Data Sufficiency

rahulvsd wrote:X, Y, and Z are positive integers. Is X% of Y bigger than Y% of Z?

A)Z - Y = Y - X
B)X = Z

Am I doing it right here? [/spoiler]

Prompt: X, Y, and Z are positive integers. Is X% of Y bigger than Y% of Z?

This is tricky, because the prompt question is about an inequality.

Statement #1: Z - Y = Y - X

One thing that concerns me about your approach was taking the inequality and setting both sides equal to see the consequences. It worked out well for you in this case, but in some cases, knowing what's true when LHS equals RHS doesn't necessarily tell you when LHS or RHS will be bigger.

I think it is far far clearer to see what Statement #1 implies if we just pick some numbers. Z - Y = Y - X means that X, Y, and Z are equally spaced. We could pick:

X = 50, Y = 100, Z = 150. Then

X% of Y = 50% of 100 = 50
Y% of Z = 100% of 150 = 150, which is clearly bigger.

But notice --- statement #1 only implies X & Y & Z are evenly spaced, not which way they increase or decrease. It's also totally consistent with statement #1 to pick:

X = 150, Y = 100, and Z = 50. Then

X% of Y = 150% of 100 = 150
Y% of X = 100% of 50 = 50, so now the first is bigger

We can pick different numbers which make the inequality point in different directions, so Statement #1, by itself, is insufficient.

Statement #2: X=Z

Now, we are comparing (X% of Y) and (Y% of X). Those are equal. In general, (A% of B) = (B% of A) = (A*B)/100. So, since they are equal, one is not greater than the other. We get a definitive NO answer to the prompt question, and since we get a definitive answer, it means Statement #2, by itself, is sufficient.

Answer = B

Remember: algebra is often a powerful shortcut, but it's not the clearest tool in every situation. In particular, algebraic expression in inequalities can sometime be unclear, and picking a few easy numbers brings a load of insight, as it did in Statement #1 here.

Does all this make sense?

Here's another algebraic inequality, for practice.
https://gmat.magoosh.com/questions/967
When you submit your answer, the following page will have a complete video explanation.

Let me know if you have any more questions.

Mike

aneesh.kg wrote:The question is:

Is (X/100) of Z > (Y/100) of Z ?

Dear aneesh.kg

With all due respect, I believe you misstated the question. It's

Is X% of Y bigger than Y% of Z?

not

Is X% of Z bigger than Y% of Z?

You gave a very good analysis for a question other than the one asked here. Does that make sense?

Mike

aneesh.kg wrote:Just corrected. Please read above. Thanks.

Very elegant analysis. Nice work.

Mike