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# What is the value of ab?

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Manager
Joined: 26 May 2013
Posts: 61
What is the value of ab? [#permalink]

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17 Aug 2014, 17:25
2
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Difficulty:

55% (hard)

Question Stats:

60% (01:17) correct 40% (01:24) wrong based on 317 sessions

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What is the value of ab?

1. |a| + b = a
2. a + |b| = b
Director
Status: Tutor - BrushMyQuant
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Location: India
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Re: What is the value of ab? [#permalink]

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18 Aug 2014, 03:04
1
1
Q What is the value of ab?

1. |a| + b = a
2. a + |b| = b

STAT1
Take two cases
Case 1: a is >=0
|a| = a
=> b = 0
so, ab=0

Case 2: a< 0
=> |a| = -a
-a + b = a
=> b = 2a

ab = 2a^2

Both are different so not sufficient

STAT2
Take two cases
Case 1: b>= 0
|b| = b
so, a+ b = b
=> a = 0
=> ab = 0

Case 2: b<0
=> |b| = -b
=> a - b = b
=> a = 2b
=> ab = 2b^2

Both are different so NoT sufficient

Takeing STAT1 and STAT2 together there will be 4 cases
adding both the equations we get
|a| + |b| +a +b = a+ b
=> |a| +|b| = 0
Only possible when both a=b=0
=> ab=0

So, asnwer will be C

Hope it helps!
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Math Expert
Joined: 02 Sep 2009
Posts: 46264
Re: What is the value of ab? [#permalink]

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18 Aug 2014, 03:21
2
What is the value of ab?

(1) |a| + b = a --> a - |a| = b --> if a = 1 and b = 0, then ab = 0 but if a = -1 and b = -2, then ab = 2. Not sufficient.

(2) a + |b| = b --> b - |b| = a --> if b = 1 and a = 0, then ab = 0 but if b = -1 and a = -2, then ab = 2. Not sufficient.

(1)+(2) Sum (1) and (2): |a| + b + a + |b| = a + b --> |a| + |b| = 0. The sum of two nonnegative values can be 0, if and only both of them are 0 --> |a| = |b| = 0 --> ab = 0. Sufficient.

Hope it's clear.
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Joined: 26 May 2013
Posts: 61
Re: What is the value of ab? [#permalink]

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18 Aug 2014, 05:18
nktdotgupta wrote:
Q What is the value of ab?

1. |a| + b = a
2. a + |b| = b

STAT1
Take two cases
Case 1: a is >=0
|a| = a
=> b = 0
so, ab=0

Case 2: a< 0
=> |a| = -a
-a + b = a
=> b = 2a

ab = 2a^2

Both are different so not sufficient

STAT2
Take two cases
Case 1: b>= 0
|b| = b
so, a+ b = b
=> a = 0
=> ab = 0

Case 2: b<0
=> |b| = -b
=> a - b = b
=> a = 2b
=> ab = 2b^2

Both are different so NoT sufficient

Takeing STAT1 and STAT2 together there will be 4 cases
adding both the equations we get
|a| + |b| +a +b = a+ b
=> |a| +|b| = 0
Only possible when both a=b=0
=> ab=0

So, asnwer will be C

Hope it helps!

Thanks. I guess in case-2 of Stat1 & Stat2, b = -2a and a = -2b respectively.
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Re: What is the value of ab? [#permalink]

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29 Nov 2015, 11:15
1
Hi Bunuel, Engr2012 et al.

Could one of the Moderators move this question to the DS Forum?

Thanks,
Rich
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Math Expert
Joined: 02 Sep 2009
Posts: 46264
Re: What is the value of ab? [#permalink]

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29 Nov 2015, 11:20
EMPOWERgmatRichC wrote:
Hi Bunuel, Engr2012 et al.

Could one of the Moderators move this question to the DS Forum?

Thanks,
Rich

Done. Thank you for noticing.
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Re: What is the value of ab? [#permalink]

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30 Nov 2015, 10:45
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

What is the value of ab?

1. |a| + b = a
2. a + |b| = b

There are 2 variables (a,b) and 2 equations are given by the 2 conditions, so there is high chance (C) will be the answer.
Looking at the conditions together,
a=b=0 --> ab=0. This is unique and sufficient, the answer becomes (C).

For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
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Re: What is the value of ab? [#permalink]

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11 Oct 2016, 07:32
Amit0507 wrote:
What is the value of ab?

1. |a| + b = a
2. a + |b| = b

1. 2 options:
a+b=a -> b=0, and ab=0
b-a=a -> b=2a - not sufficient.

2. 2 options:
a+b=b -> a=0, and ab=0
a-b=b -> a=2b - not sufficient

1+2
a=0, b=0, b=2a - true, a=2b - true
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Joined: 29 Jun 2017
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Re: What is the value of ab? [#permalink]

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24 Aug 2017, 09:55
refer to the image attached.
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Re: What is the value of ab?   [#permalink] 24 Aug 2017, 09:55
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