The greatest integer in a set of consecutive integers is 7. If the sum of the
integers is 7, how many integers are in this set?
STRATEGY: Read the question two or three times to be
sure you understand what it says.
Solve:
STRATEGY: Draw a number line to avoid careless errors.
SAT TIP: Integers are all the whole number points on
a number line. Remember zero is an integer.
---|----|----|----|----|----|----|----|----|----|----|----|----|----|----|----|----|----|--
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
The "sum" means add the integers. If the sum is 7 and the integers are
consecutive, there must be integers in the set to "cancel" 6, 5, 4, and the
other positive integers. These negative integers would be -6, -5 -4 etc.
The set would consist of -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, and 7.
Answer:
STRATEGY: Read the question again to be sure
you know what it asks.
SAT TIP: This question, like many, leads you to solve
for one answer, but it has an extra step.
When you count the number of intergers, remember zero is an integer.
The answer is 14. The number of integers in this set is 14.
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