A car dealer received a shipment of cars, half of which were black, wi

Question

A car dealer received a shipment of cars, half of which were black, with the remainder consisting of equal numbers of blue, silver, and white cars. During the next month, 70 percent of the black cars, 80 percent of the blue cars, 30 percent of the silver cars, and 40 percent of the white cars were sold. What percent of the cars in the shipment were sold during that month?

A. 36%
B. 50%
C. 55%
D. 60%
E. 72%

A. 36%
B. 50%
C. 55%
D. 60%
E. 72%

k1.saurabh · Answer

Consider total cars = 60

so Black cars = 30, Blue cars= Silver cars=White cars = 10

Black sold cars (70% of 30)= 21, Blue sold cars = 8, Silver sold cars = 3, White sold cars = 4

Total sold cars = 21+8+3+4=36

So % of total cars sold= 36/60*100= 60%

Answer D

EgmatQuantExpert · Answer

Solution

Given:  
• Out of the shipment of cars a dealer received, half were black, and the remainder consists of equal numbers of blue, silver, and white cars
• During the next month, 70% black cars, 80% blue cars, 30% silver cars, and 40% white cars were sold

To find:  
• What percent of the total cars in the shipment were sold during that month

Approach and Working:   
• Let us assume that total number of cars in the shipment were N
 o Black cars =  \frac{N}{2}  = 0.5N; remaining number of cars = N – 0.5N = 0.5N 
 o Blue cars = Silver cars = White cars =  \frac{1}{3} * 0.5N = \frac{0.5N}{3}  
• Next month,
 o Black cars sold = 70% of 0.5N = 0.7 * 0.5N = 0.35N 
 o Blue cars sold = 80% of  \frac{0.5N}{3} = 0.8 * \frac{0.5N}{3} = \frac{0.4N}{3}  
 o Silver cars sold = 30% of  \frac{0.5N}{3} = 0.3 * \frac{0.5N}{3} = \frac{0.15N}{3}  
 o White cars sold = 40% of  \frac{0.5N}{3} = 0.4 * \frac{0.5N}{3} = \frac{0.2N}{3}  
• Total cars sold = (0.35N +  \frac{0.4N}{3} + \frac{0.15N}{3} + \frac{0.2N}{3}) = \frac{1.8N}{3}  = 0.6N
• Percentage of cars sold =  \frac{0.6N}{N}  * 100 = 60%

Hence, the correct answer is option D.

Answer: D

Note 
  An alternate way to avoid the calculations is to take numerical value in place of N. 
From the given situation, N must be divided by 2, and  \frac{N}{2}  must be divided by 3. As N is an integer, N must be a multiple pf 6.
Therefore, any multiple of 6 can be assumed as the value of N, which can result in ease of calculation.

ScottTargetTestPrep · Answer

We can let the total number of cars in the shipment = 120.

So 1/2(120) = 60 are black and 60/3 = 20 = blue = silver = white.

Since 70 percent of the black cars, 80 percent of the blue cars, 30 percent of the silver cars, and 40 percent of the white cars were sold, we have:

0.7 x 60 + 0.8 x 20 + 0.3 x 20 + 0.4 x 20 = 42 + 16 + 6 + 8 = 72.

Thus, the percentage of cars sold was 72/120 = 6/10 = 60% of the cars in the shipment.

Answer: D

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

A car dealer received a shipment of cars, half of which were black, wi

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

A car dealer received a shipment of cars, half of which were black, wi

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards