jjack0310 wrote:

Is a > c?

(1) b > d

(2) a*(b^2) - b > (b^2)*c - d

The correct answer that I have is supposed to be C, but I don't know how. Thanks

Sorry if this has been posted before. I tried searching and could not find anything.

Dear

jjack0310,

This is a great question and I am happy to help.

First of all, you may find this post on DS & inequalities helpful:

http://magoosh.com/gmat/2013/gmat-quant ... qualities/I will take it for granted that each of the statements individually is not sufficient. Let's focus on what happens when we combine the statements.

In statement #2, I will add

b to both sides, and subtract

(b^2)*c. It just seems like a good idea to get both (b^2) terms on the same side.

a*(b^2) - (b^2)*c > b - d

Now, notice that since b > d, we know that (b - d) > 0

a*(b^2) - (b^2)*c > b - d > 0

Then, notice, we can

factor out (b^2) from the far left expression:

(b^2)*(a - c) > b - d > 0

This means

(b^2)*(a - c) > 0

Now, we can divide both sides by (b^2). Ordinarily, dividing both side of an inequality by a variable is a dicey business, because in general, a variable could be positive or negative, but here, we are guaranteed that, whether b is positive or negative, (b^2) must be a positive number, and therefore we can divide by it and definitely not alter the order of the inequality.

a - c > 0

a > c

Thus, from the combined information, we were able to deduce the prompt statement. Combined, the statements are

sufficient. OA =

(C).

That is a really tricky bit of algebra this question demands, but that's what the harder problems on the GMAT could demand. Please let me know if you have any further questions.

Mike

_________________

Mike McGarry

Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)