A certain movie star's salary for each film she makes consis

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alanforde800Maximus: Master | Next Rank: 500 Posts; Posts: 187; Joined: Tue Sep 13, 2016 12:46 am

by alanforde800Maximus » Sat Aug 04, 2018 1:31 am

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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

I was wondering if we can deploy number plugging approach in this question as all answer choices are evenly spread.

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Source: Beat The GMAT — Problem Solving | Sat Aug 04, 2018 1:31 am

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by Brent@GMATPrepNow » Sat Aug 04, 2018 6:59 am

alanforde800Maximus 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

Let F = the fixed amount the star receives for a movie
Let p = the percentage of the gross revenue the star receives for a movie

The star made $32 million on a film that grossed $100 million
So, we can write: F + (p/100)(100) = 32 [we'll assume that 100 and 32 represent 100 million and 32 million]

The star made $24 million on a film that grossed $60 million
So, we can write: F + (p/100)(60) = 24

We now have:
F + (p/100)(100) = 32
F + (p/100)(60) = 24

Subtract the bottom equation from the top equation to get: (p/100)(100) - (p/100)(60) = 8
Factor to get: (p/100)[100 - 60] = 8
Simplify to get: (p/100)[40] = 8
Multiply both sides by 100 to get: 40p = 800
Solve: p = 20

Now that we know the value of p, we can find the value of F
Take F + (p/100)(100) = 32 and replace p with 20 to get: F + (20/100)(100) = 32
Simplify: F + 20 = 32
So, F = 12

So, the star receives 12 million (fixed) PLUS 20% of the gross revenue

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?
Let x = gross revenue the film must generate
We can write: 12 + 20% of x = 40
Rewrite as: 12 + 0.2x = 40
Subtract 12 from both sides: 0.2x = 28
Solve: x = 140 (million)

Answer: D

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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swerve: Legendary Member; Posts: 2545; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Sat Aug 04, 2018 11:23 am

Let x be fixed income.
Let y be the % of variable income.

x + (y/100)*100 = 32
x + (y/100)*60 = 24

So, we get x = 12 and y = 20%

Then, x + 0.2(required revenue) = 40. We get required revenue = 140 million dollars.

Hence, the correct answer is the option D. Regards!

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by Scott@TargetTestPrep » Tue Apr 23, 2019 6:34 pm

alanforde800Maximus 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

We can let x = the fixed amount, in millions, the movie star receives and n/100 = the percentage of the gross revenue from the film that she receives. Therefore, we can create the equations:

32 = x + n/100(100)

32 = x + n

32 - n = x

and

24 = x + n/100(60)

24 = x + 3n/5

Substituting, we have:

24 = 32 - n + 3n/5

-8 = -2n/5

-40 = -2n

20 = n

So x is 32 - 20 = 12.

Thus, we see that she earns a fixed amount of $12 million and 20% of the film's gross revenue.

Let's determine the gross revenue for a film that allows the movie star to earn 40 million.

40 = 12 + (1/5)(m)

28 = m/5

140 = m

Answer: D

Scott Woodbury-Stewart
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[email protected]

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by [email protected] » Wed Apr 24, 2019 11:36 am

Hi All,

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% of (100 million) = 32 million
X + Y% of (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% of (40 million) = 8 million
Y% = 8/40 = 1/5 = 20%
Y = 20

Plugging back into either equation, we get...

X+ 20% of (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% of (Z) = 40 million
20% of (Z) = 28 million
Z = 140 million

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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