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505-555 Level|   Statistics and Sets Problems|                                       
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vikramnugge
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For the past n days, the average (arithmetic mean) daily 21 May 2018, 03:53
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For the past n days, the average (arithmetic mean) daily production at a company was 50 units. If today's production of 90 units raises the average to 55 units per day, what is the value of n ?

(A) 30
(B) 18
(C) 10
(D) 9
(E) 7
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WKT the sum/n = Average

Given for n days the average production was 50
there sum/n = 50
or sum = 50n ...(1)

If we include todays production the number of days will increase by 1 hence the n+1
Sum would increase by 90
new average is 65
therefor sum/n=average would imply sum+90/n+1 = 55 ...(.2 )
Substitue 1 in 2 and solve
50n + 90 = 55n + 55
0r -5n = -35
implies n = 7
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For the past n days, the average (arithmetic mean) daily 08 Sep 2018, 00:46
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90-50=40/5=8 total, since we just added the new average (90), the previous number was 8-1=7
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For the past n days, the average (arithmetic mean) daily 23 Sep 2020, 00:19
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Past 'n' days: Average is 50 units

Sum: Average * Total = 50n

A new unit [90] added to raise the average to 55

55 = \(\frac{(50 n + 90) }{ (n + 1)}\)

=> 55n + 55 = 50n + 90

=> 5n = 35

=> n = 7

Answer E
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For the past n days, the average (arithmetic mean) daily 10 Jan 2021, 10:20
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Abhishek009
Walkabout
For the past n days, the average (arithmetic mean) daily production at a company was 50 units. If today's production of 90 units raises the average to 55 units per day, what is the value of n ?

(A) 30
(B) 18
(C) 10
(D) 9
(E) 7

\(\frac{50n + 90}{n + 1}= 55\)

\(50n + 90 = 55n + 55\)

\(5n = 45\)

So, \(n = 9\)

Thus, answer must be (D) 9
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\(55(n+1)-50n=90\)

\(⇒ 55n+55-50n=90\)

\(⇒ 5n=35\)

\(∴ n=7\)

The answer E, Do you may have a typo.
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For the past n days, the average (arithmetic mean) daily 10 Jan 2021, 10:39
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Walkabout
For the past n days, the average (arithmetic mean) daily production at a company was 50 units. If today's production of 90 units raises the average to 55 units per day, what is the value of n ?

(A) 30
(B) 18
(C) 10
(D) 9
(E) 7
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The average is 50, the additional units have to be divided among the total people as the average increased.

The additional units beyond average 90-50=40

So, \(\frac{40}{n+1}=5\)
\(⇒ 5n+5=40\)
\(⇒ 5n=35\)
\(⇒n=7\)

The answer E.
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For the past n days, the average (arithmetic mean) daily 09 May 2022, 18:46
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avigutman
Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1
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avigutman

Thank you! Perhaps I am reading into this too much, but how do we necessarily know that there are not any days in between the "past n days" and today? What if there was break?
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For the past n days, the average (arithmetic mean) daily 09 May 2022, 18:54
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woohoo921

Perhaps I am reading into this too much, but how do we necessarily know that there are not any days in between the "past n days" and today? What if there was break?
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Does this help, woohoo921?
https://www.gymglish.com/en/gymglish/en ... seven-days

Posted from my mobile device
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For the past n days, the average (arithmetic mean) daily 09 May 2022, 19:19
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woohoo921

Perhaps I am reading into this too much, but how do we necessarily know that there are not any days in between the "past n days" and today? What if there was break?

Does this help, woohoo921?
https://www.gymglish.com/en/gymglish/en ... seven-days

Posted from my mobile device
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avigutman
Thank you for your quick response. As a general rule, when the GMAT says "past few days" does that just always mean a few days prior until now?
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For the past n days, the average (arithmetic mean) daily 09 May 2022, 20:07
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woohoo921
avigutman
woohoo921

Perhaps I am reading into this too much, but how do we necessarily know that there are not any days in between the "past n days" and today? What if there was break?

Does this help, woohoo921?
https://www.gymglish.com/en/gymglish/en ... seven-days
As a general rule, when the GMAT says "past few days" does that just always mean a few days prior until now?
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Yes, woohoo921. And that rule isn't limited to the GMAT.
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For the past n days, the average (arithmetic mean) daily 08 Sep 2025, 06:21
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Walkabout
For the past n days, the average (arithmetic mean) daily production at a company was 50 units. If today's production of 90 units raises the average to 55 units per day, what is the value of n ?

(A) 30
(B) 18
(C) 10
(D) 9
(E) 7
Show more
avg = sum/n

till nth day: sum/n = 50 ->1

for n+1st day : (sum+90)/n+1 = 55 -> 2

from (1)
S = 50 N

FROM (2)
S = 55(N+1)-90 = 55N +55 -90 = 55N-35

FROM BOTH S
50N = 55N-35
5N=35
N = 35/5 = 7
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