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)
OG 13 - PS 145
This topic has expert replies
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Here's another approach: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
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
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7222
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
Solution: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)
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
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
- DavidG@VeritasPrep
- Legendary Member
- Posts: 2663
- Joined: Wed Jan 14, 2015 8:25 am
- Location: Boston, MA
- Thanked: 1153 times
- Followed by:128 members
- GMAT Score:770
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: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)
If 4x = 40, then x = 10 and 6x = 6*10 = 60.
400 + 60 = 460.
-
- GMAT Instructor
- Posts: 2630
- Joined: Wed Sep 12, 2012 3:32 pm
- Location: East Bay all the way
- Thanked: 625 times
- Followed by:119 members
- GMAT Score:780
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!
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!