Bunuel wrote:
For integers a and b, is the expression ab – b even?
(1) a is odd
(2) b is odd
Target question: Is the expression ab – b even?HINT: notice that ab – b = b(a - 1)
Statement 1: a is odd What does does this tell us about the expression ab – b?
Well, ab – b = b(a - 1)
= b(ODD - 1)
= b(EVEN)
[since an odd integer minus 1 gives us a EVEN integer]= EVEN
Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: b is odd There are several values of a and b that satisfy statement 2. Here are two:
Case a: a = 3 and b = 1. In this case ab – b = (3)(1) - 1 = 2.
So, ab – b is EVENCase b: a = 2 and b = 1. In this case ab – b = (2)(1) - 1 = 1.
So, ab – b is ODDSince we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Answer:
Cheers,
Brent
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