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What is the sum a+b+c?

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Bunuel
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What is the sum a+b+c? [#permalink] New post   08 Feb 2017, 09:24
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What is the sum a + b + c?

(1) \(x^3 − x = (x + a)(x + b)(x + c)\) for all values x

(2) \(a = b + 1\) and \(c = a + 1\)
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Re: What is the sum a+b+c? [#permalink] New post   08 Feb 2017, 10:09
A
Statement 1 -> As we just have to find the sum.
(x-1)x(x+1) implies a,b,c have values -1,0,1 (not in the intended order)
But a+b+c =0
Statement 2 -> 3 unknown 2 equations => insufficient to find values of variables.
So A

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Re: What is the sum a+b+c? [#permalink] New post   08 Feb 2017, 10:17
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Bunuel wrote:
What is the sum a + b + c?

(1) x^3 − x = (x + a)(x + b)(x + c) for all values x

(2) a = b + 1 and c = a + 1


x^3 - x = x(x^2 -1) = (x-1)(x)(x+1) = (x+a)(x+b)(x+c)
By comparing we can say a b c to be 0, -1, 1 and addition = 0. But We don't know their exact values(e.g if a= 0 or -1 or 1)
Statement 1 : Sufficient.

Statement 2: a=b+1 c=a+1 means a = b+1 c = a +2, the numbers are b+1, b, b+2
From this we can only understand that a,b,c are consecutive integers on number line. We don't know their exact value.

IMO A.
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Re: What is the sum a+b+c? [#permalink] New post   08 Feb 2017, 10:36
stat 1: suff.. factorise the given equation and get the answer

stat 2 : not suff

ans A
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Re: What is the sum a+b+c? [#permalink] New post   11 Feb 2017, 20:56
What is the sum \(a+b+c\)?

(1) \(x^3−x=(x+a)(x+b)(x+c)\) for all values \(x\)
(2) \(a=b+1\) and \(c=a+1\)
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Re: What is the sum a+b+c? [#permalink] New post   11 Feb 2017, 22:20
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ziyuenlau wrote:
What is the sum \(a+b+c\)?

(1) \(x^3−x=(x+a)(x+b)(x+c)\) for all values \(x\)
(2) \(a=b+1\) and \(c=a+1\)



Let's see the statements..

(1) \(x^3−x=(x+a)(x+b)(x+c)\) for all values \(x\)
\(x^3-x=x(x^2-1)=x(x-1)(x+1)\)...
So \(x(x-1)(x+1)=(x+a)(x+b)(x+c)\)......=> a, b and c are roots of the equation and 0,1 and -1 are also roots ..
Thus a+b+c=0+1+(-1)=0
Sufficient

(2) \(a=b+1\) and \(c=a+1\)[/quote]
We will get the answer in terms of a variable..
Insufficient

A
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Re: What is the sum a+b+c? [#permalink] New post   12 Feb 2017, 01:10
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ziyuenlau wrote:
What is the sum \(a+b+c\)?

(1) \(x^3−x=(x+a)(x+b)(x+c)\) for all values \(x\)
(2) \(a=b+1\) and \(c=a+1\)


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Re: What is the sum a+b+c? [#permalink]
12 Feb 2017, 01:10
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Bunuel
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