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E
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Difficulty:
85%
(hard)
Question Stats:
45% (02:19) correct
55%
(01:58)
wrong
based on 260
sessions
History
Date
Time
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Not Attempted Yet
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
(1) b = |c|
(2) b = |a|
Hi Please help me in this.I think the answer should be , however answer is
M15-37
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Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
Sat Sep 14, 2013 11:53 am
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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.
\(a^2 - b^2 = b^2 - c^2\) --> \(a^2+c^2=2b^2\).
(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.
Wed Feb 04, 2015 8:41 pm
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Bookmarks
nroy347
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.
