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On 3 sales Tom has received commissions of $250, $95, and $175, and ha

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On 3 sales Tom has received commissions of $250, $95, and $175, and ha  [#permalink]

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New post 27 Dec 2017, 01:10
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On 3 sales Tom has received commissions of $250, $95, and $175, and has two additional sales pending. If Tom is to receive an average (arithmetic mean) commission of exactly $150 on the 5 sales, then the average (arithmetic mean) of the final two sales must be

A. 60
B. 80
C. 115
D. 230
E. 280

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Re: On 3 sales Tom has received commissions of $250, $95, and $175, and ha  [#permalink]

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New post 27 Dec 2017, 01:58
Bunuel wrote:
On 3 sales Tom has received commissions of $250, $95, and $175, and has two additional sales pending. If Tom is to receive an average (arithmetic mean) commission of exactly $150 on the 5 sales, then the average (arithmetic mean) of the final two sales must be

A. 60
B. 80
C. 115
D. 230
E. 280


We'll take a shortcut to calculation based on properties of the average.
This is a Logical approach.

Our target is to find two numbers that combine with $250, $95, $175 to give an average of $150.
These three numbers have a difference of 100, -55, 25 from 150 for a combined difference of 100-55+25=70.
So our remaining two numbers need to compensate for this with -70, which is -70/2 = -35 each.
Therefore they must have an average of 150 - 35 = 115.
(C) is our answer.

Note that the calculations here involve much smaller numbers than \(\frac{(150*5 - (250+175+95))}{2}\) which is the straightforward, Precise, approach.
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Re: On 3 sales Tom has received commissions of $250, $95, and $175, and ha  [#permalink]

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New post 27 Dec 2017, 11:34
Bunuel wrote:
On 3 sales Tom has received commissions of $250, $95, and $175, and has two additional sales pending. If Tom is to receive an average (arithmetic mean) commission of exactly $150 on the 5 sales, then the average (arithmetic mean) of the final two sales must be

A. 60
B. 80
C. 115
D. 230
E. 280


\(250 + 95 + 175 + x + y = 150*5\)

Or, \(520 + ( x + y ) = 750\)

Or, ( x + y ) = \(230\)

So, Average from the 2 additional sales must be \(\frac{230}{2} = 115\)

Thus, answer will be (C) 115
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Re: On 3 sales Tom has received commissions of $250, $95, and $175, and ha  [#permalink]

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New post 28 Dec 2017, 03:33
Bunuel wrote:
On 3 sales Tom has received commissions of $250, $95, and $175, and has two additional sales pending. If Tom is to receive an average (arithmetic mean) commission of exactly $150 on the 5 sales, then the average (arithmetic mean) of the final two sales must be

A. 60
B. 80
C. 115
D. 230
E. 280


\(Average=\frac{Total.Sales}{Number.Sales}\), and 2 more sales = \(2x\)

So \(150=\frac{(250+95+175+2x)}{5}\), \(150(5)=(520+2x)\), \(x=\frac{750-520}{2}=115\)

(C) is the answer.
Re: On 3 sales Tom has received commissions of $250, $95, and $175, and ha &nbs [#permalink] 28 Dec 2017, 03:33
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