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

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Difficulty:   55% (hard)

Question Stats: 66% (02:07) correct 34% (02:28) wrong based on 387 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. $$P(1 - 0.3x + 0.002x^2)$$

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 19 Jun 2018, 23:12, edited 2 times in total.
Edited the question.
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Posts: 3408
Re: The original price of a certain TV set is discounted by x percent, and  [#permalink]

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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)

B is the answer
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Posts: 58427
Re: The original price of a certain TV set is discounted by x percent, and  [#permalink]

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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 percent, and [#permalink] Show Tags 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  B
Joined: 01 May 2013
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Schools: ISB '16
Re: The original price of a certain TV set is discounted by x percent, and  [#permalink]

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P(1 - x/100)*(1 - 2x/100) = P(1 - 0.03x - 0.0002x^2), Option B)
Manager  Joined: 20 Dec 2013
Posts: 116
Re: The original price of a certain TV set is discounted by x percent, and  [#permalink]

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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 V Joined: 02 Sep 2009 Posts: 58427 Re: The original price of a certain TV set is discounted by x percent, and [#permalink] Show Tags 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 Re: The original price of a certain TV set is discounted by x percent, and  [#permalink]

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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! _________________
Its not over..
Manager  B
Joined: 13 Sep 2016
Posts: 115
GMAT 1: 800 Q51 V51 Re: The original price of a certain TV set is discounted by x percent, and  [#permalink]

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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 4798 times ]

Intern  B
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Location: India
Schools: Queen's MBA'20
GMAT 1: 610 Q44 V30 GMAT 2: 650 Q44 V35 GRE 1: Q160 V150 GPA: 3
Re: The original price of a certain TV set is discounted by x percent, and  [#permalink]

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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)
Math Expert V
Joined: 02 Sep 2009
Posts: 58427
Re: The original price of a certain TV set is discounted by x percent, and  [#permalink]

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alanforde800Maximus 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

"@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.

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Thank you. Edited.
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: The original price of a certain TV set is discounted by x percent, and  [#permalink]

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Hi All,

We're told that the original price of a certain TV set is discounted by X percent, the reduced price is then discounted by 2X percent and P is the original price of the TV set. We're asked which of the following represents the price of the television set after the two successive discounts. This question can be solved in a couple of different ways, including by TESTing VALUES. In addition, the design of the answer choices offers a number of different logic shortcuts that we can use to avoid a lot of redundant math.

Let's TEST P = 100 and X = 10....
IF the original price of the TV is $100, then... a 10% discount makes the reduced price =$100 - (.1)($100) =$100 - $10 =$90 and...
a 20% discount of the reduced price = $90 - (.2)($90) = $90 -$18 = $72 Looking at the first 3 answers, we can clearly see a 'decimal shift', so we're not dealing with completely unique calculations. We can quickly eliminate Answers D and E with some math and logic.... Answer D: (100)(1 - 200) = a negative Answer E: (100)(171) = a big number Answers A through C all have similar pieces, but a decimal shift on the last 'piece' of the calculation will determine which of the three is correct. We're looking for an answer that equals$72, so....

(100)(this number) = $72 The missing number in the parentheses MUST equal 0.72 (1 - .3) = .7 so we need to add another .02 to the value in that parentheses. Since X^2 = (10^2) = 100, that would shift the decimal '2 spots to the left', which would make Answer A and Answer C TOO BIG. That leaves the correct answer.... Final Answer: GMAT assassins aren't born, they're made, Rich _________________ Intern  B Joined: 13 Apr 2018 Posts: 30 Location: Zambia Concentration: Finance, Real Estate GPA: 2.98 WE: Analyst (Investment Banking) Re: The original price of a certain TV set is discounted by x percent, and [#permalink] Show Tags EMPOWERgmatRichC wrote: Hi All, We're told that the original price of a certain TV set is discounted by X percent, the reduced price is then discounted by 2X percent and P is the original price of the TV set. We're asked which of the following represents the price of the television set after the two successive discounts. This question can be solved in a couple of different ways, including by TESTing VALUES. In addition, the design of the answer choices offers a number of different logic shortcuts that we can use to avoid a lot of redundant math. Let's TEST P = 100 and X = 10.... IF the original price of the TV is$100, then...
a 10% discount makes the reduced price = $100 - (.1)($100) = $100 -$10 = $90 and... a 20% discount of the reduced price =$90 - (.2)($90) =$90 - $18 =$72

Looking at the first 3 answers, we can clearly see a 'decimal shift', so we're not dealing with completely unique calculations. We can quickly eliminate Answers D and E with some math and logic....

Answer D: (100)(1 - 200) = a negative
Answer E: (100)(171) = a big number

Answers A through C all have similar pieces, but a decimal shift on the last 'piece' of the calculation will determine which of the three is correct. We're looking for an answer that equals $72, so.... (100)(this number) =$72

The missing number in the parentheses MUST equal 0.72
(1 - .3) = .7
so we need to add another .02 to the value in that parentheses. Since X^2 = (10^2) = 100, that would shift the decimal '2 spots to the left', which would make Answer A and Answer C TOO BIG. That leaves the correct answer....

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

Hi Rich,

Please help me understand why you are using 10 instead of 0.10 (which is a percent)

Thanks
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: The original price of a certain TV set is discounted by x percent, and  [#permalink]

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Hi GloryBoy92,

I do use .10 (re: 10%) in my calculations. The prompt tells us that the initial discount is "X percent"... now, plug in a number for X and then read those words again. When we choose X = 10, those words read that the discount is "10 percent." If you were to say that X = 0.1, then those words end up reading "ten percent percent", which would make the math a bit more complicated and step-heavy.

GMAT assassins aren't born, they're made,
Rich
_________________ Re: The original price of a certain TV set is discounted by x percent, and   [#permalink] 30 Jun 2019, 15:24
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