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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: 50007
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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Difficulty:

55% (hard)

Question Stats:

62% (01:21) correct 38% (01:13) wrong based on 195 sessions

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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

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Joined: 02 Aug 2009
Posts: 6971
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
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2
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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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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

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24 Dec 2017, 02:13
Bunuel is this method correct?
Sum of two numbers = 50
HCF will be highest when LCM is least possible.
For LCM to be least one number should be equal to other but thats not possible since numbers have to be distinct so one number should be some multiple of another.
lets say one integer is a, then other number can be 2a; a+2a=50 not possible
a+3a=50 not possible.
a+4a=50, it implies a=10 and other number 40,
hence HCF=10. Option C is the correct answer. I hope my way is OK
If the sum of two distinct positive integers is 50, then what is the &nbs [#permalink] 24 Dec 2017, 02:13
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