The question stem states that x and y are prime numbers and that x is less than y. Prime numbers are positive integers that are divisible by exactly two factors: themselves and 1. The first few prime numbers are 2, 3, 5, 7, and 11.
The question asks which answer choice cannot be true. Test real, easy values that fit the given information until you get yourself down to the single correct answer.
Since x is less than y, try x = 2 and y = 3.
(A) x is even: This is indeed even, so eliminate this choice.
(B) x + y is odd: 2 + 3 = 5. This is indeed odd, so eliminate this choice.
(C) xy is even: (2)(3) = 6. This is indeed even, so eliminate this choice.
(D) y + xy is even: 3 + (2)(3) = 9. This is not even, so leave this choice in.
(E) 2x + y is even: 2(2) + 3 = 7. This is not even, so leave this choice in.
Test answers (D) and (E) again with a different pair of numbers: x = 3 and y = 5.
(D) y + xy is even: 5 + (3)(5) = 20. This is even, so eliminate this choice.
There is only one answer left, so it's not necessary to test it, but here's how it works:
(E) 2x + y is even: 2(3) + 5 = 11. This is not even, so leave this choice in.
The number 2 is the only even prime number. Many people forget that 2 is prime, so they'll end up trying only odd prime numbers (3, 5, 7, and so on), which won't get you to the right answer on this one. Whenever you see that a problem asks about prime numbers but doesn't specify which prime numbers you can use, immediately write down 2 to remind yourself to consider it as you solve.
The correct answer is (E).
