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Consecutive even numbers

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by neeti2711 » Mon Dec 26, 2016 11:36 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

The OA is [spoiler](A)[/spoiler].

The official answer explanation has counted zero (0) has one of the 18 consecutive even numbers and hence the answer is 22.

I think while counting consecutive even numbers starting with -10 as the smallest term, we should skip zero. And so the answer should be [spoiler](B) i.e. 24.[/spoiler]

Experts please help!
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by manik11 » Tue Dec 27, 2016 1:56 am
Hi,
The prompt asks you to find the range of the POSITIVE integers in the set.
Zero is not positive or negative for that matter. You should count zero as one of the even integers though.

In the question the Range of POSITIVE integers would be 24-2 = 22

OA : A
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by Jay@ManhattanReview » Tue Dec 27, 2016 5:10 am
neeti2711 wrote:The official answer explanation has counted zero (0) has one of the 18 consecutive even numbers and hence the answer is 22.

I think while counting consecutive even numbers starting with -10 as the smallest term, we should skip zero. And so the answer should be [spoiler](B) i.e. 24.[/spoiler]

Experts please help!
Zero is also an integer and we must not skip it since the elements in the set are consecutive integers. Set J: {-10, -8, -6, -4, -2, 0, 2, ..., 24}. Say the sub-set of set J, a set of all the postive integers is K, then Set K: {2, 4, 6, 8, ..., 22, 24}. Thus the range of set K = 24 - 2 = 22.

OA: A

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by melguy » Tue Dec 27, 2016 6:27 am
Properties of zero

Zero is even integer.
Zero is neither positive nor negative.

In this question 24 - 2 = 22 would be the correct answer.
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by Brent@GMATPrepNow » Tue Dec 27, 2016 7:11 am
neeti2711 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
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 [email protected] » Tue Dec 27, 2016 9:10 am
Hi neeti2711,

As everyone has already pointed out, zero IS an even integer. This prompt is an example of a 'fence post' problem - in that you have to make sure to properly 'count' all of the terms (including the first and last terms in the sequence). When the number of terms is relatively small (as it is here), it often helps to count in 'sets of 5' - so that you don't accidentally miss any of them:

-10 -8 -6 -4 -2
0 2 4 6 8
10 12 14 16 18
20 22 24

The range of the POSITIVE integers is 24 - 2 = 22

Final Answer: A

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