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

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

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New post Updated on: 29 Oct 2012, 02:27
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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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Re: Problem from GMATPrep Question Pack 1 [#permalink]

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New post 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)

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

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New post 29 Oct 2012, 02:31
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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.
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Re: The original price of a certain TV set is discounted by x [#permalink]

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New post 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.

Answer: B.

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

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

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

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New post 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.

Answer: B.

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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PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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

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

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New post 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.
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Re: The original price of a certain TV set is discounted by x [#permalink]

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New post 26 May 2018, 05:09
Answer choice B

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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