Problem Solving

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

-Jay
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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

Cheers,
Brent

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

GMAT assassins aren't born, they're made,
Rich