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Due to a sudden 20% increase in price, one is now able to buy 4 gallon

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Concentration: Technology, General Management
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Due to a sudden 20% increase in price, one is now able to buy 4 gallon  [#permalink]

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17 Oct 2017, 05:28
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Difficulty:

65% (hard)

Question Stats:

58% (01:32) correct 42% (01:59) wrong based on 55 sessions

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Due to a sudden 20% increase in price, one is now able to buy 4 gallons lesser oil than earlier on the same expenditure of
$600. What is the dollar increase in the price of oil per gallon? A.$2
B. $5 C.$10
D. $20 E.$25

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email: nkmungila@gmail.com
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Due to a sudden 20% increase in price, one is now able to buy 4 gallon  [#permalink]

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17 Oct 2017, 06:14
nkmungila wrote:
Due to a sudden 20% increase in price, one is now able to buy 4 gallons lesser oil than earlier on the same expenditure of
$600. What is the dollar increase in the price of oil per gallon? A.$2
B. $5 C.$10
D. $20 E.$25

Test the answers. The equation for this one was taking too long. Backsolving was quick.

(Price per gallon P) * (# of gallons Q) = Total cost

Q = Total cost/price per gallon

1) Find original price from given dollar increase

2) Find original # of gallons by dividing $600 by old price per gallon 3) Find new price = (1.2)($old), OR
($Old price + added$ increase)

4) Find new # gallons. Divide 600 by new price

Answer C) $10$10 is both the dollar increase in price and a .20 increase of original price, x

Original price:

$10 = .2x = $$\frac{10}{.2} = 50$$ Original number of gallons: $$\frac{600}{50PerGal} = 12$$ gallons New price:$50 + $10 (or 1.2 *$50) = $60 New number of gallons $$\frac{600}{60per} = 10$$ gallons 12 - 10 = 2 fewer gallons now. Too small. That means the dollar price increase is too large. To increase quantity, decrease price. Try B)$5

$5 = .2x Original price: $$\frac{5}{.2} = 25$$ Original quantity: $$\frac{600}{25per} = 24$$ gallons New price: (1.2)($25) or ($25 +$5) = $30 New quantity: $$\frac{600}{30per} = 20$$ gallons 24 - 20 = 4 gallons. Correct Answer B _________________ In the depths of winter, I finally learned that within me there lay an invincible summer. -- Albert Camus, "Return to Tipasa" Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 3180 Location: United States (CA) Re: Due to a sudden 20% increase in price, one is now able to buy 4 gallon [#permalink] Show Tags 19 Oct 2017, 10:16 nkmungila wrote: Due to a sudden 20% increase in price, one is now able to buy 4 gallons lesser oil than earlier on the same expenditure of$600. What is the dollar increase in the price of oil per gallon?

A. $2 B.$5
C. $10 D.$20
E. \$25

We can let the original number of gallons of oil = n and the original price = p; thus:

np = 600

and

(1.2p)(n - 4) = 600

1.2np - 4.8p = 600

Substituting 600 for np in the above equation, we have:

1.2(600) - 4.8p = 600

720 - 4.8p = 600

120 = 4.8p

25 = p

The old price was 25, and the new price is 20% more: 25 x 1.2 = 30. Thus, the increase in price is 5 dollars.

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Re: Due to a sudden 20% increase in price, one is now able to buy 4 gallon &nbs [#permalink] 19 Oct 2017, 10:16
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