Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 30 Jul 2009
Posts: 17
Location: Danbury CT
Schools: Wharton, Columbia , Cornell, CMU , Yale

If the prime numbers p and t are the only prime factors of [#permalink]
Show Tags
19 Aug 2009, 11:55
1
This post received KUDOS
4
This post was BOOKMARKED
Question Stats:
51% (01:58) correct
49% (01:08) wrong based on 191 sessions
HideShow timer Statistics
If the prime numbers p and t are the only prime factors of the integer m, is m a multiple of (p^2)*t? (1) m has more than 9 positive factors (2) m is a multiple of m^3 OPEN DISCUSSION OF THIS QUESTIONS IS HERE: iftheprimenumberspandtaretheonlyprimefactorsof85836.html
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
[b]Make your dream a reality[/b]



Senior Manager
Joined: 20 Mar 2008
Posts: 452

Re: Prime Numbers and Divisibility [#permalink]
Show Tags
19 Aug 2009, 14:15
1
This post received KUDOS
gulatin2 wrote: If the prime numbers p and t are the only prime factors of the integer m, is m a multiple of (p^2)*t?
1) m has more than 9 positive factors 2) m is a multiple of m^3 Can you please confirm this problem? St. 2 doesn't sound right



Manager
Joined: 14 Aug 2009
Posts: 123

Re: Prime Numbers and Divisibility [#permalink]
Show Tags
19 Aug 2009, 17:00
2
This post received KUDOS
gulatin2 wrote: If the prime numbers p and t are the only prime factors of the integer m, is m a multiple of (p^2)*t?
1) m has more than 9 positive factors 2) m is a multiple of m^3 2) should be : m is a multiple of \(P^3\) 1) is nsf, suppose m=p*t*t*t*t*t*t*t*t 2) is suf. p, t are the only prime factors, and m is a multiple of p^3, therefore m=n*p*p*p*t, n is an integer so, m is a multiple of (p^2)*t Answer is B.
_________________
Kudos me if my reply helps!



Intern
Joined: 16 Aug 2009
Posts: 4

Re: Prime Numbers and Divisibility [#permalink]
Show Tags
19 Aug 2009, 18:06
1
This post received KUDOS
Correct me if i am wrong.. I Have seen same question in GMATPrep ( m is a multiple of P^3) and Agree with Flyingbunny Answer B



Director
Joined: 01 Apr 2008
Posts: 881
Name: Ronak Amin
Schools: IIM Lucknow (IPMX)  Class of 2014

Re: Prime Numbers and Divisibility [#permalink]
Show Tags
20 Aug 2009, 04:50
flyingbunny wrote: gulatin2 wrote: If the prime numbers p and t are the only prime factors of the integer m, is m a multiple of (p^2)*t?
1) m has more than 9 positive factors 2) m is a multiple of m^3 2) should be : m is a multiple of \(P^3\) 1) is nsf, suppose m= p*t*t*t*t*t*t*t*t2) is suf. p, t are the only prime factors, and m is a multiple of p^3, therefore m=n*p*p*p*t, n is an integer so, m is a multiple of (p^2)*t Answer is B. Agree that answer is B. But we do not need to check 9 factors in this way because m=p*t*t*t*t*t*t*t*t will have 18 factors:) I mean the idea is right but we can as well check for m=p*t*t*t*t where number of factors is 10 > 9 and m = p*p*p*t*t where the number of factors is 12 > 9. In the first case p^2*t is not a factor, in the second case it is.



Manager
Joined: 05 Jul 2009
Posts: 146
Location: Australia
Schools: Chicago Booth class of 2012
WE 1: Consulting
WE 2: Small business/Start up
WE 3: Strategy  Large Corporate

Re: Prime Numbers and Divisibility [#permalink]
Show Tags
21 Aug 2009, 22:26
1
This post received KUDOS
I enjoyed this. Thanks.



Director
Status: Gonna rock this time!!!
Joined: 22 Jul 2012
Posts: 520
Location: India
GMAT 1: 640 Q43 V34 GMAT 2: 630 Q47 V29
WE: Information Technology (Computer Software)

Re: Prime Numbers and Divisibility [#permalink]
Show Tags
25 Jan 2013, 00:34
Economist wrote: flyingbunny wrote: gulatin2 wrote: If the prime numbers p and t are the only prime factors of the integer m, is m a multiple of (p^2)*t?
1) m has more than 9 positive factors 2) m is a multiple of m^3 2) should be : m is a multiple of \(P^3\) 1) is nsf, suppose m= p*t*t*t*t*t*t*t*t2) is suf. p, t are the only prime factors, and m is a multiple of p^3, therefore m=n*p*p*p*t, n is an integer so, m is a multiple of (p^2)*t Answer is B. Agree that answer is B. But we do not need to check 9 factors in this way because m=p*t*t*t*t*t*t*t*t will have 18 factors:) I mean the idea is right but we can as well check for m=p*t*t*t*t where number of factors is 10 > 9 and m = p*p*p*t*t where the number of factors is 12 > 9. In the first case p^2*t is not a factor, in the second case it is. Bunuel, I don't quite understand how second statement is sufficient. Please explain with a numerical example..
_________________
hope is a good thing, maybe the best of things. And no good thing ever dies.
Who says you need a 700 ?Check this out : http://gmatclub.com/forum/whosaysyouneeda149706.html#p1201595
My GMAT Journey : http://gmatclub.com/forum/endofmygmatjourney149328.html#p1197992



Current Student
Joined: 27 Jun 2012
Posts: 411
Concentration: Strategy, Finance

Re: If the prime numbers p and t are the only prime factors of [#permalink]
Show Tags
25 Jan 2013, 01:06
3
This post received KUDOS
1
This post was BOOKMARKED
Attachment:
GMAT Prob.png [ 37.3 KiB  Viewed 5236 times ]
The 2nd statement listed in this problem is incorrect. It should be \(p^3\), not \(n^3\). See attached image for the original problem. ======== If the prime numbers p and t are the only prime factors of the integer m, is m a multiple of \(p^2*t\)? 1) m has more than 9 positive factors INSUFFICIENT: it doesnt tell exponent/powers of prime factors p & t. We dont know whether m is multiple of p^2. 2) m is a multiple of \(p^3\) SUFFICIENT: If m is a multiple of \(p^3\), then m must be multiple of \(p^2\). As 't' is also a prime factor of m, then m must be multiple of \(p^2*t\) e.g. say m=24, p=2, t=3. As 24 is multiple of \(p^3 = 2^3=8\), 24 must be multiple of \(p^2=2^2=4\), and therefore 24 is also multiple of \(p^2*t=2^2*3=6\) Hence choice(C) is the answer.
_________________
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



Director
Status: Gonna rock this time!!!
Joined: 22 Jul 2012
Posts: 520
Location: India
GMAT 1: 640 Q43 V34 GMAT 2: 630 Q47 V29
WE: Information Technology (Computer Software)

Re: If the prime numbers p and t are the only prime factors of [#permalink]
Show Tags
25 Jan 2013, 03:49
PraPon wrote: Attachment: GMAT Prob.png The 2nd statement listed in this problem is incorrect. It should be \(p^3\), not \(n^3\). See attached image for the original problem. ======== If the prime numbers p and t are the only prime factors of the integer m, is m a multiple of \(p^2*t\)? 1) m has more than 9 positive factors INSUFFICIENT: it doesnt tell exponent/powers of prime factors p & t. We dont know whether m is multiple of p^2. 2) m is a multiple of \(p^3\) SUFFICIENT: If m is a multiple of \(p^3\), then m must be multiple of \(p^2\). As 't' is also a prime factor of m, then m must be multiple of \(p^2*t\) e.g. say m=24, p=2, t=3. As 24 is multiple of \(p^3 = 2^3=8\), 24 must be multiple of \(p^2=2^2=4\), and therefore 24 is also multiple of \(p^2*t=2^2*3=6\) Hence choice(C) is the answer.so say m has r also as a prime factor, then m must be a multiple of p^2*t*r and of p*t*r?
_________________
hope is a good thing, maybe the best of things. And no good thing ever dies.
Who says you need a 700 ?Check this out : http://gmatclub.com/forum/whosaysyouneeda149706.html#p1201595
My GMAT Journey : http://gmatclub.com/forum/endofmygmatjourney149328.html#p1197992



Math Expert
Joined: 02 Sep 2009
Posts: 39659

Re: If the prime numbers p and t are the only prime factors of [#permalink]
Show Tags
25 Jan 2013, 05:30



Current Student
Joined: 27 Jun 2012
Posts: 411
Concentration: Strategy, Finance

Re: If the prime numbers p and t are the only prime factors of [#permalink]
Show Tags
25 Jan 2013, 09:42
1
This post received KUDOS
Sachin9 wrote: so say m has r also as a prime factor, then m must be a multiple of p^2*t*r and of p*t*r? Yes. That 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




Re: If the prime numbers p and t are the only prime factors of
[#permalink]
25 Jan 2013, 09:42







