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

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Experta en el extranjero | Updated On - Feb 21, 2023

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.

Suggested GMAT Problem Solving Samples:

*The article might have information for the previous academic years, please refer the official website of the exam.

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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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