fozzzy wrote:
If x and y are integers, is the value of x(y + 1) even?
(1) x and y are prime numbers.
(2) y > 7
Having scanned the two statements, I can see that this question is ultimately testing whether or not we recognize that ALL prime numbers are odd
EXCEPT for 2 (which is even).
Target question: Is x(y+1) an even number? Statement 1: x and y are prime numbers. There are several values of x and y that satisfy this condition. Here are two:
Case a: x = 2 and y = 3, in which case
x(y+1) is EVENCase b: x = 3 and y = 2, in which case
x(y+1) is ODDSince we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: y > 7There are several values of x and y that satisfy this condition. Here are two:
Case a: x = 2 and y = 8, in which case
x(y+1) is EVENCase b: x = 3 and y = 8, in which case
x(y+1) is ODDSince we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined If y is a prime number
and y > 7, we know that y MUST BE ODD
If y is odd, then y+1 must be EVEN
This means that x(y+1) = x(some EVEN integer) = EVEN
So,
x(y+1) is definitely evenSince we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer:
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