Set S consists of the integers

Expert replies

aaron1981: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Tue Oct 15, 2013 4:45 am

by aaron1981 » Thu Jul 13, 2017 5:04 am

Set S consists of the integers {1, 2, 3, 4 ... Â„(2n +Â‚ 1)Â…}, where n is a positive integer. If X is the average of the odd integers in set S and Y is the average of the even integers in set S, what is the value of Â„(X - Y)Â…?

(A) 0
(B) 1/2
(C) 1
(D) 3/2
(E) 2

OA A

Like this post

Source: Beat The GMAT — Problem Solving | Thu Jul 13, 2017 5:04 am

GMAT/MBA Expert

Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Thu Jul 13, 2017 5:10 am

aaron1981 wrote:Set S consists of the integers {1, 2, 3, 4 ... Â„(2n +Â‚ 1)Â…}, where n is a positive integer. If X is the average of the odd integers in set S and Y is the average of the even integers in set S, what is the value of Â„(X - Y)Â…?

(A) 0
(B) 1/2
(C) 1
(D) 3/2
(E) 2

OA A

Since there is no restriction on n, let us try to find Â„(X - Y)Â… using a few values of n.

Case 1: n = 2, an even number

Thus, Set S = {1, 2, 3, 4, 5}

=> X = (1 + 3 + 5)/3 = 3;

=> Y = (2 + 4)/2 = 3

=> (X - Y) = 3 - 3 = 0.

Case 2: n = 3, an odd number

Thus, Set S = {1, 2, 3, 4, 5, 6, 7}

=> X = (1 + 3 + 5 + 7)/4 = 4;

=> Y = (2 + 4 + 6)/3 = 4

=> (X - Y) = 4 - 4 = 0.

The correct answer: A

Hope this helps!

Relevant book: Manhattan Review GMAT Number Properties Guide

-Jay
_________________
Manhattan Review GMAT Prep

Locations: New York | Jakarta | Nanjing | Berlin | and many more...

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

Like this post

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Thu Jul 13, 2017 6:46 am

aaron1981 wrote:Set S consists of the integers {1, 2, 3, 4 ... Â„(2n +Â‚ 1)Â…}, where n is a positive integer. If X is the average of the odd integers in set S and Y is the average of the even integers in set S, what is the value of Â„(X - Y)Â…?

(A) 0
(B) 1/2
(C) 1
(D) 3/2
(E) 2

For any evenly spaced set, AVERAGE = MEDIAN.
Thus:
X = the average of the odd integers in S = the MEDIAN of the odd integers in S.
Y = the average of the even integers in S = the MEDIAN of the even integers in S.

Let n=2, with the result that 2n+1 = (2*2) + 1 = 5.
Resulting set:
{1, 2, 3, 4, 5}.

X = the median of odd integers {1, 3, 5} = 3.
Y = the median even integers {2, 4} = 3.
Thus, X-Y = 3-3 = 0.

The correct answer is A.

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Like this post

GMAT/MBA Expert

Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Thu Jul 13, 2017 9:08 pm

aaron1981 wrote:Set S consists of the integers {1, 2, 3, 4 ... Â„(2n +Â‚ 1)Â…}, where n is a positive integer. If X is the average of the odd integers in set S and Y is the average of the even integers in set S, what is the value of Â„(X - Y)Â…?

(A) 0
(B) 1/2
(C) 1
(D) 3/2
(E) 2

OA A

Another take on this question...

We have an evenly spaced set S = {1, 2, 3, 4 ... Â„(2n +Â‚ 1)Â…}.

Thus, X = Average of {1, 3, 5, ..., (2n - 1), Â„(2n +Â‚ 1)Â…}; since (2n + 1) is an odd number for any positive integer

And Y = Average of {2, 4, 6, ..., (2n - 2), Â„2nÂ…}; since 2n is an even number for any positive integer

Since the sets {1, 3, 5, ..., (2n - 1), Â„(2n +Â‚ 1)Â…} and {2, 4, 5, ..., (2n - 2), Â„2nÂ…} are evenly spaced, their average would be the average of their first and the last term.

Thus, X = [1 + (2n+1)]/2 = n + 1

and Y = [2 + 2n]/2 = n + 1

=> X - Y = (n+1) - (n+1) = 0.

The correct answer: A

Hope this helps!

-Jay

Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide
________________
Manhattan Review GMAT Prep

Locations: New York | Jakarta | Nanjing | Berlin | and many more...

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

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review