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

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Joined: 07 Jun 2017
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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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New post 17 Oct 2017, 05:28
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Difficulty:

  65% (hard)

Question Stats:

54% (01:49) correct 46% (02:11) wrong based on 37 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
[Reveal] Spoiler: OA

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Naveen
email: nkmungila@gmail.com
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Kudos [?]: 90 [0], given: 59

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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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New post 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

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

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New post 19 Oct 2017, 10:16
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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.

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