'Average' problem
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 neelgandham
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Sam earned a $2,000 commission on a big sale, raising his average commission by $100. If Sam's new average commission is $900, how many sales has he made?
Let total number of sales prior to the big sale be S and
the average commission prior to the big sale be A
Total commission earned prior to the big sale = A*S
Total commission earned after the big sale = A*S + 2000
Total number of sales including the big sale = S+1
Question can be rephrased to What is the value of S+1 ?
900 = Average commission prior to the big sale + 100 = A+100
Implies A = 800
Average commission after the big sale be A = Total commission earned after the big sale/Total number of sales including the big sale
=> (A*S + 2000) / (S+1) = 900
=> (800S + 2000)/(S+1) = 900
=> 800S + 2000 = 900S + 900
=> 100S = 1100
=> S = 11
S+1 = 12 = Total number of sales he made !
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Let total number of sales prior to the big sale be S and
the average commission prior to the big sale be A
Total commission earned prior to the big sale = A*S
Total commission earned after the big sale = A*S + 2000
Total number of sales including the big sale = S+1
Question can be rephrased to What is the value of S+1 ?
900 = Average commission prior to the big sale + 100 = A+100
Implies A = 800
Average commission after the big sale be A = Total commission earned after the big sale/Total number of sales including the big sale
=> (A*S + 2000) / (S+1) = 900
=> (800S + 2000)/(S+1) = 900
=> 800S + 2000 = 900S + 900
=> 100S = 1100
=> S = 11
S+1 = 12 = Total number of sales he made !
p.s: For quick responses,
Please post PS questions here: https://www.beatthegmat.com/problemsolvingf6.html
Please post DS questions here: https://www.beatthegmat.com/datasufficiencyf7.html
Anil Gandham
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You could also do this using allegations.
New commission = Old + 100 = 900.
Old = 800. Resultant = 900 and Addition is 2000. ( 8 and 20 mixed to give 9)
So, (209) / (98) = 11/1. ( 11 of 8 and 1 of 20)
So, 11 + 1= 12 commissions.
New commission = Old + 100 = 900.
Old = 800. Resultant = 900 and Addition is 2000. ( 8 and 20 mixed to give 9)
So, (209) / (98) = 11/1. ( 11 of 8 and 1 of 20)
So, 11 + 1= 12 commissions.
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Solution:
Since his new average commission is $900, his old average commission must be $800. We can create the equation where n is the number of sales Sam has made before the big sale.
(800n + 2000) / (n + 1) = 900
800n + 2000 = 900n + 900
1100 = 100n
11 = n
Including the big sale, Sam has made 12 sales.
Answer: 12
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