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Is a=0?

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Math Revolution GMAT Instructor
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Joined: 16 Aug 2015
Posts: 5280
GMAT 1: 800 Q59 V59
GPA: 3.82
Is a=0? [#permalink]

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New post 28 Dec 2017, 00:41
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A
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E

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[GMAT math practice question]

Is \(a=0?\)

1) \(ab=-3a\)
2) \(b>0\)
[Reveal] Spoiler: OA

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
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Math Expert
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Re: Is a=0? [#permalink]

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New post 28 Dec 2017, 06:00
MathRevolution wrote:
[GMAT math practice question]

Is \(a=0?\)

1) \(ab=-3a\)
2) \(b>0\)


1) \(ab=-3a....ab+3a=0.....a(b+3)=0\)
so either a is 0 or b=-3 or both
insuff

2) \(b>0\)
Nothing about a..
insuff

combined..
b cannot be -3, so a=0
suff
C
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Expert Post
Math Revolution GMAT Instructor
User avatar
D
Joined: 16 Aug 2015
Posts: 5280
GMAT 1: 800 Q59 V59
GPA: 3.82
Re: Is a=0? [#permalink]

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New post 01 Jan 2018, 02:10
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.

Since we have 2 variables (x and y) and 0 equations, C is most likely to be the answer. So, we should consider conditions 1) and 2) together first.

Conditions 1) and 2)
\(ab = -3a\)
\(⇔ ab + 3a = 0\)
\(⇔ a(b+3) = 0\)
⇔ \(a = 0\) since \(b > 0\) and \(b ≠ -3.\)

The answer is C.

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.

Answer: C
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Re: Is a=0?   [#permalink] 01 Jan 2018, 02:10
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