For the past n days, the average (arithmetic mean) daily pro

Question

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 s- sum of productions in n days Average for n days is 50=s/n After adding one more day with production 90 new average 55=s+90/n+1 55=50n+90/n+1 =>n=18 But OA is different. OPEN DISCUSSION OF THIS QUESTION IS HERE: for-the-past-n-days-the-average-arithmetic-mean-daily-144784.html

beyondgmatscore · Answer

One extra data point that is 40 units higher than average increases average by 5 units, so total number of days now = 40/5 = 8. So, number of days before = 8-1 = 7.

Bunuel · Answer

(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.

fluke · Answer

Nothing wrong with your equation; something went wrong when you simplified the equation.

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

55n+55=50n+90 
 5n=35 
 n=35/5=7

Ans: "E"

KarishmaB · Answer

The problem in your calculation has already been identified above.

Let me discuss the concept of average in another way:
It helps to think of average as the number that makes all the numbers equal. That is, if I say average of 4 numbers is 50, the first thing you should do is imagine having 4 numbers, each of them 50. Most probably, all of them will actually not be equal to 50 but the overall effect would be the same as if they were 50 each because their sum would be 200.

So when you say that for n days, production was 50 on average, I imagine the production of each day as 50. If on (n+1)th day too, the production is 50, the average will remain the same i.e. 50. But actually, the production is 90. i.e. 40 extra. To get to the average, we divide the sum equally among all. So the 40 extra needs to be divided equally among all the days including the (n+1)th day. Since the average increases by 5 (becomes 55), it means there must have been a total of 8 days (because 40/8 = 5). So n must be 7.

YourMom · Answer

Number line:

Old---------Change--------------New
50----------55--------------------90
55-50 = 5
90-55 = 35
35/5 = 7

I can't really explain this but Karishma's explanation does.

For the past n days, the average (arithmetic mean) daily pro

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