What is the average (arithmetic mean) of a sequence of N consecutive

Question

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.

This is a  Data Sufficiency Butler Question

Check the links to other Butler Projects: 
 
   Data Sufficiency Butler 
   Problem Solving Butler  
   Sentence Correction Butler  
   Reading Comprehension Butler  
   Integrated Reasoning Butler

IshanSaini · Answer

To answer this question make a basic series of such consecutive odd numbers :
series 1 : 2k-3, 2k-1, 2k+1, 2k+3
series 2 : 2k +1, 2k + 3, 2k + 5, 2k+7
Note both series have 4 terms.

Now (1) N is even.
N = 4,
so take series 1 : 8k/4 = 2k
take series 2 : 8k + 16 = 8(k+2)/4 = 2k + 4
Hence not sufficient.

Furthermore lets now consider (2) Half of the terms in the sequence are negative.
This infers that N is even as how will half terms be negative if N is Odd.

"Should I select C or B because B is indirectly C"

.
Take series 1 for instance here we get 8k/4 = 2k
Take note further even if we increase the N to 6 3-ve 3 +ve we will see we get 12k/6 = 2k
Hence B is sufficient.

IMO B

"Should I select C or B because B is indirectly C"

. Take series 1 for instance here we get 8k/4 = 2k Take note further even if we increase the N to 6 3-ve 3 +ve we will see we get 12k/6 = 2k Hence B is sufficient. IMO B

GrandGG · Answer

(2) infers that N is odd since 0 is neither even or odd. Ex: -3,-1,0,1,3. Here half of the terms are negative, thus the mean is always 0

Tinytrotter · Answer

Zero (0) is an even number, so it will never be in the sequence.

Statement 2 tells that half of the terms in a series of consecutive odd INTEGERS are negative. Which means by default that N cannot be odd becuase N/2 will always result in a fraction/decimal. Hence N is always even and if N is even and N/2 is negative and balance N/2 is positive in a consecutive sequence, then mean is definitely going to be zero.

Hence, Answer becomes B.

What is the average (arithmetic mean) of a sequence of N consecutive

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

What is the average (arithmetic mean) of a sequence of N consecutive

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards