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16 Sep 2014, 00:33
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If \(a\), \(b\), and \(c\) are positive and \(a^2 + c^2 = 202\), what is the value of \(b - a - c\)?
(1) \(b^2 + c^2 = 225\)
(2) \(a^2 + b^2 = 265\)
(1) \(b^2 + c^2 = 225\)
(2) \(a^2 + b^2 = 265\)
16 Sep 2014, 00:33
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Official Solution:
If \(a\), \(b\), and \(c\) are positive and \(a^2 + c^2 = 202\), what is the value of \(b - a - c\)?
(1) \(b^2+c^2=225\). Not sufficient on its own.
(2) \(a^2+b^2=265\). Not sufficient on its own.
(1)+(2) Subtract \(a^2+c^2=202\) from \(b^2+c^2=225\):
\(b^2-a^2=23\).
Now, sum this with \(a^2+b^2=265\):
\(2b^2=288\).
So, \(b^2=144\), giving \(b=12\) (since it is given that \(b\) is a positive number). Since \(b=12\), then from \(b^2-a^2=23\) we get that \(a=11\) and from \(a^2+c^2=202\) we get that \(c=9\). Sufficient.
Answer: C
If \(a\), \(b\), and \(c\) are positive and \(a^2 + c^2 = 202\), what is the value of \(b - a - c\)?
(1) \(b^2+c^2=225\). Not sufficient on its own.
(2) \(a^2+b^2=265\). Not sufficient on its own.
(1)+(2) Subtract \(a^2+c^2=202\) from \(b^2+c^2=225\):
\(b^2-a^2=23\).
Now, sum this with \(a^2+b^2=265\):
\(2b^2=288\).
So, \(b^2=144\), giving \(b=12\) (since it is given that \(b\) is a positive number). Since \(b=12\), then from \(b^2-a^2=23\) we get that \(a=11\) and from \(a^2+c^2=202\) we get that \(c=9\). Sufficient.
Answer: C
General Discussion
madhavmarda
Joined: 06 Aug 2014
Last visit: 06 Jun 2015
Posts: 12
Given Kudos: 44
Concentration: Entrepreneurship, Marketing
Schools: ISB '17 (A)
GMAT 1: 720 Q50 V37
GPA: 3.3
23 Sep 2014, 02:01
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Hi Bunuel,
In this question, if I take only the first statement and subtract the two equations given we get:-
b^2-a^2=23.
Thus possible values positive values will be- b=12, a=11.
Upon substitution in any of the two equations we get c=9.
Thus can we not answer the question using only statement 1.
Please kindly point out the flaw in this reasoning. Is it because the question does not give us that only integer values are possible?
In this question, if I take only the first statement and subtract the two equations given we get:-
b^2-a^2=23.
Thus possible values positive values will be- b=12, a=11.
Upon substitution in any of the two equations we get c=9.
Thus can we not answer the question using only statement 1.
Please kindly point out the flaw in this reasoning. Is it because the question does not give us that only integer values are possible?
