Consider the set S = {2, 3, 4, ...., 2n+1), where n is a positive inte

Question

Consider the set S = {2, 3, 4, ...., 2n+1), where n is a positive integer larger than 2007. Define X as the average of the odd integers in S and Y as the average of the even integers in S. What is the value of X – Y?

(A) 0
(B) 1
(C) 2008
(D) n/2
(E) (n + 1)/(2n)

Show Answer

Official Answer

B

(A) 0
(B) 1 
(C) 2008 
(D) n/2 
(E) (n + 1)/(2n)

firas92 · Accepted Answer

Even set = {2,4,6,8,...2n}
Odd set = {3,5,7,9,...2n+1}

By property, if a certain number x is added to all elements of a set, the average of the set increases by x

By this property, since the odd set is just the even set with 1 added to all elements, the average of the odd set must be 1 greater than the average of the even set

So X-Y=1

Answer is (B)

Posted from my mobile device

PiyushPanda1 · Answer

Take smaller values of n, such as n=5 or n=6.

Notice that n=5 => X=7,Y=6
n=6 => X=8, Y=7.

As we can see, X=n+2 and Y=n+1.

Hence,  X-Y = 1.

Option  B

btsaami · Answer

S(odd)= {3, 5, ...., 2n+1}
Avg: First term + Last term /2 
Therefore, X=(3+2n+1)/2
X= n+2

Similarly, S(even)= {2, 4, ...., 2n}
Y= (2+2n)/2
Y= n+1

Therefore X-Y= 1

Consider the set S = {2, 3, 4, ...., 2n+1), where n is a positive inte

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 Problem Solving (PS) Questions

Consider the set S = {2, 3, 4, ...., 2n+1), where n is a positive inte

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