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If a, b, and c are positive and a^2+c^2=202, what is the val [#permalink]
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04 Jul 2013, 17:59
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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 M0634
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Re: If a, b, and c are positive [#permalink]
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Re: If a, b, and c are positive [#permalink]
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08 Jul 2013, 02:02
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^2a^2=(ba)*(b+a)=23 b+a must be 23 and ba 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,



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Re: If a, b, and c are positive [#permalink]
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08 Jul 2013, 02:28
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^2a^2=(ba)*(b+a)=23 b+a must be 23 and ba 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, It is not mentioned that a,b and c are integer values, so we cannot say that b+a =23 and ba = 1 Regards



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Re: If a, b, and c are positive [#permalink]
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29 May 2014, 04:59
Bunuel wrote: If a, b, c and are positive and a^2+c^2=202, what is the value of bac?
(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 \(b^2+c^2=225\): \(b^2a^2=23\). 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 \(b^2a^2=23\) we get that \(a=11\) and from \(a^2+c^2=202\) we get that \(c=9\). Sufficient.
Answer: C.
M0634 Hi bunnel, Following is my logic following is my logic here in question it is given that a^2+c^2=202 1 from st1 b^2+c^2=2252 subtract 2 from 1 a^2b^2 = 23 (ab)(a+b) = 23 here we are given that a.b.c are positive so (a+b) can not be 23 or 1 as some of two positive no can not be negative ab=1 a+b=23 resolving this we get a=11, b=12 now I will put b=12 in equation so I can get value of C. b^2+c^2=225 same I can get with st2. Bunnel could you please clarify this. What is the issue with my logic as official ans. is different Thanks.



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Re: If a, b, and c are positive [#permalink]
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29 May 2014, 06:51
PathFinder007 wrote: Bunuel wrote: If a, b, c and are positive and a^2+c^2=202, what is the value of bac?
(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 \(b^2+c^2=225\): \(b^2a^2=23\). 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 \(b^2a^2=23\) we get that \(a=11\) and from \(a^2+c^2=202\) we get that \(c=9\). Sufficient.
Answer: C.
M0634 Hi bunnel, Following is my logic following is my logic here in question it is given that a^2+c^2=202 1 from st1 b^2+c^2=2252 subtract 2 from 1 a^2b^2 = 23 (ab)(a+b) = 23 here we are given that a.b.c are positive so (a+b) can not be 23 or 1 as some of two positive no can not be negative ab=1 a+b=23 resolving this we get a=11, b=12 now I will put b=12 in equation so I can get value of C. b^2+c^2=225 same I can get with st2. Bunnel could you please clarify this. What is the issue with my logic as official ans. is different Thanks. The problem with your solution is that you assume, with no ground for it, that variables represent integers only. From (b+a)(ba)=23 you cannot say that b+a=23 and ba=1, because for example b+a can be 46 and ba can be 1/2.
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Re: If a, b, and c are positive and a^2+c^2=202, what is the val [#permalink]
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29 May 2014, 08:36
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Why not D?
Using bruteforce we can deduce each variable.
Initial equation a^2+c^2=202 202 is a sum of squares, so we need to find 'em: 201 and 1  no 198 and 4  no 193 and 9  no 186 and 16  no 177 and 25  no 166 and 36  no 153 and 49  no 138 and 64  no 121 and 81  yes 102 and 100  no
So a and c could be 11 or 9
Using the same method whith both statements: (1) b^2 + c^2 = 225 The only pair is 81 and 144, so b and c could only be 9 or 12 => c=9, b=12, a=11
(2) a^2 + b^2 = 265 There are two pairs: a) 256 and 9 => a and b could be 16 or 3, but we know that "a" could only be 11 or 9, so eliminating this pair. b) 144 and 121 => a and b could be 12 or 11 => b=12, a=11 , c=9
Of course it is time consuming process and I run out of 2 minutes, but still it solvable using each statement alone. So i'm little bit confused.



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Re: If a, b, and c are positive and a^2+c^2=202, what is the val [#permalink]
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29 May 2014, 08:51
Valrus wrote: Why not D?
Using bruteforce we can deduce each variable.
Initial equation a^2+c^2=202 202 is a sum of squares, so we need to find 'em: 201 and 1  no 198 and 4  no 193 and 9  no 186 and 16  no 177 and 25  no 166 and 36  no 153 and 49  no 138 and 64  no 121 and 81  yes 102 and 100  no
So a and c could be 11 or 9
Using the same method whith both statements: (1) b^2 + c^2 = 225 The only pair is 81 and 144, so b and c could only be 9 or 12 => c=9, b=12, a=11
(2) a^2 + b^2 = 265 There are two pairs: a) 256 and 9 => a and b could be 16 or 3, but we know that "a" could only be 11 or 9, so eliminating this pair. b) 144 and 121 => a and b could be 12 or 11 => b=12, a=11 , c=9
Of course it is time consuming process and I run out of 2 minutes, but still it solvable using each statement alone. So i'm little bit confused. Please check here: ifabandcarepositiveanda2c2202whatistheval155421.html#p1369107 We are NOT told that a, b, and c are integers! So, you cannot make the chart you made.
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If a, b, and c are positive and a^2 + c^2 = 202, what is the [#permalink]
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05 Jul 2014, 01:57
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
M0634
Last edited by Bunuel on 05 Jul 2014, 05:05, edited 1 time in total.
Renamed the topic and edited the question.



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Re: If a, b, and c are positive and a^2 + c^2 = 202, what is the [#permalink]
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05 Jul 2014, 02:02
Though the OA is C, i got A as an answer. Reasoning. a^2+c^2=202 (1) b^2+c^2=225 (2) (2)(1) b^2a^2=23 (ba)(b+a)=23 Since 23 is prime , the only way we can have 23 as a product of 23 and 1. Solving , ba=1 b+a=23 we get , b=12 ,a=11 and c=9. Is there something i am missing? Thanks, Gaurav  Kudos??



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Re: If a, b, and c are positive and a^2 + c^2 = 202, what is the [#permalink]
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05 Jul 2014, 05:06
gaurav245 wrote: Though the OA is C, i got A as an answer. Reasoning. a^2+c^2=202 (1) b^2+c^2=225 (2) (2)(1) b^2a^2=23 (ba)(b+a)=23 Since 23 is prime , the only way we can have 23 as a product of 23 and 1. Solving , ba=1 b+a=23 we get , b=12 ,a=11 and c=9. Is there something i am missing? Thanks, Gaurav  Kudos?? The problem with your solution is that you assume, with no ground for it, that variables represent integers only. From (b+a)(ba)=23 you cannot say that b+a=23 and ba=1, because for example b+a can be 46 and ba can be 1/2. If a, b, c and are positive and a^2+c^2=202, what is the value of bac?(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^2a^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^2a^2=23 we get that a=11 and from a^2+c^2=202 we get that c=9. Sufficient. Answer: C. Hope it's clear.
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Re: If a, b, and c are positive and a^2 + c^2 = 202, what is the [#permalink]
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05 Jul 2014, 05:43
Thanks Bunuel... That makes sense.. I tend to make a lot of such mistakes in DS questions.. Anything that you can suggest so that these things become alot more visible?



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Re: If a, b, and c are positive and a^2+c^2=202, what is the val [#permalink]
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Re: If a, b, and c are positive and a^2+c^2=202, what is the val [#permalink]
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09 May 2017, 06:03
ichauhan.gaurav wrote: 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
M0634 question stem says: a=9, c=11 or, a=11, c=9 Statement 1: c=12, b=9 or, c=9, b=12 > not sufficient. Statement 2: a=12, b=11 or, a=11, b=12 >not sufficient Statement 1+2: a=11, b=12, c=9 Which gives a definite value of bac. So, C is ok
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Re: If a, b, and c are positive and a^2+c^2=202, what is the val [#permalink]
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11 May 2017, 07:44
ichauhan.gaurav wrote: 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
M0634 I think it's a common mistake to assume that the variables would be integers. Hence, the sum of squares have also been kept as sum of squares of two integers to entice that error.
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Re: If a, b, and c are positive and a^2+c^2=202, what is the val
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