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# If x, y, and z are integers greater than 1, and

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Manager
Joined: 04 Jan 2008
Posts: 120
Followers: 2

Kudos [?]: 22 [0], given: 0

If x, y, and z are integers greater than 1, and [#permalink]  22 Sep 2008, 01:03
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If x, y, and z are integers greater than 1, and (3^27)(5^10)(z) = (5^8)(9^14)(x^y), then what is the value of x?

(1) y is prime

(2) x is prime
Director
Joined: 23 May 2008
Posts: 840
Followers: 3

Kudos [?]: 37 [0], given: 0

Re: Zumit DS 030 [#permalink]  22 Sep 2008, 21:34
25/3 = x^y/z

1) x is prime, must be 5
2) y is prime, must be 2

D
Director
Joined: 20 Sep 2006
Posts: 658
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Kudos [?]: 77 [0], given: 7

Re: Zumit DS 030 [#permalink]  22 Sep 2008, 21:44
IMO B.

5^2 * 3 * K = X ^Y where Z= 3*k

If X is prime then K has to be 1 (i.e Z = 1) and Y = 2 to maintain the equality in the equation.
Intern
Joined: 13 Aug 2008
Posts: 17
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Kudos [?]: 2 [0], given: 0

Re: Zumit DS 030 [#permalink]  23 Sep 2008, 02:00
IMO B as well, from statement 1 x can be 5 or 10 or so on..

25z = 3 x^y

25 * 12 = 3 * 10^2

25*3 = 3 * 5 ^ 2
Re: Zumit DS 030   [#permalink] 23 Sep 2008, 02:00
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