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Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.
We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.
As x^3-x=(x-a)(x-b)(x-c) is true for ALL x-es than it must be true for x=0, x=1 and x=-1 too. Substituting these values you get the values of a, b, and c. _________________
Re: If a, b, and c are constants, a > b > c, and x^3 - x = (x - [#permalink]
02 Mar 2015, 12:11
Bunuel wrote:
bankerboy30 wrote:
How do we know so is equal the numbers are -1,0,1. I know there consecutive but why not 2,3,4?
As x^3-x=(x-a)(x-b)(x-c) is true for ALL x-es than it must be true for x=0, x=1 and x=-1 too. Substituting these values you get the values of a, b, and c.
I still dont understand this logic. Are we simply looking for any value of X that makes the entire equation 0? What do you specifically mean by "as x^3.... is true for all x-es" - I really dont understand this.
Re: If a, b, and c are constants, a > b > c, and x^3 - x = (x - [#permalink]
02 Mar 2015, 18:18
4
This post received KUDOS
Expert's post
Hi erikvm,
This is a "layered" concept and it's easy to get "lost" in this prompt because you're used to solving for the final values in most Quant questions.
Here, the 3 "final" numbers are (X - A), (X - B) and (X - C), but the question is NOT asking for any of the 3 final numbers...it's asking for a "piece" of one of them....the value of B.
To answer it, you have to ignore the A, B and C for a moment and go back to the prior "term"
X^3 - X
This can be factored down into 3 pieces. Here's how...
X^3 - X
First, factor out an X...
(X)(X^2 - 1)
Next, reverse-FOIL the other term.... (X)(X+1)(X-1)
Since we're multiplying 3 terms, it doesn't matter what the order is. I'm going to put them in order from least to greatest...
(X-1)(X)(X+1)
Now, looking at THIS, you can figure out what A, B and C are. Since A>B>C, then....
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