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# If the sum of two distinct positive integers is 50, then what is the

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Math Expert
Joined: 02 Sep 2009
Posts: 42250

Kudos [?]: 132495 [0], given: 12323

If the sum of two distinct positive integers is 50, then what is the [#permalink]

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05 Nov 2017, 02:52
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If the sum of two distinct positive integers is 50, then what is the maximum possible value of the greatest common factor of these 2 integers ?

(A) 2
(B) 5
(C) 10
(D) 25
(E) 50
[Reveal] Spoiler: OA

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Kudos [?]: 132495 [0], given: 12323

Math Expert
Joined: 02 Aug 2009
Posts: 5199

Kudos [?]: 5816 [0], given: 117

Re: If the sum of two distinct positive integers is 50, then what is the [#permalink]

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05 Nov 2017, 04:48
Bunuel wrote:
If the sum of two distinct positive integers is 50, then what is the maximum possible value of the greatest common factor of these 2 integers ?

(A) 2
(B) 5
(C) 10
(D) 25
(E) 50

hi...

here the choices will help us..
we are looking for the largest so lets start from highest
1) $$50$$
a+b=50
GCF cannot be GREATER than the number...NO
2) $$25$$..
Only possibility is when both numbers are 25 ......25+25=50
numbers have to be DISTINCT...NO
3) $$10$$
10(a+b)=50
so a+b= 5..
various possibility a=1,b=4 that is 10 and 40
then 2, and 3 will give 20 and 30...YES

ans C
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 5816 [0], given: 117

Re: If the sum of two distinct positive integers is 50, then what is the   [#permalink] 05 Nov 2017, 04:48
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