Solution:
Given that, x and y are integers. We are asked to find the value of y.
Statement 1: y^x=1
For x=0, y can take any integer value.
Integer Property: Any number (except zero) raised to power zero is one; zero raised to power zero is undefined.
So, y can be any number.
For instance, 2^0=1, (-2)^0=1, 4^0=1
Since we do not get an unique value of y from Statement 1, this statement is NOT sufficient.
Statement 2: (16 - 2x)/x = -x - 10
x^2 + 8x + 16 = 0
(x + 4)^2 = 0
Solving the quadratic equation, we get two equal root of x, i.e. x = -4, -4
From Statement 2, we can only know the value of x, but not y. So, Statement 2 by itself NOT sufficient.
Combining Statement 1 & Statement 2y^x=1 and x = -4
y^(-4)=1
Therefore, y^4 = 1
Two value of y satisfies the above equation, i.e. y = 1 & y = -1
Since we do not get an unique value of y even after combining Statement 1 & Statement 2, these statements are together NOT sufficient. Hence, the correct answer is Option E.divyadamahe - Could you please review the OA?
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