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For the past n days, the average (arithmetic mean) daily [#permalink]

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27 Dec 2012, 06:28

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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 ?

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

(average production for n days) * n = (total production for n days) --> 50n=(total production for n days); (total production for n days) + 90 = (average production for n+1 days) * (n+1) --> 50n + 90 = 55 * (n+1) --> n=7.

Or as 40 extra units increased the average for n+1 days by 5 units per day then 40/(n+1)=5 --> n=7.

Re: For the past n days, the average (arithmetic mean) daily [#permalink]

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18 Jul 2014, 11:52

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Re: For the past n days, the average (arithmetic mean) daily [#permalink]

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21 Oct 2014, 13:25

Bunuel wrote:

Walkabout wrote:

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

(average production for n days) * n = (total production for n days) --> 50n=(total production for n days); (total production for n days) + 90 = (average production for n+1 days) * (n+1) --> 50n + 90 = 55 * (n+1) --> n=7.

Or as 40 extra units increased the average for n+1 days by 5 units per day then 40/(n+1)=5 --> n=7.

Answer: E.

Could you explain why there is n+1 days? I don't quite get the logic here. Thanks in advance.

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

(average production for n days) * n = (total production for n days) --> 50n=(total production for n days); (total production for n days) + 90 = (average production for n+1 days) * (n+1) --> 50n + 90 = 55 * (n+1) --> n=7.

Or as 40 extra units increased the average for n+1 days by 5 units per day then 40/(n+1)=5 --> n=7.

Answer: E.

Could you explain why there is n+1 days? I don't quite get the logic here. Thanks in advance.

The past n days plus today, so one more day = n + 1 days.
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Re: For the past n days, the average (arithmetic mean) daily [#permalink]

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23 Oct 2014, 22:16

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Walkabout wrote:

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

For "N" days avg production was 50 Units

Today production of 90 Units raises avg to 55 Units

So 90 Units of today raises each of N days avg unit by 5 Units + 55 Units of today.

Considering that if 55 Units were produced today then remaining 35 Units of today add up to raise value from 50 Units to 55 Units. Implies that if 5 units each are given to "N" days then the avg will be 55 Units

Re: For the past n days, the average (arithmetic mean) daily [#permalink]

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10 Aug 2015, 23:28

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I thought about this like a weighted average problem. Since 90 (the last day; weight of 1) is +35 above 55 (the new average) and 50 (all the previous days; weight of n) is -5 below 55. In order to reach the new average, the sum of everything above and below 55 must equal to 0, so...

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

We start with the formula for calculating the average.

average = sum/quantity

We are given that the initial quantity is n days and that the average for those n days is 50 units. We can use this to determine a sum for the n days.

Since sum = average x quantity, we know:

sum = (50) (n) = 50n

We are next given that today, the production was 90 units. This means we can add “1” to the current quantity and “90” to the current sum. We are also given that this new average is 55 units per day. Substituting this information into the average formula we get:

55 = (50n + 90)/(n + 1)

55(n + 1) = 50n + 90

55n + 55 = 50n + 90

5n = 35

n = 7 days

The answer is E.
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Re: For the past n days, the average (arithmetic mean) daily [#permalink]

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01 Apr 2017, 09:44

Walkabout wrote:

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

Total production for past n days= 50n

The new average after today's production= 55(n+1) (past n days+today's production) 55n+55-50n= 90 5n=35 n=7

Re: For the past n days, the average (arithmetic mean) daily [#permalink]

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01 Apr 2017, 23:56

Walkabout wrote:

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 _________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

Re: For the past n days, the average (arithmetic mean) daily [#permalink]

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02 Apr 2017, 06:25

Abhishek009 wrote:

Walkabout wrote:

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 ?

Re: For the past n days, the average (arithmetic mean) daily [#permalink]

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24 Jul 2017, 09:21

My 50 cents here.

I guess Using the Differential way (Or thinking of average in terms of Sums) is the quickest way to answer this questions. Also the scope of error is less. Pardon me if the explanation looks abstruse

Given: Average of n days is 50. Production of 90 on (n+1)th day "pulls" the average of n+1 days to 55.

In terms of overall sum of n+1 what this means is - for n days we lost 50 - 55 = -5 per day on the total sum needed to make the average of 55. Meaning, over n days we lost a total of -5n that would be needed to make the average of 55. The 90 on the (n+1)th day makes up for all the Lost sum and brings the average to 55. Meaning, a value of 90-55 = +35 will offset all the sum that we lost in last n days.

Mathematically we can simply write -5n+35 = 0 => n = 7.

Hope this makes sense and als helps
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