varun289 wrote:At the end of the year, the six members of the board of directors of a large computer company each receive a different number of the twelve shares of an executive bonus package. The total amount of the bonus is equal to the average of 1.5% of the company's net profit and 5 times the number of computers sold. If the Chief Technology Officer receives 2 shares of the bonus and was paid $1.65 million in bonus money at the end of a year when the company sold 2.6 million computers, what was the company's net profit for that year?
$6.8 million
$453 million
$906 million
$1,147 million
$2,293 million
To avoid tedious math, BALLPARK and use the answer choices, which represent the net profit.
CTO's shares/total shares = 2/12 = 1/6.
Thus, the 1.65 million received by the CTO is equal to 1/6 of the total bonus:
1.65 = (1/6)T.
T = 6(1.65) ≈ 10 million.
Since 2.6 million computers were sold, 5 times the number of computers = 5(2.6) = 13 million.
Since the bonus of 10 million is the AVERAGE of 13 million and 1.5% of the net profit, 10 million must be HALFWAY between 13 million and 1.5% of the net profit.
Thus, 1.5% of the correct answer choice must yield a value around 7 million.
Since (.015)(400) = 6 million, the only viable answer choice is 453 million.
The correct answer is
B.
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