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# If a, b, and c are positive

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If a, b, and c are positive [#permalink]  04 Jul 2013, 16:59
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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

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[Reveal] Spoiler: OA

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Chauahan Gaurav
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Re: If a, b, and c are positive [#permalink]  04 Jul 2013, 21:21
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If a, b, c and 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 --> b^2=144 --> b=12 (since 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.

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Re: If a, b, and c are positive [#permalink]  08 Jul 2013, 01:02
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.

Many thanks,
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Re: If a, b, and c are positive [#permalink]  08 Jul 2013, 01:28
hfiratozturk wrote:
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.

Many thanks,

It is not mentioned that a,b and c are integer values, so we cannot say that b+a =23 and b-a = 1

Regards
Re: If a, b, and c are positive   [#permalink] 08 Jul 2013, 01:28
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