priyankaparanjape wrote:
$686,000 in bonus money is to be divided among 6 employees. No employee is to receive a bonus more than 20% greater than the bonus received by any other employee. What is the minimum possible bonus that an employee can receive?
A. $96,000
B. $97,000
C. $98,000
D. $99,000
E. $100,000
I often struggle with such questions. I can understand that for minimum value , we need to consider highest salary 20%, however I cannot understand how to put other 4 intermediate values. When I read the explanation I understand, but do not seem to apply it while solving. Can someone pls help in how to think through such problems.
Thanks.
Since "no employee is to receive a bonus more than 20% greater than the bonus received by any other employee", then the bonuses of 6 employees must be in the range: \($x\) and \($1.2x\).
So we want to minimize \(x\). To minimize \(x\) we should make
only one employee to receive that bonus (minimum possible) and the
rest 5 employees to receive \(1.2x\) bonus (maximum possible).
\(x+5*1.2x=686\) --> \(7x=686\) --> \(x=98\).
Answer: C.
General rule for such kind of problems: to maximize one quantity, minimize the others;
to minimize one quantity, maximize the others.
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