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Question 17, page 38 in Numbers Properties Guide

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Thumbdrive
 Post subject: Question 17, page 38 in Numbers Properties Guide
 Post Posted: Sun Jan 25, 2009 6:40 pm 
So...

a,b and c are positive integers. If a<b<c and abc = 286, what is c - b?

Answer in the back says to take the prime factorization of 286 (13,11,2) and it states that 'Furthermore, a, b and c must each be larger than one'. That neatly gives you 2 as the answer (13-11) but my question is - why do a,b and c have to be larger than one? It doesn't say that in the question and you can use a=1, b=2 and c=143 to get c-b=141.

What am I missing here? Thanks in advance.

-TD
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JonathanSchneider
 Post subject: Re: Question 17, page 38 in Numbers Properties Guide
 Post Posted: Wed Feb 11, 2009 1:03 pm 
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ManhattanGMAT Staff


Posts: 480
Location: Durham, NC
Good catch, Thumbdrive! We need to update that one. You are entirely correct. The next update should replace the word "integers" with "prime numbers."
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alexambroz
 Post subject: Re: Question 17, page 38 in Numbers Properties Guide
 Post Posted: Wed Feb 11, 2009 5:52 pm 
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Course Students


Posts: 11
I'd just replace it with 'integers greater than 1' because if you say 'prime numbers' you make the method to find the answer a little easier to spot.
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esledge
 Post subject: Re: Question 17, page 38 in Numbers Properties Guide
 Post Posted: Sun Feb 22, 2009 3:46 pm 
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ManhattanGMAT Staff


Posts: 901
Location: St. Louis, MO
True :-) On the other hand, our intent is to get students to the point that they see something like "abd = 286" and automatically think "prime factorization." Maybe a little reinforcement of "prime" in practice problems is not a bad thing...

Great discussion. Keep up the good work!

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Emily Sledge
Instructor
ManhattanGMAT
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