A reduction in the price of petrol by 10% enables a motorist : GMAT Problem Solving (PS)
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# A reduction in the price of petrol by 10% enables a motorist

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A reduction in the price of petrol by 10% enables a motorist [#permalink]

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17 Feb 2012, 20:29
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55% (hard)

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68% (02:42) correct 32% (01:51) wrong based on 333 sessions

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A reduction in the price of petrol by 10% enables a motorist to buy 5 gallons more for $180. Find the original price of petrol? A.$11
B. $5 C.$45
D. $400 E.$4
[Reveal] Spoiler: OA

Last edited by LM on 17 Feb 2012, 20:44, edited 1 time in total.
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17 Feb 2012, 21:16
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LM wrote:
A reduction in the price of petrol by 10% enables a motorist to buy 5 gallons more for $180. Find the original price of petrol? A.$11
B. $5 C.$45
D. $400 E.$4

Price decreased by 10%, so 9/10 times, which means that original gallons bought increased 10/9 times. Since this increase equals to 5 gallons then 45 gallons were bought originally (45*10/9=50 --> increase 5 gallons). Hence original price was 180/45=$4. Answer: E. P.S. One can also use backsolving to get the answer. Hope it's clear. _________________ Math Expert Joined: 02 Sep 2009 Posts: 36583 Followers: 7087 Kudos [?]: 93284 [4] , given: 10555 Re: Percentages-PS [#permalink] ### Show Tags 17 Feb 2012, 22:29 4 This post received KUDOS Expert's post 1 This post was BOOKMARKED LM wrote: Thanks a lot! How did you quickly arrive at this short method (which I was looking to!) 9/10 decrease will lead to increase of 10/9. This seems to be the key and short cut! Little more explanation or any hint or link within posts would be helpful. Awesome approach! Consider this: original price of an item is$10, decrease the price by 50%: new price $5 ($10*1/2=$5). Now, for some fixed amount of money, say for$100, you'll be able to buy twice as many items for $5 (100/$5=20) than for $10 (100/$10=10): reduction in price (1/2) reciprocal of increase in quantity (2) (or simply for half of the price you'll buy twice as many in quantity). The same for the original question.

Hope it helps.
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Re: A reduction in the price of petrol by 10% enables a motorist [#permalink]

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05 Jan 2013, 02:25
3
KUDOS
LM wrote:
A reduction in the price of petrol by 10% enables a motorist to buy 5 gallons more for $180. Find the original price of petrol? A.$11
B. $5 C.$45
D. $400 E.$4

Here is a short-cut:

Since price decreased by 10% ( i e 1/10) so for same 180$, quantity increase will be 11.11% (i e 1/9). So the increase in quantity will be 1/9 of original which is given to be 5. So original quantity was 5*9 = 45. Thus original price was 180$/45 = 4 $. Concept explanation: When ever there are problems involving change (like increase decrease) the numerator is either added or substracted from the denominator to change base. Ex. SP = 600$. Profit % = 20%. Now, Profit in $? Profit % is calculated on CP. Profit% = (P*100/CP) but wee are given SP. SO we change the base from CP to SP. 20% of CP = 1/5 of CP = 1/6 of SP = 1/6 of 600 = 100$.
We have added numerator to denominator because new base required is SP, which is larger in case of profit. If it were loss, we would have subtracted.
(P/CP )*100% is on base CP (denominator). which can be base changed to SP. SP = P+CP. thus, Profit % can also be shown like (P/(P+CP))*100%

I will be posting so more examples soon... hope this helps and add value to this wonderfull site!!!

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Re: A reduction in the price of petrol by 10% enables a motorist [#permalink]

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27 Jan 2013, 03:55
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NP=180
0.9P(N+5)=180

0.9P(N+5)=NP
N=45

P=180/45=4
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Re: A reduction in the price of petrol by 10% enables a motorist [#permalink]

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04 Sep 2012, 07:16
2
KUDOS
LM wrote:
A reduction in the price of petrol by 10% enables a motorist to buy 5 gallons more for $180. Find the original price of petrol? A.$11
B. $5 C.$45
D. $400 E.$4

initially he got $$x$$ gallons for $180 so 1 gallon = $$\frac{180}{x}$$-- old price per gallon after reduction of price he got 5 gallons more , $$x+5$$ gallons for$180 so 1 gallon = $$\frac{180}{x+5}$$----new price per gallon

now old price decreased by 10%, so 90% of old price = new price

$$(\frac{90}{100})(\frac{180}{x}) = \frac{180}{x+5}$$ --> simplifying $$\frac{162}{x} = \frac{180}{x+5}$$
now solving for x we get x= 45 ,so initially he got 45 gallons for 180 hence price of 1gallon $$\frac{180}{45} = 4$$
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Re: A reduction in the price of petrol by 10% enables a motorist [#permalink]

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10 Jan 2013, 11:54
1
KUDOS
I have a slightly different approach where we can directly arrive at the original unit price.

Let x be the unit price. We know that we get 5 gallons more after the discount. So the difference is 5.
This difference can be expressed as below

180/.9x minus 180/x = 5 where 180/.9x is the no. of gallons we get after discount and 180/x is the no. of gallons we get before discount

solving for x gives you 180/45 = 4

Hope this approach helps.
thanks,
Mohan
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Re: A reduction in the price of petrol by 10% enables a motorist [#permalink]

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03 Jan 2014, 06:45
1
KUDOS
LM wrote:
A reduction in the price of petrol by 10% enables a motorist to buy 5 gallons more for $180. Find the original price of petrol? A.$11
B. $5 C.$45
D. $400 E.$4

This is more of a word problem, but anyways

One gets (0.9P)(Q+5)=180

Now, once we have this it is better to backsolve. Obviously, D is total out.
I'll start with E since answer choices are not in order and I'm guessing GMAT expects me to work in order

180/4 = 45

Replacing in original equaiton one gets (9/10*4)(50) = 180

It matches so answer is E

Hope it helps
Gimme Kuddos if it does ok?

Cheers!
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17 Feb 2012, 20:41
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I think this is the way to solve it not really sure

Let X be no of litres of petrol & n be the price per litre

Eqn 1 : x*n = 180

Eqn 2 : (x+5) * (0.9n) = 180

Simplifying eqn 2

0.9xn + 4.5n = 180

Substituting eqn 1 in eqn 2

0.9 ( 180) + 4.5n = 180

n = 18/4.5 = 4

Hence E

PS : Thanxs LM for pointing out my error
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Last edited by boomtangboy on 17 Feb 2012, 20:54, edited 1 time in total.
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17 Feb 2012, 20:44
boomtangboy wrote:
I think this is the way to solve it not really sure

$100 - > 100 Litre$ 90 -> 105 Litre
$180 - > ? => 180 * 105 /90 => 210 180/210 => 6/7 =>$ 0.14 / Litre

=> 210 Litres

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17 Feb 2012, 21:00
boomtangboy wrote:
I think this is the way to solve it not really sure

Let X be no of litres of petrol & n be the price per litre

Eqn 1 : x*n = 180

Eqn 2 : (x+5) * (0.9n) = 180

Simplifying eqn 2

0.9xn + 4.5n = 180

Substituting eqn 1 in eqn 2

0.9 ( 180) + 4.5n = 180

n = 18/4.5 = 4

Hence E

PS : Thanxs LM for pointing out my error

Correct and systematic approach. I was just wondering whether it can be solved within a minute or so without making efforts of too much calculations. Any fast method to solve percentages in such kind of questions?
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17 Feb 2012, 22:12
Bunuel wrote:
LM wrote:
A reduction in the price of petrol by 10% enables a motorist to buy 5 gallons more for $180. Find the original price of petrol? A.$11
B. $5 C.$45
D. $400 E.$4

Price decreased by 10%, so 9/10 times, which means that original gallons bought increased 10/9 times. Since this increase equals to 5 gallons then 45 gallons were bought originally (45*10/9=50 --> increase 5 gallons). Hence original price was 180/45=$4. Answer: E. P.S. One can also use backsolving to get the answer. Hope it's clear. Thanks a lot! How did you quickly arrive at this short method (which I was looking to!) 9/10 decrease will lead to increase of 10/9. This seems to be the key and short cut! Little more explanation or any hint or link within posts would be helpful. Awesome approach! Intern Joined: 09 Oct 2013 Posts: 5 Followers: 1 Kudos [?]: 6 [0], given: 1 Re: A reduction in the price of petrol by 10% enables a motorist [#permalink] ### Show Tags 21 Oct 2013, 10:58 LM wrote: A reduction in the price of petrol by 10% enables a motorist to buy 5 gallons more for$180. Find the original price of petrol?

A. $11 B.$5
C. $45 D.$400
E. \$4

The question never explicitly states that .9P(X+5) = PX...
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04 Nov 2016, 00:42
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Re: A reduction in the price of petrol by 10% enables a motorist [#permalink]

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06 Dec 2016, 17:35
pq=180
0.90p(q+5)=180

0.90pq+4.5p=180
0.90(180)+4.5p=180
4.5p=18
p=4

E.
Re: A reduction in the price of petrol by 10% enables a motorist   [#permalink] 06 Dec 2016, 17:35
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