Basic Ability Quantitative Problem Solving Questions and Answers — Questions and Answers
Question 1: A clothing store increases the price of a shirt by 20%. After a month, the shirt goes on sale for 20% off the new price. What is the net percentage change in the price of the shirt from its original price?
- No change
- 4% increase
- 4% decrease (Correct answer)
- 10% decrease
Correct answer: 4% decrease
Let the original price of the shirt be $100. A 20% increase makes the new price $100 * 1.20 = $120. A 20% sale on this new price means a discount of $120 * 0.20 = $24. The final price is $120 - $24 = $96. The difference from the original price is $100 - $96 = $4. This represents a 4% decrease from the original price.
Question 2: Machine A can complete a production order in 6 hours. Machine B can complete the same order in 9 hours. If both machines work together at their respective constant rates, how many hours will it take to complete the order?
- 7.5 hours
- 3.6 hours (Correct answer)
- 4.5 hours
- 3.0 hours
Correct answer: 3.6 hours
The work rate of Machine A is 1/6 of the job per hour. The work rate of Machine B is 1/9 of the job per hour. When working together, their combined rate is the sum of their individual rates: (1/6) + (1/9) = (3/18) + (2/18) = 5/18 of the job per hour. To find the total time to complete the job (which is 1 whole job), we take the reciprocal of the combined rate: Time = 1 / (5/18) = 18/5 = 3.6 hours.
Question 3: A car travels from City A to City B at an average speed of 50 miles per hour and returns from City B to City A along the same route at an average speed of 75 miles per hour. If the distance between the two cities is 150 miles, what is the average speed for the entire round trip?
- 62.5 mph
- 65 mph
- 60 mph (Correct answer)
- 67.5 mph
Correct answer: 60 mph
Average Speed = Total Distance / Total Time. The trip from A to B takes 150 miles / 50 mph = 3 hours. The return trip from B to A takes 150 miles / 75 mph = 2 hours. The total distance for the round trip is 150 + 150 = 300 miles. The total time is 3 hours + 2 hours = 5 hours. Therefore, the average speed for the entire trip is 300 miles / 5 hours = 60 mph.
Question 4: A grocer wants to create a 50-pound mixture of nuts that will sell for $4.50 per pound. He will mix peanuts that sell for $3.00 per pound and cashews that sell for $7.00 per pound. Which of the following is closest to the number of pounds of peanuts he should use?
- 19 pounds
- 25 pounds
- 31 pounds (Correct answer)
- 38 pounds
Correct answer: 31 pounds
Let P be the weight of peanuts and C be the weight of cashews. We have two equations: 1) P + C = 50 (total weight) and 2) 3P + 7C = 50 * 4.50 = 225 (total value). From equation 1, C = 50 - P. Substitute this into equation 2: 3P + 7(50 - P) = 225. This simplifies to 3P + 350 - 7P = 225. Then, -4P = -125. Solving for P gives P = 31.25. The closest answer is 31 pounds.
Question 5: The bar chart below shows the number of units sold for five different products in a given month. What percentage of the total units sold were for Product C? Product A: 120 units Product B: 150 units Product C: 180 units Product D: 90 units Product E: 60 units
- 25%
- 30% (Correct answer)
- 33%
- 20%
Correct answer: 30%
First, calculate the total number of units sold: 120 (A) + 150 (B) + 180 (C) + 90 (D) + 60 (E) = 600 units. Next, find the percentage for Product C: (Number of Product C units / Total units) * 100. This is (180 / 600) * 100. Simplifying the fraction gives 18/60, which is 3/10. As a percentage, 3/10 is 30%.
Question 6: In a class, the ratio of boys to girls is 5:3. If there are a total of 40 students in the class, how many boys are there?
- 15
- 20
- 24
- 25 (Correct answer)
Correct answer: 25
The ratio 5:3 means that for every 5 boys, there are 3 girls. This creates a total of 5 + 3 = 8 parts in the ratio. To find the value of one part, divide the total number of students by the total number of parts: 40 students / 8 parts = 5 students per part. Since the boys represent 5 parts of the ratio, the number of boys is 5 parts * 5 students/part = 25 boys.
Basic Ability Quantitative Problem Solving Questions and Answers
A clothing store increases the price of a shirt by 20%.
After a month, the shirt goes on sale for 20% off the new price.
What is the net percentage change in the price of the shirt from its original price?