Plug these values into the formula:
average × number of items = sum
↓ ↓ ↓
60 × 33 = 1, 980- 16 Though it might be difficult to see, the numbers in this set are evenly
spaced. Think of numbers that yield a remainder of 1 when divided by 6: 7, 13,
19, and so on. The spacing is thus 6. Use Property 3 to determine the number
of items in the set:
last – first
spacing + 1
The last term will be the greatest number smaller than 100 that yields a
remainder of 1 when divided by 6: 97. The first term will be the smallest
number greater than 5 that yields a remainder of 1 when divided by 6: 7. Now
plug these values into the formula:
97 – 7
6 + 1 = 16 - D Use Property 4 to determine the sum:
average × number of items = sum
You are told that the set contains eight consecutive integers, so to calculate the
sum, you must determine the average. The average of an evenly spaced set =
the median. Since the given set has an even number of terms, the median will
be the average of the two middle terms (in this case, the 4th and 5th terms). If
the third term is 7, then the 4th term is 8 and the 5th term is 9. The average of
these two terms is 8.5. Now substitute 8.5 for the average and 8 for the number
of items:
average × number of items = sum
↓ ↓ ↓
8.5 × 8 = 68 - D Though you can use the previously discussed formulas, it would be faster
to recognize that from 1–100, there are an equal number of odd integers and
even integers. Since there are 100 terms in the set, 50 will be odd and 50 will
be even. Each even term will be 1 greater than each corresponding odd term.
Since there are 50 terms, the sum of the even terms will be 50 more than the
sum of the odd terms. - D Use Property 3 to determine the number of integers from 50–60, inclusive:
last – first
spacing + 1
60 – 50
1 + 1 = 11
Use Property 4 to determine the sum of the integers in the set:
average × number of items = sumCHAPTER 9 ■ NUMBER PROPERTIES 20503-GRE-Test-2018_173-312.indd 205 12/05/17 11:51 am