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# The original price of a certain TV set is discounted by x

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Intern
Joined: 28 Oct 2012
Posts: 15
The original price of a certain TV set is discounted by x [#permalink]

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Updated on: 29 Oct 2012, 02:27
1
15
00:00

Difficulty:

55% (hard)

Question Stats:

66% (01:19) correct 34% (01:41) wrong based on 337 sessions

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The original price of a certain TV set is discounted by x percent, and the reduced price is then discounted by 2x percent. If P is the original price of the TV 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 - 0.03x + 0.002x^2)
D: P(1 - 2x^2)
E: P(1 - 3x + 2x^2)

Question Code is QPS05959

Originally posted by clarkkent0610 on 28 Oct 2012, 12:05.
Last edited by Bunuel on 29 Oct 2012, 02:27, edited 1 time in total.
Renamed the topic and edited the question.
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Posts: 3416
Re: Problem from GMATPrep Question Pack 1 [#permalink]

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28 Oct 2012, 16:43
2
2
is difficult as problem and in this case picking numbers lead to something even harder

use percent change formula ( 1 - x/100) or ( 1 + x/100)

Follow the problem step by step

Now P have 2 % decrease consecutive

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

Multiply

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

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

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

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Posts: 46146
Re: The original price of a certain TV set is discounted by x [#permalink]

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29 Oct 2012, 02:31
2
clarkkent0610 wrote:
The original price of a certain TV set is discounted by x percent, and the reduced price is then discounted by 2x percent. If P is the original price of the TV 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 - 0.03x + 0.002x^2)
D: P(1 - 2x^2)
E: P(1 - 3x + 2x^2)

Question Code is QPS05959

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 rprice would become $0. Now, since P is not zero, then the expression in the brackets must be zero for x=50. Only answer choice B works. Answer: B. Hope it's clear. _________________ Intern Joined: 25 May 2014 Posts: 3 Concentration: Healthcare, General Management GPA: 3.61 WE: Operations (Health Care) Re: The original price of a certain TV set is discounted by x [#permalink] ### Show Tags 30 May 2014, 17:23 Bunuel wrote: clarkkent0610 wrote: The original price of a certain TV set is discounted by x percent, and the reduced price is then discounted by 2x percent. If P is the original price of the TV 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 - 0.03x + 0.002x^2) D: P(1 - 2x^2) E: P(1 - 3x + 2x^2) Question Code is QPS05959 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 rprice would become$0.

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

Hope it's clear.

On this problem - number pluggin is not giving me the answer.. I initially used x = 10, then 2x = 20 and P = 100. Answer should after both consecutive discounts = 72. I plug in the respective values and I keep getting 68. Can you double check my math.

100 (1-0.03(10) + 0.0002 (10)^2)
100 (1-0.3 + 0.0002 (100))
100 (0.7 + 0.02)
100 (0.68) = 68????

double check my math. Am I missing something? I also plugged in your numbers and still did not get zero as final answer with choice B..
Intern
Joined: 01 May 2013
Posts: 5
Schools: ISB '16
Re: The original price of a certain TV set is discounted by x [#permalink]

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30 May 2014, 20:51
P(1 - x/100)*(1 - 2x/100) = P(1 - 0.03x - 0.0002x^2), Option B)
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Joined: 20 Dec 2013
Posts: 123
Re: The original price of a certain TV set is discounted by x [#permalink]

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30 May 2014, 22:27
clarkkent0610 wrote:
The original price of a certain TV set is discounted by x percent, and the reduced price is then discounted by 2x percent. If P is the original price of the TV 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 - 0.03x + 0.002x^2)
D: P(1 - 2x^2)
E: P(1 - 3x + 2x^2)

Question Code is QPS05959

Simply plug in:
Let us say that P = 100 $and x = 10 % Now if there are two successive discounts of 10 % and 20 % then the effective discount percentage will be -10 - 20 + (-10) (-20)/100 = -30 + 2 = 28 % Hence the new price will be 100 - 28 = 72 Hence by plugging in P = 100 and x = 10 the answer should be 72 A: P(1 - 0.03x + 0.02x^2) = 100 (1 - 0.3 + 2) = 100(2.7) B: P(1 - 0.03x + 0.0002x^2) = 100 (1 - 0.3 + 0.02) = 100 (1 - 0.28) = 72 (BINGO!) (Lets still eliminate all other answer options - what if another one gives me 72) C: P(1 - 0.03x + 0.002x^2) = 100 (1 - 0.3 + 0.2) D: P(1 - 2x^2) = 100 ( 1 - 200) E: P(1 - 3x + 2x^2) = 100 ( 1 - 0.2 + 200) Hence the answer is B _________________ 76000 Subscribers, 7 million minutes of learning delivered and 5.6 million video views Perfect Scores http://perfectscores.org http://www.youtube.com/perfectscores Math Expert Joined: 02 Sep 2009 Posts: 46146 Re: The original price of a certain TV set is discounted by x [#permalink] ### Show Tags 31 May 2014, 04:13 anyibuofu wrote: Bunuel wrote: clarkkent0610 wrote: The original price of a certain TV set is discounted by x percent, and the reduced price is then discounted by 2x percent. If P is the original price of the TV 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 - 0.03x + 0.002x^2) D: P(1 - 2x^2) E: P(1 - 3x + 2x^2) Question Code is QPS05959 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 rprice would become$0.

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

Hope it's clear.

On this problem - number pluggin is not giving me the answer.. I initially used x = 10, then 2x = 20 and P = 100. Answer should after both consecutive discounts = 72. I plug in the respective values and I keep getting 68. Can you double check my math.

100 (1-0.03(10) + 0.0002 (10)^2)
100 (1-0.3 + 0.0002 (100))
100 (0.7 + 0.02)
100 (0.68) = 68????

double check my math. Am I missing something? I also plugged in your numbers and still did not get zero as final answer with choice B..

100(0.7 + 0.02) = 100(0.72) = 72.

Plugging the numbers from my solution:
10(1 - 0.03*50 + 0.0002*2500) = 10(1 - 1.5 + 0.5) = 10*0 = 0.

Hope it helps.
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GMAT 1: 600 Q41 V31
The original price of a certain TV set is discounted by x [#permalink]

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04 Sep 2015, 12:48
Although bunuel's way of taking discounts that amount to 0 as final price is much more intelligent way to solving this question, this is how I solved it

discount 1 - x%
discount 2 - 2x%

Successive discounts ->
=> $$-x -2x + [(-x * -2x)/100]$$
=> $$-3x - 0.02x^2 = -(3x + 0.02x^2)$$or which is nothing but a discount of $$3x + 0.02x^2$$
Now, while we may calculate
$$P - P(3x + 0.02x^2)/100$$

we know that the discount will have an additional power of 10^-2 making the figures look like $$0.03$$ and $$0.0002$$ which are present only in one answer, i.e Answer B

+Kudos if this helped!
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Posts: 124
Re: The original price of a certain TV set is discounted by x [#permalink]

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10 May 2018, 02:26
clarkkent0610 wrote:
The original price of a certain TV set is discounted by x percent, and the reduced price is then discounted by 2x percent. If P is the original price of the TV 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 - 0.03x + 0.002x^2)
D: P(1 - 2x^2)
E: P(1 - 3x + 2x^2)

Question Code is QPS05959

"@Bunuel"

I just want to update in actual question option C is "P(1 - 0.3x + 0.002x^2)". Attached image as an evidence for reference.
Attachments

Capture_1.PNG [ 19.59 KiB | Viewed 544 times ]

Intern
Joined: 16 May 2018
Posts: 13
Location: India
GMAT 1: 610 Q44 V30
Re: The original price of a certain TV set is discounted by x [#permalink]

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26 May 2018, 05:09

This is how I solved it -
Original price - P
Price after the first discount -
(P - Px/100)
Price after the second discount -
= (P - Px/100) - [(2x/100)(P - Px/100)]
=> (P - Px/100) common in both the terms hence,
= (P - Px/100) [1 - 2x/100]
= P(1 - x/100)(1 - 2x/100)
=Multiply both the terms
= P(1 - x/100 -2x/100 +2x^2/10000)
= P(1 - 3x/100 + 2x^2/10000)
= P(1 - 0.03x + 0.0002x^2)
Re: The original price of a certain TV set is discounted by x   [#permalink] 26 May 2018, 05:09
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