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payments - algebra (m08q17) [#permalink]
 27 Dec 2007, 13:50
Question Stats:
44% (02:46) correct
55% (02:05) wrong based on 1 sessions
Two payment schemes are available for customers in the N'K store. The first scheme includes a downpayment of 20% of the purchase price and 10 monthly payments of 10% each. The second includes a downpayment 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% Source: GMAT Club Tests - hardest GMAT questions
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Two comments, One, it's much eaiser to solve this question if you ignore the $216 figure in your calculation. So you know the cost is 120 for scheme one and 170 for scheme two. The difference is 50. Then you calculate the percentage. Second, when we say how much cheaper is A than B we use B as the base. Therefore you calcuate the percentage by 50/170 and gets 30% since 17*3=51. Now the problem is often in a test we are not sure if we should do 50/120 or 50/170. Fortunetaly for this question 50/120 is over 40% (50>12*4=48) and it is not in the list of choices. So you know 120 cannot be the base and then you go back to the question to verify that 170 is indeed the base. These little tricks may not sound significant but they could be big time savers at your test.
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Director
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Scheme 1: you end up paying 120% of the $216 price (20+10(10))
Scheme 2: you end up paying 170% of the $216 price (10+8(20))
this means that scheme 2 costs more by 50% (170-120) of the purchase price. In other words, the customer would pay $108 more that way (.5*216).
now the question:
Quote: by what percent will he find the first scheme cheaper than the second (approximately)?
so what percent is 108 of the price of the second scheme? this is important, you're making the comparison against scheme 2, not scheme 1!
we know that 108 is .5P (let P = price) and scheme 2 costs 170% of P. so what percent of 1.7P is .5P?
.5/1.7 = ~30% (without doing the math you can see that 10% of 1.7 = .17 and that .5/.17 = ~3)
C. 30%
tricky stuff man 
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Director
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You're comparing overall costs, not just monthly payments. So...
216+43.2 = 259.2
345.6+21.6 = 367.2
367.2-259.2=108
108/367.2 = 30%
it's 30% cheaper to do it the first way.
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Re: payments - algebra (m08q17) [#permalink]
18 Aug 2010, 04:46
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Answer is C The key to this question is to realise that since everything is asked in percents we do not need to get in to the math with 216 just take 100 as a based and do it. 50/170 is the answer. ALso the question is how much cheaper is first from second so it is difference / second. If the question would ahve been how much expensive is second from first then equation would have been 50/ 120. Right?? Vivek Kudos if you agree 
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weird ... the answer i get isnt one of the options
scheme 1:
down payment = $43.20
remaining payment = 216-43.20 = 172.80
10% of this is $17.28
10 months of this payment is 172.80
total payment = 43.20+172.80 = 216
scheme 2
down payment = $21.60
remaining payment = 216-21.60 = 194.40
8% of this is $15.52
20 months of this payment is 311.04
total payment = 21.60+311.01 = 332.64
difference = 332.64-216 / 216 = 45%
maybe i didnt understand the question properly
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Director
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pmenon: I know it doesn't make any sense when compared to the "real world" but you don't subtract the down payment before figuring out the monthly payments. It's a 20% down payment and then 10 payments of 10% of the original price
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eschn3am wrote: pmenon: I know it doesn't make any sense when compared to the "real world" but you don't subtract the down payment before figuring out the monthly payments. It's a 20% down payment and then 10 payments of 10% of the original price
thanks ! that does seem a little strange though, lol.
ok, if i go that route, i seem to be ending up with 34% as the answer
downpayments are 43.2 and 21.6
monthly payments are 21.6 and 17.28
total monthly is 216 and 345.6
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I get 27%.
1. 216+43.20+((216-43.20)10/100)10= 432
2. 216+21.60+((216-21.60)8/100))20= 548.64
432-548.64/432= 27%
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Cooper2248817 wrote: I get 27%.
1. 216+43.20+((216-43.20)10/100)10= 432
2. 216+21.60+((216-21.60)8/100))20= 548.64
432-548.64/432= 27%
once again, you're taking 10% and 8% of the NEW total AFTER you remove the initial down payment. The question doesn't specify where it's taking the monthly percentage from so I believe it comes straight from the original $216. Poorly worded question where the answer depends on where you're getting your numbers from.
Do we have an OA for it? I think if they wanted us to pull the percent from another number they would specify that.
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for first scheme, total cost is $120 and it is $170 and since question is how cheaper is first the anser would be 100*(170-120)/170 ~=30 % so answer should be C
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bmwhype2 wrote: Two payment schemes are available for customers in the N'K store.
The first scheme implies a downpayment of 20% of the purchase price and 10 monthly payments of 10% each.
The second implies a downpayment 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)?
14%
27%
30%
34%
35% first way: 0.20*216 + 216 (10% of 216 per 10 payments)=(216/5) +216=1296/5 second way: 0.10*216+8*216*0.20 (8% of 216 per 20 payments)=(216+3456)/10=3672/10 difference: (3672-2592)/10=108 %: 108/367.2=30% OA is C
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Let P be the purchase price then
for 1st scheme:
0.2*P + 0.1*10*P
= 1.2P
For 2nd Scheme: 0.1P + 0.08*20P = 1.7P
(1.7P - 1.2P)/(1.2P) * 100
= 0.5/1.2 * 100
= 42 (Approx).
Why this isn't our answer? they get answer by dividing with second scheme[0.5/1.7 *100 = 30(approx)]. Why?
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Re: payments - algebra (m08q17) [#permalink]
17 Aug 2010, 18:32
Fully agree. The result will be the same whatever the price. It is just here to make things confusing. Whatever it is you will pay 170 percent in one case and 120 percent in the other. Hence 30 percent difference (50/170). The real world difference would be different as time value for money would have to be accounted for. Here we assume 100 paid now has the same value has 100 paid in few months. Posted from my mobile device 
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Re: payments - algebra (m08q17) [#permalink]
18 Aug 2010, 03:55
Tricky question
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Re: payments - algebra (m08q17) [#permalink]
22 Aug 2011, 06:12
agree with wvivek )
1st payment - 20% + 10 * 10% = 120%
2nd payment - 10% + 20 * 8% = 170%
percentage difference = (170%-120%)/170% = 5/17 ~ 30%
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Re: payments - algebra (m08q17) [#permalink]
22 Aug 2011, 10:28
When taken into percentages the problem becomes a lot easier.
Its easier to think in terms of 120% and 170% rather than jump to the numbers and start solving.
Need to think like this going forward.
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Re: payments - algebra (m08q17) [#permalink]
03 Sep 2011, 14:02
Is there a way to speed up calculating something like 108/367.2?
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HongHu wrote: Two comments,
One, it's much eaiser to solve this question if you ignore the $216 figure in your calculation. So you know the cost is 120 for scheme one and 170 for scheme two. The difference is 50. Then you calculate the percentage.
Second, when we say how much cheaper is A than B we use B as the base. Therefore you calcuate the percentage by 50/170 and gets 30% since 17*3=51. Now the problem is often in a test we are not sure if we should do 50/120 or 50/170. Fortunetaly for this question 50/120 is over 40% (50>12*4=48) and it is not in the list of choices. So you know 120 cannot be the base and then you go back to the question to verify that 170 is indeed the base. These little tricks may not sound significant but they could be big time savers at your test. Can someone please explain, how to calculate cost of schemes i.e 120 & 170. 
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shrive555 wrote: HongHu wrote: Two comments,
One, it's much eaiser to solve this question if you ignore the $216 figure in your calculation. So you know the cost is 120 for scheme one and 170 for scheme two. The difference is 50. Then you calculate the percentage.
Second, when we say how much cheaper is A than B we use B as the base. Therefore you calcuate the percentage by 50/170 and gets 30% since 17*3=51. Now the problem is often in a test we are not sure if we should do 50/120 or 50/170. Fortunetaly for this question 50/120 is over 40% (50>12*4=48) and it is not in the list of choices. So you know 120 cannot be the base and then you go back to the question to verify that 170 is indeed the base. These little tricks may not sound significant but they could be big time savers at your test. Can someone please explain, how to calculate cost of schemes i.e 120 & 170. whats up guys ??? 
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