Question

What is the maximum possible numbers(below 10,000)which when divided by 13leaves remainder 2 and when divided by 6leaves remainder 3?

Answer 1

Answer: 9999

Step-by-step explanation: There might be a better answer out there, but I had an approach that got a quick answer so here it goes

for a number to be divisible by 13 and leave a remainder of 2 it must be of the form

13x + 2 - (I)

for the same number to be divible by 6 and leave a remainder of 3 it must be of the form

6x + 3 or 2x+1  - (2)          i.e. it must be divisible by 3 but not by 2

So, we're looking at an odd number here that's divisible by 3,

From (1) I can try finding the highest multiple of 13 less than 10,000

which turns out to be. 13 x 769 = 9997

Now to add in the extra 2 for the remainder 9997 + 2 = 9999

which also happens to be a odd number divisible by 3 ( if sum of digits of a number are divisible by 3 then the number is divisible by 3 )

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