Problem Solving

This is from the GMATPrep:

The original price of a TV is discounted by X percent, and then reduced further by 2X percent. If P is the original price of the TV, which of the following represents the price of the TV after both discounts are applied?

A) P(1-.03X + .02X^2)
B) P(1-.03X + .0002X^2)
C) P(1-.03X + .002X^2)
D) P(1-2X^2)
E) P(1-3X+2X^2)

OA is B

My problem though is in the answer explanation:

It says as follows:

After the first discount the price of the TV was P(1-.01X)
And after the second discount the price was P(1-.01X)[1-(.01X)(2X)]

Then it goes on to expand and solve. My question is:

Why for the first reduction do we take X percent as ".01X" and then the during the second reduction take 2X percent as "2X"? SHouldn't it be .02X?

Thanks!

joshhowatt wrote:This is from the GMATPrep:

The original price of a TV is discounted by X percent, and then reduced further by 2X percent. If P is the original price of the TV, which of the following represents the price of the TV after both discounts are applied?

A) P(1-.03X + .02X^2)
B) P(1-.03X + .0002X^2)
C) P(1-.03X + .002X^2)
D) P(1-2X^2)
E) P(1-3X+2X^2)

OA is B

Let P = 100
Let X = 10.
Price after the first discount of 10% = 90.
Price after the second discount of 20% = 90 - 18 = 72. This is our target.

Now we plug P=100 and X=10 into the answers to see which yields our target of 72.
Only answer choice B works:
P(1 -. 03X + .0002X²) = 100(1 - (3/100)(10) + (2/10�)(10²)) = 100 - 30 + 2 = 72.

The correct answer is B.

joshhowatt wrote:This is from the GMATPrep:


My problem though is in the answer explanation:

It says as follows:

After the first discount the price of the TV was P(1-.01X)
And after the second discount the price was P(1-.01X)[1-(.01X)(2X)]

Then it goes on to expand and solve. My question is:

Why for the first reduction do we take X percent as ".01X" and then the during the second reduction take 2X percent as "2X"? SHouldn't it be .02X?

Thanks!

Hi joshhowatt:

Your thinking is correct.
If the first one is a reduction by x% , then price after that = P(1-x%)= P(1-0.01x)
Also, after the second reduction by 2x%, the price will be P(1-x%)(1-(2x)%) = P(1-0.01x)(1-0.02x)
When you expand P(1-0.01x)(1-0.02x) it indeed gives P(1-0.03x+0.0002x^2) which is the correct answer.

Let me know if this helps

Hi Mitch,
Which approach do you suggest...solving it algebraically or putting in number as you did.
I am more used to algebra than plugging in numbers.
But I think number plugging might be faster with some practice.

Thanks

GMATGuruNY wrote:

joshhowatt wrote:This is from the GMATPrep:

The original price of a TV is discounted by X percent, and then reduced further by 2X percent. If P is the original price of the TV, which of the following represents the price of the TV after both discounts are applied?

A) P(1-.03X + .02X^2)
B) P(1-.03X + .0002X^2)
C) P(1-.03X + .002X^2)
D) P(1-2X^2)
E) P(1-3X+2X^2)

OA is B

Let P = 100
Let X = 10.
Price after the first discount of 10% = 90.
Price after the second discount of 20% = 90 - 18 = 72. This is our target.

Now we plug P=100 and X=10 into the answers to see which yields our target of 72.
Only answer choice B works:
P(1 -. 03X + .0002X²) = 100(1 - (3/100)(10) + (2/10�)(10²)) = 100 - 30 + 2 = 72.

The correct answer is B.