Bunuel wrote:
GMAT CLUB'S FRESH QUESTION
If x and y are positive integers, is x odd?
(1) x/y is a prime number
(2) x^y is a prime number
The data is sufficient if we can determine conclusively whether x is odd or even.
Statement 1: x/y is a prime number
Approach - Counter exampleExample: x = 100 and y = 20. x/y = 5, is prime. x is even.
Counter Example: x = 85 and y = 17. x/y = 5, is prime. x is odd.
Because both possibilities exist, statement 1 ALONE is NOT sufficient.
Statement 2: x^y is a prime number
Because the question stem clearly states that x and y are positive integers, we can deduce that x is prime and y is 1.
Example: x = 5 and y = 1. x^y = 5, is prime. x is odd.
Counter Example: x = 2 and y = 1. x^y = 2, is prime. x is even.
Because both possibilities exist, statement 2 ALONE is NOT sufficient.
Combine the two statements.
Let us use the deduction from statement 2 as the starting point.
It narrows down our choice for y to just one value. y = 1.
Example: x = 5 and y = 1. x/y = 5 and x^y = 5, is prime. Satisfies both statements. x is odd.
Counter Example: x = 2 and y = 1. x/y = 2 and x^y = 2, is prime. This example also satisfies both statements. x is even.
Despite combining the two statements, we are not able to deduce whether x is odd, choice E is the answer.
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