GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Sep 2018, 22:10

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

Hide Tags

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

Show Tags

Updated on: 19 Jun 2018, 23:12
1
20
00:00

Difficulty:

55% (hard)

Question Stats:

65% (01:25) correct 35% (01:45) wrong based on 413 sessions

HideShow timer Statistics

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.
Board of Directors
Joined: 01 Sep 2010
Posts: 3463
Re: The original price of a certain TV set is discounted by x percent, and  [#permalink]

Show Tags

28 Oct 2012, 16:43
4
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)

_________________
General Discussion
Math Expert
Joined: 02 Sep 2009
Posts: 49258
Re: The original price of a certain TV set is discounted by x percent, and  [#permalink]

Show Tags

29 Oct 2012, 02:31
4
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 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 percent, and  [#permalink]

Show Tags

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

Show Tags

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: 49258 Re: The original price of a certain TV set is discounted by x percent, and [#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.
_________________
Manager
Joined: 11 Oct 2013
Posts: 112
Concentration: Marketing, General Management
GMAT 1: 600 Q41 V31
Re: The original price of a certain TV set is discounted by x percent, and  [#permalink]

Show Tags

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!
_________________

Its not over..

Manager
Joined: 13 Sep 2016
Posts: 121
Re: The original price of a certain TV set is discounted by x percent, and  [#permalink]

Show Tags

10 May 2018, 02:26
1
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 1608 times ]

Intern
Joined: 16 May 2018
Posts: 15
Location: India
GMAT 1: 610 Q44 V30
Re: The original price of a certain TV set is discounted by x percent, and  [#permalink]

Show Tags

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)
Math Expert
Joined: 02 Sep 2009
Posts: 49258
Re: The original price of a certain TV set is discounted by x percent, and  [#permalink]

Show Tags

19 Jun 2018, 23:13
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.

________________
Thank you. Edited.
_________________
Re: The original price of a certain TV set is discounted by x percent, and &nbs [#permalink] 19 Jun 2018, 23:13
Display posts from previous: Sort by

Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.