The monthly performance bonus of a salesman depends...

[swerve]

The monthly performance bonus of a salesman depends on the number of units of a product sold by him in a particular month. Till he sells 10 units of the product, the amount of his monthly performance bonus is given by the formula ax^2+ax, where x is the number of units sold, x ≤ 10 and a is a positive number. If he sells more than 10 units, he gets an added bonus equivalent to ab^2+50b, where b is the number of additional units sold. If the salesman sells 28 units in the month of June, how much will he receive as his monthly performance bonus?

(1) Had the salesmman sold 5 units he would have received a bonus of $300.
(2) Had the salesman sold 15 units he would have received an added bonus of $500.

The OA is D.

I'm really confused with this DS question. Please, can any expert assist me with it? Thanks in advanced.

[Jay@ManhattanReview]

The monthly performance bonus of a salesman depends on the number of units of a product sold by him in a particular month. Till he sells 10 units of the product, the amount of his monthly performance bonus is given by the formula ax^2+ax, where x is the number of units sold, x ≤ 10 and a is a positive number. If he sells more than 10 units, he gets an added bonus equivalent to ab^2+50b, where b is the number of additional units sold. If the salesman sells 28 units in the month of June, how much will he receive as his monthly performance bonus?

(1) Had the salesmman sold 5 units he would have received a bonus of $300.
(2) Had the salesman sold 15 units he would have received an added bonus of $500.

The OA is D.

I'm really confused with this DS question. Please, can any expert assist me with it? Thanks in advanced.

We have the performance bonus criterion as follows.

1. If the number of units sold x ≤ 10, then the performance bonus = ax^2 + ax. Since the number of units sold = 28 > 10, the performance bonus for the first 10 units = ax^2 + ax = a.10^2 + a.10 = 100a + 10 a = 110a

2. If the number of units sold > 10, then the performance bonus = ab^2 + 50b, where b is the number of additional units sold.
The performance bonus for the additional 18 (= 28 - 10) units = a.18^2 + 50.18 = 324a + 900

Total performance bonus = 110a + 324a + 900 = 434a + 900

Question rephrased: What's the value of a?

(1) Had the salesman sold 5 units he would have received a bonus of $300.

The performance bonus for 5 (< 10) units = ax^2 + ax = a.5^2 + a.5 = 25a + 5a = 30 a = 300 => a = 10. Sufficient.

(2) Had the salesman sold 15 units he would have received an added bonus of $500.

Additiona performance bonus (number of units sold > 10) = ab^2 + 50b = a.(15 - 10)^2 + 50.(15 - 10) = 25a + 250 => 25a + 250 = 500 => 25a = 250 => a = 10. Sufficient.

The correct answer: D

Hope this helps!

-Jay
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