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# The average wages of a worker during a fortnight comprising 15 consecu

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Math Expert
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The average wages of a worker during a fortnight comprising 15 consecu  [#permalink]

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13 Mar 2016, 12:44
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91% (01:32) correct 9% (02:16) wrong based on 48 sessions

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The average wages of a worker during a fortnight comprising 15 consecutive working days was $90 per day. During the first 7 days, his average wages was$87 per day and the average wages during the last 7 days was $92 per day. What was his wage on the 8th day? A.$83
B. $90 C.$92
D. $97 E.$104

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Re: The average wages of a worker during a fortnight comprising 15 consecu  [#permalink]

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13 Mar 2016, 19:37
Average daily wage of a worker for 15 consecutive working days = 90$During the first 7 days , the daily average daily wage = 87$
During the last 7 days , the daily average daily wage = 92$Wage on 8th day = 90*15 -( 87*7 + 92 *7) = 1350 - (609 + 644) =1350 - 1253 = 97 Answer D Alternatively , During the first 7 days , since the daily average daily wage = 87$
Amount by which sum of first 7 days varies from average for entire 15 days = -3*7 = -21

During the last 7 days , since the daily average daily wage = 92$Amount by which sum of last 7 days varies from average for entire 15 days = 2*7 = 14 Amount by which sums first 7 and last 7 days varies from average for entire 15 days = -21 +14 = -7 Therefore , in order to make average for entire 15 days to be 90 , the wage on 8th day needs to be = 90 + 7 = 97 Answer D _________________ When everything seems to be going against you, remember that the airplane takes off against the wind, not with it. - Henry Ford The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long Math Expert Joined: 02 Aug 2009 Posts: 8006 Re: The average wages of a worker during a fortnight comprising 15 consecu [#permalink] ### Show Tags 13 Mar 2016, 20:56 Bunuel wrote: The average wages of a worker during a fortnight comprising 15 consecutive working days was$90 per day. During the first 7 days, his average wages was $87 per day and the average wages during the last 7 days was$92 per day. What was his wage on the 8th day?

A. $83 B.$90
C. $92 D.$97
E. $104 Hi, Ofcourse calculation of averages and subtraction etc here is not very cumbersome.. But another approach which cuts down on calculations and could help in some other Q of same type with cumbersome calculations.. Solution- we are given averages for 7 days on either side.. the average of these 7+7 days can be easily found out as 92-87=5 so 5/2=2.5 from each number.. so average is 87+2.5= 89.5 for these 14 numbers.. 15th number increases this by 90-89.5=0.5.. so 15th number= the final average + increase required in other 14 numbers= 90+14*(90-89.5)=90+14*0.5=90+7=97 _________________ Director Joined: 17 Dec 2012 Posts: 626 Location: India Re: The average wages of a worker during a fortnight comprising 15 consecu [#permalink] ### Show Tags 13 Mar 2016, 21:12 Total wages = 15*90 -- (1) Total wages excluding the 8th day= 7(87+92) = 7*179-- (2) The difference between 1 and 2 should end in 7. Hence D. _________________ Srinivasan Vaidyaraman Sravna Test Prep http://www.sravnatestprep.com Holistic and Systematic Approach Manager Joined: 09 Jun 2015 Posts: 86 Re: The average wages of a worker during a fortnight comprising 15 consecu [#permalink] ### Show Tags 13 Mar 2016, 21:22 Bunuel wrote: The average wages of a worker during a fortnight comprising 15 consecutive working days was$90 per day. During the first 7 days, his average wages was $87 per day and the average wages during the last 7 days was$92 per day. What was his wage on the 8th day?

A. $83 B.$90
C. $92 D.$97
E. $104 First 7 days the worker gets$3 less than average and the last 7 days the worker gets $2 more than the average. Hence during these 14 days the net change is negative$7.
Therefore, on the 8th he has to get $97. Intern Joined: 16 Apr 2015 Posts: 31 Re: The average wages of a worker during a fortnight comprising 15 consecu [#permalink] ### Show Tags 14 Mar 2016, 12:00 Bunuel wrote: The average wages of a worker during a fortnight comprising 15 consecutive working days was$90 per day. During the first 7 days, his average wages was $87 per day and the average wages during the last 7 days was$92 per day. What was his wage on the 8th day?

A. $83 B.$90
C. $92 D.$97
E. $104 short cut only applicable for similar problem to save calculation time (in case we have tedious calc) => since total wage will be product of $$90 * 15$$ it will always end with 0, and 8th day wage =$$TOTAL - 1st 7day - last 7 days$$ or $$Total - (1st 7days + last 7 days)$$we can only do summation of products of Unit digits of 7 days and subtract the unit digit from 10, any option with that number is candidate answers. 1st 7 days = 7*7 = unit digit 9 last 7 days = 2*7 = unit digit 4 Unit digit of summation of these two = 3 So possible answer must end with 7 as unit digit, only possible answer is D Large method total 15 day of wages =>$$15*90 = 1350$$ 1st 7 days wages =>$$7*87 = 609$$ last 7 days of wages =>$$7*92 = 644$$ 8th day wage => $$1350 - 609 - 644 = 97$$ EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 15309 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: The average wages of a worker during a fortnight comprising 15 consecu [#permalink] ### Show Tags 04 Jan 2018, 16:46 Hi All, We're told that the average pay a worker received for 15 consecutives working days was$90 per day. During the first 7 days, his average wages was $87 per day and the average wages during the last 7 days was$92 per day. We're asked for his wage on the 8th day.

There are a number of different ways to approach the 'math' in this question. Here's an approach that allows you to avoid a lot of 'step-heavy' math and focus on the 'relationships' between the numbers.

Since the average pay was $90/day, we can track how much 'below average' or 'above average' the individual days are... -For the first 7 days, the average pay was$87/day, thus each of those days was $3 BELOW the average... meaning that we're (7)($3) = $21 'below' in total here. -For the last 7 days, the average pay was$92/day, thus each of those days was $2 ABOVE the average... meaning that we're (7)($2) = $14 'above' in total here. With those 14 days, we're a total of '$7 below' what the average is supposed to be, so that final day (the 8th day) has to make up for that difference...

8th day = $90 +$7 = \$97

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Re: The average wages of a worker during a fortnight comprising 15 consecu   [#permalink] 04 Jan 2018, 16:46
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