GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 18 Dec 2018, 10:17

# In Progress:

Admit Calls from Ross Join Chat Room | McCombs Join Chat Room for Latest Updates

### 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

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

## Events & Promotions

###### Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### Happy Christmas 20% Sale! Math Revolution All-In-One Products!

December 20, 2018

December 20, 2018

10:00 PM PST

11:00 PM PST

This is the most inexpensive and attractive price in the market. Get the course now!
• ### Key Strategies to Master GMAT SC

December 22, 2018

December 22, 2018

07:00 AM PST

09:00 AM PST

Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.

# If the arithmetic mean of a set of n measurements was found to be m, a

Author Message
TAGS:

### Hide Tags

Manager
Joined: 02 Jun 2015
Posts: 191
Location: Ghana
If the arithmetic mean of a set of n measurements was found to be m, a  [#permalink]

### Show Tags

29 Jun 2017, 12:44
3
00:00

Difficulty:

35% (medium)

Question Stats:

67% (01:29) correct 33% (01:22) wrong based on 75 sessions

### HideShow timer Statistics

If the arithmetic mean of a set of n measurements was found to be m, and then it was discovered that there was an error of +k% in each measurement. What is the percentage error in the mean?

(1) m = 6
(2) n = 7

_________________

Kindly press kudos if you find my post helpful

Senior Manager
Joined: 24 Apr 2016
Posts: 331
Re: If the arithmetic mean of a set of n measurements was found to be m, a  [#permalink]

### Show Tags

29 Jun 2017, 15:02
Let us say that there are n measurements and each represented by$$a_1,a_2,a_3,a_4,a_5.......a_n$$

Mean of the above measurements is given by =$$\frac{(a_1+a_2+a_3+a_4+a_5+.......+a_n)}{n}$$ = m -------Equation 1

now if each original value had an error of +K%, this means

$$(1+ \frac{k}{100})$$Original value = new value

Therefore, Original value = new value * $$[\frac{100}{(100+k)}]$$

Correct Mean = $$[a_1*[\frac{100}{(100+k)}]+a_2*[\frac{100}{(100+k)}]+a_3*[\frac{100}{(100+k)}]+a_4*[\frac{100}{(100+k)}]+.......+a_n*[\frac{100}{(100+k)}]]/n$$

Correct Mean =$$[\frac{100}{(100+k)}]\frac{[a1+a2+a3+a4+....+an]}{n}$$ ------------------Equation 2

Replacing the value from Equation 1 in Equation 2

Correct Mean =$$\frac{100m}{(100+k)}$$

Percentage error in the Mean = (Given Mean - Old Mean)*100 / Given Mean = [(m - $$\frac{100m}{(100+k)}$$)*100]/m = [1 - $$\frac{100}{(100+k)}$$]*100 = $$\frac{(100+k-100)}{(100+k)}$$ * 100 = $$\frac{100k}{100+k}$$

So we need the of k to find the Percentage error in the Mean

Statement 1: m = 6
This statement does not given the value of k, Hence is insufficient.

Statement 2: n = 7
This statement does not given the value of k, Hence is insufficient.

Combining both statement is also not sufficient. Answer is E
VP
Joined: 05 Mar 2015
Posts: 1003
Re: If the arithmetic mean of a set of n measurements was found to be m, a  [#permalink]

### Show Tags

29 Jun 2017, 17:55
duahsolo wrote:
If the arithmetic mean of a set of n measurements was found to be m, and then it was discovered that there was an error of +k% in each measurement. What is the percentage error in the mean?

(1) m = 6
(2) n = 7

avg. /mean(M) = Sum(s) / No. of samples(s)

Actual mean without error= M = s/ n

Mean with error(Let M') = s(1+k%) / n

%age error = M' - M /M

= s(1+k%)/n - s/n / s/n

= k/100

so for knowing the percentage error in the mean we must know k...

(1) no info of k...insuff

(2) no info of k...insuff

combined..again
no info of k...insuff

Ans E
Senior Manager
Joined: 08 Jun 2015
Posts: 435
Location: India
GMAT 1: 640 Q48 V29
GMAT 2: 700 Q48 V38
GPA: 3.33
Re: If the arithmetic mean of a set of n measurements was found to be m, a  [#permalink]

### Show Tags

26 Jun 2018, 05:24
+1 for option E. The error for mean will be k% itself. Both options individually and together are not sufficient. Hence option E it is.
_________________

" The few , the fearless "

Re: If the arithmetic mean of a set of n measurements was found to be m, a &nbs [#permalink] 26 Jun 2018, 05:24
Display posts from previous: Sort by