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Data sufficiency modulus question

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by uniyal01 » Wed Jun 22, 2016 11:58 am
Data sufficiency question.

What is the value of a?

(1) |a|−|b|=0

(2) |a|+|b|=0

The answer is B (statement 2 is enough) but I can't figure out why.
TIA.
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by [email protected] » Wed Jun 22, 2016 8:31 pm
Hi uniyal01,

You can deal with this DS question conceptually or by TESTing VALUES.

We're asked for the value of A.

1) |A| - |B| = 0

IF...
A = 0, B = 0, then the answer to the question is 0.

IF...
A = 1, B = 1, then the answer to the question is 1.
Fact 1 is INSUFFICIENT.

1) |A| + |B| = 0

With this Fact, we're ADDING two absolute values and ending up with a sum of 0. Since the result of an individual absolute value is either 0 or positive, the ONLY way for the sum of two absolute values to total 0 is if BOTH A and B are 0. Thus, the answer to the question is ALWAYS 0.
Fact 2 is SUFFICIENT

Final Answer: B

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by MartyMurray » Wed Jun 22, 2016 11:49 pm
uniyal01 wrote:What is the value of a?

(1) |a|−|b|=0

(2) |a|+|b|=0
Statement 1:

a and b could be any two numbers with the same absolute value. Here are some examples.

a = 5, b = 5, |5| − |5| = 0

a = 2, b = -2, |2| − |-2| = 0

a = 0, b = 0, |0| − |0| = 0

So a could represent infinite different values.

Insufficient.

Statement 2:

Since absolute values can only be positive, the only way that the sum of two absolute values can be 0 is their both being 0.

So the value of a must be 0.

Sufficient.

The correct answer is B.
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by ceilidh.erickson » Thu Jun 23, 2016 6:53 am
Just to be a total stickler... absolute values must be either positive or zero. Zero is neither positive nor negative.

In statement 2, if the sum of two absolute values is zero, and neither can be negative, then they must both be zero.
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by Matt@VeritasPrep » Thu Jun 23, 2016 3:50 pm
S1

|a| = |b|

So we could have a = b or a = -b; NOT SUFFICIENT

S2

|a| = -|b|

The left side CAN'T be negative, and the right side CAN'T be positive - so there's only way they can be equal, if a = b = 0. (Zero strikes again!) SUFFICIENT
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