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Manager  Joined: 22 Sep 2010
Posts: 62
In a small snack shop, the average (arithmetic mean) revenue  [#permalink]

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Question Stats: 90% (01:24) correct 10% (01:47) wrong based on 1915 sessions

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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 Originally posted by pzazz12 on 22 Oct 2010, 04:49. Last edited by Bunuel on 09 Oct 2012, 02:55, edited 1 time in total. Edited the question. ##### Most Helpful Expert Reply Math Expert V Joined: 02 Sep 2009 Posts: 65785 Re: In a small snack shop......... [#permalink] ### Show Tags 4 2 pzazz12 wrote: 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

The average revenue was $400 per day over a 10-day period --> total revenue over 10-day period is 10*$400=$4,000; The average daily revenue was$360 for the first 6 days --> total revenue for the first 6 days is 6*$360=2,160; Total revenue for the last 4 days is$4,000-2,160=$1,840; Average daily revenue for the last 4 days is$1,840/4=$460. Answer: D. _________________ ##### Most Helpful Community Reply Intern  Joined: 17 Aug 2010 Posts: 48 Re: In a small snack shop......... [#permalink] ### Show Tags 5 pzazz12 wrote: 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

D. $460 is my answer. 400 = x/10 x = 4000 For first 6 days = 360 * 6 =$2160

therefore for the last 4 days revenue is $4000 -$2160 = 3840
hence, airthmatic mean = 3840/4 = $460 Please let me know the OA. Also, I am very bad in explaining things. I am waiting for Bunuel to respond. He is extremly good in explaining solution. ##### General Discussion Intern  Joined: 17 Aug 2010 Posts: 48 Re: In a small snack shop......... [#permalink] ### Show Tags 1 Like I said, what Bunuel says is OA for me. Intern  Joined: 30 Sep 2010 Posts: 1 Re: In a small snack shop......... [#permalink] ### Show Tags 1 I solved it in another way, but not sure whether its correct. Can some one help me by validating.. Let 'x' be the average daily revenue for last 4 days. [6(360)+4(x)]/10 = 400 solving, x = 460 Thanks in advance Intern  Joined: 15 Apr 2010 Posts: 36 Re: In a small snack shop......... [#permalink] ### Show Tags 3 1 weighted average total 10 days, avg10 of this period is 400 first 6 days avg6 is 360 which is deltaAvg6 = 40 away from the overall avg10 last 4 day avg4 must have more weight to pull the avg10 to 400 (if 5 days-5 days then last 5 must have 440 so that avg10 is pulled back to 400, but this is 6/4, so we know last 4 days avg must have much more weight, so avg4 > 440, eliminate few choices) since ratio of weight of 2 periods is 6/4 = 3/2, the avg4 must compensate for the loss of deltaAvg6 a 3/2 amount of deltaAvg6 so that the avg10 is pulled back to 400. therefore the last 4 days must have deltaAvg4 = 3/2 * deltaAvg6 = 3/2 * 40 = 60. so avg4 = 400 + deltaAvg4 = 400 + 60 = 460 --> D Director  Status: My Thread Master Bschool Threads-->Krannert(Purdue),WP Carey(Arizona),Foster(Uwashngton) Joined: 27 Jun 2011 Posts: 799 Re: In a small snack shop, the average (arithmetic mean) revenue [#permalink] ### Show Tags 460 400 x 10= 4000 360 x 6 = 2160 4000-2160 = 1840/4=460 Manager  B Joined: 13 Feb 2012 Posts: 126 Location: Italy Concentration: General Management, Entrepreneurship GMAT 1: 560 Q36 V34 GPA: 3.1 WE: Sales (Transportation) Re: In a small snack shop, the average (arithmetic mean) revenue [#permalink] ### Show Tags Bunuel's way of solving is definitely the most straight forward one; thanks! Intern  Joined: 24 Apr 2012 Posts: 44 Re: In a small snack shop, the average (arithmetic mean) revenue [#permalink] ### Show Tags Ans: the total revenue for 10 days is 10x400=4000 and the total revenue for first 6 days is 6x360=2160, so the average for last 4 days will be (4000-2160)/4 = 460 (D). Senior Manager  Joined: 23 Oct 2010 Posts: 312 Location: Azerbaijan Concentration: Finance Schools: HEC '15 (A) GMAT 1: 690 Q47 V38 Re: In a small snack shop, the average (arithmetic mean) revenue [#permalink] ### Show Tags (400-360)*6/4=60 400+60=460 _________________ Happy are those who dream dreams and are ready to pay the price to make them come true I am still on all gmat forums. msg me if you want to ask me smth Current Student B Joined: 10 Mar 2013 Posts: 448 Location: Germany Concentration: Finance, Entrepreneurship Schools: WHU MBA"20 (A$)
GMAT 1: 580 Q46 V24
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In a small snack shop, the average (arithmetic mean) revenue  [#permalink]

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I've solved it using weighted average formula:
So, 360 is 40 less then the average of 400 -> -40 * 6 Days; We have 4 Days and need to calculate the revenue =X

6*(-40) + 4*x=0
X=60, so it means that for the last 4 days the revenue was 60 above the average = 400+60 =460 (D)

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Manager  Joined: 26 Nov 2014
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In a small snack shop, the average (arithmetic mean) revenue  [#permalink]

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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?

Avg revenue per day = 400
Total revenue for 10 days = 4000

Avg Revenue for first 6 days = 360
Total revenue for first 6 days = 360 x 6 = 2160

Total revenue for 10 days = Total revenue for first 6 days + Total revenue for last 4 days
4000 = 2160 + X

X=1840, which is Total revenue for last 4 days

Avg revenue for last 4 days = $$\frac{1840}{4}$$ = 460.
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Re: In a small snack shop, the average (arithmetic mean) revenue  [#permalink]

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pzazz12 wrote:
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 This is a problem testing us on our knowledge of weighted averages. To solve, we can 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. 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

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In a small snack shop, the average (arithmetic mean) revenue  [#permalink]

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pzazz12 wrote:
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 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 =$460

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Re: In a small snack shop, the average (arithmetic mean) revenue  [#permalink]

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pzazz12 wrote:
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 Total revenue for 10 days= 400*10= 4000 Total revenue for 6 days= 360*6= 2160 Thus the total revenue for remaining 4 days would be 4000-2160=1840 The average revenue for 4 days= 1840/4= 460 Manager  G Joined: 09 Jan 2016 Posts: 97 GPA: 3.4 WE: General Management (Human Resources) Re: In a small snack shop, the average (arithmetic mean) revenue [#permalink] ### Show Tags pzazz12 wrote: 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

Total revenue 400* 10 = 4000
first 6 days = 360 *6 = 2160
rest of the four days = 1840
4x = 1840
X= 360
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Re: In a small snack shop, the average (arithmetic mean) revenue  [#permalink]

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The below is another method(easier)
400-360 = 40
for 6 days 40*6 = 240
this 240 need to be divide by remaining 4 days = 60
60 need to added to the average = 400+60 = 460
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Joined: 31 Oct 2016
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Re: In a small snack shop, the average (arithmetic mean) revenue  [#permalink]

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360*6 +4x= 400*10
4x= 1840
x= 460
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Re: In a small snack shop, the average (arithmetic mean) revenue  [#permalink]

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Hi All,

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.

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Re: In a small snack shop, the average (arithmetic mean) revenue  [#permalink]

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Hello,

To avoid calculations we can use deviation method

400=360+(4x/10)
4x= 400
x= 100
=360+100= 460
hence option D
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~You Just Can't beat the person who never gives up~ Babe Ruth Re: In a small snack shop, the average (arithmetic mean) revenue   [#permalink] 17 Aug 2018, 11:30

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