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.
Jan 1507:30 AM PST
-08:30 AM PST
Studying for the GMAT can feel like a long journey, but having the right plan can keep you on track. In this live session, Julia, who scored a perfect 805, will share her step-by-step study plan for 2025. Join for help with key strategies and tips...
Jan 1610:00 AM EST
-12:00 PM EST
The Target Test Prep team is proud to introduce GMAT OnDemand, a video course created by Scott Woodbury-Stewart, founder and CEO, designed to provide you with everything you need to master the GMAT and achieve your score goals.- Jan 16
10:00 AM PST
-11:00 AM PST
Meet Kseniia, a former Public Relations Head at Google in Russia, whose inspiring journey defied the odds and landed her admissions to Wharton, Chicago Booth, and Yale SOM. - Jan 17
10:00 AM PST
-11:00 AM PST
Keshav who scored 99 percentile with near-perfect quant score shares his strategies and techniques to identify and overcome the weaknesses in his GMAT preparation. Learn the preparation tips and study strategies that worked for him. - Jan 18
10:00 AM PST
-11:00 AM PST
In this video, we talked to Rishi, an ambitious Indian student who successfully secured admission into HEC Paris and ESSEC Business School, two of the top Masters in Management (MiM) programs in Europe. 
Jan 1811:00 AM IST
-01:00 PM IST
Do RC/MSR passages scare you? e-GMAT is conducting a masterclass to help you learn – Learn effective reading strategies Tackle difficult RC & MSR with confidence Excel in timed test environment- Jan 19
11:00 AM IST
-01:00 PM IST
Attend this session to evaluate your current skill level, learn process skills, and solve through tough Arithmetic questions
Updated on: 30 Mar 2020, 12:33
Originally posted by MathRevolution on 27 Mar 2020, 02:07.
Last edited by MathRevolution on 30 Mar 2020, 12:33, edited 1 time in total.
Last edited by MathRevolution on 30 Mar 2020, 12:33, edited 1 time in total.
Kudos
Bookmarks
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
63% (02:13) correct
37%
(02:19)
wrong
based on 188
sessions
History
Date
Time
Result
Not Attempted Yet
[GMAT math practice question]
The average and standard deviation of x1, x2, x3, x4 is 5 and \(\sqrt{2}\), respectively. What is the average of x1^2, x2^2, x3^2, x4^2?
A. 11
B. 17
C. 22
D. 27
E. 33
The average and standard deviation of x1, x2, x3, x4 is 5 and \(\sqrt{2}\), respectively. What is the average of x1^2, x2^2, x3^2, x4^2?
A. 11
B. 17
C. 22
D. 27
E. 33
ArunSharma12
Joined: 25 Oct 2015
Last visit: 20 Jul 2022
Posts: 514
Own Kudos:
Given Kudos: 74
Location: India
Schools: IIML-IPMX '22 (A)
GMAT 1: 650 Q48 V31
GMAT 2: 720 Q49 V38 (Online)
GPA: 4
Products:
29 Mar 2020, 00:26
Kudos
Bookmarks
MathRevolution
[GMAT math practice question]
The average and standard deviation of x1, x2, x3, x4 is 5 and 2, respectively. What is the average of x1^2, x2^2, x3^2, x4^2?
A. 11
B. 17
C. 22
D. 27
E. 33
The average and standard deviation of x1, x2, x3, x4 is 5 and 2, respectively. What is the average of x1^2, x2^2, x3^2, x4^2?
A. 11
B. 17
C. 22
D. 27
E. 33
S.D = \(\sqrt{\frac{\sum(x-m)^2}{n}}\); where x is individual element, m is average/mean, n is the number of elements
2 = \(\sqrt{\frac{(x_1-5)^2+(x_2-5)^2+(x_3-5)^2+(x_4-5)^2}{4}}\)
squaring both sides,
4 = \(\frac{(x_1-5)^2+(x_2-5)^2+(x_3-5)^2+(x_4-5)^2}{4}\)
16 =\((x_1-5)^2+(x_2-5)^2+(x_3-5)^2+(x_4-5)^2\)
16 =\({x_1}^2+25-10*x_1+{x_2}^2+25-10*x_2+{x_3}^2+25-10*x_3+{x_4}^2+25-10*x_4\)
16 =\(({x_1}^2+{x_2}^2+{x_3}^2+{x_4}^2)+100-10*(x_1+x_2+x_3+x_4)\)
16 =\(({x_1}^2+{x_2}^2+{x_3}^2+{x_4}^2)+100-10*(20)\);sum of the four numbers is 20
116 = \({x_1}^2+{x_2}^2+{x_3}^2+{x_4}^2\)
\(\frac{{x_1}^2+{x_2}^2+{x_3}^2+{x_4}^2}{4}=\frac{116}{4}\)=29
I think option D needs to be changed to 29.
Updated on: 30 Mar 2020, 12:32
Originally posted by MathRevolution on 30 Mar 2020, 00:34.
Last edited by MathRevolution on 30 Mar 2020, 12:32, edited 1 time in total.
Last edited by MathRevolution on 30 Mar 2020, 12:32, edited 1 time in total.
Kudos
Bookmarks
=>
We have (x1+x2+x3+x4)/4 = 5 or x1+x2+x3+x4 = 20.
Since we know the standard deviation of x1,x2,x3, and x4 is 2, we have
((x1 - 5)^2 + (x2 - 5)^2 + (x3 - 5)^2 + (x4 - 5)^2)/4 = \((\sqrt{2})^2\)
=> (x1 - 5)^2 + (x2 - 5)^2 + (x3 - 5)^2 + (x4 - 5)^2 = 8
=> (x1^2 - 10x1 + 25) + (x2^2 - 10x2 + 25) + (x3^2 - 10x3 + 25) + (x4^2 - 10x4 + 25) = 8
=> (x1^2 + x2^2 + x3^2 + x4^2) - 10(x1 + x2 + x3 + x4) + 25 + 25 + 25 + 25 = 8
=> (x1^2 + x2^2 + x3^2 + x4^2) - 10(20) + 100 = 8
=> (x1^2 + x2^2 + x3^2 + x4^2) = 108
=> (x1^2 + x2^2 + x3^2 + x4^2)/4 = 27
Therefore, D is the answer.
Answer: D
We have (x1+x2+x3+x4)/4 = 5 or x1+x2+x3+x4 = 20.
Since we know the standard deviation of x1,x2,x3, and x4 is 2, we have
((x1 - 5)^2 + (x2 - 5)^2 + (x3 - 5)^2 + (x4 - 5)^2)/4 = \((\sqrt{2})^2\)
=> (x1 - 5)^2 + (x2 - 5)^2 + (x3 - 5)^2 + (x4 - 5)^2 = 8
=> (x1^2 - 10x1 + 25) + (x2^2 - 10x2 + 25) + (x3^2 - 10x3 + 25) + (x4^2 - 10x4 + 25) = 8
=> (x1^2 + x2^2 + x3^2 + x4^2) - 10(x1 + x2 + x3 + x4) + 25 + 25 + 25 + 25 = 8
=> (x1^2 + x2^2 + x3^2 + x4^2) - 10(20) + 100 = 8
=> (x1^2 + x2^2 + x3^2 + x4^2) = 108
=> (x1^2 + x2^2 + x3^2 + x4^2)/4 = 27
Therefore, D is the answer.
Answer: D
