Discount of a TV

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joshhowatt: Junior | Next Rank: 30 Posts; Posts: 18; Joined: Mon Mar 19, 2012 12:53 pm

by joshhowatt » Thu Jun 07, 2012 3:52 pm

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!

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Source: Beat The GMAT — Problem Solving | Thu Jun 07, 2012 3:52 pm

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Thu Jun 07, 2012 6:33 pm

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 + .0002XÂ²) = 100(1 - (3/100)(10) + (2/10â�´)(10Â²)) = 100 - 30 + 2 = 72.

The correct answer is B.

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eagleeye: Legendary Member; Posts: 520; Joined: Sat Apr 28, 2012 9:12 pmFollowed by: 49 members; Thanked: 339 times; GMAT Score:770

by eagleeye » Thu Jun 07, 2012 7:32 pm

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

Last edited by eagleeye on Fri Jun 08, 2012 2:59 am, edited 1 time in total.

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1947: Master | Next Rank: 500 Posts; Posts: 215; Joined: Sat Jun 14, 2008 4:24 pmFollowed by: 1 member; Thanked: 13 times

by 1947 » Thu Jun 07, 2012 10:01 pm

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 + .0002XÂ²) = 100(1 - (3/100)(10) + (2/10â�´)(10Â²)) = 100 - 30 + 2 = 72.

The correct answer is B.

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