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a^2 - b^2 = b^2 - c^2 . Is a = |b| ? 1) b = |c| 2) b = |a| * [#permalink]

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29 Aug 2008, 00:48

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

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

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient * Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient * BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient * EACH statement ALONE is sufficient * Statements (1) and (2) TOGETHER are NOT sufficient

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient * Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient * BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient * EACH statement ALONE is sufficient * Statements (1) and (2) TOGETHER are NOT sufficient

Guessing E

not sure if I interpret what the question is asking correctly.

The question is asking if a is positive.

rearrange the stem to

a^2 + c^2 = b^2 + b^2

statement 1: b^2 = c^2 leads to a^2 = b^2 a could be positive or negative insuff

statement 2: a^2 = b^2, it is the same as statement 1, so insuff

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient * Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient * BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient * EACH statement ALONE is sufficient * Statements (1) and (2) TOGETHER are NOT sufficient

1) b = |c| a^2 - b^2 =0 a=b or a=-b ( b is positive and a can be -ve or +ve) Is a = |b| ? Yes or No multiple answers not suffcieint 2) b = |a| b= a or b=-a (a is -ve and b is positive) Is a = |b| ? Yes or No insuffcient

combine. not suffcient E
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1) b = |c|, thus b is positive. Nothing about a. INSUFF. 2) b = |a|, thus b is positive. Again, nothing about a. INSUFF Clearly 1+2 taken together are also INSUFF. Anwer: E for me.

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient * Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient * BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient * EACH statement ALONE is sufficient * Statements (1) and (2) TOGETHER are NOT sufficient

Interesting problem. If I take a look at this problem more abstractly, the question is asking whether a is positive or zero.

(1) b is zero or positive. So, if you take the absolute value of b from this restriction, a will be either positive or zero. True

(2) we don't know the actual sign of a, however, because b is either positive or zero, the absolute value of that will also be positive or a zero, so suff.

Damn, I really hate these kind of problems, but I believe that it should be D?

by the way, what is the abstract meaning behind \(a^2-b^2=b^2-c^2\)? This expression must be telling us something, but I can't seem to figure out what it is. For example, if we would have the expresion \(|x+y|<|x|+|y|\), then you would know instantly that the signs for x and y are opposite from each other. So what is the expression from this problem trying to tell us without doing any math. There must be a message behind this expression.