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Recently, fuel price has seen a hike of 20%. Mr X is planning to buy a new car with better mileage as compared to his current car. By what % should the new mileage be more than the previous mileage to ensure that Mr X’s total fuel cost stays the same for the month? (assuming the distance traveled every month stays the same)[/b]

Recently, fuel price has seen a hike of 20%. Mr X is planning to buy [#permalink]

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07 Jul 2017, 02:18

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Bunuel wrote:

Recently, fuel price has seen a hike of 20%. Mr X is planning to buy a new car with better mileage as compared to his current car. By what % should the new mileage be more than the previous mileage to ensure that Mr X’s total fuel cost stays the same for the month? (assuming the distance traveled every month stays the same)[/b]

(A) 10% (B) 17% (C) 20% (D) 21% (E) 25%

Answer: B Lets say Price and Mileage before hike are P1 and M1 respectively. After Hike, they are P2 and M2 respectively.

If price per mile is to stay the same, we need to have this equation.

\(P1 / M1 = P2 / M2\)

\(M2 = P2 * M1/P1\)

but P2 is 1.2 times P1.

\(P1 / M1 = 1.2P1 / M2 * P1\)

\(M2 = 1.2M1\)

Difference is 1.2 or 20%.

Edit: Editing after mistake was pointed out by chetan2u _________________

Please hit Kudos if this post helped you inch closer to your GMAT goal. Procrastination is the termite constantly trying to eat your GMAT tree from the inside. There is one fix to every problem, working harder!

Last edited by jedit on 07 Jul 2017, 19:51, edited 2 times in total.

Recently, fuel price has seen a hike of 20%. Mr X is planning to buy a new car with better mileage as compared to his current car. By what % should the new mileage be more than the previous mileage to ensure that Mr X’s total fuel cost stays the same for the month? (assuming the distance traveled every month stays the same)[/b]

(A) 10% (B) 17% (C) 20% (D) 21% (E) 25%

Answer: B Lets say Price and Mileage before hike are P1 and M1 respectively. After Hike, they are P2 and M2 respectively.

We need them to be Equal.

\(P1 * M1 = P2 * M2\)

Hi.. We have to be very careful while making the equation Even the Q tells you that the new mileage INCREASE, so the increase cannot be together both in P and M as the equation taken by you..

What is mileage? D/L... D is same ..

So \(\frac{P_1}{M_1}=\frac{P_2}{M_2}.......m_2=\frac{p_2*m_1}{p_1}\) Ans 20% C
_________________

Re: Recently, fuel price has seen a hike of 20%. Mr X is planning to buy [#permalink]

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07 Jul 2017, 18:30

lets take 1 gallon of gas - 10$ - gives 30miles same eq : 1 gallon of gas - 12$ - give x miles to breakeven. 12*30/10 = 36 , so miles should increase by 6 means 20% increase. Ans C.

Re: Recently, fuel price has seen a hike of 20%. Mr X is planning to buy [#permalink]

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07 Jul 2017, 23:31

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Total cost initially = C * fuel => C * Distance/mileage ( mileage = distance/litre) Let initial mileage be m1 and later mileage be m2 Later cost = 1.2C* Distance/m2 Cost has to remain same => C*D/m1 = 1.2 C* D/m2 =>m2 = 1.2m1 => 20% increase in mileage IMO C

Recently, fuel price has seen a hike of 20%. Mr X is planning to buy a new car with better mileage as compared to his current car. By what % should the new mileage be more than the previous mileage to ensure that Mr X’s total fuel cost stays the same for the month? (assuming the distance traveled every month stays the same)[/b]

(A) 10% (B) 17% (C) 20% (D) 21% (E) 25%

Since the fuel price is directly proportional to mileage of a car; if the fuel price is increased by 20%, the mileage of the car should be increased by 20% as well to keep the total fuel cost the same.

Answer: C
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GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

Re: Recently, fuel price has seen a hike of 20%. Mr X is planning to buy [#permalink]

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20 Jul 2017, 04:10

chetan2u wrote:

jedit wrote:

Bunuel wrote:

Recently, fuel price has seen a hike of 20%. Mr X is planning to buy a new car with better mileage as compared to his current car. By what % should the new mileage be more than the previous mileage to ensure that Mr X’s total fuel cost stays the same for the month? (assuming the distance traveled every month stays the same)[/b]

(A) 10% (B) 17% (C) 20% (D) 21% (E) 25%

Answer: B Lets say Price and Mileage before hike are P1 and M1 respectively. After Hike, they are P2 and M2 respectively.

We need them to be Equal.

\(P1 * M1 = P2 * M2\)

Hi.. We have to be very careful while making the equation Even the Q tells you that the new mileage INCREASE, so the increase cannot be together both in P and M as the equation taken by you..

What is mileage? D/L... D is same ..

So P1/M1=P2/M2.......m2=p2*m1p1 Ans 20% C

Hi Chetan2u,

I guess you mentioned to say, m2 = p2*(m1/p1) _________________

Re: Recently, fuel price has seen a hike of 20%. Mr X is planning to buy [#permalink]

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30 Aug 2017, 08:26

jedit wrote:

Bunuel wrote:

Recently, fuel price has seen a hike of 20%. Mr X is planning to buy a new car with better mileage as compared to his current car. By what % should the new mileage be more than the previous mileage to ensure that Mr X’s total fuel cost stays the same for the month? (assuming the distance traveled every month stays the same)[/b]

(A) 10% (B) 17% (C) 20% (D) 21% (E) 25%

Answer: B Lets say Price and Mileage before hike are P1 and M1 respectively. After Hike, they are P2 and M2 respectively.

If price per mile is to stay the same, we need to have this equation.

\(P1 / M1 = P2 / M2\)

\(M2 = P2 * M1/P1\)

but P2 is 1.2 times P1.

\(P1 / M1 = 1.2P1 / M2 * P1\)

\(M2 = 1.2M1\)

Difference is 1.2 or 20%.

Edit: Editing after mistake was pointed out by chetan2u

hi

okay with your solution ...

can you, however, apply the same logic to the following problem ....??

The cost of fuel increases by 10%. By what % must the consumption of fuel decrease to keep the overall amount spent on the fuel same?

Re: Recently, fuel price has seen a hike of 20%. Mr X is planning to buy [#permalink]

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01 Dec 2017, 06:03

Bunuel wrote:

Recently, fuel price has seen a hike of 20%. Mr X is planning to buy a new car with better mileage as compared to his current car. By what % should the new mileage be more than the previous mileage to ensure that Mr X’s total fuel cost stays the same for the month? (assuming the distance traveled every month stays the same)[/b]

(A) 10% (B) 17% (C) 20% (D) 21% (E) 25%

Hi, please explain whether mileage is miles/gallon or dollars/mile?

Please also help to solve this question in the most efficient manner. VeritasPrepKarishma your help is greatly appreciated.
_________________

Re: Recently, fuel price has seen a hike of 20%. Mr X is planning to buy [#permalink]

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05 Jan 2018, 20:18

ShashankDave wrote:

Bunuel wrote:

Recently, fuel price has seen a hike of 20%. Mr X is planning to buy a new car with better mileage as compared to his current car. By what % should the new mileage be more than the previous mileage to ensure that Mr X’s total fuel cost stays the same for the month? (assuming the distance traveled every month stays the same)[/b]

(A) 10% (B) 17% (C) 20% (D) 21% (E) 25%

Hi, please explain whether mileage is miles/gallon or dollars/mile?

Please also help to solve this question in the most efficient manner. VeritasPrepKarishma your help is greatly appreciated.

---------------------------

This can be seen as a problem with 2 inverse variations: 1. Since Mr.X want to be keep his fuel cost = const , the fuel hike would mean low fuel consumption i.e cost = fuel price * fuel consumption = constant after 20% hike, new fuel price = (fuel price)*(120/100) ---(a) (fuel price) * (fuel consumption) = (new fuel price)*(fuel consumption) On substituting (a) in the above, we get: => new fuel consumption = (fuel consumption) 100/120 {meaning fuel consumption has decreased now)

2. Next is about mileage, now Mr.X wants better mileage to handle the decreased fuel consumption

(old Mileage) * (fuel consumption) = (new mileage) * (new fuel consumption)

since new fuel consumption = (fuel consumption) 100/120

new mileage = (old mileage) * 120/100 => indicating a 20 % increase needed in mileage