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OG 13 - PS 145

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by gdshamain » Sat May 03, 2014 1:34 pm
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145. In a small snack shop, the average(arithmetic mean)
revenue was $400 per day overall 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

Just wanted to know an alternate method for this one.
Can we solve this problem using weighted average logic ? ( with the horizontal axes logic)
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by [email protected] » Sat May 03, 2014 2:02 pm
Hi gdshamain,

There are a number of ways to "do the math" on this type of question. Using the standard Average Formula will work perfectly here, and you'll be asked to use it a couple of times over the course of the Quant section, so you shouldn't try to avoid it.

That having been said, there's a weighted average "pattern" that can be used against this question:

The average of the 10 days = $400

The average for the first 6 days = $360. This means that, on each of the first 6 days, each day was $40 "behind" the average. To get the average "up" to $400, the remaining 4 days have to "make up" for that deficit…

6 x $40 = $240 "behind"

The last 4 days have to be above 400 by an amount that will make up for the $240.

$240/4 = $60. This means that each of the last 4 days needs to be $460 for the overall average to be $400.

Final Answer: D

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by gdshamain » Sat May 03, 2014 2:29 pm
Thanks for the explanation Rich.
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by Brent@GMATPrepNow » Sat May 03, 2014 4:51 pm
gdshamain wrote:145. In a small snack shop, the average(arithmetic mean)
revenue was $400 per day overall 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
Here's another approach:

If the average (mean) daily revenue over 10 days is $400/day, then the TOTAL 10-DAY REVENUE = (10)($400) = $4000

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 = [spoiler]$460[/spoiler]

Answer: D

Cheers,
Brent
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by Scott@TargetTestPrep » Mon Jun 29, 2015 7:20 am
gdshamain wrote:145. In a small snack shop, the average(arithmetic mean)
revenue was $400 per day overall 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

Just wanted to know an alternate method for this one.
Can we solve this problem using weighted average logic ? ( with the horizontal axes logic)
Solution:

This problem tests us on our knowledge of weighted averages. To solve, we set up a weighted average equation:

(Revenue for first 6 days + Revenue for final 4 days)/10 days = 400

We know that the average revenue for the first 6 days was $360, resulting in total revenue for the first 6 days as 2,160. We let r be the average daily revenue for the final four days, so we have

(360 x 6 + 4r)/10 = 400

2,160 + 4r = 4,000

4r = 1,840

r = 460

Answer:D

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by DavidG@VeritasPrep » Mon Jun 29, 2015 7:54 am
145. In a small snack shop, the average(arithmetic mean)
revenue was $400 per day overall 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

Just wanted to know an alternate method for this one.
Can we solve this problem using weighted average logic ? ( with the horizontal axes logic)
We could also do a little fancy number line action. If the average revenue was $360 for the first 6 days, and we're looking for the average revenue for last 4 days, we can depict the distance of each value from the overall average ($400) as 4x and 6x. See here:


Image

If 4x = 40, then x = 10 and 6x = 6*10 = 60.
400 + 60 = 460.
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by Matt@VeritasPrep » Mon Jun 29, 2015 3:19 pm
Another approach:

To have an average of $400 over 10 days, we need total revenue of $400*10 = $4000.

So far we have $360*6 = $2160, so we need $4000 - $2160 = $1840 over four days. $1840 / 4 = $460, and we're done!
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