During a special promotion, a certain filling station is offering a 10

Question

During a special promotion, a certain filling station is offering a 10 percent discount on gas purchased after the first 10 gallons. If Kim purchased 20 gallons of gas, and Isabella purchased 25 gallons of gas, then Isabella‟s total per-gallon discount is what percent of Kim‟s total per-gallon discount?

(A) 80%

(B) 100%

(C) 116.7%

(D) 120%

(E) 140%

(A) 80%

(B) 100%

(C) 116.7%

(D) 120%

(E) 140%

Bunuel · Accepted Answer

Kim purchased 20 gallons of gas. She paid for 10 + 0.9*10 = 19 gallons, so the overall discount she got was 1/20 = 5%.

Isabella purchased 25 gallons of gas. She paid for 10 + 0.9*15 = 23.5 gallons, so the overall discount she got was 1.5/25 = 6%.

6 is 6/5*100 = 120% of 5.

Answer: D.

chetan2u · Answer

hi,
just take the discount to be 1 unit on every gallon above 10..
kim saved 10 on 20 gallons or \frac{1}{2} per gallon...
isabella saved 15 on 25 gallons or  \frac{15}{25}=\frac{3}{5} per gallon..
%= 100*(\frac{3}{5})/(\frac{1}{2})=\frac{600}{5}=120% ...ans B

HarisinghKhedar · Answer

Hi Bunuel,

Thanks for the explanation. A small clarification required though..

You have applied the specified discount on #Units of Gallons. Though it doesn't matter but I chose to look at the given discount in terms of Price/Gallon ($1/G) and then followed the same approach.

I usually take time on percent questions if they're of 700+ level. Do you see any obvious flaw in my approach? I could work on some particular concept files if you think that may help me provide a direct and efficient approach to percent problems. Accuracy is moderate on higher level percent question but time is of concern. This includes my accuracy on Manhattan CATS.

Hari

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shashankism · Answer

Let R be the fixed rate of the gas per gallon.
So for first 10 gallon, rate = 10 R

After this the gas will be available at 10 percent discount.

Kim purchased 20 gallon of gas. So, price = 10R +.9*10 R = 19R
Discount per gallon = 1/20

Isabella purchased 25 gallons of gas. So, price = 10 R + .9*15 R = 22.5 R
Discount per gallon = 1.5/25 = 3/50

So, percentage of Isabella‟s total per-gallon discount w.r.t Kim‟s total per-gallon discount = (3/50)/(1/20) *100 = 120%

Answer D

ScottTargetTestPrep · Answer

Let’s assume that the price per gallon of gas is $10. Thus, the discounted price per gallon of gas after the first 10 gallons is 0.9 x 10 = $9. In other words, after the first 10 gallons, each additional gallon has a $1 discount in price.

Now let’s calculate the total discount for each person. Since Kim purchased 20 gallons of gas, the 10 additional gallons (that is, after the initial 10 gallons) will receive a $10 discount, so her total per-gallon discount is 10/20 = $0.50. Since Isabella purchased 25 gallons of gas, the 15 additional gallons (that is, after the initial 10 gallons) will receive a $15 discount, so her total per-gallon discount is 15/25 = $0.60. Therefore, Isabella’s total per-gallon discount is 0.60/0.50 = 6/5 = 1.2 = 120% of Kim’s total per-gallon discount.

Answer: D

ezzo · Answer

I think you made a typo error in the highlighted portion, It should be 23.5 R

gps5441 · Answer

Let the cost of fuel be $10 per gallon.
 Kim 
First, 10 gallons price=10*$10=$100
2nd 10 gallon Price=10*$9=90 (Discount of 10% or $1 after first 10 gallons)
Total Paid $190
In case there would have been no discount than amount paid would have been $200(20*10)
Savings $10.
Total savings on Total fuel purchased= \frac{10}{20} = \frac{1}{2} 
 Isabella 
First 10 gallon price=10*$10=100
2nd 15 gallon Price=15*$9=135 (Discount of 10% or $1 after first 10 gallons)
Total Paid $235
In case there would have been no discount than amount paid would have been $250(25*$10)
 Savings $15. 
Total savings on Total fuel purchased= \frac{15}{25} = \frac{3}{5}

% of  \frac{Isabella}{Kim} =  \frac{3}{5} ÷ \frac{1}{2} = \frac{6}{5} =1.2*100=120%

shisingh · Answer

I tried a more straightforward method :

total per-gallon discount 
Kim : 0.9p*10 / 20 
Isa: 0.9p*15/ 25
Kim/Isa * 100 = 120%

During a special promotion, a certain filling station is offering a 10

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