12 Days of Christmas GMAT Competition - Day 2: This week, Alice drove

Question

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This week, Alice drove a total distance that is 20% less than what she covered the previous week. Yet, her petrol expenditure for the week rose by 20%. Assuming petrol consumption directly proportional with distance driven, by what percentage has the price of petrol increased this week?

A. 20%
B. 25%
C. 40%
D. 50%
E. 100%

Last week drove X, this week drove 0.8X
Last week consumed Y, this week consumed 1.2Y
so (1.2Y/0.8X-Y/X)/y/x*100 = 50% -->D

A. 20%
B. 25%
C. 40%
D. 50%
E. 100%

Bunuel · Accepted Answer

GMAT Club Official Explanation:

This week, Alice drove a total distance that is 20% less than what she covered the previous week. Yet, her petrol expenditure for the week rose by 20%. Assuming petrol consumption directly proportional with distance driven, by what percentage has the price of petrol increased this week?

A. 20%
B. 25%
C. 40%
D. 50%
E. 100%

Last week drove X, this week drove 0.8X
Last week consumed Y, this week consumed 1.2Y
so (1.2Y/0.8X-Y/X)/y/x*100 = 50% -->D

A. 20%
B. 25%
C. 40%
D. 50%
E. 100%

Assume that last week Alice drove 100 km and spent $100 on petrol. This gives a price per kilometer of $1.

This week, Alice drove 80 km (20% less) and spent $120 (20% more), resulting in a price per kilometer of $120/80 = $1.5.

Therefore, the price of petrol increased by 50% this week.

Answer: D.

Kinshook · Answer

Given:  This week, Alice drove a total distance that is 20% less than what she covered the previous week. Yet, her petrol expenditure for the week rose by 20%. 
 Asked:  Assuming petrol consumption directly proportional with distance driven, by what percentage has the price of petrol increased this week?

Let the percentage increase in petrol price be x%

Petrol expenditure = Petrol consumption * Petrol Price = Constant * Distance driven * Petrol Price

(Petrol expenditure this week / Petrol expenditure last week) = (Distance driven this week / Distance driven last week) * (Petrol price this week/ Petrol price last week)
(1+20%/100) = 1.2/1 = (1-20%/100)*(1+x%/100)/1 = .8/1 * (1+x%/100)/1 
1 + x%/100 = 1.2/.8 = 1.5
x = 50%

IMO D

Median · Answer

Alice drove 20% less distance this week compared to the previous week, but her petrol expenses increased by 20%. Assuming that fuel consumption is directly proportional to distance, the increase in petrol cost can be attributed solely to the rise in petrol prices. If we let the previous week's petrol price be 100%, then the new price is 120% of the cost for 80% of the distance. To find the percentage increase in petrol price, we calculate the new price for the same distance as before (which would be 120% / 80% of the original price), and then subtract 100% to find the percentage increase.

sj296 · Answer

Last week

Total distance = d
Petrol price per ltr = P

Total petrol consumed = k*d where k is some constant and d is the distance traveled.

petrol expenditure = k*d*P..............(1)

This week

Total distance traveled = 0.8d.......(given)
Total petrol consumed = 0.8kd................where k is some constant

Petrol price per ltr = P'

petrol expenditure = P'*0.8k*d..........(2)

Now, we are given P'*0.8k*d = 1.2 k*d*P

After solving P' = 1.5 P

% increase =  \frac{(P'-P)}{P}  = 50%

OA should be D

limuengaoey · Answer

This week, Alice drove a total distance that is 20% less than what she covered the previous week. Yet, her petrol expenditure for the week rose by 20%. Assuming petrol consumption directly proportional with distance driven, by what percentage has the price of petrol increased this week?

A. 20%
B. 25%
C. 40%
D. 50%
E. 100%

Last week drove X, this week drove 0.8X
Last week consumed Y, this week consumed 1.2Y
so (1.2Y/0.8X-Y/X)/y/x*100 = 50% -->D

A. 20%
B. 25%
C. 40%
D. 50%
E. 100%

Last week drove X, this week drove 0.8X
Last week consumed Y, this week consumed 1.2Y
so (1.2Y/0.8X-Y/X)/y/x*100 = 50% -->D

missionmba2025 · Answer

Distance covered last week = 100 miles

Cost of petrol last week = $100

Cost of petrol per mile = $1/mile

Distance covered this week = 80 miles

Cost of petrol this week = $120

Cost of petrol per mile = $120/80 = 3/2 = $1.5 / mile

Increase in cost = $0.50

Percentage increase = 0.5/1 * 100 = 50%

IMO D

vishal_gupta · Answer

Let distance travelled pvs week = x
distance travelled this week = 0.8x
Price of petrol/liter pvs week = y
Price of petrol/liter this week= z
Given,
Total petrol expenditure this week = 1.2 * Total petrol expenditure pvs week
Petrol consumption(liter)* price/liter pvs week = k*x*y
Petrol consumption(liter)* price/liter this week = k*0.8x*z

So,
k*0.8x*z = 1.2*k*x*y
=> z/y = 1.5.

Hence % increase in petrol price = 50%

D is correct.

amitgangane00 · Answer

Last week distance = 100km
This week distance (-20%) = 80km

Petrol expenditure last week - Rs 100
Petrol expenditure this week(+20%) = Rs 120

Price per Km (Last week) = Rs 1
Price Per Km(This week) = Rs 1.5

%Increase = (1.5-1)/1 *100 = 50%

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12 Days of Christmas GMAT Competition - Day 2: This week, Alice drove

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