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by akhilsuhag » Thu May 28, 2015 11:18 am
a^2−b^2=b^2−c^2. Is a=|b|?

(1) b=|c|
(2) b=|a|

OA [spoiler](E) although i feel (A) could be the answer[/spoiler]
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by Brent@GMATPrepNow » Thu May 28, 2015 11:31 am
akhilsuhag wrote:a² − b² = b² − c². Is a = |b|?

(1) b = |c|
(2) b = |a|
Target question: Is a = |b|

Given: a² − b² = b² − c²

Statement 1: b = |c|
If b = |c|, then we know that b² = c², which means b² − c² = 0
So, from the given information (a² − b² = b² − c²), we can conclude that a² − b² = 0
This tells us that a² = b²
Is this enough information to answer the target question?
No.
Consider these two conflicting cases, that meet the condition that a² = b²:
Case a: a = 1 and b = 1, in which case a = |b|
Case b: a = -1 and b = 1, in which case a ≠ |b|
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: b = |a|
Consider these two conflicting cases, that meet the condition that b = |a|:
Case a: a = 1, b = 1 and c = 1, in which case a = |b|
Case b: a = -1, b = 1 and c = 1, in which case a ≠ |b|
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Consider these two conflicting cases, that meet BOTH conditions:
Case a: a = 1, b = 1 and c = 1, in which case a = |b|
Case b: a = -1, b = 1 and c = 1, in which case a ≠ |b|
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

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by [email protected] » Thu May 28, 2015 11:33 am
Hi akhilsuhag,

This question can be solved by TESTing VALUES.

While it certainly looks complex, the 'key' to this question is at each variable can be positive OR negative.

We're told that A^2 - B^2 = B^2 - C^2.....

Thus, we could make all of the variables equal 1, make all equal -1 or ANY combination of 1s and -1s that we choose.

We're asked if A = |B|. This is a YES/NO question.

Fact 1: B = |C|

IF....
C = 1
B = 1
A^2 - 1 = 1 - 1 = 0
A = 1 and the answer to the question is YES
OR
A = -1 and the answer to the question is NO
Fact 1 is INSUFFICIENT

Fact 2: B = |A|

IF....
A = 1
B = 1
The answer to the question is YES

IF....
A = -1
B = 1
The answer to the question is NO
Fact 2 is INSUFFICIENT

Combined, the same TESTs fit BOTH Facts....

IF....
C = 1
B = 1
A^2 - 1 = 1 - 1 = 0
A = 1 and the answer to the question is YES
OR
A = -1 and the answer to the question is NO
Combined, INSUFFICIENT

Finan Answer: E

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by jain2016 » Sat Nov 28, 2015 10:23 pm
Hi Experts ,

Please check and correct me.

Target Question = a=|b| .... either a=b or a=-b

Given equation = a^2-b^2=b^2-c^2

Statement 1 : b=|c|

either b=c or b=-c right?

if I put b=c in given equation, then will get a^2=c^2

which mean a=c so a=b.. YES to target question


now what next please advise..

Thanks in advance.

SJ
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by DavidG@VeritasPrep » Sun Nov 29, 2015 9:28 am
then will get a^2=c^2

which mean a=c so a=b..
If a^2 = c^2, all we know is that |a| = |c|. (or |a| = |b|) Take another look at the explanations that Brent and Rich offered. Note that they test scenarios in which a = 1 and c = 1, or a = -1 and c = 1. We still don't know if 'a' is positive or negative, so we still don't know if it's equal to |b|
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by Max@Math Revolution » Thu Dec 03, 2015 7:56 am
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.

a^2-b^2=b^2-c^2. Is a=|b|?

(1) b=|c|
(2) b=|a|

There are 3 variables (a,b,c) and one equation (a^2-b^2=b^2-c^2) in the original condition, and 2 more equations are given in the conditions, so there is high chance (C) will be the answer.
Looking at the conditions together, the answer becomes 'yes' for a=c=1, b=1, but 'no' for a=c=-1, b=1. This is insufficient and the answer becomes (E).

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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