12 Days of Christmas GMAT Competition - Day 9: A parking lot contains

Question

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A parking lot contains 60 vehicles, a mix of cars and trucks. Each car weighs 1.5 tons, and each truck weighs 3.5 tons. The current average (arithmetic mean) weight of the vehicles in the lot is 3 tons. Assuming no cars leave the lot, how many trucks must leave to reduce the average weight of the remaining vehicles to 2 tons?

A. 5
B. 25
C. 30
D. 40
E. 45

Bunuel · Accepted Answer

GMAT Club's Official Explanation:

The current average weight of all vehicles is 3 tons. Cars weigh 1.5 tons, which is 1.5 tons below the average, while trucks weigh 3.5 tons, which is 0.5 tons above the average. To maintain this average, there must be three times as many trucks as cars. With a total of 60 vehicles, this gives 15 cars and 45 trucks.

We need to remove only trucks so that the average weight drops to 2 tons. Similarly, 2 tons is 0.5 away from the weight of cars (1.5 tons) and 1.5 away from the weight of trucks (3.5 tons). Therefore, after removing some number of trucks, there must be three times as many cars as trucks remaining.

Since there are 15 cars, the remaining number of trucks must be 15/3 = 5 trucks.

Thus, 45 - 5 = 40 trucks must leave the lot.

Answer: D

siddhantvarma · Answer

Let x = number of cars, y = number of trucks
x + y = 60 (total vehicles) ........... (1)
1.5x + 3.5y = 180 (total weight = 60 × 3 tons) .......... (2)

From first equation: x = 60 - y
Substituting into second equation:
 1.5(60 - y) + 3.5y = 180
 90 - 1.5y + 3.5y = 180
 90 + 2y = 180
 y = 45 trucks, so x = 15 cars

After z trucks leave:
New total vehicles = 60 - z
New total weight = (1.5 × 15) + (3.5 × (45-z))
New average = 2 tons

(22.5 + 157.5 - 3.5z)/(60-z) = 2
 180 - 3.5z = 120 - 2z
 -3.5z + 2z = 120 - 180
 -1.5z = -60
 z = 40

Therefore, 40 trucks must leave to reduce the average to 2 tons.

Answer: D. 40

GraCoder · Answer

Total initial weight = 180 tons
Let number of cars = x
Number of trucks = 60 - x
Total weight = 3.5(60-x) + 1.5x = 210 - 2x = 180
x => 15 cars and 45 trucks

Now if y trucks leave => total vehicles = 60 - y
New total weight = 2*(60-y)
2*(60-y) = 15(1.5) + (45 - y)*3.5
y = 40

AbhiS101 · Answer

We are given the total number of vehicles (60), the average weight of all vehicles (3 tons), and the individual weights of cars (1.5 tons) and trucks (3.5 tons).
We also know that the goal is to reduce the average weight of the remaining vehicles to 2 tons by removing some trucks.
 Solve for the initial number of cars and trucks:
 Let 'c' represent the number of cars and 't' represent the number of trucks.
We have two equations:
c + t = 60 (total number of vehicles)
1.5c + 3.5t = 180 (total weight of all vehicles)
Solving these equations simultaneously gives us:
c = 15
t = 45
 Calculate the new conditions after removing 'x' trucks:
 After removing 'x' trucks:
Number of remaining vehicles = 60 - x
Number of remaining trucks = 45 - x
Number of remaining cars = 15
New total weight = 1.5(15) + 3.5(45 - x) = 180 - 3.5x
 Solve for the number of trucks to remove ('x'):
 We set up the equation for the new average weight:
(New total weight) / (Number of remaining vehicles) = 2
(180 - 3.5x) / (60 - x) = 2
x=40

IMO D

Kinshook · Answer

A parking lot contains 60 vehicles, a mix of cars and trucks. Each car weighs 1.5 tons, and each truck weighs 3.5 tons. The current average (arithmetic mean) weight of the vehicles in the lot is 3 tons.

Assuming no cars leave the lot, how many trucks must leave to reduce the average weight of the remaining vehicles to 2 tons?

Ratio of number of cars to number of trucks = (3.5-3): (3-1.5) = .5:1.5 = 1:3

Number of cars = 60*1/4 = 15
Number of trucks = 60*3/4 = 45

Let us assume that x trucks must leave to reduce the average weight of the remaining vehicles to 2 tons.

15*1.5 + (45-x)*3.5 = (60-x)*2
22.5 + 157.5 - 3.5x = 120 - 2x
60 = 1.5x
x = 60/1.5 = 40

40 trucks must leave to reduce the average weight of the remaining vehicles to 2 tons

IMO D

ManifestDreamMBA · Answer

Using the weighted average,

trucks/cars = (3-1.5)/(3.5-3) = 3/1
So cars = 1/4*60 = 15
trucks = 3/4 * 60 = 45

For the avg weight to be 20
remaining trucks/remaining car = (2-1.5)/(3.5-2) = 1/3
1/3 = remaining trucks/15
remaining trucks = 5

Trucks to leave = 45-5 = 40

Sanjay9822 · Answer

We have a parking lot with 60 vehicles, a mix of cars and trucks. The cars weigh 1.5 tons, and the trucks weigh 3.5 tons. The current average weight is 3 tons, and we want to reduce the average weight to 2 tons by having some trucks leave. Let’s figure out how many trucks need to leave.

Step 1: Define Variables
Let:

c = number of cars
t = number of trucks
We know:

c + t = 60 (total number of vehicles)
Each car weighs 1.5 tons, each truck weighs 3.5 tons.
Average weight = 3 tons, so total weight = 60 * 3 = 180 tons.
Step 2: Write the Total Weight Equation
Total weight of cars and trucks: 1.5c + 3.5t = 180

Step 3: Solve the System of Equations
From c + t = 60, solve for c: c = 60 - t

Substitute into the total weight equation: 1.5(60 - t) + 3.5t = 180 90 - 1.5t + 3.5t = 180 2t = 90 t = 45

So, there are 45 trucks and 15 cars in the lot.

Step 4: Determine How Many Trucks Must Leave
Let x be the number of trucks that need to leave.

After x trucks leave:

Remaining trucks = 45 - x
Remaining vehicles = 60 - x
Total remaining weight = 1.5 * 15 + 3.5 * (45 - x)

We want the new average weight to be 2 tons: (1.5 * 15 + 3.5 * (45 - x)) / (60 - x) = 2

Multiply both sides by (60 - x): 1.5 * 15 + 3.5 * (45 - x) = 2 * (60 - x)

Simplify: 22.5 + 3.5 * (45 - x) = 120 - 2x 22.5 + 157.5 - 3.5x = 120 - 2x 180 - 3.5x = 120 - 2x

Move x terms to one side: 180 - 120 = 3.5x - 2x 60 = 1.5x x = 40

Final Answer:
40 trucks must leave. The answer is 40.

missionmba2025 · Answer

Using the concept of weighted average we can determine that the ratio of cars to truck currently is 1:3

Number of cars = 1/4 * 60 = 15
Number of trucks currently = 3/4 * 60 = 45

The number of cars remain the same, hence the total weight of the cars = 1.5 * 15 = 22.5

Let the number of trucks = x

2 = 22.5 + 3.5x / (15 + x)

30 + 2x = 22.50 + 3.5x

1.5x = 7.5

x = 5

Hence number of trucks that need to leave = 45 - 5 = 40

Option D

HarshaBujji · Answer

Total Cars c and Trucks t = 60.

This is like a mixture problem. We need to find the ratio in which they are mixed.

Current Scenario :

C -------------------A------T
 1.5 3 3.5
 So c:t = 0.5:1.5 => 1:3.

So #cars = 15, #trucks=45.

Later Scenario :

C -----A--------------------T
 1.5 2 3.5

So c:t = 1.5:0.5 => 3:1. We know no car left. Hence #cars is the same as 15, Hence #trucks = 15/3=5. 
 
#trucks left = 45-5 =40

IMO D

A_Nishith · Answer

Step 1:  Define variables
Let x be the number of cars in the parking lot.
Let y be the number of trucks in the parking lot.
We know:
x+y=60 (total number of vehicles).

Step 2:  Weight information
Each car weighs 1.5 tons.
Each truck weighs 3.5 tons.
The current average weight of all vehicles is 3 tons.
This gives:(1.5x+3.5y) / 60 =3
Multiply through by 60: 1.5x+3.5y=180

Step 3:  Solve for x and y
We now have the system of equations:
x+y=60
1.5x+3.5y=180

From the first equation:
y=60−x
Substitute 
y=60−x into the second equation:
1.5x+3.5(60−x)=180

Simplify:
1.5x+210−3.5x=180
−2x+210=180
2x=30⇒x=15
Substitute 
x=15 into y=60−x:

y=60−15=45
Thus, there are 15 cars and 45 trucks.

Step 4:  Trucks leaving the lot
The goal is to reduce the average weight of the remaining vehicles to 2 tons. 
Let z be the number of trucks that leave the lot. 
After z trucks leave:

The number of cars remains 15.
The number of trucks becomes 45−z.
The total weight of the remaining vehicles is: 1.5(15)+3.5(45−z)
The total number of vehicles remaining is:
15+(45−z)=60−z

The new average weight is 2, so:
1.5(15)+3.5(45−z) / (60−z) =2

Step 5:  Solve for z
Simplify the numerator:
1.5(15)+3.5(45−z)=22.5+157.5−3.5z=180−3.5z

Thus:
(180−3.5z)/ (60−z) =2

Multiply through by 60−z:
180−3.5z=2(60−z)

Simplify:
180−3.5z=120−2z
180−120=3.5z−2z
60=1.5z
z=40

Final answer : D  
The number of trucks that must leave is:  40 
​

Navya442001 · Answer

The parking lot has 60 vehicles, a mix of cars and trucks. Each car weighs 1.5 tons, and each truck weighs 3.5 tons. The current average weight of the vehicles is 3 tons. The total weight of all vehicles is:
Total weight=3×60=180 tons

Let x be the number of trucks that leave the lot. After removing x trucks, the remaining number of vehicles is 60−x, and the new total weight is:
180−3.5x

The new average weight is given as 2 tons:
(180−3.5x)/(60−x)=2
Multiply through by 60−x to eliminate the fraction:
180−3.5x=2(60−x)
Simplify:
180−3.5x=120−2x
Combine like terms:
180−120=3.5x−2x
60=1.5x
Solve for x:
x=40

Therefore  40 trucks  should leave the parking lot to bring down the average to 2 tons.

Heix · Answer

Let's approach this step-by-step using the concepts we've learned about adding sums and averages.

1. First, let's find the total weight of all vehicles and the number of cars and trucks:
* Total vehicles = 60
* Average weight = 3 tons
* Total weight = 60 × 3 = 180 tons

2. Let x be the number of cars. Then (60 - x) is the number of trucks. We can set up an equation:
1.5x + 3.5(60 - x) = 180

3. Solve for x:
* 1.5x + 210 - 3.5x = 180
* -2x + 210 = 180
* -2x=-30
* x=15

4. So there are 15 cars and 45 trucks initially.

5. Now, let y be the number of trucks that leave. The new average should be 2 tons. We can set up another equation:
(15 × 15 + 3.5 * (45 - y)) ÷ (60 - y) = 2

6. Simplify and solve for y:
* (22.5 + 157.5 - 3.5y) ÷ (60 - y) = 2
* 180 - 3.5y = 120 - 2y
* 60 = 1.5y
* y= 40

Therefore, 40 trucks must leave to reduce the average weight to 2 tons.

The correct answer is D. 40.

Krunaal · Answer

C + T = 60 ...........(1)

The average weight is 3 tons, therefore total weight of vehicles is 3 * 60 = 180 tons

Weight of each car is 1.5 ton and of each truck is 3.5 ton => 1.5C + 3.5T = 180 ........(2)

Solving (1) and (2), we get C = 15 and T = 45

Let x be the no. of Trucks to be removed, therefore the new average can be written as,

/ 60 - x = 2
  / 60 - x = 2
  / 60 - x = 2
180 - 3.5*x = 120 - 2*x
1.5*x = 60
 x = 40

Answer D.

Jayesh20201 · Answer

To such questions about weighted averages, I follow a technique:

Cars Trucks
1.5 Tonnes 3.5 Tonnes

Average
 3 Tonnes

Ratio of the Cars to Trucks 
 |3.5-3| : |1.5-3|
 0.5 : 1.5
 1 : 3

Therefore there are 15 Cars and 45 Trucks from the 60 Vehicles

If you apply the same logic to the expected average, 
 Cars Trucks
1.5 Tonnes 3.5 Tonnes

Average
 2 Tonnes

Ratio of the Cars to Trucks 
 |3.5-2| : |1.5-2|
 1.5 : 0.5
 3 : 1

Therefore, if the cars represent 15 vehicles and are 3/4 of the total expected vehicles, then trucks will be the 1/4th portion representing 5 trucks. Hence The number of trucks = 45-5 = 40 Trucks

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