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What is your strategy for the divisibility problems ?? Are there any specifc posts that deals with tough questions on divisibility
Lets say the question you posed.
A number when divided by a divisor leaves a remainder of 24. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?
My approach will be
y = x*q + 24
2*y = x*(2q) + 48 = x*2q + 37 + 11 => (11 is remainder as per problem)
=> 2*y = [x*2q + 37] + 11
Since 37 is a prime no. There are no common factors between 2q and 37
=> x must be 37 for
2*y = 37 (2q+1) + 11
I have to admit, I took long time to solve this. I won't have that luxury in test.
What is the quick approach.
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