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What are the greatest and smallest positive differences

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GMAT Club Legend
GMAT Club Legend
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Joined: 07 Jun 2014
Posts: 4710
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 91

Kudos [?]: 1612 [0], given: 375

CAT Tests
What are the greatest and smallest positive differences [#permalink] New post 01 Nov 2016, 17:18
Expert's post
00:00

Question Stats:

75% (01:01) correct 25% (00:00) wrong based on 8 sessions
What are the greatest and smallest positive differences between any of the factors of 210?

A. 103 and 1
B. 209 and 0
C. 210 and 1
D. 103 and 11
E. 209 and 1


Drill 3
Question: 8
Page: 290
[Reveal] Spoiler: OA

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Sandy
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GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4710
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 91

Kudos [?]: 1612 [0], given: 375

CAT Tests
Re: What are the greatest and smallest positive differences [#permalink] New post 01 Nov 2016, 17:21
Expert's post
Explanation

First, list all of the factors of 210. The easiest way to do this is in pairs, starting with 1 and 210 (remember, the number itself is considered one of its factors). Count up from one and check to see if each number you count is a factor of 210.

1 and 210
2 and 105
3 and 70
5 and 42
7 and 3
10 and 21
14 and 15

When you reach 14, you’ll see that you’ll just repeat 15 and 14 if you keep counting, so you know you’re finished. The question asked for the greatest and smallest positive difference between any two factors. (It’s helpful that the question specified positive difference so you know you don’t need to count negative differences, though once you look at the answer choices you can see that’s not what the question is asking for). The way you listed the factors makes this easy because as you look down the list, the difference between factors decreases.

So the greatest difference is between 210 and 1, and the smallest difference is between 14 and 15. The final answer is 209 and 1.

Hence option E is correct.
_________________

Sandy
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Re: What are the greatest and smallest positive differences   [#permalink] 01 Nov 2016, 17:21
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What are the greatest and smallest positive differences

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