Author 
Message 
TAGS:

Hide Tags

Manager
Status: Never ever give up on yourself.Period.
Joined: 23 Aug 2012
Posts: 151
Location: India
Concentration: Finance, Human Resources
GMAT 1: 570 Q47 V21 GMAT 2: 690 Q50 V33
GPA: 3.5
WE: Information Technology (Investment Banking)

If y^4 is divisible by 60, what is the minimum number of dis [#permalink]
Show Tags
06 Jan 2013, 06:50
5
This post received KUDOS
15
This post was BOOKMARKED
Question Stats:
51% (01:22) correct 49% (01:17) wrong based on 337 sessions
HideShow timer Statistics
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
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Don't give up on yourself ever. Period. Beat it, no one wants to be defeated (My journey from 570 to 690) : http://gmatclub.com/forum/beatitnoonewantstobedefeatedjourney570to149968.html
Last edited by Bunuel on 07 Jan 2013, 02:05, edited 1 time in total.
Edited the question.



Intern
Joined: 23 Nov 2012
Posts: 35
Location: France
Concentration: Finance, Economics
WE: Sales (Investment Banking)

Re: If y^4 is divisible by 60, what is the minimum number of dis [#permalink]
Show Tags
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!



Manager
Status: Never ever give up on yourself.Period.
Joined: 23 Aug 2012
Posts: 151
Location: India
Concentration: Finance, Human Resources
GMAT 1: 570 Q47 V21 GMAT 2: 690 Q50 V33
GPA: 3.5
WE: Information Technology (Investment Banking)

Re: If y^4 is divisible by 60, what is the minimum number of dis [#permalink]
Show Tags
06 Jan 2013, 08:38
3
This post received KUDOS
1
This post was BOOKMARKED
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) : http://gmatclub.com/forum/beatitnoonewantstobedefeatedjourney570to149968.html



Current Student
Joined: 28 Apr 2012
Posts: 306
Location: India
Concentration: Finance, Technology
GMAT 1: 650 Q48 V31 GMAT 2: 770 Q50 V47
WE: Information Technology (Computer Software)

Re: If y^4 is divisible by 60, what is the minimum number of dis [#permalink]
Show Tags
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!



VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1372
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75

Re: If y^4 is divisible by 60, what is the minimum number of dis [#permalink]
Show Tags
06 Jan 2013, 10:41
1
This post received KUDOS
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.
_________________
Prepositional Phrases ClarifiedElimination of BEING Absolute Phrases Clarified Rules For Posting www.UnivScholarships.com



VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1372
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75

Re: If y^4 is divisible by 60, what is the minimum number of dis [#permalink]
Show Tags
06 Jan 2013, 10:43
1
This post received KUDOS
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.
_________________
Prepositional Phrases ClarifiedElimination of BEING Absolute Phrases Clarified Rules For Posting www.UnivScholarships.com



Math Expert
Joined: 02 Sep 2009
Posts: 43789

Re: If y^4 is divisible by 60, what is the minimum number of dis [#permalink]
Show Tags
07 Jan 2013, 02:22
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.
_________________
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? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 18 Nov 2011
Posts: 36
Concentration: Strategy, Marketing
GMAT Date: 06182013
GPA: 3.98

Re: If y^4 is divisible by 60, what is the minimum number of dis [#permalink]
Show Tags
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?



VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1372
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75

Re: If y^4 is divisible by 60, what is the minimum number of dis [#permalink]
Show Tags
08 Jan 2013, 18:24
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.
_________________
Prepositional Phrases ClarifiedElimination of BEING Absolute Phrases Clarified Rules For Posting www.UnivScholarships.com



Manager
Joined: 25 Jun 2012
Posts: 67
Location: India
WE: General Management (Energy and Utilities)

Re: If y^4 is divisible by 60, what is the minimum number of dis [#permalink]
Show Tags
09 Jan 2013, 02:12
1
This post was BOOKMARKED
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... I got answer 12.



VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1372
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75

Re: If y^4 is divisible by 60, what is the minimum number of dis [#permalink]
Show Tags
09 Jan 2013, 02:50
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... 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.
_________________
Prepositional Phrases ClarifiedElimination of BEING Absolute Phrases Clarified Rules For Posting www.UnivScholarships.com



VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1372
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75

Re: If y^4 is divisible by 60, what is the minimum number of dis [#permalink]
Show Tags
09 Jan 2013, 03:03
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: mathnumbertheory88376.html
_________________
Prepositional Phrases ClarifiedElimination of BEING Absolute Phrases Clarified Rules For Posting www.UnivScholarships.com



Manager
Joined: 04 Oct 2011
Posts: 212
Location: India
Concentration: Entrepreneurship, International Business
GPA: 3

Re: If y^4 is divisible by 60, what is the minimum number of dis [#permalink]
Show Tags
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: 401
Concentration: Strategy, Finance

Re: If y^4 is divisible by 60, what is the minimum number of dis [#permalink]
Show Tags
09 Jan 2013, 19:50
2
This post received KUDOS
3
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) Hence answer choice(C) is correct.
_________________
Thanks, Prashant Ponde
Tough 700+ Level RCs: Passage1  Passage2  Passage3  Passage4  Passage5  Passage6  Passage7 Reading Comprehension notes: Click here VOTE GMAT Practice Tests: Vote Here PowerScore CR Bible  Official Guide 13 Questions Set Mapped: Click here Looking to finance your tuition: Click here



VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1372
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75

Re: If y^4 is divisible by 60, what is the minimum number of dis [#permalink]
Show Tags
09 Jan 2013, 20:48
1
This post received KUDOS
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.
_________________
Prepositional Phrases ClarifiedElimination of BEING Absolute Phrases Clarified Rules For Posting www.UnivScholarships.com



NonHuman User
Joined: 09 Sep 2013
Posts: 13849

Re: If y^4 is divisible by 60, what is the minimum number of dis [#permalink]
Show Tags
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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



Board of Directors
Joined: 17 Jul 2014
Posts: 2723
Location: United States (IL)
Concentration: Finance, Economics
GPA: 3.92
WE: General Management (Transportation)

If y^4 is divisible by 60, what is the minimum number of dis [#permalink]
Show Tags
18 Dec 2015, 17:20
minimum value y can be is 2*3*5. all raised to the power of 4 is divisible by 60. thus, to find the number of factors that y can have: 2*2*2 = 8. C.
bumped into this one again. did the same way  under 50 seconds.



NonHuman User
Joined: 09 Sep 2013
Posts: 13849

Re: If y^4 is divisible by 60, what is the minimum number of dis [#permalink]
Show Tags
10 Feb 2017, 01:26
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



Intern
Joined: 14 Oct 2014
Posts: 17

Re: If y^4 is divisible by 60, what is the minimum number of dis [#permalink]
Show Tags
10 Feb 2017, 05:06
I got 6 as ans Since factor of 60 2^2*3*5 and since minimum factor of y is asked so it much contain one nos of 2,3,5 so the min no of distinct factors are 6.
Sent from my iPhone using GMAT Club Forum



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2179
Location: United States (CA)

Re: If y^4 is divisible by 60, what is the minimum number of dis [#permalink]
Show Tags
15 Feb 2017, 09:44
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 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
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions




Re: If y^4 is divisible by 60, what is the minimum number of dis
[#permalink]
15 Feb 2017, 09:44



Go to page
1 2
Next
[ 23 posts ]



