# Re-discovering Remainders

by on October 1st, 2010

If you are similar to most GMAT preppers, you were probably surprised the first time you encountered a remainder question in your GMAT preparation.  You probably remember learning about remainders in third grade, when you learned long division.  Your teacher probably told you something along the lines of, “a remainder is what is left over after you divide.”  You took your long division test and dutifully noted the remainder each time.  You passed that test and finished third grade.  The next year, in fourth grade, you are suddenly allowed to use a calculator and remainders disappeared.  And you did not see them again until you opened up your GMAT prep materials.

## Reminder on Remainders

So, where did remainders go all of those years?  Well, they really did not go anywhere.  Instead of writing out remainders, you started using fractions or decimals to indicate when numbers did not divide evenly.  The remainders are the numerator part of those fractions – and this is the first key to remember when you see remainders on the GMAT.

For example, if you were asked to calculate five divided by two, you would end up with 2.5 or 2 1/2.  This is the same as 2 remainder 1, because when we divide five by two, we end up with two 2’s, with a one left over.

## Two Ways to Think About Remainders

This means that when we see a remainder question on the GMAT we have two ways to think about it.  One option is to convert to a fraction and work with it as such.  The other option is to think of it as what is left over.  For example, if we are looking for a number which gives us a remainder of 4 when it is divided by 5, we know that the number must be four more than a multiple of five.  So the number could be 9, 14, 19, etc.

• Hey good pointers Bret. I always feel using fractions instead of decimals is better because then we have a possibility of cancellation and making the calculations easier. Imagine what would you prefer

1) 0.125 * 1.6 = 0.2
or
2)1/8 * 8/5 = 1/5

and of course remainders have many other applications as well in more complicated questions
thanks again

Ishaan

• Bret, what an elucidative and important article. The information you reviewed is so critical to a creating a strong foundation - and especially for understanding Data Sufficiency questions.

Also, many thanks for making the article just the right length for stressed out GMAT students.

Michele