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Sam earned a $2,000 commission on a big sale, raising his average comm

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Sam earned a $2,000 commission on a big sale, raising his average comm  [#permalink]

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New post 08 Jan 2019, 09:10
3
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

75% (01:58) correct 25% (01:57) wrong based on 58 sessions

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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?

a) 12
b) 13
c) 15
d) 21
e) 8

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Sam earned a $2,000 commission on a big sale, raising his average comm  [#permalink]

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New post 08 Jan 2019, 10:16
Okay, So we need to consider a few variables here:

Total Sales = Ts
Total commission (before $2000) =T1


New Average Commission = 900 = \(\frac{T1+2000}{Ts}\) = Old Average Commission + 100 ------ (According to the question)
Old Average Commission =\(\frac{T1}{(Ts-1)}\)

Therefore we have 2 equations now

900 = \(\frac{T1+2000}{Ts}\) ----- (i)
900 = \(\frac{T1}{(Ts-1)}\) + 100 -----(ii)

Simplifying them..

900xTs = T1 + 2000 ----- (i)
800xTs = T1 + 800 -----(ii)

Subtracting eq(ii) from eq(i), we eliminate T1

We get, Ts = 12;

ANSWER: (A) 12
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Re: Sam earned a $2,000 commission on a big sale, raising his average comm  [#permalink]

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New post 08 Jan 2019, 20:25
An alternative solution,
Let, total sales before=s
Then, total revenue=800s
New average,900= (800s+2000)/(s+1)
Solve for, s= 11
Total sale=11+1 (new sale)=12 (Answer)
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Re: Sam earned a $2,000 commission on a big sale, raising his average comm  [#permalink]

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New post 08 Jan 2019, 22:17
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CLIMBTHELADDER wrote:
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?

a) 12
b) 13
c) 15
d) 21
e) 8


By Rule of Alligations :

\(\frac{n_1}{n_2}\) = \(\frac{(A_2-A)}{(A-A_1)}\)

Here, \(n_1\) is unknown, \(n_2\) = 1, \(A_2\) = 2000, \(A_1\) = 800, and A = 900

\(\frac{n_1}{1}\)= \(\frac{(2000-900)}{(900-800)}\)

\(n_1\) =11

So, total number of Sales = \(n_1 + n_2\) = 11 + 1 = 12

Choice A
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Re: MGMAT problem   [#permalink] 15 Mar 2019, 21:24
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