Find all School-related info fast with the new School-Specific MBA Forum

It is currently 15 Sep 2014, 18:59

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

A reduction in the price of petrol by 10% enables a motorist

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Director
Director
User avatar
Joined: 03 Sep 2006
Posts: 893
Followers: 6

Kudos [?]: 126 [0], given: 33

A reduction in the price of petrol by 10% enables a motorist [#permalink] New post 17 Feb 2012, 20:29
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

66% (02:23) correct 34% (01:48) wrong based on 182 sessions
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.
Expert Post
4 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 26582
Followers: 3487

Kudos [?]: 26167 [4] , given: 2705

Re: Percentages-PS [#permalink] New post 17 Feb 2012, 21:16
4
This post received
KUDOS
Expert's post
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.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Expert Post
4 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 26582
Followers: 3487

Kudos [?]: 26167 [4] , given: 2705

Re: Percentages-PS [#permalink] New post 17 Feb 2012, 22:29
4
This post received
KUDOS
Expert's post
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.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

2 KUDOS received
Manager
Manager
avatar
Joined: 28 Dec 2012
Posts: 50
Schools: LBS '14
Followers: 1

Kudos [?]: 15 [2] , given: 55

Re: A reduction in the price of petrol by 10% enables a motorist [#permalink] New post 05 Jan 2013, 02:25
2
This post received
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!!!

Some kudos please.. I need 50.. am working hard to get them!!!
2 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 23 Oct 2010
Posts: 384
Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38
Followers: 12

Kudos [?]: 134 [2] , given: 73

GMAT ToolKit User
Re: A reduction in the price of petrol by 10% enables a motorist [#permalink] New post 27 Jan 2013, 03:55
2
This post received
KUDOS
NP=180
0.9P(N+5)=180

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

P=180/45=4
_________________

Happy are those who dream dreams and are ready to pay the price to make them come true

1 KUDOS received
Manager
Manager
avatar
Joined: 27 May 2012
Posts: 213
Followers: 0

Kudos [?]: 47 [1] , given: 169

Re: A reduction in the price of petrol by 10% enables a motorist [#permalink] New post 04 Sep 2012, 07:16
1
This post received
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
_________________

- Stne

1 KUDOS received
Intern
Intern
avatar
Joined: 08 Jan 2013
Posts: 4
Followers: 0

Kudos [?]: 3 [1] , given: 1

Re: A reduction in the price of petrol by 10% enables a motorist [#permalink] New post 10 Jan 2013, 11:54
1
This post received
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
Senior Manager
Senior Manager
User avatar
Status: May The Force Be With Me (D-DAY 15 May 2012)
Joined: 06 Jan 2012
Posts: 292
Location: India
Concentration: General Management, Entrepreneurship
Followers: 1

Kudos [?]: 83 [0], given: 16

Reviews Badge
Re: Percentages-PS [#permalink] New post 17 Feb 2012, 20:41
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 :-D
_________________

Giving +1 kudos is a better way of saying 'Thank You'.


Last edited by boomtangboy on 17 Feb 2012, 20:54, edited 1 time in total.
Director
Director
User avatar
Joined: 03 Sep 2006
Posts: 893
Followers: 6

Kudos [?]: 126 [0], given: 33

Re: Percentages-PS [#permalink] New post 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


Please check again, what the question is asking.
Director
Director
User avatar
Joined: 03 Sep 2006
Posts: 893
Followers: 6

Kudos [?]: 126 [0], given: 33

Re: Percentages-PS [#permalink] New post 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 :-D


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?
Director
Director
User avatar
Joined: 03 Sep 2006
Posts: 893
Followers: 6

Kudos [?]: 126 [0], given: 33

Re: Percentages-PS [#permalink] New post 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
Intern
avatar
Joined: 09 Oct 2013
Posts: 5
Followers: 0

Kudos [?]: 3 [0], given: 1

Re: A reduction in the price of petrol by 10% enables a motorist [#permalink] New post 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...
SVP
SVP
User avatar
Joined: 06 Sep 2013
Posts: 1661
Location: United States
Concentration: Finance
GMAT 1: 710 Q48 V39
WE: Corporate Finance (Investment Banking)
Followers: 12

Kudos [?]: 164 [0], given: 268

GMAT ToolKit User
Re: A reduction in the price of petrol by 10% enables a motorist [#permalink] New post 03 Jan 2014, 06:45
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!
J :)
Re: A reduction in the price of petrol by 10% enables a motorist   [#permalink] 03 Jan 2014, 06:45
    Similar topics Author Replies Last post
Similar
Topics:
1 On a certain road, 10 percent of the motorist exceed the GMATT73 6 22 Jan 2006, 04:28
On a certain road, 10% of the motorists exceed the posted ludwigvb 2 20 Nov 2005, 07:36
Experts publish their posts in the topic On a certain road, 10% of the motorists exceed the posted rahulraao 4 03 Sep 2005, 05:12
7 Experts publish their posts in the topic On a certain road 10% of the motorists exceed the posted spe mandy 6 14 Jun 2005, 08:00
On a certain road 10 percent of hte motorists exceed the vprabhala 5 16 Jan 2005, 11:33
Display posts from previous: Sort by

A reduction in the price of petrol by 10% enables a motorist

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.