Bunuel wrote:
If m and n are integers, what is the value of m + n ?
(1) (x + m)(x + n) = x² + 5x + mn and x ≠ 0.
(2) mn = 4
Given: m and n are integers Target question: What is the value of m + n ? Statement 1: (x + m)(x + n) = x² + 5x + mn and x ≠ 0. Use FOIL to expand the left side: x² + nx + mx + mn = x² + 5x + mn
Factor the two middle terms: x² + x(n + m) + mn = x² + 5x + mn
At this point, we should see that
m+n = 5Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
If you're not convinced, we can take a few more steps.
Take: x² + x(n + m) + mn = x² + 5x + mn
Subtract x² from both sides: x(n + m) + mn = 5x + mn
Subtract mn from both sides: x(n + m) = 5x
Divide both sides by x to get:
n + m = 5Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: mn = 4There are many values of m and n that satisfy statement 2. Here are two:
Case a: m = 4 and n = 1. In this case, the answer to the target question is
m + n = 4 + 1 = 5Case b: m = 2 and n = 2. In this case, the answer to the target question is
m + n = 2 + 2 = 4Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent
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