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M08-17

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M08-17 [#permalink]

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New post 16 Sep 2014, 00:37
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Two payment schemes are available for customers in the N'K store. The first scheme includes a down payment of 20% of the purchase price and 10 monthly payments of 10% each. The second includes a down payment of 10% and 20 monthly payments of 8% each. If a customer buys a TV for $216, by what percent will he find the first scheme cheaper than the second (approximately)?

A. 14%
B. 27%
C. 30%
D. 34%
E. 35%

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Re: M08-17 [#permalink]

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New post 16 Sep 2014, 00:37
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Official Solution:

Two payment schemes are available for customers in the N'K store. The first scheme includes a down payment of 20% of the purchase price and 10 monthly payments of 10% each. The second includes a down payment of 10% and 20 monthly payments of 8% each. If a customer buys a TV for $216, by what percent will he find the first scheme cheaper than the second (approximately)?

A. 14%
B. 27%
C. 30%
D. 34%
E. 35%


The price of $216 is irrelevant to finding the answer.

For any price \(X\) the customer would pay:
  • First scheme: \(0.2X + 10*0.1X = 1.2X\)
  • Second scheme: \(0.1X + 20*0.08X = 1.7X\)

The percentage difference = \(100\% * \frac{1.7X - 1.2X}{1.7X} = 100\% * \frac{0.5}{1.7} \approx 100\% * \frac{0.51}{1.7} = 30\%\)


Answer: C
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Re: M08-17 [#permalink]

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New post 06 Aug 2015, 02:56
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Bunuel wrote:
Official Solution:

Two payment schemes are available for customers in the N'K store. The first scheme includes a down payment of 20% of the purchase price and 10 monthly payments of 10% each. The second includes a down payment of 10% and 20 monthly payments of 8% each. If a customer buys a TV for $216, by what percent will he find the first scheme cheaper than the second (approximately)?

A. 14%
B. 27%
C. 30%
D. 34%
E. 35%


The price of $216 is irrelevant to finding the answer.

For any price \(X\) the customer would pay:
  • First scheme: \(0.2X + 10*0.1X = 1.2X\)
  • Second scheme: \(0.1X + 20*0.08X = 1.7X\)

The percentage difference = \(100\% * \frac{1.7X - 1.2X}{1.7X} = 100\% * \frac{0.5}{1.7} \approx 100\% * \frac{0.51}{1.7} = 30\%\)


Answer: C


Hi Bunuel,

The mistake I made was that I took 1.2 instead of 1.7 in the base. \(\frac{1.7X - 1.2X}{1.2X}\)

How do you decide what to take as denominator ? For any case if possible . I always followed\(\frac{Final-Initial}{Initial}\) but clearly I am not able to it here.Please help me out !!


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Re: M08-17 [#permalink]

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New post 17 Aug 2015, 03:13
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anurag356 wrote:
Bunuel wrote:
Official Solution:

Two payment schemes are available for customers in the N'K store. The first scheme includes a down payment of 20% of the purchase price and 10 monthly payments of 10% each. The second includes a down payment of 10% and 20 monthly payments of 8% each. If a customer buys a TV for $216, by what percent will he find the first scheme cheaper than the second (approximately)?

A. 14%
B. 27%
C. 30%
D. 34%
E. 35%


The price of $216 is irrelevant to finding the answer.

For any price \(X\) the customer would pay:
  • First scheme: \(0.2X + 10*0.1X = 1.2X\)
  • Second scheme: \(0.1X + 20*0.08X = 1.7X\)

The percentage difference = \(100\% * \frac{1.7X - 1.2X}{1.7X} = 100\% * \frac{0.5}{1.7} \approx 100\% * \frac{0.51}{1.7} = 30\%\)


Answer: C


Hi Bunuel,

The mistake I made was that I took 1.2 instead of 1.7 in the base. \(\frac{1.7X - 1.2X}{1.2X}\)

How do you decide what to take as denominator ? For any case if possible . I always followed\(\frac{Final-Initial}{Initial}\) but clearly I am not able to it here.Please help me out !!


Thanks


Put in the denominator the value you are comparing to: "If a customer buys a TV for $216, by what percent will he find the first scheme cheaper than the second?"
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Re: M08-17 [#permalink]

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New post 07 Dec 2015, 11:33
i subtracted the origional amount ie..20% of x and made them in 10% each in 10 installment..Logically the question does not say that but i thought this is how it should be..
Can you please guide as how should i read this question ?
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Re: M08-17 [#permalink]

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New post 29 Sep 2016, 15:48
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jevish wrote:
i subtracted the origional amount ie..20% of x and made them in 10% each in 10 installment..Logically the question does not say that but i thought this is how it should be..
Can you please guide as how should i read this question ?


Down payment means you are paying certain percentage of item up front.

Therefore, 20% down payment means you are paying 20% of the price at the time of purchase.

I agree that 10% each part may be confusing and could have been worded better as "10 payments, each payment being 10% of the purchase price."
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Re: M08-17 [#permalink]

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New post 06 Oct 2016, 01:05
can you explain how you got the equation of first scheme to=0.2x+10.0.1x=1.2x?
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Re: M08-17 [#permalink]

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New post 06 Oct 2016, 02:21
manchitkapoor wrote:
can you explain how you got the equation of first scheme to=0.2x+10.0.1x=1.2x?


20% down payment + 10% monthly payment X 10 months.

x is the price of purchase, which is being financed with above terms.
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Re: M08-17 [#permalink]

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New post 22 Feb 2017, 08:00
Hi,

though I followed the same process, when I found the final ratio 5/17 I simply noticed that 5/20 < 5/17 < 5/15, thus I picked 27% since that ratio is slightly less than 5/15

How did you come up to 30% from 0,5/1,7 ? Or maybe the Answer choice B should be eliminated in order to avoid ambiguity?
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Re: M08-17 [#permalink]

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New post 22 Feb 2017, 08:17
Nipson wrote:
Hi,

though I followed the same process, when I found the final ratio 5/17 I simply noticed that 5/20 < 5/17 < 5/15, thus I picked 27% since that ratio is slightly less than 5/15

How did you come up to 30% from 0,5/1,7 ? Or maybe the Answer choice B should be eliminated in order to avoid ambiguity?


0.5/1.7 = 0.294...

The way we got 30% is as follows:

\(100\% * \frac{0.5}{1.7} \approx 100\% * \frac{0.51}{1.7} = 30\%\)
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Re: M08-17 [#permalink]

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New post 18 Apr 2017, 01:39
if we don't take approx. value then answer is 27.4% that is close to choice B. Therefore answer options should be kept distant from one another
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Re: M08-17 [#permalink]

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New post 18 Apr 2017, 01:46
Oh sorry ! I made a calculation mistake ... it's 29.4 %
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Re: M08-17 [#permalink]

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New post 18 Apr 2017, 14:51
Hi Bunuel,

Is it wrong to assume from the statement "The first scheme includes a down payment of 20% of the purchase price and 10 monthly payments of 10% each" that 10 monthly payments of 10% may be different?
For instance the initial cost is 100$ with 10 monthly payments of 10% each. So first you pay 10$, remaining is 90$, then you pay 10% of 90$ i.e 9$ and so on. In that case we cannot use the equation 0.2X+10*0.1X = 1.2X.

Please correct me if I am wrong!!
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New post 06 May 2017, 15:04
First :
0.2a+10∗0.1a=1.2X0.2a+10∗0.1a=1.2a
Second :
0.1a+20∗0.08a=1.7a
(1.7-1.2)/1.7=30%
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Re: M08-17 [#permalink]

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New post 24 Jul 2017, 07:49
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I think this is a poor-quality question and I agree with explanation. I agree the cost plays no role in solving this question but I feel the question is really poorly worded. If we are talking about real world examples, if we buy a car or a house, a down payment is paid upfront and the monthly payments are calculated on the rest of the amount not on the principal amount. If you are going to calculate on the principal amount then that should be clearly intended in the question stem. Secondly, if you are going to calculate the payments on the rest of the principal amount at least give different answer options. I am sure that majority of the question takers must be marking D/E as the answer and that is why this question is in the 700 category.
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New post 06 Jul 2018, 04:05
Rookie84 wrote:
jevish wrote:
i subtracted the origional amount ie..20% of x and made them in 10% each in 10 installment..Logically the question does not say that but i thought this is how it should be..
Can you please guide as how should i read this question ?


Down payment means you are paying certain percentage of item up front.

Therefore, 20% down payment means you are paying 20% of the price at the time of purchase.

I agree that 10% each part may be confusing and could have been worded better as "10 payments, each payment being 10% of the purchase price."


I agree the wording of this question is very poor & does not communicate clearly whether the installments are calculated on remaining amount after the down payment or purchase price.

What is the source of this question?
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New post 06 Jul 2018, 07:21
vil1 wrote:
I think this is a poor-quality question and I agree with explanation. I agree the cost plays no role in solving this question but I feel the question is really poorly worded. If we are talking about real world examples, if we buy a car or a house, a down payment is paid upfront and the monthly payments are calculated on the rest of the amount not on the principal amount. If you are going to calculate on the principal amount then that should be clearly intended in the question stem. Secondly, if you are going to calculate the payments on the rest of the principal amount at least give different answer options. I am sure that majority of the question takers must be marking D/E as the answer and that is why this question is in the 700 category.


Thank you. The question is removed from the database.
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Re: M08-17 [#permalink]

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New post 07 Jul 2018, 12:24
Bunuel wrote:
Two payment schemes are available for customers in the N'K store. The first scheme includes a down payment of 20% of the purchase price and 10 monthly payments of 10% each. The second includes a down payment of 10% and 20 monthly payments of 8% each. If a customer buys a TV for $216, by what percent will he find the first scheme cheaper than the second (approximately)?

A. 14%
B. 27%
C. 30%
D. 34%
E. 35%


Dear Bunuel

I rarely comment on the wording but the highlighted is very vague and unclear? what does 10% or 8% represent? Also, 10% of the remaining or from original price?
I could not interpret them until I saw your solution. I hope you can re-word those part.
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New post 07 Jul 2018, 12:27
Mo2men wrote:
Bunuel wrote:
Two payment schemes are available for customers in the N'K store. The first scheme includes a down payment of 20% of the purchase price and 10 monthly payments of 10% each. The second includes a down payment of 10% and 20 monthly payments of 8% each. If a customer buys a TV for $216, by what percent will he find the first scheme cheaper than the second (approximately)?

A. 14%
B. 27%
C. 30%
D. 34%
E. 35%


Dear Bunuel

I rarely comment on the wording but the highlighted is very vague and unclear? what does 10% or 8% represent? Also, 10% of the remaining or from original price?
I could not interpret them until I saw your solution. I hope you can re-word those part.


The question is removed from the database.
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Collection of Questions:
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

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: M08-17 [#permalink]

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New post 07 Jul 2018, 12:30
Bunuel wrote:

The question is removed from the database.
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Thanks for your reply but which database? it is till in the GMATclub test directory.
Re: M08-17   [#permalink] 07 Jul 2018, 12:30

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