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# What is the greatest possible common divisor of two

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Manager
Joined: 10 Jan 2006
Posts: 117
Followers: 1

Kudos [?]: 1 [0], given: 0

What is the greatest possible common divisor of two [#permalink]  15 Mar 2006, 21:23
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0% (00:00) correct 0% (00:00) wrong based on 0 sessions
What is the greatest possible common divisor of two different positive integers which are less than 144?

143
142
72
71
12
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5078
Location: Singapore
Followers: 22

Kudos [?]: 184 [0], given: 0

We can take out 143 and 142 because they are too large to be the divisor of any 2 numbers below 144.

72 is also out as the second multiple of 144 and we need the number to be below 144.

71 is the best choice.

I'll take D
SVP
Joined: 14 Dec 2004
Posts: 1707
Followers: 1

Kudos [?]: 50 [0], given: 0

144/2 = 72.

It has to be less than 72.
Should be 71.
Manager
Joined: 30 Jan 2006
Posts: 146
Followers: 1

Kudos [?]: 9 [0], given: 0

Riuscita, I had problems really understanding the concept to this one when I first saw it in the Kaplan book. But the concept is easier to comprehend if you look at it backwards.

In order for a number to be the greatest common divisor for two different positive integers that are less than 144, we need to be able to multiply that number with two different positive integers and still get a result that is less than 144.

143 * 1 = 143; 143 * 2 = .... obviously this would be greater than 144. No need to calculate.

142 * 1 = 142; 142 * 2 = .... same as above

72 * 1 = 72; 72 * 2 = 144 .... 144 is not less than 144.

71 * 1 = 71; 71 * 2 = 142 .... eureka! there we have it...

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