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The original price of a certain Television set is discounted

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The original price of a certain Television set is discounted

by alanforde800Maximus » Thu May 10, 2018 1:07 am

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The original price of a certain Television set is discounted by x percent, and the reduced price is then discounted by 2x percent. If P is the original price of the television Set, which of the following represents the price of the television set after the two successive discounts?

A: P(1 - 0.03x + 0.02x^2)
B: P(1 - 0.03x + 0.0002x^2)
C: P(1 - 0.3x + 0.002x^2)
D: P(1 - 2x^2)
E: P(1 - 3x + 2x^2)

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by GMATGuruNY » Thu May 10, 2018 2:46 am
alanforde800Maximus wrote:The original price of a certain Television set is discounted by x percent, and the reduced price is then discounted by 2x percent. If P is the original price of the television Set, which of the following represents the price of the television set after the two successive discounts?

A: P(1 - 0.03x + 0.02x^2)
B: P(1 - 0.03x + 0.0002x^2)
C: P(1 - 0.3x + 0.002x^2)
D: P(1 - 2x^2)
E: P(1 - 3x + 2x^2)
Let P = 100 and x = 10, implying that 2x = 20.
Price after an x% discount = 100 - (10% of 100) = 100 - 10 = 90.
Price after a 2x% discount = 90 - (20% of 90) = 90 - 18 = 72.

The correct answer must yield a resulting price of $72 when x=10.
Only B works:
100(1 - 0.03*10 + 0.0002*10²) = 100(1 - 0.3 + 0.02) = 100(0.72) = 72.

The correct answer is B.
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by swerve » Thu May 10, 2018 10:42 am
You can solve this problem with number plugging.

Say the original price was $10 and x = 50. Then after the first reduction, the price would become $5 and after the second reduction of 2*50 = 100%, the price would become $0.

Now, since P is not zero, then the expression in the brackets must be must be zero for x = 50. Only answer choice B works.

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by Scott@TargetTestPrep » Sun May 13, 2018 5:01 pm
alanforde800Maximus wrote:The original price of a certain Television set is discounted by x percent, and the reduced price is then discounted by 2x percent. If P is the original price of the television Set, which of the following represents the price of the television set after the two successive discounts?

A: P(1 - 0.03x + 0.02x^2)
B: P(1 - 0.03x + 0.0002x^2)
C: P(1 - 0.3x + 0.002x^2)
D: P(1 - 2x^2)
E: P(1 - 3x + 2x^2)
We can create the expression:

P(1 - x/100)(1 - 2x/100)

P(1 - 3x/100 + 2x^2/10000)

P(1 - 0.03x + 0.0002x^2)

Answer: B

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