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Can we use non integer value here to get the solution

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Source: — Data Sufficiency |
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by GMATGuruNY » Fri Aug 08, 2014 3:26 am
[email protected] wrote:If ab ≠ 0, is ab > a/b ?

(1) |b| > 1

(2) ab + a/b > 0
ab > a/b?

ab - a/b > 0

ab²/b - a/b > 0

(ab² - a) / b > 0

[ (a)(b² - 1) ] / b > 0

(a/b)(b² - 1) > 0?

Question stem, rephrased: Are a/b and b² - 1 the SAME SIGN?

Statement 1: |b| > 1
Thus, b² - 1 > 0.
No information about a/b.
INSUFFICIENT.

Statement 2: ab + a/b > 0
ab²/b + a/b > 0

(ab² + a) / b > 0

[ (a)(b² + 1) ] / b > 0

(a/b)(b² + 1) > 0.

Since it is not possible for b² + 1 to be negative, the inequality above holds true only if a/b > 0.
No information about b² - 1.
INSUFFICIENT.

Statements combined:
Statement 1: b² - 1 > 0.
Statement 2: a/b > 0.
Thus, a/b and b² - 1 are the SAME SIGN.
SUFFICIENT.

The correct answer is C.
Last edited by GMATGuruNY on Fri Aug 08, 2014 6:15 am, edited 1 time in total.
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by Brent@GMATPrepNow » Fri Aug 08, 2014 4:54 am
Hi [email protected],

What do you mean when you ask, "Can we use non integer value here to get the solution?"
If you're referring to plugging in values for a and b, it's perfectly fine to plug in ANY kind of number (integer and non-integer), since there's nothing in the question that restricts what kind of numbers a and b are.
Having said that, the question does tell us that ab ≠ 0, so we can't plug in 0 for a or b.

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by [email protected] » Fri Aug 08, 2014 6:13 pm
HI shibsriz,

This question is perfect for TESTing Values (and there are some useful Number Properties that are worth noting).

We're told and A and B cannot = 0. We're asked if AB > A/B? This is a YES/NO question.

Fact 1: |B| > 1

This tells us that B can be greater than 1 OR less than -1.

B = 2
A = 0
Is 0 > 0? NO.

B = 2
A = 1
Is 2 > 1/2? YES
Fact 1 is INSUFFICIENT

Fact 2: AB + A/B > 0

Here, we know that A and B must have the SAME SIGN (either both positive OR both negative)

B = 2
A = 1
Is 2 > 1/2? YES

B = 1
A = 1
Is 1 > 1/1? NO
Fact 2 is INSUFFICIENT

Combined, we know
B is greater than 1 OR less than -1
A and B have the same sign

Here we have some interesting Number Property:
First, since A and B have the same sign, both AB and A/B will be positive.
Second, since B is either greater than 1 or less than -1, multiplying by B makes AB "bigger" and dividing by B makes A/B "smaller"

This means that in all possibilities, AB will be greater than A/B. You can plug in as many cases as you need to, but the answer will always be YES.
Combined, SUFFICIENT

Final Answer: C

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