GRE Exam: A Simple Guide To Number Properties - Remainders

Recall that 15 is a multiple of 5 since 5 divides evenly into 15.

What about 16?

16 is not a multiple of 5, because , which is a noninteger.

When doing division, if the numerator is not divisible by the denominator, the value left over after the denominator divides into the numerator is called the remainder.

The remainder essentially tells you how many units the numerator is past a given multiple of the denominator.

It follows that the remainder must always be smaller than the divisor.

Look at the remainders yielded by each of the following:

Once you come to , the remainder cycles back to zero.

Unknowns and Remainders
It helps to express remainders algebraically, especially when the numerator of the fraction is an unknown.

For example: When x is divided by 7, the remainder is 2.
You can translate this to mean: x is two units to the right of a multiple of 7.

As illustrated in the diagram, x can equal 9, 16, 23, 30, 37, and so on.

There are infinite values for x, but they are all two units to the right of a multiple of 7.

You can also express the previous mathematical sentence algebraically.

Any given multiple of 7 can be expressed as 7I, where I = any integer. Since x is two units to the right of a multiple of 7, it follows that: x = 7I + 2.

When x is divided by 6, the remainder is 2. Which of the following could be a value of x?
10
12
14
16
18

SOLUTION: Express x algebraically: x = 6I + 2. Determine which of the choices will yield an integer value for I.


SOLUTION: The correct answer is C.