jenl2881 wrote:

Is 0 < a/b < 1?

(1) ab> 1

(2) a - b < 1

Kaplan gives the answer but I am still unsure of how they got their answers. They used a = 3, b=2 and a=-3, b=-2 to test. I could use some explanation on this one. Maybe I am just over thinking it?

Dear

jenl2881I'm happy to help. This is a good question, and it is designed to punish folks who think of numbers only in terms of what they can count on their fingers. It's always good to have your antennae up for the whole family of numbers --- positives, negatives, zero, fractions, decimals.

Here, we have a straightforward prompt question.

Statement #1:

ab> 1Clearly, we could have a = 3 and b = 2, or a = 2 and b = 3. The first choice would produce a "no" answer to the prompt, the second a "yes" answer to the prompt. Two different answers are possible, so this statement does not lead to a definitive answer. This statement, alone and by itself, is

insufficient.

I'll just mention, in passing, if ab > 1, that could meant that both numbers are positive, but it could also mean that both numbers are negatives. We didn't need that here, but we will come back to that.

Statement #2:

a - b < 1a = 2, b = 7, a - b < 1, and 0 < a/b < 1 --- an answer of "yes" to the prompt

a = 5, b = 5, a - b < 1, and a/b = 1, so it is not between 0 and 1 --- an answer of "no" to the prompt

Two different answers are possible, so this statement does not lead to a definitive answer. This statement, alone and by itself, is

insufficient.

Combined:

(1) ab> 1

(2) a - b < 1This is very tricky.

The choice a = 3 and b = 5 satisfies both statements, and a/b = 3/5 is between 0 and 1, so this produces a "yes" answer.

The choice a = 8 and b = 8 also satisfies both statements, and a/b = 8/8 = 1 is not between 0 and 1, so this produces a "no" answer.

BTW, the choice a = -7 and b = -4 would also produce a "no" answer.

Two different answers are possible, so the combined statements do not lead to a definitive answer. Everything is

insufficient.

Answer =

(E)Here's a blog about inequalities:

http://magoosh.com/gmat/2013/gmat-quant ... qualities/Here's a blog about DS tips:

http://magoosh.com/gmat/2013/gmat-data- ... ency-tips/Does all this make sense?

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)