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# If x^5-5x^3+4x is the product of consecutive positive integers

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Joined: 07 Dec 2014
Posts: 1192
If x^5-5x^3+4x is the product of consecutive positive integers  [#permalink]

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06 Jul 2017, 19:37
1
1
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(N/A)

Question Stats:

67% (00:42) correct 33% (02:33) wrong based on 6 sessions

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If x^5-5x^3+4x is the product of consecutive positive integers, what is the range of the sequence?

A. 3
B. 4
C. 5
D. 6
E. 7

source:self

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Joined: 28 Jun 2015
Posts: 290
Concentration: Finance
GPA: 3.5
Re: If x^5-5x^3+4x is the product of consecutive positive integers  [#permalink]

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06 Jul 2017, 19:47
gracie wrote:
If x^5-5x^3+4x is the product of consecutive positive integers, what is the range of the sequence?

A. 3
B. 4
C. 5
D. 6
E. 7

source:self

Let the integers be $$y-2, y-1, y, y+1, y+2$$
Range = $$y + 2 - y + 2 = 4$$. Ans - B.
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Re: If x^5-5x^3+4x is the product of consecutive positive integers  [#permalink]

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06 Jul 2017, 19:54
1
x^5 - 5x^3 + 4x can be written as:
x (x^4 - 5x^2 + 4) = (take out x common)
x (x^4 - 4x^2 - x^2 + 4) = (factorising)
x {x^2(x^2-4) - 1(x^2-4)} =
x (x^2-1) (x^2-4) =
x (x-1)(x+1)(x-2)(x+2) OR (x-2)(x-1)x(x+1)(x+2)

Thus the above algebraic expression is the product of 5 consecutive integers.. Thus range = x+2 - (x-2) = 4.

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

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Re: If x^5-5x^3+4x is the product of consecutive positive integers   [#permalink] 06 Jul 2017, 19:54
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