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What is the value of ab?

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What is the value of ab? [#permalink]

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New post 17 Aug 2014, 17:25
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What is the value of ab?

1. |a| + b = a
2. a + |b| = b
[Reveal] Spoiler: OA

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Re: What is the value of ab? [#permalink]

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New post 18 Aug 2014, 03:04
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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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Re: What is the value of ab? [#permalink]

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New post 18 Aug 2014, 03:21
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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.

Answer: C.

Hope it's clear.
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Re: What is the value of ab? [#permalink]

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New post 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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Re: What is the value of ab? [#permalink]

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

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

Thanks,
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Re: What is the value of ab? [#permalink]

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Re: What is the value of ab? [#permalink]

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New post 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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New post 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
answer is C.

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Re: What is the value of ab? [#permalink]

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New post 24 Aug 2017, 09:55
Clearly the answer is C
refer to the image attached.
Attachments

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Re: What is the value of ab?   [#permalink] 24 Aug 2017, 09:55
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