If ab^2 = 50, what is the value of a(a – b)(a + b)? (1) a^3 = 8

Question

If ab^2 = 50, what is the value of a(a – b)(a + b)?

(1) a^3 = 8

(2) ab = –10

IanStewart · Answer

(a)(a-b)(a+b) = (a)(a^2 - b^2) = a^3 - ab^2, and since we know ab^2 = 50, the question is just asking for the value of a^3 - 50. So Statement 1 is immediately sufficient.

Using Statement 2, we have two equations:

ab^2 = 50
ab = -10

and dividing the first equation by the second (or by using substitution) we find b = -5, and we can plug that in to ab = -10 to find that a = 2 and answer the question. So the answer is D.

cnjames · Answer

Why can you simply divide the first equation by the second to find b = -5?

IanStewart · Answer

We know ab^2 = 50, and ab = -10. So, just by substituting "50" for "ab^2" and "-10" for "ab" in "ab^2 / ab", we find

ab^2 / ab = 50/(-10)

and canceling on both sides,

b = -5

So that's correct just using substitution. But notice that's exactly what you'd also get if you just divide the first equation by the second -- dividing one equation by another is really the same thing as substitution. So it's always fine to do, just as it's fine to add or subtract (or multiply, etc) equations, except in the one case when you might be dividing by zero.

If ab^2 = 50, what is the value of a(a – b)(a + b)? (1) a^3 = 8

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