lheiannie07 wrote:What is the average (arithmetic mean) of a sequence of N consecutive odd integers?

(1) N is even.

(2) Half of the terms in the sequence are negative.

Can some experts find the best option?

OA B

We have to get the value of the average (arithmetic mean) of a sequence of N consecutive odd integers.

(1) N is even.

We do not have any information from which number the sequence starts. Say the sequence is 1, 3, 5 and 7, then the average = 4; however, say the sequence is 11, 13, 15 and 17, then the average = 14. No unique answer. Insufficient.

(2) Half of the terms in the sequence are negative.

This implies that the total number of the terms in the sequence is even. It also implies that Statement 1 is also implied in Statement 2. Thus, the correct answer would either be B or E.

The negative odd terms will awlays include -1, ie, the negative terms would be -1, -3, -5, -7, and so on. This is because if they do not include -1, the consecutive nature of the terms will break since exactly half the terms must be positive and odd.

So, if the negative terms are -1, -3, -5, -7, the positive terms would be 1, 3, 5, and 7, making the sequence {-7, -5, -3, -1, 1, 3, 5, 7}. Thus, the average would be 0.

If the negative terms are -1, -3, -5, -7, -9, the positive terms would be 1, 3, 5, 7 and 9, making the sequence {-9, -7, -5, -3, -1, 1, 3, 5, 7, 9}. Thus, the average would be 0.

So irrespecitve of how many terms are there in the sequence, the average would be 0. Sufficient.

The correct answer: B

Hope this helps!

-Jay
_________________
Manhattan Review GMAT Prep

Locations: New York | Singapore | London | Dubai | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

lheiannie07 wrote:What is the average (arithmetic mean) of a sequence of N consecutive odd integers?

(1) N is even.

(2) Half of the terms in the sequence are negative.

Statement One Alone:

N is even.

We can't determine the average since we know neither the value of N nor the integers in the sequence.

For example, if N = 2, the average of 3 and 5 is not equal to the average of 5 and 7.

Statement one alone is not sufficient to answer the question.

Statement Two Alone:

Half of the terms in the sequence are negative.

Since half of the terms in the sequence are negative, the other half of the terms must be positive, and each negative term has a positive counterpart that is its opposite. For example,

1) If -3 and -1 are in the sequence, then 1 and 3 are also in the sequence.

2) If -5, -3, and -1 are in the sequence, then 1, 3, and 5 are also in the sequence.

Thus, we see that the sum of all the numbers in the sequence must be 0, and hence the average is also 0.

Answer: B