GMAT Prep Now - GMAT Integer Properties Video # 32

shounakjoshi wrote:GMAT Prep Now - GMAT Integer Properties Video # 32 - K Divided by 67.

https://www.gmatprepnow.com/module/gmat- ... /video/851

If I rewrite the same question using 100 instead of 2345. Can you please explain how will the 'Possible values of N' method would help?

I tried to solve it by this method :

Possible values of K : 89, 100+89, 200+89 and so on.

If i plug in K= 89, then dividing by 67 will result in remainder as 22.

But if I plug in k = 100+ 89 = 189, then remainder would be 55.

Am i missing something here? Can we call this method full proof?

Here's the actual question - https://www.gmatprepnow.com/module/gmat- ... /video/851

The assumption we have to make here is that 89 and (2345+89) will both have the same remainder when divided by 67. Otherwise, there would not be a single correct answer.

Now, we COULD find the remainder when we divide (2345+89) by 67, or we can go the easier route and find the remainder when we divide 89 by 67.

The reason that 89 and (2345+89) both have the same remainder when divided by 67 is that 2345 is a MULTIPLE of 67.

In your example, 100 is not a multiple of 67, so we get different remainders.
Let's change the question to similar numbers that DO work with your example using 100:

When positive integer K is divided by 100, the remainder is 7. What is the remainder when K is divided by 10?

In this case, possible values of K are: 7, 107, 207, 307, etc
When we divide any of these by 10, the remainder is 7.

The purpose of this question is the highlight a common mistake that students make. For example, if I tell students that an integer K has remainder 2 when we divide K by 5, students often omit 2 from the list of possible values of K.

I hope that helps.

Cheers,
Brent