My Tip to Solving Remainder Problems

[DennaMueller]

I am having trouble with these problems, so I came up with a way to memorize the formula. The instructors can post if there is anything wrong with my logic.

This is the formula from Manhattan GMAT Number Properties Guide:
x=QN+R
x = Dividend
Q = Quotient
N = Divisor
R = Remainder

I changed the symbols in the formula to this:
T=QB+R
This I can remember with the phrase 'a touchdown equals the quarterback plus the receiver'.
T = Top of the fraction
Q = Quotient
B = Bottom of the fraction
R = Remainder

The Question:

If T divided by B equals 8.12 what is a possible remainder?
2
8
9
26
44

Set up your equation T=QB+R
T=800B+.12
Now make .12 an integer
100T=800B+12
Simplify by dividing by 4
25T=200B+3
Now the Remainder is (3), so any remainder of T/B must be a multiple of 3
This makes my answer to the problem C - 9

[tomslawsky]

I remember this by just remembering that the remainder must be a whole multiple of the decimal:

18/.12= whole number

[Ben Ku]

This formula can be a helpful way to approach remainder problems. I would recommend it when you know the reason why the formula works. This way you know when to use it and when not to.

Thanks!

[garimaash]

Sorry.. Pls refer to the post below..

[garimaash]

I remember this by just remembering that the remainder must be a whole multiple of the decimal:

18/.12= whole number

I didn't understand this.. Could you pls elaborate?

[ryan.vineyard]

your logic is not logical..

check your math again

[Ben Ku]

I changed the symbols in the formula to this:
T=QB+R
This I can remember with the phrase 'a touchdown equals the quarterback plus the receiver'.
T = Top of the fraction
Q = Quotient
B = Bottom of the fraction
R = Remainder

A numerical example is this:
13 ÷ 4 = 3 R 1
However, you should remember that it really is just 13 ÷ 4 = 3 + 1/4 or 3.25. So you see that the ".25" part of the answer is just "R / B". If we can write the decimal part as a fraction, then we can determine what might be the remainder.

In your example:

The Question:

If T divided by B equals 8.12 what is a possible remainder?
2
8
9
26
44

We just need to figure out how express ".12" into a fraction. Well, the easy fraction here is "12/100." This can be simplified to "3 / 25" which is "R / B". So we know that the remainder must be a multiple of 3 for this to be true.

Hope that makes sense.