ab>a/b

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ab>a/b

by j_shreyans » Wed Oct 01, 2014 2:42 am
If ab ≠ 0, is ab > a/b ?

(1) |b| > 1

(2) ab + a/b > 0

Guys ,

Our target question is ab>a/b

we can rephrase and get b^2>1

Statement 1- |b|>1

this means b>1 or b<-1 right?

so statement 1 is sufficient right?

Pls correct me and explain me really need help...

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by GMATGuruNY » Wed Oct 01, 2014 5:55 am
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.
Our target question is ab>a/b

we can rephrase and get b^2>1
When an inequality is multiplied or divided by a negative value, the direction of the inequality must FLIP.
Here, the signs of a and b are unknown.
Thus, if we multiply each side by b and divide each side by a, we cannot be certain whether the resulting inequality should be b²>1 or b²<1.
For this reason, it is safer to eschew algebra or to simplify as I did in my solution above.
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by j_shreyans » Wed Oct 01, 2014 7:23 am
Thanks Guru for your explanation it helps a lot, one more thing which i need to be cleared.

What else should be given in the question so that i can rephrase my target question from ab>a/b to b^2>1.

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by GMATGuruNY » Wed Oct 01, 2014 7:53 am
j_shreyans wrote:Thanks Guru for your explanation it helps a lot, one more thing which i need to be cleared.

What else should be given in the question so that i can rephrase my target question from ab>a/b to b^2>1.
If the question stem indicated that ab > 0, then we could rephrase ab > a/b as b² > 1.
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by [email protected] » Wed Oct 01, 2014 10:19 pm
Hi j_shreyans,

"Rewriting" a DS question can be a rather useful tactic on Test Day (in certain circumstances). You have to decide two things though before (and sometimes after) you try to rewrite the question:

1) Do you know the math rules perfectly, so that you don't make a mistake?
2) Is the "new" question easier for you to deal with than the original question?

Here, we're told that A and B CANNOT = 0. We're asked if AB > A/B? This is a YES/NO question.

*Of all the various calculations that the GMAT might ask you to perform, multiplying 2 numbers and dividing 2 numbers are relatively simple tasks, so I'm not going to try to change this question at all.*

Since there are variables, this looks like a great opportunity to TEST VALUES and use some Number Properties to your advantage.

Fact 1: |B| > 1

Here, we have some minor restrictions on the the value of B, but no restrictions on A (other than the fact that it can't be 0)

If...
A = 1
B = 2
(1)(2) > 1/2 and the answer to the question is YES

A = 1
B = -2
1(-2) is NOT > 1/-2 and the answer to the question is NO
Fact 1 is INSUFFICIENT

Fact 2: AB + A/B > 0

Here, we can use the first TEST from Fact 1....
A = 1
B = 2
The answer to the question is YES.

If...
A = 1
B = 1
The answer to the question is NO.
Fact 2 is INSUFFICIENT.

Combined, we know:
|B| > 1
AB + A/B > 0

Using Number Properties, we can deduce that....
B > 1 OR B < -1
If B is Negative, then A MUST be Negative (which would make AB + A/B > 0)
If B is Positive, then A MUST be Positive (which would make AB + A/B > 0)
So A and B MUST have the SAME SIGN.

With the restrictions on B, multiplying A by B will lead to a BIGGER VALUE; and dividing A by B lead to a SMALLER VALUE. Thus AB will ALWAYS > A/B. The answer to the question is ALWAYS YES.
Combined, SUFFICIENT

Final Answer: C

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