nroy347 wrote:

a^2 − b^2 = b^2 − c^2. Is a = |b|?

(1) b = |c|

(2) b = |a|

Hi Please help me in this.I think the answer should be

, however answer is

M15-37Good question! This is what came to my mind when I read it:

\(a^2 - b^2 = b^2 - c^2\)

The difference between \(a^2\) and \(b^2\) is same as difference between \(b^2\) and \(c^2\) so \(a^2, b^2\) and \(c^2\) form an Arithmetic Progression.

Question: Is a = |b|?

(1) b = |c|

This means \(b^2 = c^2\). So difference between a^2 and b^2 is also 0.

\(a^2 = b^2 = c^2\)

If a = 5 and b = 5, a = |b|

But if a = -5 while b = 5, \(a \neq |b|\)

Not sufficient

(2) b = |a|

Same analysis as above.

If a = 5 and b = 5, a = |b|

But if a = -5 while b = 5, \(a \neq |b|\)

Not sufficient

Using both statements, we see that

If a = 5 and b = 5, a = |b|

But if a = -5 while b = 5, \(a \neq |b|\)

Hence, both together are not sufficient.

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Karishma

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