Data Sufficiency

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]

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

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|

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.