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# if p, s, and t are positive prime numbers, what is the value

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Director
Joined: 12 Oct 2008
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if p, s, and t are positive prime numbers, what is the value [#permalink]  10 May 2009, 21:09
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if p, s, and t are positive prime numbers, what is the value of p^3s^3t^3?
(1) p^3st=728
(2) t=13
Director
Joined: 27 Jun 2008
Posts: 547
WE 1: Investment Banking - 6yrs
Followers: 1

Kudos [?]: 48 [0], given: 92

Re: DS: Prime numbers [#permalink]  11 May 2009, 02:56
if p, s, and t are positive prime numbers, what is the value of p^3s^3t^3?
(1) p^3st=728
(2) t=13

(1) 728 = 2*2*2*7*13, so we know p=2, s=7or13, t=13or7. The values for s & t doesn't really matter because we need to find the value of (p*s*t)^3. So, its (2*7*13)^3
Suff
(2) nothing about s * t
Insuff

A
Manager
Joined: 16 Apr 2009
Posts: 246
Schools: Ross
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Re: DS: Prime numbers [#permalink]  11 May 2009, 09:57
if p, s, and t are positive prime numbers, what is the value of p^3s^3t^3?
(1) p^3st=728
(2) t=13

Stat(1)
p^3st=728
728=2*2*2*7*13

Therefore suff

Stat(2)
t=13
but we don't know either s or p value so insuff

Hence A
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Manager
Joined: 13 May 2009
Posts: 195
Schools: Stanford, Harvard, Berkeley, INSEAD
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Re: DS: Prime numbers [#permalink]  14 May 2009, 13:11
1
KUDOS
If p, s, and t are positive prime numbers, what is the value of p^3s^3t^3?
(1) p^3st=728
(2) t=13

Question:($$p^3s^3t^3$$)?
Question:( $$(pst)^3$$ )?

(1) $$p^3*s*t=728$$
Factorize 728
$$728 = 2(364)=2(2)(182)=2(2)(2)(91)=2^3(7)(13)$$

So, $$p^3st=2^3(7)(13)$$
This gives us that p=2, and s=7,t=13 or s=13,t=7.
But in either case it doesn't matter, because the order in which we multiply the primes has no effect on the answer. For example, $$(2)(7)(13) = (2)(13)(7))$$, yes? So $$((2)(7)(13))^3 = ((2)(13)(7))^3$$ as well.

Sufficient.

(2) By itself this is insufficient as it tells us nothing about $$p$$ or $$s$$.

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Re: DS: Prime numbers   [#permalink] 14 May 2009, 13:11
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# if p, s, and t are positive prime numbers, what is the value

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