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
_________________
Brent Hanneson – Creator of gmatprepnow.com
I’ve spent the last 20 years helping students overcome their difficulties with GMAT math, and the biggest thing I’ve learned is…
Students often get questions wrong NOT because they lack the skills to solve the question, but because they don’t understand what the GMAT is testing Learn more