RBBmba@2014 wrote: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
OA: B
@ Experts - sort of lost here. What is the best way to approach this kind of problem ? Please help!
(3²�)(5¹�)(z) = (5�)(9¹�)(x^y)
(3²�)(5¹�)(z) = (5�)(3²)¹�(x^y)
(3²�)(5¹�)(z) = (5�)(3²�)(x^y)
(5²)(z) = (3)(x^y)
z = (3) * (x^y)/5².
Since z is an INTEGER, the resulting equation implies that z is a multiple of 3 and that x^y is a multiple of 5².
Statement 1: y is prime
Given that x^y is a multiple of 5² and y is prime, the following cases are possible:
x=5 and y=2
x=25 and y=2.
Since x can be different values, INSUFFICIENT.
SUFFICIENT.
Statement 2: x is prime
Since x^y is a multiple of 5² and x is prime, x=5 and y≥2.
SUFFICIENT.
The correct answer is
B.
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