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04 Jul 2013, 17:59
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C
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Difficulty:
55%
(hard)
Question Stats:
62% (02:03) correct
38%
(02:34)
wrong
based on 317
sessions
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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
M06-34
(1) b^2 + c^2 = 225
(2) a^2 + b^2 =265
M06-34
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04 Jul 2013, 22:21
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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) \(b^2+c^2=225\). 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
M06-34
(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
M06-34
General Discussion
08 Jul 2013, 02:02
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I think the answer should be A since statement1 is enough by itself.
Lets consider statement 1
a^2+c^2=202 given in the question
b^2+c^2=225 given in the statement1
(b^2+c^2)-(a^2+c^2)=23
b^2-a^2=(b-a)*(b+a)=23 b+a must be 23 and b-a must be 1 since a,b,c given positive and 23 is prime number. b=12 and a=11
if we know a and b then we could calculate c by using a^2+c^2=202.
Could you please elaborate?
Many thanks,
Lets consider statement 1
a^2+c^2=202 given in the question
b^2+c^2=225 given in the statement1
(b^2+c^2)-(a^2+c^2)=23
b^2-a^2=(b-a)*(b+a)=23 b+a must be 23 and b-a must be 1 since a,b,c given positive and 23 is prime number. b=12 and a=11
if we know a and b then we could calculate c by using a^2+c^2=202.
Could you please elaborate?
Many thanks,
