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# If x is a perfect square and x=p^a*q^b*r^c*s^d , are prime

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VP
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If x is a perfect square and x=p^a*q^b*r^c*s^d , are prime [#permalink]  09 Mar 2008, 08:47
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If x is a perfect square and x=p^a*q^b*r^c*s^d , are prime numbers p, q, r and s
distinct?

(1) 18 is a factor of ab and cd
(2) 4 is not a factor of ab and cd

Last edited by marcodonzelli on 15 Mar 2008, 00:32, edited 1 time in total.
Current Student
Joined: 28 Dec 2004
Posts: 3391
Location: New York City
Schools: Wharton'11 HBS'12
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Re: integers and prime numbers [#permalink]  09 Mar 2008, 10:03
I get A for this

i know that (prime)^even=perfect sq.

since x=perfect sq, then p, a, q,b, r, ,c,s,d must all be raised to an even power

1) says ab, cd =18M which means the have prime factors 3,2 since these appear 4 times in a, b c and d..the other prime factors p, q, r and s have to be such that either p=q and r=s or they are all equalp=q=r=s..eiter way sufficient to answer they are not distinct

2) says 2 is not a factor of ab, cd, which means ab=3*3 cd=7*3 or 5*11 , 5*3 etc, which leaves pqrs to be 7 11 5 and 3..we cant tell..
insufficient
Director
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Re: integers and prime numbers [#permalink]  10 Mar 2008, 19:08
Got 'E'

Stmt1:
plug in numbers;
p 5
q 7
r 7
s 5
ab 18
cd 18
pqrsabcd is a perfect sq and p,q,r,s are not distinct primes.

p 3
q 5
r 7
s 11
ab 18
cd 18*3*5*7*11
pqrsabcd is a perfect sq and p,q,r,s are distinct primes.
so Insuff

Stmt2:above two set of numbers satisfy this.
So insuff

Combining togther
still insuff
VP
Joined: 22 Nov 2007
Posts: 1105
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Re: integers and prime numbers [#permalink]  15 Mar 2008, 00:32
vshaunak@gmail.com wrote:
Got 'E'

Stmt1:
plug in numbers;
p 5
q 7
r 7
s 5
ab 18
cd 18
pqrsabcd is a perfect sq and p,q,r,s are not distinct primes.

p 3
q 5
r 7
s 11
ab 18
cd 18*3*5*7*11
pqrsabcd is a perfect sq and p,q,r,s are distinct primes.
so Insuff

Stmt2:above two set of numbers satisfy this.
So insuff

Combining togther
still insuff

sorry, look at the question now
Re: integers and prime numbers   [#permalink] 15 Mar 2008, 00:32
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