3^1, 5^1 - where p =2, q = 1, and r = 1. My initial reaction is to plug in and get 12. I understand that we need y, not y^4, but why does that change things?

I guess my question is, why exactly are we making each power 1 (changing 2^2 to 2^1) in this case? When would we do this vs when would we not do this? I need to understand what makes this problem unique so that on test day, I don't get a question like this wrong.

If it was y is divisible by 60 (instead of y^4), then would the answer be 12? Also, if it was y^2 or y^3 instead of y^4, would that change things? :|

Thank you very much to whoever can set me straight on this! :-D

Best,
Max
User avatar
chesstitans
Joined: 12 Dec 2016
Last visit: 20 Nov 2019
Posts: 991
Own Kudos:
Given Kudos: 2,562
Location: United States
GMAT 1: 700 Q49 V33
GPA: 3.64
GMAT 1: 700 Q49 V33
Posts: 991
Kudos: 1,896
Kudos
Add Kudos
Bookmarks
Bookmark this Post
in this question, the assumption is that y is an integer. Then, the question can be paraphrased into the following idea: if y is a minimum integer that y^4 can be divisible by 60 , how many distinct factors y has?

3 distinct prime factors of the minimum y are 2,3,5 => distinct factors will be 8
User avatar
arvind910619
Joined: 20 Dec 2015
Last visit: 18 Oct 2024
Posts: 851
Own Kudos:
Given Kudos: 755
Status:Learning
Location: India
Concentration: Operations, Marketing
GMAT 1: 670 Q48 V36
GRE 1: Q157 V157
GPA: 3.4
WE:Engineering (Manufacturing)
Products:
GMAT 1: 670 Q48 V36
GRE 1: Q157 V157
Posts: 851
Kudos: 599
Kudos
Add Kudos
Bookmarks
Bookmark this Post
mbah191
Hi all,

I read through all responses but I'm still having some trouble understanding this. Going by the formula... Number of distinct factors = (p+1)(q+1)(r+1)... I have 2^2, 3^1, 5^1 - where p =2, q = 1, and r = 1. My initial reaction is to plug in and get 12. I understand that we need y, not y^4, but why does that change things?

I guess my question is, why exactly are we making each power 1 (changing 2^2 to 2^1) in this case? When would we do this vs when would we not do this? I need to understand what makes this problem unique so that on test day, I don't get a question like this wrong.

If it was y is divisible by 60 (instead of y^4), then would the answer be 12? Also, if it was y^2 or y^3 instead of y^4, would that change things? :|

Thank you very much to whoever can set me straight on this! :-D

Best,
Max
Hi y^4 is divisible by 60
We have to find the minimum value
So prime factors of 60 are 2^2*3*5
Now the tricky part in this question is that y has a power of 4
So we have to have 2*3*5 in Y because to divide and get the integer we should have common factors.
And we should have only one 2 in numerator because this that 2 will rise to power 4 in y^4 so ultimately it will be divisible by 60 so minimum factors are 8
Now coming in to your second question it y is divided by 60 , the the situation changes we should have all the powers of prime factors in order to divide
Y/60
Y/(2^2*3*5)
In this the factors are 12
Hope it helps

Sent from my ONE E1003 using GMAT Club Forum mobile app
User avatar
sb995
Joined: 20 Jan 2025
Last visit: 23 Jun 2025
Posts: 24
Given Kudos: 53
Products:
Posts: 24
Kudos: 0
Kudos
Add Kudos
Bookmarks
Bookmark this Post
1) Prime factorize 60: \((2^2)\) * (3) * (5)
2) \(Y^4\) factors: 4 * 3 * 5
3) Total number of distinct factors using formula: (1+1) * (1+1) * (1+1) = 2 * 2 * 2 = 8


daviesj
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
Moderators:
Math Expert
102253 posts
PS Forum Moderator
657 posts