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A credit card company plans to give rebate to users whose

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A credit card company plans to give rebate to users whose [#permalink] New post 31 May 2007, 10:49
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
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 [#permalink] New post 31 May 2007, 11:03
#2 is B, but I don't know an efficient way of solving it.
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 [#permalink] New post 31 May 2007, 11:20
#1 (x-5000)*.02 + 3000*.01=.013x

x=10,000
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 [#permalink] New post 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%

:-D
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Re: prep questions [#permalink] New post 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
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 [#permalink] New post 31 May 2007, 17:59
Thanks for the explanation, Kevin! It was very helpful!
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 [#permalink] New post 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.
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Confused a little about the solution [#permalink] New post 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?
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Re: Confused a little about the solution [#permalink] New post 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.

:-D

Last edited by KillerSquirrel on 31 May 2007, 22:32, edited 1 time in total.
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Re: prep questions [#permalink] New post 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.
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Re: Confused a little about the solution [#permalink] New post 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] New post 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.

:-D


Ohh ...Could you please explain once more in more simple way!!! Urrghhhh



sure :-D

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).

:-D

Last edited by KillerSquirrel on 01 Jun 2007, 00:40, edited 2 times in total.
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 [#permalink] New post 01 Jun 2007, 00:31
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?
  [#permalink] 01 Jun 2007, 00:31
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