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# A credit card company plans to give rebate to users whose

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Manager
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A credit card company plans to give rebate to users whose [#permalink]  31 May 2007, 10:49
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1. A credit card company plans to give rebate to users whose amount of transaction by its credit card is over a certain level. It will give back 1% of amount that is more than $2,000 and less than or equal to$ 5,000 and 2% for the portion that is more than $5,000. If a person receives 1.3% of total amount as a rebate, what is the amount he used with the credit card? (answer is 10000) 2. a, b, and c are consecutive integers where a<b<c. Which of the following values are not possible for the equation c^2-b^2-a^2 A. -12 B. -6 C. 0 D. 3 E. 4 Manager Joined: 22 May 2007 Posts: 121 Followers: 1 Kudos [?]: 2 [0], given: 0 [#permalink] 31 May 2007, 11:03 #2 is B, but I don't know an efficient way of solving it. Manager Joined: 22 May 2007 Posts: 121 Followers: 1 Kudos [?]: 2 [0], given: 0 [#permalink] 31 May 2007, 11:20 #1 (x-5000)*.02 + 3000*.01=.013x x=10,000 VP Joined: 08 Jun 2005 Posts: 1146 Followers: 6 Kudos [?]: 151 [0], given: 0 [#permalink] 31 May 2007, 12:19 Yes ! agree with Hayabusa since 1.3% is more then 1% we know that he/she used more then$5000.

if they used less then $5000 the rebate can't be more then 1% !!! x is the amount over$5000

Note ! that the rebate starts at $2000. (0.01*(5000-2000)+0.02*x)/(5000+x) = 0.013 30+0.02*x = 0.013*x+65 0.007*x = 35 x = 5000 rebate = 1%*3000+2%*5000 = 130 rebate percent 130/10,000 = 1.3% GMAT Instructor Joined: 04 Jul 2006 Posts: 1264 Location: Madrid Followers: 26 Kudos [?]: 196 [0], given: 0 Re: prep questions [#permalink] 31 May 2007, 14:37 Jamesk486 wrote: 2. a, b, and c are consecutive integers where a<b<c. Which of the following values are not possible for the equation c^2-b^2-a^2 A. -12 B. -6 C. 0 D. 3 E. 4 x=(b+1)^2 -b^2 - (b-1)^2 = 2b +1 - b^2 +2b - 1=4b- b^2 Thus b^2 - 4b + x =0 , b= (4 +- sqrt (16 - 4x))/2. Note that b is an integer if x is -12, 0, 3 and 4, but not if x = -6. B Manager Joined: 18 Apr 2007 Posts: 121 Followers: 1 Kudos [?]: 5 [0], given: 0 [#permalink] 31 May 2007, 17:59 Thanks for the explanation, Kevin! It was very helpful! CEO Joined: 29 Mar 2007 Posts: 2584 Followers: 17 Kudos [?]: 290 [0], given: 0 [#permalink] 31 May 2007, 20:48 Followed u all the way to here Thus b^2 - 4b + x =0 Ok got u here. How does the following step come about? Im confused on how you got it from here. b= (4 +- sqrt (16 - 4x))/2. Note that b is an integer if x is -12, 0, 3 and 4, but not if x = -6. Intern Joined: 31 May 2007 Posts: 1 Followers: 0 Kudos [?]: 0 [0], given: 0 Confused a little about the solution [#permalink] 31 May 2007, 22:05 Why are we subtracting 5000 from 2000. i understand that these are the highest and lowest range values . But if there is 1% rebate refund on the portion which is any where btw 2000 and 5000. Then it can be 4000, or 2500. Right? VP Joined: 08 Jun 2005 Posts: 1146 Followers: 6 Kudos [?]: 151 [0], given: 0 Re: Confused a little about the solution [#permalink] 31 May 2007, 22:30 001ash wrote: Why are we subtracting 5000 from 2000. i understand that these are the highest and lowest range values . But if there is 1% rebate refund on the portion which is any where btw 2000 and 5000. Then it can be 4000, or 2500. Right? according to the stem - the rebate starts at$2000 and not from the first $(i.e person buying$1000 worth will get no rebate !!) so max rebate is $3000*0.01 on buying less then$5000.

Last edited by KillerSquirrel on 31 May 2007, 22:32, edited 1 time in total.
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Re: prep questions [#permalink]  31 May 2007, 22:31
Jamesk486 wrote:
1. A credit card company plans to give rebate to users whose amount of transaction by its credit card is over a certain level. It will give back 1% of amount that is more than $2,000 and less than or equal to$ 5,000 and 2% for the portion that is more than $5,000. If a person receives 1.3% of total amount as a rebate, what is the amount he used with the credit card? (answer is 10000) Amount = X ;$2,000 < X <5> $5,000 Returned Back = (X - 5,000)/50 ( because 2% is only for the portion more than$ 5,000 )

Interest received is more than 1%. Therefore the amount ( X ) should be greater than $5000. Therefore, (2/100)*(X-5000) = (1.3/100)*X......................... ( i ) X = 14280 Please explain what is the mistake in the equation ..( i ) Why is the answer 10,000 2. a, b, and c are consecutive integers where a<b<c. Which of the following values are not possible for the equation c^2-b^2-a^2 A. -12 B. -6 C. 0 D. 3 E. 4 b = a+1 c=b+1 = a+2 c^2-b^2-a^2 = (a+2)^2 - (a+1)^2 - a^2 = (-a^2+2*a-3) This equation is equal to -6, will not result in any solution for the value of "A". thus the answer is B. Director Joined: 03 Sep 2006 Posts: 878 Followers: 6 Kudos [?]: 416 [0], given: 33 Re: Confused a little about the solution [#permalink] 01 Jun 2007, 00:15 KillerSquirrel wrote: 001ash wrote: Why are we subtracting 5000 from 2000. i understand that these are the highest and lowest range values . But if there is 1% rebate refund on the portion which is any where btw 2000 and 5000. Then it can be 4000, or 2500. Right? according to the stem - the rebate starts at$2000 and not from the first $(i.e person buying$1000 worth will get no rebate !!) so max rebate is $3000*0.01 on buying less then$5000.

:-D

Ohh ...Could you please explain once more in more simple way!!! Urrghhhh
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Re: Confused a little about the solution [#permalink]  01 Jun 2007, 00:30
LM wrote:
KillerSquirrel wrote:
001ash wrote:
Why are we subtracting 5000 from 2000. i understand that these are the highest and lowest range values . But if there is 1% rebate refund on the portion which is any where btw 2000 and 5000. Then it can be 4000, or 2500. Right?

according to the stem - the rebate starts at $2000 and not from the first$ (i.e person buying $1000 worth will get no rebate !!) so max rebate is$3000*0.01 on buying less then $5000. Ohh ...Could you please explain once more in more simple way!!! Urrghhhh sure this is the question: credit card company plans to give rebate to users whose amount of transaction by its credit card is over a certain level. It will give back 1% of amount that is more than$2,000 and less than or equal to $5,000 and 2% for the portion that is more than$5,000. If a person receives 1.3% of total amount as a rebate, what is the amount he used with the credit card?

look at the bold part - the company will give a rebate of 1% only when you buy more then $2000 so if you buy$10,000 worth, then:

from 0 to $2000 = no rebate from$2000 to $5000 =$30 rebate (1%)

from $5000 to$10,000 = $100 rebate (2%) if you want to find the avarege rebate (given as 1.3%) ($2000*0%+$3000*1%+$5000*2%)/$10,000 I think you are missing$2000*0 = 0

we use 3000, because if the avarege rebate is more then 1% you can say thet the purchase amount has to be ! more then \$5000 (in order to reach 1.3% rebate).

Last edited by KillerSquirrel on 01 Jun 2007, 00:40, edited 2 times in total.
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Hayabusa wrote:
#1 (x-5000)*.02 + 3000*.01=.013x

x=10,000

Hayabusa, Could you please explain the " 3000 " in your equation? Why is it there and how is it calculated to be precisely 3000 and not any other value?
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