I write down 3 different positive whole numbers that add up to 96.The sum of any two is divisible by the third.
What is the largest of these three numbers?
 

Asked by neilsgpac | 13th Jul, 2017, 07:47: PM

Expert Answer:

begin mathsize 16px style The space sum space of space any space two space numbers space is space divisible space by space the space third.
That space means comma space pairwise comma space their space HCF space will space be space same.
Let space the space HCF space be space straight x.
Then comma space the space three space numbers space can space be space straight x comma space 2 straight x space and space 3 straight x.
as space HCF left parenthesis straight x comma space 2 straight x right parenthesis space equals space HCF left parenthesis 2 straight x comma space 3 straight x right parenthesis space equals space HCF space left parenthesis straight x comma space 3 straight x right parenthesis space equals space straight x
Sum space of space the space numbers equals 96
rightwards double arrow straight x plus 2 straight x plus 3 straight x equals 96
rightwards double arrow 6 straight x equals 96
rightwards double arrow straight x equals 16
rightwards double arrow Largest space number equals 3 straight x equals 3 cross times 16 equals 48 end style

Answered by Rashmi Khot | 14th Jul, 2017, 09:00: AM

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