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For integers b and c, what is the sum of all unique solutions to the

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New post 08 Jul 2017, 05:19
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Question Stats:

55% (01:15) correct 45% (01:19) wrong based on 78 sessions

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Re: For integers b and c, what is the sum of all unique solutions to the  [#permalink]

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New post 08 Jul 2017, 05:42
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Bunuel wrote:
For integers b and c, what is the sum of all unique solutions to the equation \(x^2−bx+c=10\)?

(1) c = 59
(2) b = 14


In an equation ax^2 +bx +c

sum of roots is -b/a
multiplication of roots is c/a

in our question a=1, b=b, c= c-10

Hence B is sufficient
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New post 08 Jul 2017, 05:57
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mynamegoeson wrote:
Bunuel wrote:
For integers b and c, what is the sum of all unique solutions to the equation \(x^2−bx+c=10\)?

(1) c = 59
(2) b = 14


sum of roots is -b/a
in our question a=1, b=b, c= c-10
Hence B is sufficient


Hi..

Superb Q Bunuel
You are absolutely correct in your approach.
But have missed out on a word UNIQUE

If you do not know c, it any be that the equation is perfect square..

SUm of roots is -b/a where a is 1 in the equation
Let's see the statements..
1) C=49
Insuff as we don't know b.

2) b=14..
Very tempting
Ans 14/1=14... But ONLY if the roots are NOT UNIQUE.
What if equation is \(x^2-14x+49=0\)
Here roots are 7 and 7, but only one unique solution.
Here and will be 7
So we require to know c
Insuff

Combined..
The equation is \(x^2-14x+59=10....x^2-14x+49=0.....(x-7)^2=0\)
So solution is 7
Sufficient

May be if b were some odd number, B would be sufficient..
Say 7, then C wouldn't be an integer in any case for the equation to have unique solution

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For integers b and c, what is the sum of all unique solutions to the   [#permalink] 08 Jul 2017, 05:57
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