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# a^2 − b^2 = b^2 − c^2. Is a = |b|?

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Intern
Joined: 18 Jul 2012
Posts: 11
a^2 − b^2 = b^2 − c^2. Is a = |b|?  [#permalink]

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Updated on: 14 Sep 2013, 11:46
1
4
00:00

Difficulty:

85% (hard)

Question Stats:

43% (02:13) correct 57% (02:04) wrong based on 164 sessions

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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

M15-37

Originally posted by nroy347 on 14 Sep 2013, 11:24.
Last edited by Bunuel on 14 Sep 2013, 11:46, edited 2 times in total.
RENAMED THE TOPIC.
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Joined: 02 Sep 2009
Posts: 52294
Re: a^2 − b^2 = b^2 − c^2. Is a = |b|?  [#permalink]

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14 Sep 2013, 11:53
2
1
a^2 − b^2 = b^2 − c^2. Is a = |b|?

$$a^2 - b^2 = b^2 - c^2$$ --> $$a^2+c^2=2b^2$$.

(1) b = |c| --> $$b^2=c^2$$. From above: $$a^2+b^2=2b^2$$ --> $$a^2=b^2$$ --> $$|a|=|b|$$. Not sufficient.

(2) b = |a|. Not sufficient.

(1)+(2) $$b=|a|$$ and $$|a|=|b|$$. Still not sufficient. Consider $$a=b=c=1$$, for an YES answer and $$a=-1$$ and $$b=c=1$$, for a NO answer. Not sufficient.

Answer: E.

Or: notice that in the stem and both statements $$a$$ is either squared or in the modulus, so both negative and positive values of $$a$$ can satisfy each equation. Now, if $$a$$ is negative, then the answer would be NO (absolute value of b cannot equal to a negative number) but if $$a$$ is not negative, then the answer would be YES.

Hope it's clear.
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a^2 − b^2 = b^2 − c^2. Is a = |b|?  [#permalink]

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04 Feb 2015, 20:41
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

M15-37

Good 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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Re: a^2 − b^2 = b^2 − c^2. Is a = |b|?  [#permalink]

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10 Jun 2018, 00:25
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Re: a^2 − b^2 = b^2 − c^2. Is a = |b|? &nbs [#permalink] 10 Jun 2018, 00:25
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# a^2 − b^2 = b^2 − c^2. Is a = |b|?

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