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

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If x, y, and z are integers greater than 1, and [#permalink] New post 30 Jul 2008, 06:07
If x, y, and z are integers greater than 1, and (3^27)(35^10)(z) = (5^8)(7^10)(9^14)(x^y), then what is the value of x?

(1) z is prime

(2) x is prime
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Re: UNKNOWN EQN.... [#permalink] New post 30 Jul 2008, 06:39
arjtryarjtry wrote:
If x, y, and z are integers greater than 1, and (3^27)(35^10)(z) = (5^8)(7^10)(9^14)(x^y), then what is the value of x?

(1) z is prime

(2) x is prime



(3^27)(35^10)(z) = (5^8)(7^10)(9^14)(x^y)
--> (3^27)(7^10)(5^10)(z) = (5^8)(7^10)(3^28)(x^y)
--> (5^2)(z) =3(x^y)
-->25 z = 3(x^y)
(x^y) = 25 z /3

(1) z is prime -- Sufficient.
(x^y) = 25 z /3
x and Y are integers 25 z /3 --> must be integer (not fraction..)
Z prime number --> it should be divided by itself and only with one..
so -- it must be 3
z=3
(x^y) =25
5^2 = 25
x=5

2) x is prime -- Sufficient.

(x^y) = 25 z /3 = (5 * 5 * Z) /3 -- > z must be divisible by 3
(x^y) = 25 z /3 = 5*5 K ( k=z/3 which is integer)

If x is prime it must be 5..
only if x=5 (prime number) --> 5*5 K is possible.
x=5 y=2 k =3
x=5 y=3 k =3*5=15
if you try any other prime number.. e.g 3, 7, 11.. it wont' lead to 5*5*K..
so x=5

Each statement alone sufficient.
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Re: UNKNOWN EQN.... [#permalink] New post 30 Jul 2008, 08:36
arjtryarjtry wrote:
If x, y, and z are integers greater than 1, and (3^27)(35^10)(z) = (5^8)(7^10)(9^14)(x^y), then what is the value of x?

(1) z is prime

(2) x is prime


(3^27)(35^10)(z) = (5^8)(7^10)(9^14)(x^y)
(3^27)(5^10)(7^10)(z) = (5^8)(7^10)(3^28)(x^y)
(5^2)z = 3(x^y)

(1) z is prime
because there is a 3 on the right, there should be a 3 on the left
As z is prime, z must be equal to 3
then (5^2) = (x^y)
Suff

(1) x is prime
because there is a 5 on the left, there should be a 5 on the right
As x is prime, x must be equal to 5
then (5^2) = (x^y)
Suff

Ans is D
Suff
Re: UNKNOWN EQN....   [#permalink] 30 Jul 2008, 08:36
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If x, y, and z are integers greater than 1, and

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