Help on Arithmetic

[divya.1024]

When the positive integer n is divided by 3, the remainder is 2 and when n s divided by 5, the remainder is 1. What is the least possible value of n? Answer is 11. Can anyone please explain?

[vikasapkal]

when 'n' is divided by divisor 'd' and leaving a remainder of 'r', then,

All possible values of n = r , r+d, r+2d, r+3d, r+4d and so on....

Your example -

When the positive integer n is divided by 3, the remainder is 2 and when n s divided by 5, the remainder is 1. What is the least possible value of n? Answer is 11.

>>>

When Positive integer n is divided by 3, the remainder is 2, hence
All values of n = 2,5,8,11,14,17 and so on..

When n is divided by 5, the remainder is 1, hence
All values of n = 1,6,11,16,21,26,31 and so on..

Now, we have to find the value of 'n' which is common between the two set = 11 ( which is least).

[divya.1024]

thank you for the explanation.

[tommywallach]

Thanks for the speedy reply, Vikas. That's absolutely right.

Just so you know, the way that we know we'll have to do something like this (look at lots of numbers, instead of "solving") is because of the way the question is worded:

What is the least possible value of n?

Notice that it's not asking: What is n?

Because it's asking for the "least possible," you know there will multiple POSSIBLE values. This means there will be no single-value solution.

-t

[divya.1024]

Hi Tommy,

so the above solution is one of the ways of doing it? Is there an easy way of doing it?

Appreciate your response. Thanks!

[tommywallach]

Uh-oh. I think you missed my point entirely!

My point was that the wording of this question tells you that you must do it this way, as opposed to some "easier," or at least straight-forwardly algebraic way.

Hope that makes sense!

-t