In a small snack shop, the average (arithmetic mean) revenue was $400 per day over a 10-day period. During this period, if the average daily revenue was $360 for the first 6 days, what was the average daily revenue for the last 4 days?
A. $420
B. $440
C. $450
D. $460
E. $480
Answer: D
Source: GMAT Prep
In a small snack shop, the average (arithmetic mean) revenue was $400 per day over a 10-day period. During this period,
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Given that
Average revenue over a 10 period is 400
Average revenue over the first 6 days is 360
Let the revenue per day be given by D1, D2, .... D10
Converting the above statements into equations we have
Statement (2)
\(\frac{D_1+D_2+D_3+D_4+D_5+D_6}{6}=360\)
Solving it we have
\(D_1+D_2+D_3+D_4+D_5+D_6\) = 360*6
\(D_1+D_2+D_3+D_4+D_5+D_6\) = 2160
Similarly statement (1) can be written as
\(D_1+D_2+D_3+D_4+D_5+D_6+D_7+D_8+D_9+D_10\) = 4000
Substituting the \(D_1+D_2+D_3+D_4+D_5+D_6\) value in the above equation we get
2160+\(D_7+D_8+D_9+D_10\) =4000
\(D_7+D_8+D_9+D_10\) =4000-2160
\(D_7+D_8+D_9+D_10\) = 1840
Now to find the average revenue over the last 4 days we need to divide \(D_7+D_8+D_9+D_10\) by 4
Average revenue over the last 4 days = \(\frac{D_7+D_8+D_9+D_{10}}{4}=\frac{1840}{4}=460\)
hence the OA is D
Average revenue over a 10 period is 400
Average revenue over the first 6 days is 360
Let the revenue per day be given by D1, D2, .... D10
Converting the above statements into equations we have
Statement (2)
\(\frac{D_1+D_2+D_3+D_4+D_5+D_6}{6}=360\)
Solving it we have
\(D_1+D_2+D_3+D_4+D_5+D_6\) = 360*6
\(D_1+D_2+D_3+D_4+D_5+D_6\) = 2160
Similarly statement (1) can be written as
\(D_1+D_2+D_3+D_4+D_5+D_6+D_7+D_8+D_9+D_10\) = 4000
Substituting the \(D_1+D_2+D_3+D_4+D_5+D_6\) value in the above equation we get
2160+\(D_7+D_8+D_9+D_10\) =4000
\(D_7+D_8+D_9+D_10\) =4000-2160
\(D_7+D_8+D_9+D_10\) = 1840
Now to find the average revenue over the last 4 days we need to divide \(D_7+D_8+D_9+D_10\) by 4
Average revenue over the last 4 days = \(\frac{D_7+D_8+D_9+D_{10}}{4}=\frac{1840}{4}=460\)
hence the OA is D
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If the average (mean) daily revenue over 10 days is $400/day, then the TOTAL 10-DAY REVENUE = (10)($400) = $4000Gmat_mission wrote: ↑Sat Aug 22, 2020 3:50 amIn a small snack shop, the average (arithmetic mean) revenue was $400 per day over a 10-day period. During this period, if the average daily revenue was $360 for the first 6 days, what was the average daily revenue for the last 4 days?
A. $420
B. $440
C. $450
D. $460
E. $480
Answer: D
Source: GMAT Prep
The average daily revenue for the first 6 days is $360. So, the TOTAL 6-DAY REVENUE = (6)($360) = $2160
So, the TOTAL REVENUE for the last 4 days = $4000 - $2160 = $1840
So, the AVERAGE daily revenue for those 4 days = $1840/4 = $460
Answer: D