Forum Home > GMAT > Quantitative > Problem Solving (PS)
Events & Promotions
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Jul 2710:00 AM PDT
-11:00 AM PDT
Are you struggling with the GMAT verbal section? Do tricky questions and lengthy passages overwhelm you? Don't worry—I've got you covered! In this video, I'll provide a detailed, actionable plan to help you significantly boost your verbal score.
Jul 2508:00 AM EDT
-11:59 PM EDT
More and more TTP students are earning impressive scores on the GMAT. Now is the perfect time to join the many GMAT students who made the switch to TTP and surpassed their wildest expectations on test day.- Jul 28
10:00 AM PDT
-11:00 AM PDT
We will learn how to guess an answer choice better on the GMAT. If you are running out of time and want to guess on a few questions, these effective techniques will help you in making a smart guess. 
Jul 2811:00 AM IST
-01:00 PM IST
Attend this free GMAT Algebra Webinar and learn how to master the most challenging Inequalities and Absolute Value problems with ease.- Jul 31
05:55 AM PDT
-12:30 PM PDT
MBA Application Walkthrough and Essay Review. You will have a chance to hear from experts covering the Top 15 MBA programs, covering details of the application and essays. 
Jul 3110:00 AM EDT
-11:59 PM PDT
Save 20% on Target Test Prep and Score in the 100th Percentile in GMAT Verbal! Our course uses techniques such as topical study and spaced repetition to maximize knowledge retention and make studying simple and fun.
The average (arithmetic mean) of 11 numbers is 50. When the numbers
[#permalink]
19 Nov 2023, 03:10
19 Nov 2023, 03:10
15
Bookmarks
Show timer
00:00
A
B
C
D
E
Difficulty:
35%
(medium)
Question Stats:
79% (02:16) correct
21%
(02:19)
wrong
based on 216
sessions
The average (arithmetic mean) of 11 numbers is 50. When the numbers are arranged in order from least to greatest, the average of the 6 smallest numbers is 44 and the average of the 6 greatest numbers is 57. What is the median of the 11 numbers?
A) 47
B) 50
C) 50.5
D) 53.5
E) 56
2023-12-03_20-07-31.png [ 39.36 KiB | Viewed 4437 times ]
A) 47
B) 50
C) 50.5
D) 53.5
E) 56
Attachment:
2023-12-03_20-07-31.png [ 39.36 KiB | Viewed 4437 times ]
Quant Chat Moderator
Joined: 22 Dec 2016
Posts: 3125
Given Kudos: 1859
Location: India
Concentration: Strategy, Leadership
Re: The average (arithmetic mean) of 11 numbers is 50. When the numbers
[#permalink]
19 Nov 2023, 03:23
19 Nov 2023, 03:23
1
Kudos
6
Bookmarks
pablovaldesvega wrote:
The average (arithmetic mean) of 11 numbers is 50. When the numbers are arranged in order from least to greatest, the average of the 6 smallest numbers is 44 and the average of the 6 greatest numbers is 57. What is the median of the 11 numbers?
A) 47
B) 50
C) 50.5
D) 53.5
E) 56
A) 47
B) 50
C) 50.5
D) 53.5
E) 56
A = {\(x_1, \quad x_2,\quad ...\quad, x_5,\quad x_6,\quad x_7,\quad....\quad x_{10},\quad x_{11}\)}
The median of the set = \(x_6\)
The average (arithmetic mean) of 11 numbers is 50.
\(x_1 +x_2+x_3+...x_{10}+x_{11} = 11*50 = 550\) --- (1)
...the average of the 6 smallest numbers is 44...
\(x_1 +x_2+x_3+...x_{5}+x_{6} = 6*44\) --- (2)
...the average of the 6 greatest numbers is 57...
\(x_6 +x_7+x_8+...x_{10}+x_{11} = 6*57\) --- (3)
Adding equations (2) and (3) we see that \(x_6\) has been added twice as the term is common both in equation (2) and equation (3)
\((x_1 +x_2+x_3+...x_{10}+x_{11}) + x_6 = 6*(44+57)\)
Substituting the value of (1)
\(550 + x_6 = 6*(44+57)\)
\( x_6 =606 - 550 = 56\)
Option E
General Discussion
Intern
Joined: 31 Oct 2023
Posts: 31
Given Kudos: 11
Location: India
Concentration: Finance, Technology
GMAT 1: 710 Q50 V35
GMAT 2: 750 Q50 V41
GPA: 3.15
WE:Sales (Other)
Re: The average (arithmetic mean) of 11 numbers is 50. When the numbers
[#permalink]
19 Nov 2023, 11:38
19 Nov 2023, 11:38
Average of 11 numbers = 50
Therefore total sum of 11 numbers = 50 * 11 = 550
Average of first 6 = 44
Sum of first 6 = 44*6 = 264
Average of last 6 = 57
Sum of last 6 = 57*6 = 342
Common number is the 6th number in both of these, which is also the median.
Therefore sum of both of above = sum of 11 numbers + median = 550+ median = 264 + 342
thus median = 606 - 550 = 56.
Therefore total sum of 11 numbers = 50 * 11 = 550
Average of first 6 = 44
Sum of first 6 = 44*6 = 264
Average of last 6 = 57
Sum of last 6 = 57*6 = 342
Common number is the 6th number in both of these, which is also the median.
Therefore sum of both of above = sum of 11 numbers + median = 550+ median = 264 + 342
thus median = 606 - 550 = 56.
