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Standard X

Mathematics

Real Numbers

A positive in...

Question

A positive integer a is written as a=3q+r and a=4k+r, where q,k and r are whole numbers. Find the possibilities of q and k?

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Solution

Given a=3q+r and a=4k+r
Where k,q,r are whole numbers, So
3q+rv = 4k+r
=> 3q=4k
therefore q=(4/3)k
r can be any whole number
Whole numbers are 0,1,2,3...
When k=0,3,6,9,.... That is multiples of 3( Then only we get q as a whole number,given that q is whole number)
q=0,4,8,12,... That is multiples of 4

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