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If b≠0, and |ab|=ab, is b>0?

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Math Revolution GMAT Instructor
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Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42
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If b≠0, and |ab|=ab, is b>0?  [#permalink]

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New post 21 Mar 2018, 23:52
00:00
A
B
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E

Difficulty:

  35% (medium)

Question Stats:

66% (01:22) correct 34% (01:26) wrong based on 90 sessions

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[GMAT math practice question]

If \(b≠0\), and \(|ab|=ab,\) is \(b>0\)?

\(1) a<0\)
\(2) \frac{a}{b}>0\)

_________________

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Re: If b≠0, and |ab|=ab, is b>0?  [#permalink]

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New post 22 Mar 2018, 00:46
MathRevolution wrote:
[GMAT math practice question]

If \(b≠0\), and \(|ab|=ab,\) is \(b>0\)?

\(1) a<0\)
\(2) \frac{a}{b}>0\)



mod ab always has a positive value

hence ab = positive

a and b can both be negative
or a and b can both be positive

1) a is negative

sufficient to answer


2) a/b > 0 here again both a and b can positive/negative - insufficient

a clear A
Math Revolution GMAT Instructor
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Joined: 16 Aug 2015
Posts: 6827
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: If b≠0, and |ab|=ab, is b>0?  [#permalink]

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New post 25 Mar 2018, 17:18
=>
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

\(|ab| = ab\)
\(=> ab ≥ 0\)

Condition 1)
Since \(a < 0, b≠0\) and \(ab ≥ 0\), we have \(b < 0\).
Thus, the answer is ‘no’.
Since ‘no’ is also a unique answer by CMT (Common Mistake Type) 1, condition 1) is sufficient.

Condition 2)
If \(a = 1\) and \(b = 1\), the answer is ‘yes’.
If \(a = -1\) and \(b = -1\), the answer is ‘no’.
Since we don’t have a unique solution, condition 2) is not sufficient.

Therefore, A is the answer.

Answer: A
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Re: If b≠0, and |ab|=ab, is b>0? &nbs [#permalink] 25 Mar 2018, 17:18
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