Question 15

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 ?

Name: 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 ?
Uploaded: Nov. 9, 2021, 7 p.m.
Duration: 1 min 48 s
Description: 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 ?

Solution

The odd numbers in the set are 3, 5, 7, ...2n+1

Sum of the odd numbers = 3+5+7+...+(2n+1) = $$n^2 + 2n$$

Average of odd numbers = $$n^2 + 2n$$/n = n+2

Sum of even numbers = 2 + 4 + 6 + ... + 2n = 2(1+2+3+...+n) = 2*n*(n+1)/2 = n(n+1)

Average of even numbers = n(n+1)/n = n+1

So, difference between the averages of even and odd numbers = 1

Share on Whatsapp Share on Whatsapp

Boost your CAT prep: Take All-India 3 free CAT mock tests with Video solutions

Video Solution

Click on the Email ☝️ to Watch the Video Solution

Create a FREE account and get:

All Quant CAT complete Formulas and shortcuts PDF
38+ CAT previous year papers with video solutions PDF
5000+ Topic-wise Previous year CAT Solved Questions for Free

CAT Quant Questions | CAT Quantitative Ability

CAT Profit, Loss and Interest Questions CAT Remainders Questions CAT Geometry Questions CAT Averages Mixtures Alligations Questions CAT Averages Questions

CAT DILR Questions | LRDI Questions For CAT

CAT Data Interpretation Questions CAT Selection With Condition Questions CAT Charts Questions CAT DI Miscellaneous Questions CAT Special Charts Questions

CAT Verbal Ability Questions | VARC Questions For CAT

CAT Odd One Out Questions CAT Reading Comprehension Questions CAT Vocabulary Questions CAT Para Summary Questions CAT Critical Reasoning Questions

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 ?

Video Solution

CAT Quant Questions | CAT Quantitative Ability

CAT DILR Questions | LRDI Questions For CAT

CAT Verbal Ability Questions | VARC Questions For CAT

Also Read

Related Formulas With Tests

CAT 2007 QA 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 ?

Video Solution

CAT Quant Questions | CAT Quantitative Ability

CAT DILR Questions | LRDI Questions For CAT

CAT Verbal Ability Questions | VARC Questions For CAT

Also Read

Free CAT Quant Questions

Related Formulas With Tests

Login to your Cracku account

Hello! 👋

Ready to Unlock Your Success?

Please Enter Your OTP

Please enter the following details

Create a free Cracku account

Get Started with 5000+ Free CAT Questions & Mock Tests with Detailed Solutions!