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M06-34

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M06-34  [#permalink]

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New post 16 Sep 2014, 00:33
1
5
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

54% (02:09) correct 46% (02:20) wrong based on 117 sessions

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Re M06-34  [#permalink]

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New post 16 Sep 2014, 00:33
1
2
Official Solution:


(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
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Re: M06-34  [#permalink]

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New post 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?
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Re: M06-34  [#permalink]

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New post 23 Sep 2014, 02:07
madhavmarda wrote:
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?


The problem with your solution is that you assume, with no ground for it, that variables represent integers only. From b^2 - a^2 = 23 you cannot say that b = 12 and a = 11. For example b could be \(\sqrt{24}\) and a could be 1.
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New post 29 Nov 2014, 22:25
Tricky question but a good one. -- I also had assumed that B = 12 , A = 11 C = 9.
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Re: M06-34  [#permalink]

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New post 11 Apr 2015, 09:10
good question..I also did the same mistake of assuming the numbers as integers.
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Re: M06-34  [#permalink]

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New post 27 Nov 2015, 16:17
To solve 3 different variables, you need 3 different equations. hence it was simple to identify 'C' as the option. Is the approach correct
? I did this question in less than 30 seconds
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New post 18 Apr 2017, 22:24
HK17 wrote:
To solve 3 different variables, you need 3 different equations. hence it was simple to identify 'C' as the option. Is the approach correct
? I did this question in less than 30 seconds


I did it the same way without calculating the individual values. Is there a possiblity that this assumption will not hold?
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Re M06-34  [#permalink]

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New post 03 Aug 2017, 23:08
I think this is a high-quality question and I agree with explanation.
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Re: M06-34  [#permalink]

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New post 21 Oct 2017, 19:54
In my onion A is the answer

1) a^2 + c^2 = 202 ( given )
2) b^2 + c^2 = 225 ( statement 1 )

subtracting 1 from 2, we get b^2 - a^2 = 23 ( prime number )

its given that a,b and c are positive. therefore the only solution is b+c = 23 and b-c = 1 -> b= 12, c = 11

we can substitute the value of b in equation 2 -> 12^2 + c^2 = 225 -> c = 9 ( since -9 can be negated since c has to be +ve )

also similarly for statement 2, b^2 - c^2 = 63; but 63 is not prime -> therefore we cant get a solution ( it can be 21 * 3 or 9*7 )

I think the answer is A. High quality question -> but wrong answer marked.

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New post 21 Oct 2017, 22:57
TheGMATcracker wrote:
In my onion A is the answer

1) a^2 + c^2 = 202 ( given )
2) b^2 + c^2 = 225 ( statement 1 )

subtracting 1 from 2, we get b^2 - a^2 = 23 ( prime number )

its given that a,b and c are positive. therefore the only solution is b+c = 23 and b-c = 1 -> b= 12, c = 11

we can substitute the value of b in equation 2 -> 12^2 + c^2 = 225 -> c = 9 ( since -9 can be negated since c has to be +ve )

also similarly for statement 2, b^2 - c^2 = 63; but 63 is not prime -> therefore we cant get a solution ( it can be 21 * 3 or 9*7 )

I think the answer is A. High quality question -> but wrong answer marked.

Ashwin


The problem with your solution is that you assume that the variables are integers. We are not given that. b^2 - a^2 = 23 has infinitely many solutions for b ans a.
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Re: M06-34  [#permalink]

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New post 22 Oct 2017, 09:56
Bunuel wrote:
Official Solution:


(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 it would've been given that a,b,c are integers then can we mark D?

Explanation:
if a,b,c are integers-

a^2+C^2=202 => a=9/11, C=11/9

or
Solving with b^2+C^2=225 => b^2-a^2=23 => (b-a)(b+a)=23, 23 is prime number so b and a must be consecutive numbers.=> b=12,a=11 for c=9(integer value)

Similarly, we can do for a^2+b^2=265
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New post 14 Jun 2018, 22:11
For this question no need of solving. AS we are given that positive values only, we know that only c will work. no need what the solution is as long as we can confirm that a solution does exist. saves time.
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New post 08 Jan 2019, 12:44
Hi Bunuel,

I don't agree with the solution to this question. In the question stem, a^2+c^2 = 202 can have only two sets of values

a= 11
c= 9

OR
a= 9
c= 11

Each of the statements would then be sufficient to solve the question by giving separate values for a, b and c.

Please let me know if there is something incorrect with this approach.

Thanks :D
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New post 08 Jan 2019, 21:23
samsam00 wrote:
Hi Bunuel,

I don't agree with the solution to this question. In the question stem, a^2+c^2 = 202 can have only two sets of values

a= 11
c= 9

OR
a= 9
c= 11

Each of the statements would then be sufficient to solve the question by giving separate values for a, b and c.

Please let me know if there is something incorrect with this approach.

Thanks :D


Please read the thread before posting. Your doubt is addressed here: https://gmatclub.com/forum/m06-183731.html#p1419052
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Re M06-34  [#permalink]

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New post 25 Feb 2019, 13:30
I think this is a high-quality question and I agree with explanation.
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New post 02 Jul 2019, 01:40
Fairly meaty question. The amount of quadratics present can be overwhelming. I got this one incorrect.

Once you get one value of any variable you can find the rest. That saves a bit of time!
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Re: M06-34   [#permalink] 02 Jul 2019, 01:40
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