McGraw-Hill Education GRE 2019

What is the average of x, x + 4, x + 8, x + 12, and x + 16?

SOLUTION: Recognize that each term is 4 greater than the previous term. You

thus have an evenly spaced set. To find the average, you need the median,

which in this case, is x + 8.

What is the average of the integers from 15–21, inclusive?

SOLUTION: Since average = median for an evenly spaced set, you could list out

all the terms and find the median. But a faster approach would be to take the

average of the endpoints: 15 + 21 2 = 18. The average is 18.

Property 3: Use the following formula to determine the number of terms in an

evenly spaced set:

(last item in the set – first item in the set)

increment + 1

Example: How many integers are there from 6–10, inclusive?

SOLUTION: Note that inclusive means that you will include both endpoints of

the set when determining the answer. You might be tempted to simply take

the difference of 10 and 6 and arrive at 4 as your answer, but this would omit

one of the items. If you list out the numbers, you will see that there are five

(6, 7, 8, 9, and 10). Using the preceding formula, you arrive at:

10 – 6

1 + 1 = 5

How many multiples of 15 are there from 40–160, inclusive?

SOLUTION: Before using the formula, note that the endpoints of this set are

not multiples of 15. To use the formula, you need the endpoints to have

the property that the formula specifies (in this case, multiples of 15). Your

endpoints will thus be 45 (the smallest multiple of 15 that is greater than 40)

and 150 (the greatest multiple of 15 that is less than 160). Now you know that

your endpoints are 45 and 150, and the increment between each term in the

set is 15. Plug these values into the formula:

150 – 45

15 + 1 =

105

15 + 1 = 7 + 1 = 8

Property 4: To determine the sum of the values in an evenly spaced set, use the

average formula: A × N = S.

Properties 2 and 3 specified how to determine the average and number of items

in a set, so using these properties, you can determine the sum of a set.

What is the sum of the even integers from 4–180, inclusive?

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