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

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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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A
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E

Difficulty:

  75% (hard)

Question Stats:

57% (02:36) correct 43% (02:44) wrong based on 94 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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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
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]

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New post 20 Oct 2018, 12:35
Can we solve this using a logical approach??
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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 20 Oct 2018, 12:51
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Let the price of gasoline be x. New Price = 1.2x

\(\frac{600}{x} - \frac{600}{1.2x} = 4\)

120 = 4.8x
x = 25
New price = 30
Increase = 5$
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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 20 Oct 2018, 13:12
1
castiel wrote:
Can we solve this using a logical approach??

Apart from algebra you could solve it using percentage.

Initial amount = 100
Now price increased by 20% = 120
Since the price increased , you need to decrease consumption by 20/120 * 100 = 16.67% or 1/6 to keep your expenditure the same.

This 16.67% decrease = 4 units of gasoline
Therefore , 100% = 24 units of gasoline
Initial quality = 24 units ; Initial price = 600/24 = 25$
Final quantity = 20 units ; Final Price = 600/20 = 30$

Increase = 5$
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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 21 Oct 2018, 01:34
Got it!

Thanks pandeyashwin :thumbup:
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Due to a sudden 20% increase in price, one is now able to buy 4 gallon   [#permalink] 21 Oct 2018, 01:34
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