Karina is deciding whether to use Brand A or Brand B motor oil in her

Question

Karina is deciding whether to use Brand A or Brand B motor oil in her car. Brand A costs 50% more per liter than Brand B. But, according to the recommendations for frequency of oil changes, if she uses Brand A, she will be able to drive 2.5 times as many kilometers before she changes her oil as she will if she uses Brand B. The cost per kilometer driven is what percent less when using Brand A than when using Brand B ?

A. $33\frac{1}{3}$%

B. 40%

C. 50%

D. 60%

E. $66\frac{2}{3}$%

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Official Answer

B

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JeffTargetTestPrep · Accepted Answer

Brand B:

cost = c

total kilometers = d

cost per kilometer = c/d

Brand A:

cost = 1.5c

total kilometers = 2.5d

cost per kilometer = 1.5c/2.5d = (3/5)(c/d)

Therefore,

percent less =  /(c/d)

percent less = 1 – 3/5 = 2/5 = 40%

Answer: B

gmatophobia · Answer

Let's jot down the information provided in the question stem in a tabular format.

Assume that the price per liter of Brand B oil = $100 
 The price per liter of Brand A oil = $100 (1+0.5) = $150

Assume that the distance that can be traveled using Brand B oil = 100 km 
 The distance that can be traveled using Brand A oil = $100 (2.5) = 250 km

Cost per kilometer for Brand B oil =  \frac{100 }{ 100} = $1  
 Cost per kilometer for Brand A oil =  \frac{150 }{ 250} = $\frac{3}{5}

Difference = $ (1-\frac{3}{5}) = \frac{2}{5}

Percentage =  \frac{2}{5} * 100 = 40 %

katkot · Answer

Okay I am slightly confused about this question. How do you decide the percentage has to be taken with respect to brand A or brand B? It is slight confusion, but if I take percentage with respect to brand A, I get E as an answer which seems incorrect

Bunuel · Answer

The percentage decrease should be calculated with respect to Brand B's cost because you're comparing how much cheaper Brand A is  than  Brand B per kilometer.

The general formula for calculating percent increase or decrease (percent change) is:  \frac{	ext{Difference in values}}{	ext{Reference value}}*100 . The reference value is the value you are comparing to.

Therefore, for the correct interpretation of 'The cost per kilometer driven is what percent less when using Brand A  than  when using Brand B?', would be  \frac{	ext{Brand B cost per kilometer} - 	ext{Brand A cost per kilometer}}{	ext{Brand B cost per kilometer}} *100 . In this instance, Brand B serves as the reference point since the question asks how much less is cost per kilometer when using Brand A  than  when using Brand B.

Hope it's clear.

Jayam12 · Answer

gmatophobia  - I didn't understand something. How do we know what is the mileage in this question. Do we simple assume that if the cost of 1 litre of brand B oil is 100, then the mileage is also 1litre/km. What if the distance covered is 100km using brand B oil but its mileage is 50 km/litre. That would be mean the total cost incurred to cover that distance would be 200 bucks and not 100

gmatophobia · Answer

Jayam12

The question mentions motor oil and not gasoline. Hence, mileage has no impact here.

KarishmaB · Answer

We are dealing with motor oil here, not fuel, but the handling is no different. You need certain amount of fuel (petrol/diesel) for each km driven. Similarly, you need certain amount of motor oil which "gets used" as you drive and after some kms, it needs to be replaced. When dealing with confusing quantities such as 'mileage' or 'cost per km' etc focus on the units. Here we are given: Brand A - Cost per litre = 1.5x , Distance per oil change = 2.5y km Brand B - Cost per litre = x, Distance per oil change = y km Same amount of oil will be filled at each change whether it is brand A or B so let's just assume its 1 ltr. Cost per kilometer = Cost per litre/Distance per litre Cost per kilometer for Brand A = \frac{1.5x}{2.5y} = \frac{3x}{5y} Cost per kilometer for Brand B = \frac{x}{y} Hence, cost per km is 40% less for Brand A. Answer (B) Check out another question in which using units to solve helps here: https://youtu.be/_s5vZE-csgY

lavanya.18 · Answer

Brand A Brand B
150 Rs/litre 100 Rs/litre
2.5x km x km

150/2.5x=60/x 100/x

100/x-60/x= 40/x ie. 40 %

bhealy757 · Answer

Had a different approach but got the correct answer.
Since brand a is 50 percent greater that brand b I started my equations a=1.5b
Since brand a extends the amount of kilometers before oil change by 2.5 I divided this (2.5) by the price of a, new equation. a=1.5b/2.5 then solved.
2.5a=1.5b or 5a/2=3b/2
10a=6b
a=6b/10 or a=60% of b which is 40% less

GulfTube · Answer

since no real values are given and everything is relative, we can pick smart numbers to make our lives easier:

Price per liter of motor oil:
B: $50
A: 150% of $50 = $75

kilometers driven before she changes her oil:
B: 10 km
A: 2.5*10 = 25 km

Cost per kilometer:
A: 75/25 = $3/km
B: 50/10 = $5/km

cost per kilometer driven is what percent less when using Brand A than when using Brand B? 
(5-3)/5 * 100 =  40%

AndyRugger · Answer

This is a question where paying attention to units (dimensions) pays dividends. It can almost create the solution road map for you. 
- Cost (x) is given as $/liter.
- Distance (d) is given as km.
- We are asked to find percentage (dimensionless) of the quantities in  cost/km.

So we have three units: $, liters, and km. This is where a lot of people get tripped up.  Don't I need to know km (distance)? Or assume a "smart" number for the distance? 
 
You can, but you don't have to. Distance, as well as the actual price per liter, will cancel out. Alternatively, you might have the insight that cost-per-liter-per-km will be proportional to cost-per-kilometer, and therefore the percentage differences will be the same. Either way, not necessary.

So cost/km for A and B, respectively, are 1.5x/2.5d and x/d. The (A-B)/B percentage difference equation cancels out quickly to (3/5-1)/1, which is -2/5, which is negative 40 percent.

If you have trouble seeing exactly where the ratios come from ... well, that's the point of the units! You can't subtract apples from oranges, only apples from apples. So you "assign" the numbers you have to the dimensions you need, and wallah! - the equation falls into place.

HarshavardhanR · Answer

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Karina is deciding whether to use Brand A or Brand B motor oil in her

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