Problem Solving

LUANDATO wrote:John, Steve, and Mary are buying a car with a list price of $24,000. John contributes three times as much as Steve, who contributes half as much as Mary. At the dealership, the trio buys the car and receives a 15% rebate. If they split the rebate funds proportional to each person's initial investment, how much more money does John receive back compared to Mary?

A. $400
B. $600
C. $1,200
D. $1,800
E. $3,600

The OA is B.

I need help with this PS question. Can any expert explain it please? Thanks.

Say Steve contributes $x, thus John contributes $3x, and Mary contributes $2x.

Total share = 3x + x + 2x = $6x

Rebate received = 15% of $24000 = $(15/100)*24000 = 15*240

On the ratio scale, John received back 3x - 2x = x more money compared to Mary.

Thus, the more money John received back compared to Mary = (x/6x)*(15*240) = $600.

The correct answer: B

Hope this helps!

-Jay

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Hi LUANDATO,

We're told that John, Steve, and Mary are joining up to buy a car with a list price of $24,000 and receives a 15% rebate. John contributes three times as much as Steve, who contributes half as much as Mary. They split the rebate funds proportional to each person's initial investment. We're asked how much MORE money does John receive back than Mary.

To start, we need to determine what fraction of the purchase price each person contributed. It might help to TEST VALUES to determine those fractions.

Since John contributed THREE TIMES as much as Steve....
For every $1 that Steve contributes....
John contributes $3.

We also know that Steve contributed HALF as much as Mary...
For every $1 that Steve contributes....
Mary contributes $2.

Thus, for every $6 contributed, John gave $3, Steve gave $1 and Mary gave $2.....
John gives $3/$6 = 1/2 of the money
Steve gives $1/$6 = 1/6 of the money
Mary gives $2/$6 = 1/3 of the money

Since the rebate is 15% of the $24,000, the rebate is (.15)($24,000) = $3600
John receives (1/2)($3600) = $1800
Mary receives (1/3)($3600) = $1200
The difference is $1800 - $1200 = $600

Final Answer: B

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