gmatophobia wrote:
If \(p, q, x,\) and \(y\) are non-zero integers and '\(x\)' is even, is \(p * (x^q * y)\) = even
1) '\(q\)' is an odd integer
2) '\(p\)' is an even integer
Official Explanation Given- \(p, q, x,\) and \(y\) are non-zero integers
- \(x\) is even
QuestionIs \(p * (x^q * y)\) = even
Statement 11) '\(q\)' is an odd integer
While we know that the value of q is odd, we do not know whether the value is positive or negative. Without that information, we cannot determine the even/odd nature of \(x^q\)
Consider the following -
Case 1\(x = 2, p = 2 , q = -1, y = 1\)
\(2 * (2^{-1} * 1) = 2 * (\frac{1}{2} * 1) = 1\)
The value is odd.
Case 2\(x = 2, p = 2 , q = 1, y = 1\)
\(2 * (2^{1} * 1) = 2 * (2 * 1) = 4\)
The value is even.
As we have multiple possible answers, the statement alone is not sufficient and we can eliminate A and D.
Statement 22) '\(p\)' is an even integer
We know that \(p\) is even, however, we do not know the positive-negative nature of \(q\). The cases taken to evaluate Statement 1 are valid in this case as well.
We know that Statement 1 is not sufficient, hence Statement 2 is also not sufficient to arrive at a definite answer.
Eliminate B.
CombinedStatement 2 doesn't provide any additional information to resolve the positive negative nature of q. Hence, the statements combined are not sufficient as well.
Option E