prashanthichennupati wrote:If x,y,and z are integers, is x Even?
(1) 10^x= (4^y)(5^z)
(2) 3^(x+5)= 27^(y+1)
From my analysis I think C should be the answer but A is the answer. Can anyone explain how statement 1 alone is sufficient?
Statement 1: 10^x= (4^y)(5^z)
(2*5)^x = (2²)^y * 5^z
(2^
x)(5^x) = 2^
(2y) * 5^z
In order for the lefthand side to be equal to the righthand side, the exponents in red must be equal:
x = 2y.
x = 2(integer)
x = even.
SUFFICIENT.
Statement 2: 3^(x+5)= 27^(y+1)
3^(x+5) = (3³)^(y+1)
3^
(x+5) = 3^
(3y+3).
In order for the lefthand side to be equal to the righthand side, the exponents in red must be equal:
x+5 = 3y+3
x = 3y-2.
If y=1, then x=1.
In this case, x is not even.
If y=2, then x=4.
In this case, x is even.
INSUFFICIENT.
The correct answer is
A.
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