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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: 64216
If the sum of two distinct positive integers is 50, then what is the  [#permalink]

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05 Nov 2017, 01:52
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55% (hard)

Question Stats:

59% (01:16) correct 41% (01:14) wrong based on 255 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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Math Expert
Joined: 02 Aug 2009
Posts: 8602
Re: If the sum of two distinct positive integers is 50, then what is the  [#permalink]

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05 Nov 2017, 03:48
2
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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Joined: 27 May 2015
Posts: 6
Schools: ISB '18
If the sum of two distinct positive integers is 50, then what is the  [#permalink]

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24 Dec 2017, 01:13
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
Math Expert
Joined: 02 Sep 2009
Posts: 64216
Re: If the sum of two distinct positive integers is 50, then what is the  [#permalink]

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24 Dec 2018, 03:51
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

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Joined: 03 Jun 2019
Posts: 2899
Location: India
GMAT 1: 690 Q50 V34
WE: Engineering (Transportation)
If the sum of two distinct positive integers is 50, then what is the  [#permalink]

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08 Oct 2019, 01:34
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

E 50 is not possible since there are 2 distinct positive integers

D 25 is not possible since they are distinct

C 10 is possible since 10a + 10b = 50 ; a+b=5 ; (a,b) = {(1,4),(2,3),(4,1)}

IMO C
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Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com
If the sum of two distinct positive integers is 50, then what is the   [#permalink] 08 Oct 2019, 01:34