Forum Home > GMAT > Quantitative > Problem Solving (PS)
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Giulia is planning to sell her car, which is fueled by gasoline (petro
[#permalink]
03 Feb 2024, 06:40
03 Feb 2024, 06:40
2
Kudos
13
Bookmarks
Expert Reply
Show timer
00:00
Difficulty:
95%
(hard)
Question Stats:
38% (03:34) correct
62%
(04:15)
wrong
based on 112
sessions
Giulia is planning to sell her car, which is fueled by gasoline (petrol) and averages 20 miles per gallon (mpg), and purchase a diesel-fueled car that averages 30 mpg. She estimates that her future cost per gallon of diesel fuel will be 5% higher than is her present cost per gallon of gasoline. She wishes to estimate (1) the annual cost of fuel for her new car if she maintains her present annual total miles driven and (2) the annual total miles she can drive her new car if she maintains her present annual expenditure on fuel.
Let x represent Giulia's present annual cost per gallon of gasoline in US dollars, and let y equal her present annual total of miles driven. Select for Cost an appropriate expression for Giulia's estimate of (1) above, and select for Miles an appropriate expression for her estimate of (2) above. Make only two selections, one in each column.
Let x represent Giulia's present annual cost per gallon of gasoline in US dollars, and let y equal her present annual total of miles driven. Select for Cost an appropriate expression for Giulia's estimate of (1) above, and select for Miles an appropriate expression for her estimate of (2) above. Make only two selections, one in each column.
| Cost | Miles | |
| \(\frac{2}{3} * 1.05x\) | ||
| \(\frac{3}{2} * \frac{y}{1.05}\) | ||
| \(\frac{3}{2} * 1.05y\) | ||
| \(\frac{1.05xy}{30} \) | ||
| \(\frac{1.05xy}{20} \) | ||
| \(\frac{20xy}{1.05} \) |
ShowHide Answer
Official Answer
Cost: \(\frac{1.05xy}{30} \)
Miles: \(\frac{3}{2} * \frac{y}{1.05}\)
Re: Giulia is planning to sell her car, which is fueled by gasoline (petro
[#permalink]
15 Mar 2024, 04:16
15 Mar 2024, 04:16
8
Kudos
Expert Reply
An amazing question that shows how using a simple concept like ‘unitary method’ one can make a difficult question – by adding various different layers of complexity.
1. Layer 1 – Applying unitary method twice.
2. Layer 2 – Incorporating translation to understand the scenario on which unitary method is to be applied.
3. Layer 3 – Incorporating variables instead of numbers.
Watch the solution and tell me which layer(s) made this question difficult for you!
Happy Learning!
1. Layer 1 – Applying unitary method twice.
2. Layer 2 – Incorporating translation to understand the scenario on which unitary method is to be applied.
3. Layer 3 – Incorporating variables instead of numbers.
Watch the solution and tell me which layer(s) made this question difficult for you!
Happy Learning!
General Discussion
Tutor
Joined: 11 Aug 2023
Posts: 925
Given Kudos: 83
GMAT 1: 800 Q51 V51
Giulia is planning to sell her car, which is fueled by gasoline (petro
[#permalink]
Updated on: 03 Feb 2024, 09:03
Updated on: 03 Feb 2024, 09:03
1
Kudos
Expert Reply
Giulia is planning to sell her car, which is fueled by gasoline (petrol) and averages 20 miles per gallon (mpg), and purchase a diesel-fueled car that averages 30 mpg. She estimates that her future cost per gallon of diesel fuel will be 5% higher than is her present cost per gallon of gasoline. She wishes to estimate (1) the annual cost of fuel for her new car if she maintains her present annual total miles driven and (2) the annual total miles she can drive her new car if she maintains her present annual expenditure on fuel.
Let x represent Giulia's present annual cost per gallon of gasoline in US dollars, and let y equal her present annual total of miles driven. Select for Cost an appropriate expression for Giulia's estimate of (1) above, and select for Miles an appropriate expression for her estimate of (2) above. Make only two selections, one in each column.
Cost
To find (1) the annual cost of fuel for her new car if she maintains her present annual total miles driven, we need to multiply cost per gallon by total gallons.
Miles
To find (2) the annual total miles she can drive her new car if she maintains her present annual expenditure on fuel, we can just take her current miles and adjust for her new miles per gallon and new cost per gallon.
Correct answer:
Let x represent Giulia's present annual cost per gallon of gasoline in US dollars, and let y equal her present annual total of miles driven. Select for Cost an appropriate expression for Giulia's estimate of (1) above, and select for Miles an appropriate expression for her estimate of (2) above. Make only two selections, one in each column.
Cost
To find (1) the annual cost of fuel for her new car if she maintains her present annual total miles driven, we need to multiply cost per gallon by total gallons.
- Cost per gallon for her new car = current cost * 1.05 = x * 1.05
Total gallons used by her new car annually = miles driven/miles per gallon = y/30
Annual cost of fuel for her new car = x * 1.05 * y/30 = 1.05xy/30
Miles
To find (2) the annual total miles she can drive her new car if she maintains her present annual expenditure on fuel, we can just take her current miles and adjust for her new miles per gallon and new cost per gallon.
- The passage says that her current car "averages 20 miles per gallon" and that the new car "averages 30 mpg." So, for every gallon of gas, she will go 30/20 as far in the new car as she does in her current car. According, to adjust for the new miles per gallon, multiply by 30/20 = 3/2.
To adjust for the new cost per gallon, divide by 1.05 since each gallon she buys will now cost 5% more.
So the new annual total miles she can drive = 3/2 * old total annual miles/1.05 = 3/2 * y/1.05
Correct answer:
1.05xy/30, 3/2 * y/1.05
Originally posted by MartyMurray on 03 Feb 2024, 07:02.
Last edited by MartyMurray on 03 Feb 2024, 09:03, edited 1 time in total.
Last edited by MartyMurray on 03 Feb 2024, 09:03, edited 1 time in total.
