granite wrote:Set J consists of 18 consecutive even numbers. If the smallest term in the set is -10, what is the range of the positive integers in set J?
(A) 22
(B) 24
(C) 34
(D) 36
(E) 38
Answer A
I got B by omitting 0 (since it's neither negative nor positive) as one of the numbers in the set and having the range be -10 to 26. Can someone explain why we include 0 in the set?
When 0 is divided by 2, the remainder is 0.
Thus, 0 is EVEN.
To count evenly spaced integers:
Number of integers = (biggest - smallest)/increment + 1.
The INCREMENT is the distance between successive terms.
In the problem at hand:
Number of integers = 18.
Smallest = -10.
Increment = 2, since the distance between successive even integers is 2.
Thus:
18 = ( biggest - (-10) )/ 2 + 1
34 = biggest + 10
Biggest = 24.
Range of the POSITIVE integers = biggest - smallest = 24-2 = 22.
The correct answer is
A.
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