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# If a, b, and c are positive integers, with a < b < c,

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Senior Manager
Joined: 16 Jul 2009
Posts: 253
If a, b, and c are positive integers, with a < b < c, [#permalink]

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23 Oct 2009, 09:24
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If a, b, and c are positive integers, with a < b < c, are a, b, and c consecutive integers?

(1) 1/a – 1/b = 1/c

(2) a + c = b2 – 1
Intern
Joined: 26 Sep 2009
Posts: 43
Location: Los Angeles

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26 Oct 2009, 11:56

This was my approach:

This is a yes/no question

statement 1:
Since the question is asking if a, b, and c are consecutive integers and we know that a<b<c... test the equation using:

a=a
b=a+1
c=a+2

1/a = 1/(a+1)+ 1/(a+2)
Without even solving, you can see pretty quickly that this is going to be a cubed polynomial and it won't yield an integer solution. Since it's given that a, b, and c have to be positive integers...then it follows that for this statement to be true, a, b and c cannot be consecutive integers. sufficient.

statement 2:
plug in the same variables from statement 1.

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

again, consecutive integers will not yield a positive integer for a, b, or c. Variables a, b, and c cannot be consecutive integers, so sufficient.

Since statement 1 and 2 are sufficient, ans should be D
_________________

Paul

Focused GMAT Prep
http://www.thegmatbootcamp.com

Re: Number Properties   [#permalink] 26 Oct 2009, 11:56
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