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Set

by granite » Tue Nov 20, 2012 12:43 pm
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?
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by Brent@GMATPrepNow » Tue Nov 20, 2012 12:50 pm
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?
0 is an even number, so it must be included in the set of consecutive even numbers.

So, we get J: {-10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
The positive even integers are from 2 to 24.
So, the range = 24 - 2 = 22 = A

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by GMATGuruNY » Tue Nov 20, 2012 12:56 pm
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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by LalaB » Tue Nov 20, 2012 9:47 pm
an=a1+d(n-1)

a18=a1+2(18-1)=24

the first positive number in this set is 2

24-2=22
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