A certain movie star's salary for each film she makes consists of a fixed amount, along with a percentage of the gross revenue the film generates. In her last two roles, the star made $32 million on a film that grossed $100 million, and $24 million on a film that grossed $60 million. If the star wants to make at least $40 million on her next film, what is the minimum amount of gross revenue the film must generate?
A)$110 million
B)$120 million
C)$130 million
D)$140 million
E)$150 million
OAD
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
Salary
This topic has expert replies
-
j_shreyans
- Legendary Member
- Posts: 510
- Joined: Thu Aug 07, 2014 2:24 am
- Thanked: 3 times
- Followed by:5 members
GMAT/MBA Expert
-
[email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
Hi j_shreyans,
This question involves what's called "system math", which is an algebra concept. We need to translate the given prompt into a couple of algebra equations, then solve.
We're told that a total is based on a fixed amount + a percentage of a gross. From the two roles, we can create the following equations:
X = fixed amount
Y = % of the gross
X + Y%(100 million) = 32 million
X + Y%(60 million) = 24 million
We now have a "system" of equations (2 variables with 2 equations, so we CAN solve for X and Y).
Subtracting the second equation from the first gives us...
Y%(40 million) = 8 million
Y% = 8/40 = 1/5 = 20%
Y = 20
Plugging back into either equation, we get...
X = 20%(100 million) = 32 million
X = 12 million
With the value of X and Y, we can now answer the question: To make at least 40 million, the minimum gross revenue must be...
12 million + 20%(Z) = 40 million
20%(Z) = 28 million
Z = 140 million
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
This question involves what's called "system math", which is an algebra concept. We need to translate the given prompt into a couple of algebra equations, then solve.
We're told that a total is based on a fixed amount + a percentage of a gross. From the two roles, we can create the following equations:
X = fixed amount
Y = % of the gross
X + Y%(100 million) = 32 million
X + Y%(60 million) = 24 million
We now have a "system" of equations (2 variables with 2 equations, so we CAN solve for X and Y).
Subtracting the second equation from the first gives us...
Y%(40 million) = 8 million
Y% = 8/40 = 1/5 = 20%
Y = 20
Plugging back into either equation, we get...
X = 20%(100 million) = 32 million
X = 12 million
With the value of X and Y, we can now answer the question: To make at least 40 million, the minimum gross revenue must be...
12 million + 20%(Z) = 40 million
20%(Z) = 28 million
Z = 140 million
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
-
GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Let x= the film's gross revenue and y = star's salary.j_shreyans wrote:A certain movie star's salary for each film she makes consists of a fixed amount, along with a percentage of the gross revenue the film generates. In her last two roles, the star made $32 million on a film that grossed $100 million, and $24 million on a film that grossed $60 million. If the star wants to make at least $40 million on her next film, what is the minimum amount of gross revenue the film must generate?
A)$110 million
B)$120 million
C)$130 million
D)$140 million
E)$150 million
The formula for determining the star's salary is the same as the EQUATION OF A LINE:
y = mx + b.
In the equation above:
m = the percentage of the film's gross revenue.
b = the fixed amount.
When we INPUT the value of x (the film's gross), the OUTPUT is the value of y (the star's salary).
The star made $32 million on a film that grossed $100 million.
Thus, when x=100, y=32, implying that one point on the line is (100, 32).
The star made $24 million on a film that grossed $60 million.
Thus, when x=60, y=24, implying that a second point on the line is (60, 24).
Since m = (y₂-y�)/(x₂-x�), we get:
m = (32-24)/(100-60) = 8/40 = 1/5.
The star wants to make at least $40 million on her next film.
Thus, when x is equal to a certain value, y=40, implying that a third point on the line is (x, 40).
Since (x, 40) and (60, 24) are both on the line -- and (y₂-y�)/(x₂-x�) = 1/5 for any two points on the line -- we get:
(40-24)/(x-60) = 1/5
16/(x-60) = 1/5
80 = x-60
x = 140.
The correct answer is D.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
