Understanding Remainders

[byuwadd]

So I've run into a few problems that say something like, "When positive integer X is divided by positive integer Y, the remainder is 3." If X/Y = 74.11 then what is the value of Y?

The problem I have with this is that I thought that you could break up 74.11 into 74 + 11/100 and that 11 was by definition the remainder and that 100 is by definition the divisor.

How can 11 and 3 both be remainders?

I know how to solve for these problems, but they make no sense to me.

[jnelson0612]

So I've run into a few problems that say something like, "When positive integer X is divided by positive integer Y, the remainder is 3." If X/Y = 74.11 then what is the value of Y?

The problem I have with this is that I thought that you could break up 74.11 into 74 + 11/100 and that 11 was by definition the remainder and that 100 is by definition the divisor.

How can 11 and 3 both be remainders?

I know how to solve for these problems, but they make no sense to me.

I totally understand! I found this very confusing when I was going through training.

Consider a very simple example: 7 divided by 2. If I divide 7 by 2, I get the result 3 remainder 1. So 1 is the remainder. However, the actual value of 7 divided by 2 is 3.5. Where did I get the .5? I took the remainder, 1, and divided it by the divisor, 2.

Using your example, the remainder of 3 divided by Y = .11. In other words, 3/Y = 11/100. I then cross multiply and get 3 * 100 = Y * 11. Now, this is a madeup problem; a real GMAT problem would allow you to come up with a Y that would make this equation equal.

Does this make more sense? Write this all out and work it through, and hopefully it will become clear.

[byuwadd]

Hey JNelson,

It finally makes sense. Thanks a lot. I've been spinning my wheels over this problem for a while now.

I have always understood the 7/2 example intuitively: 7/2 = 3.5. You can rewrite this as 3+5/10 which would simplify to 3+1/2. There is your remainder of 1.

However, on the OG problems you can't easily reduce to find your remainder. The problem I was looking at gave me a decimal of .12 with a remainder of 9. I couldn't simplify 12/100 to 9/Y intuitively so I was stuck.

In retrospect I now see that you can simplify 12/100 to 3/25. Then to get your remainder to 9 you multiply it by 3. You also need to multiply the divisor (25) by 3 and you get the divisor the question is asking for, 75.

Thanks for your help. This forum is great.

Nate

[jnelson0612]

Hey JNelson,

It finally makes sense. Thanks a lot. I've been spinning my wheels over this problem for a while now.

I have always understood the 7/2 example intuitively: 7/2 = 3.5. You can rewrite this as 3+5/10 which would simplify to 3+1/2. There is your remainder of 1.

However, on the OG problems you can't easily reduce to find your remainder. The problem I was looking at gave me a decimal of .12 with a remainder of 9. I couldn't simplify 12/100 to 9/Y intuitively so I was stuck.

In retrospect I now see that you can simplify 12/100 to 3/25. Then to get your remainder to 9 you multiply it by 3. You also need to multiply the divisor (25) by 3 and you get the divisor the question is asking for, 75.

Thanks for your help. This forum is great.

Nate

YES!!!!

Trust me, I found this stuff completely baffling when I first saw it and had to work hard to understand it. Glad that I could help you with it!