The monthly performance bonus of a salesman depends...

This topic has expert replies
Legendary Member
Posts: 2218
Joined: Sun Oct 29, 2017 2:04 pm
Followed by:6 members
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.

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3008
Joined: Mon Aug 22, 2016 6:19 am
Location: Grand Central / New York
Thanked: 470 times
Followed by:34 members

by Jay@ManhattanReview » Thu Nov 09, 2017 9:40 pm
swerve wrote: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
_________________
Manhattan Review GMAT Prep

Locations: New York | Singapore | Doha | Lausanne | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.