In a Town of 8,000 Residents, 65 Percent of All Residents Own a Car GMAT Problem Solving

bySayantani Barman Experta en el extranjero

Question: In a town of 8,000 residents, 65 percent of all residents own a car, 55 percent own a motorcycle, and 25 percent own neither a car nor a motorcycle. How many residents own a car but not a motorcycle?

800
1,600
2,000
3,600
4,400

Correct Answer: B
Solution and Explanation:
Approach Solution 1:
The problem statement states that:
Given:

In a town of 8,000 residents, 65 percent of all residents own a car
55 percent own a motorcycle,
25 percent own neither a car nor a motorcycle.

Find out:

The number of residents who own a car but not a motorcycle.

Let the total number of residents be 100
As per the conditions of the question:
No. of Residents who own a car = 65
No. of Residents who own a motorcycle = 55
No. of Residents who own neither = 25
Therefore no. of residents who own either car or motorcycle = 100 – 25 = 75
No. of residents who own both car and motorcycle= (55 + 65) – 75 = 45
Hence no. of residents who own only car = 65 – 45 = 20
Therefore when the no. of residents is 100, no. of residents who own only car = 20
When no of residents = 8000, no of residents who own only car = 20/100 * 8000 = 1600
Hence, the number of residents who own a car but not a motorcycle = 1600

Approach Solution 2:
The problem statement suggests that:
Given:

In a town of 8,000 residents, 65 percent of all residents own a car
55 percent own a motorcycle,
25 percent own neither a car nor a motorcycle.

Find out:

The number of residents who own a car but not a motorcycle.

We can solve the problem with this easier and quicker approach.
Let the total number of residents be 100
Therefore, the equation will be:
Total - neither = first + second - both
100 - 25 = 65 + 55 - Both
Both = 45
Only CAR = Car - Both = 65 - 45 = 20
But 20 is percent, then 20% of 8000 = 1600.
Hence, the number of residents who own a car but not a motorcycle = 1600

Approach Solution 3:
The problem statement indicates that:
Given:

In a town of 8,000 residents, 65 percent of all residents own a car
55 percent own a motorcycle,
25 percent own neither a car nor a motorcycle.

Find out:

The number of residents who own a car but not a motorcycle.

65 percent of all residents own a car: {Car} = 0.65 * 8,000 = 5,200
55 percent own a motorcycle: {Motorcycle} = 0.55 * 8,000 = 4,400;
25 percent own neither a car nor a motorcycle: {Neither} = 0.25 * 8,000 = 2,000.
{Total} = {Car} + {Motorcycle} - {Both} + {Neither};
8,000 = 5,200 + 4,400 - {Both} + 2,000;
{Both} = 3,600.
The number of residents who own a car but not a motorcycle = {Car} - {Both}
= 5,200 - 3,600
= 1,600.
Hence, the number of residents who own a car but not a motorcycle = 1600

“In a town of 8,000 residents, 65 percent of all residents own a car”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. To solve the GMAT Problem Solving questions, the candidates must have a basic understanding of mathematics. The candidates can follow GMAT Quant practice papers to practice varieties of questions that will enable them to strengthen their mathematical knowledge.

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In a Town of 8,000 Residents, 65 Percent of All Residents Own a Car GMAT Problem Solving

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