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

Question

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

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

Carcass · Accepted Answer

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

Bunuel · Answer

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.

anyibuofu · Answer

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..

deepakpandey028 · Answer

P(1 - x/100)*(1 - 2x/100) = P(1 - 0.03x - 0.0002x^2), Option B)

PerfectScores · Answer

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

Bunuel · Answer

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.

swanidhi · Answer

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!

Nanobotstv · Answer

"@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.

naturalimproviser · Answer

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) -  
=> (P - Px/100) common in both the terms hence,
= (P - Px/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)

Bunuel · Answer

________________
Thank you. Edited.

EMPOWERgmatRichC · Answer

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:  B

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

GloryBoy92 · Answer

Hi Rich,

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

Thanks

EMPOWERgmatRichC · Answer

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

Basshead · Answer

Lets plug numbers:

let original price P = $100
price is discounted by 10% = $90
further discounted by 20% = 90(0.8) = $72

The correct answer, when plugging in numbers, will give us $72.

Now lets look at the answer choices:

A)  P(1 - 0.03x + 0.02x^2) 
 100(1 - 3 + 2) 
 100 - 300 + 200 = $0

B)  P(1 - 0.03x + 0.0002x^2) 
 100(1 - 0.03(10) + 0.0002(10)^2) 
 100(1 - 0.3 + 0.02) 
 100 - 30 + 2 = $72

CORRECT.

C.  P(1 - 0.3x + 0.002x^2) 
 100(1 - 3 + .2) 
 100 - 300 + 20 = -$180

Answer is B.

Fdambro294 · Answer

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

(1 - x/100 - 2x/100 + 2(x)^2/10,000) * P

-x/100 -----> (-1/100)x ------> (-1 * (10)^-2)x ------> -0.01x

-2x/100 -------> -0.02x

+2(x)^2 / 10,000 -----> 0.0002(x)^2

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

-B-

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