Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL.

Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

Re: If a, b, and c are constants, a > b > c, and x^3 - x = (x - a)(x - b)
[#permalink]

Show Tags

02 Mar 2015, 18:18

8

1

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....

Re: If a, b, and c are constants, a > b > c, and x^3 - x = (x - a)(x - b)
[#permalink]

Show Tags

07 Feb 2016, 18:31

There is some bit of knowledge I'm missing. How are we supposed to innately know that (x-a)(x-b)(x-c)=(x+1)(x-0)(x-1)?

I'm even more confused after reading through these approaches. When I attempted to 'pull' x out of x^3-x I got x^2(x−1) which is different that the approach I'm seeing here.

Re: If a, b, and c are constants, a > b > c, and x^3 - x = (x - a)(x - b)
[#permalink]

Show Tags

07 Feb 2016, 18:39

1

Anonamy wrote:

There is some bit of knowledge I'm missing. How are we supposed to innately know that (x-a)(x-b)(x-c)=(x+1)(x-0)(x-1)?

I'm even more confused after reading through these approaches. When I attempted to 'pull' x out of x^3-x I got x^2(x−1) which is different that the approach I'm seeing here.

Thanks in advance

You need to practice algebra a bit more.

\(x^3-x = x*x*x-x=x(x^2-1) = x*(x+1)(x-1)\) as \((a^2-b^2)=(a+b)(a-b)\)

So once you are able to get to \(x^3-x = x*(x+1)(x-1)\), you are now set to compare it with \((x-a)(x-b)(x-c)\)

Thus, you get \(x*(x+1)(x-1) = (x-a)(x-b)(x-c)\) ---> \((x-0)(x+1)(x-1) = (x-a)(x-b)(x-c)\) ---> \((x-0)(x- (-1))(x-1) = (x-a)(x-b)(x-c)\), giving you 3 values of -1,0,1 .

Re: If a, b, and c are constants, a > b > c, and x^3 - x = (x - a)(x - b)
[#permalink]

Show Tags

21 Jul 2016, 16:53

EMPOWERgmatRichC wrote:

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....

What I found confusing about this problem is that we are not told that the left side of the equation is equal to 0 (x^3-x=0), so how do we know to begin factoring x^3-x here into x(x-1)(x=1)? Am I missing something really basic here?

Re: If a, b, and c are constants, a > b > c, and x^3 - x = (x - a)(x - b)
[#permalink]

Show Tags

24 Dec 2016, 09:16

Hi Schnauss,

The 'act' of factoring does not require an equation - it's just a way of re-writing information that you've been given.

For example, if you're told that you have 'two boxes that each contain the same number of widgets', then you can write that as (2)(W)... even though you don't have an actual equation yet. If I wanted to, I could rewrite 2W as (W + W). Certain GMAT questions just come down to organizing information in a way that makes it easy to answer the given question, so you should think about how you choose to take notes and 'translate' sentences ('your way' might not be the only way, and there might be additional 'steps' that you can take to simplify what you have written).

Re: If a, b, and c are constants, a > b > c, and x^3 - x = (x - a)(x - b)
[#permalink]

Show Tags

26 Jan 2017, 06:51

If you dont know the algebra for this most probably you cannot solve this question.

x^3 - x = x(x^2 - 1) . GMAT algebra fundamentals require you to know/memorise that x^2 - 1 = (x-1) * (x+1)

So long story short: x^3 - x = x * (x-1) * (x+1) = (x - a)(x - b)(x - c)

x * (x-1) * (x+1) = (x - a)(x - b)(x - c)

We know that a > b > c

Hence (x-c) > (x-b) > (x-a) . This is because in this question x is a constant rather than a variable. So the maximum value of any of the three operation, (x-c), (x-b) or (x-a) is the one that uses the SMALLEST value (i.e. c):

Then you just do the mapping

out of x, (x-1) and (x+1) the (x+1) has the GREATEST value. Hence (x+1) = (x - c) => x+1 = x -c which gives c = -1 out of x, (x-1) and (x+1) the (x-1) has the SMALLEST value . Hence (x-1) = (x - a) which gives a = 1

therefore the only case that left is the x = (x-b) which gives b = 0

Re: If a, b, and c are constants, a > b > c, and x^3 - x = (x - a)(x - b)
[#permalink]

Show Tags

16 Jul 2017, 14:33

metallicafan wrote:

ezhilkumarank wrote:

Quote:

However, why could we assume that (x-0)=(x-b), (x+1)=(x-c) and (x-1)=(x-a)? Probably, x(x-1)(x+1) are different factors which produce the same result as (x-a)(x-b)(x-c) do. For example, 6*2=3*4, but we cannot say that 6 = 3. Am I missing something?

We are not assuming anything. We are just equating the left hand side to the right hand side of the equation.

Any other thoughts?????

Yes, as I said, for example, 6*2=3*4, but we cannot say that 6 = 3. Based on this, we cannot say that (x-0)=(x-b) Well, I am studying too much, probably I am seeing things that probably don't really matter LOL.

Hi in your example --- 6 * 2 * 1 = 3 *4 * 1 will not fit in the equation (x-0) (x+1) (x-1) = (x +a) (x+b) (x+C) with a>b>c ... put in values and see if it works ...here are some of my attempts ..

hence not an applicable test

trying random values, assuming X = 5 and a = 3 b = 2 c = 1

that is 5 (x-0) * 6 (x+1) * 4 (x-1) = 8 (x+a) * 7 (x+b) * 6 (x+c)

not working

trying random values, assuming X = 5 and a = -1 b = -2 c = -3

that is 5 (x-0) * 6 (x+1) * 4 (x-1) = 4 (x+a) * 3 (x+b) * 2 (x+c)

not feasible ...

only way this is possible is the following

assuming X = 5 and a = 1 b = 0 c = -1

that is 5 (x-0) * 6 (x+1) * 4 (x-1) = 6 (x+a) * 5 (x+b) *4 (x+c)....working

Whatever the value of x but with a = 1 | b = 0 | c = -1 ...below equation will hold ..

Re: If a, b, and c are constants, a > b > c, and x^3 - x = (x - a)(x - b)
[#permalink]

Show Tags

20 Jul 2017, 15:36

2

jpr200012 wrote:

If a, b, and c are constants, a > b > c, and x^3-x=(x-a)(x-b)(x-c) for all numbers x, what is the value of b?

A. -3 B. -1 C. 0 D. 1 E. 3

Let’s simplify the given equation:

x^3 - x = (x-a)(x-b)(x-c)

x(x^2 - 1) = (x-a)(x-b)(x-c)

x(x - 1)(x + 1) = (x-a)(x-b)(x-c)

(x - 1)x(x + 1) = (x-a)(x-b)(x-c)

Since a > b > c:

(x - b) = x

b = 0

Alternate Solution:

If we let x = a in the equation, we get a^3 - a = 0; i.e., a^3 = a. Similarly, letting x = b and x = c, we get b^3 = b and c^3 = c. We know that the only three numbers whose cube is equal to the number itself are 1, 0, and -1. We have a > b > c; therefore, we must have a = 1, b = 0, and c = -1.

Answer: C
_________________

Jeffery Miller Head of GMAT Instruction

GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

If a, b, and c are constants, a > b > c, and x^3 - x = (x - a)(x - b)
[#permalink]

Show Tags

19 Oct 2017, 11:00

JeffTargetTestPrep wrote:

jpr200012 wrote:

If a, b, and c are constants, a > b > c, and x^3-x=(x-a)(x-b)(x-c) for all numbers x, what is the value of b?

A. -3 B. -1 C. 0 D. 1 E. 3

Let’s simplify the given equation:

x^3 - x = (x-a)(x-b)(x-c)

x(x^2 - 1) = (x-a)(x-b)(x-c)

x(x - 1)(x + 1) = (x-a)(x-b)(x-c)

(x - 1)x(x + 1) = (x-a)(x-b)(x-c)

Since a > b > c:

(x - b) = x

b = 0

Alternate Solution:

If we let x = a in the equation, we get a^3 - a = 0; i.e., a^3 = a. Similarly, letting x = b and x = c, we get b^3 = b and c^3 = c. We know that the only three numbers whose cube is equal to the number itself are 1, 0, and -1. We have a > b > c; therefore, we must have a = 1, b = 0, and c = -1.

Answer: C

Silly question, but how do we get algebraically get to the 0? Is it because we are subtracting x from both sides? Why is it not replaced with 1? & what about the negative?

If a, b, and c are constants, a > b > c, and x^3 - x = (x - a)(x - b)
[#permalink]

Show Tags

31 Mar 2018, 07:08

EMPOWERgmatRichC wrote:

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....