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If a,b and c are consecutive positive integers and a>b>c. What can be

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If a,b and c are consecutive positive integers and a>b>c. What can be [#permalink]

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If a,b and c are consecutive positive integers and a>b>c. What can be the value of (a^2-b^2)(b^2-c^2)?

A. 21
B. 79
C. 143
D. 231
E. 450
[Reveal] Spoiler: OA

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Re: If a,b and c are consecutive positive integers and a>b>c. What can be [#permalink]

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New post 12 Sep 2016, 02:26
C. 143. From the condition that a,b, c are consecutive,it's clear that (a^2-b^2)(b^2-c^2) = (a+b)*(b+c)
Therefore, the product should have factors with a difference of 2. 143 = 11*13 hence this is the option

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Re: If a,b and c are consecutive positive integers and a>b>c. What can be [#permalink]

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As a,b and c are consecutive, cleary a-b = b-c = 1

hence (a^2-b^2)(b^2-c^2) = (a+b)*(a-b)*(b+c)*(b-c) = (a+b)*(b+c)
as a,b,c are consecutive
either a ans c will be odd or they will be even.
Now (a+b) and (b+c) both will be odd with a difference of 2.
only option that satisfies this is C.
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Re: If a,b and c are consecutive positive integers and a>b>c. What can be [#permalink]

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Since a,b and c are consecutive positive integers and a>b>c, we can write them as (x + 1), x and (x - 1) respectively
(a^2-b^2)(b^2-c^2) can be simplified into (2x + 1)(2x - 1) = 4x^2 - 1

using the options to find the product,
only C. 143 satisfactorily gives us x as an integer
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Re: If a,b and c are consecutive positive integers and a>b>c. What can be [#permalink]

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Re: If a,b and c are consecutive positive integers and a>b>c. What can be   [#permalink] 28 Dec 2017, 12:05
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