Bunuel wrote:

If the greatest common factor of positive integers A and B is 20, what is the value of A – B?

(1) The least common multiple of A and B is 400.

(2) A = 80

Target question: What is the value of A – B? Given: The greatest common factor of positive integers A and B is 20 Statement 1: The least common multiple of A and B is 400 USEFUL RULE: (greatest common factor x and y)(least common multiple of x and y) = xySo, (greatest common factor A and B)(least common multiple of A and B) = AB

Replace values to get: (20)(400) = AB

In other words,

AB = 8000Is knowing the value of AB enough to determine

the value of A - B?

No.

There are several values of A and B that satisfy statement 1 (and the given information). Here are two:

Case a: A = 20 and B = 400, in which case

A - B = 20 - 400 = -380Case b: A = 400 and B = 20, in which case

A - B = 400 - 20 = 380Since we cannot answer the

target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: A = 80There's no information about B, so statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined Statement 1 tells us that

AB = 8000Statement 2 tells us that A = 80

This means that B = 100

So,

A - B = 80 - 100 = -20Since we can answer the

target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,

Brent

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Brent Hanneson – Founder of gmatprepnow.com