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During a special promotion, a certain filling station is off

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by BTGmoderatorDC » Thu Dec 06, 2018 3:54 pm

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Difficulty—

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"Ÿs total per-gallon discount is what percent of Kim"Ÿs total per-gallon discount?

(A) 80%

(B) 100%

(C) 116.7%

(D) 120%

(E) 140%

OA D

Source: Princeton Review
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by Iakgmat » Thu Dec 06, 2018 6:27 pm
Not too sure about this approach... but..
Let P be the price per gallon
Kim = 10P+0.9(10P) = 19P (versus 20P originally)
Isabelle = 10P+0.9(15P) = 22P (versus 25P originally)

Thus Kim has a discount of $$\frac{1}{20}P$$
Isabelle has a discount of $$\frac{3}{25}P$$

This corresponds to 5% discount for Kim and 12% discount for Isabelle

Next to calculate the % of Isabelle's discount in terms of % Kim's discount
$$\frac{12-5}{5}$$

Which gives us 140%
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by [email protected] » Thu Dec 06, 2018 8:04 pm
Hi All,

We're told that during a special promotion, a certain filling station is offering a 10 percent discount on gas purchased AFTER the first 10 gallons. Kim purchased 20 gallons of gas, and Isabella purchased 25 gallons of gas. We're asked for Isabella's total PER-GALLON DISCOUNT as a percent of Kim's total PER-GALLON DISCOUNT. This question can be approached in a couple of different ways, including by TESTing VALUES.

To start, let's set the price at $1 for 1 gallon gallon of gasoline.

Kim purchased 20 gallons, with the last 10 gallons discounted 10%, meaning that she saved (10)($1)(.1) = $1.00 off of 20 gallons
Isabella purchased 25 gallons, with the last 15 gallons discounted 10%, meaning that she saved (15)($1)(.1) = $1.50 off of 25 gallons

Kim's per-gallon discount is 1/20 = .05; Isabella's per-gallon discount 1.5/25 = 3/50 = .06

Thus, the percent would be .06/.05 = 6/5 = 1.2 = 120%

Final Answer: D

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by Scott@TargetTestPrep » Fri Mar 22, 2019 8:18 am
BTGmoderatorDC wrote: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"Ÿs total per-gallon discount is what percent of Kim"Ÿs total per-gallon discount?

(A) 80%

(B) 100%

(C) 116.7%

(D) 120%

(E) 140%

OA D

Source: Princeton Review
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

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