Last year a credit card company gave each of its cardholders a rebate

Question

Last year a credit card company gave each of its cardholders a rebate on the amount charged during the year. The rebate was 1 percent of the portion of the amount charged in excess of $2,000 but less than or equal to $5,000, and 2 percent of the portion of the amount charged in excess of $5,000. If a cardholder received a total rebate equal to 1.3 percent of the amount charged, how much did the cardholder charge on the card?

A) $6,000
B) $7,000
C) $8,000
D) $9,000
E) $10,000

A) $6,000
B) $7,000
C) $8,000
D) $9,000
E) $10,000

gmatophobia · Accepted Answer

Assume that the person charged $x on their card.

We can observe that the person got a rebate of more than 1%, hence we can be sure that the person's expense was more than $5000. This is also evident in the options presented.

The rebate was 1 percent of the portion of the amount charged in excess of $2,000 but less than or equal to $5,000

Rebate Earned upto $5000=  \frac{5000 - 2000 }{ 100} = \frac{3000}{100}

Rebate Earned for value above $5000=  \frac{2 }{ 100} * (x - 5000)

If a cardholder received a total rebate equal to 1.3 percent of the amount charged, how much did the cardholder charge on the card?

\frac{3000}{100} + \frac{2 }{ 100} * (x - 5000) = \frac{1.3}{100} * x

Multiplying both sides by 100

3000 + 2x - 10000 = 1.3x

0.7x = 7000

x = $10,000

Option E

YB10 · Answer

Amount charged = x

0.01*3000+0.02(x-5000)=1.3x

Solving x=10,000

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NoviceBoy · Answer

YB10  Why did you take 3000??

YB10 · Answer

It says the combined interest is 1.3%, so that means the total amount is greater than the 5,000 threshold. 3,000 because the rebate is only for amount over 2,000 and less than or equal to 5,000

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Anki111 · Answer

If we use allegation method, we can directly get 7:3 ratio. So, that can be a valid solution?

Vanshikakataruka · Answer

how did u proceed from allegations? I got the ratio 7:3 but i didnt understand how to go further with that.

KarishmaB · Answer

You can use weighted averages too. 1.3% is the rebate on the entire amount, including the first $2000. First $2000, 0% rebate Next $3000 (from 2000 to 5000), 1% rebate Next $x (5000+), 2% rebate 1.3 = \frac{0*2 + 1*3 + 2*x}{(2+3+x)} x = 5 Hence the charge was 5000 above $5000 i.e. a total of $10,000 Answer (E) Weighted Averages Video: https://www.youtube.com/watch?v=_GOAU7moZ2Q

einstein801 · Answer

Hi  MartyMurray , would you be able to help here?

taking X as the amount between 2k and 5k; Y as the amount in excess of 5k:

1x + 2y = 1.3(x+y) --> 3x = 7y.

Since X = 3000, --> 7y = 9000. Y = ~1000+. 5k+1k = 6k.

ShuGMATTutor · Answer

Ok lets dumb this down for us. "A problem well defined is halfway through to the solution - Kidlins law"

Visualization  
 The first step would be to visualize the problem; something similar to attached

Translation  
 So for the first 5000$ they get a rebate of 300$ (1% of $3000) that is 0.6%  
 For the next bit they get a rebate at 2%  
 Collectively their rebate is 1.3$

Approach  
 so using alligation we see they are in 1:1 ratio, thus the "next bit" would also be $5000

Conclusion  
 The total amount eligible for rebates is $10,000, split evenly into two $5,000 segments, with weighted rebate rates producing an average of 1.3%.

Shu "TheGMATTutor"
    T    he GMAT concepts are relatively basic   , but they require a deep understanding to tackle nuanced questions effectively. So  lets dumb it down for us . This is    not just a math and English test   —it is a    deductive test designed to assess your problem-solving skills

tickoo47 · Answer

I dont think by solving it we are getting x = 10000

equation should be 0.01*3000+0.02(x-5000)=1.3/100x
as its 1.3% ie 1.3/100

or

1*3000+2(x-5000)=1.3x

Aviralmanit111 · Answer

on RHS it should be 1.3x/100

GMATinsight · Answer

Please find the video solution of this question.

https://www.youtube.com/watch?v=QfAX71hJfoQ

Last year a credit card company gave each of its cardholders a rebate

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Last year a credit card company gave each of its cardholders a rebate

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