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Percentage Applications Quiz 4 (10 MCQs)

This set of multiple-choice questions evaluates skills in depreciation calculation using the reducing balance method, percentage applications, and numerical computation. Concepts covered include asset depreciation, decimal conversion, multiplication, and division. Students will apply these skills to solve problems related to price after discount, total savings, and time reduction.

Quiz Instructions

Select an option to see the correct answer instantly.

1. Mary decreased her time in the mile walk from 30 minutes to 24 minutes. What was the percent of decrease?

Correct Answer: Correct answer is: (B) 20%.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Easy

Concept notes: The concept of percentage decrease is used to determine the reduction in a quantity as a percentage of the original quantity.

Common Mistakes: A common mistake is to calculate the percentage decrease based on the new value instead of the original value.

Explanations: To find the percent decrease, we use the formula: \[ \text{Percent Decrease} = \left( \frac{\text{Original Value} - \text{New Value}}{\text{Original Value}} \right) \times 100 \] Here, the original time is 30 minutes and the new time is 24 minutes. \[ \text{Percent Decrease} = \left( \frac{30 - 24}{30} \right) \times 100 \] \[ \text{Percent Decrease} = \left( \frac{6}{30} \right) \times 100 \] \[ \text{Percent Decrease} = 0.2 \times 100 \] \[ \text{Percent Decrease} = 20\% \]

Option Analysis:

Option A: 25% is incorrect because the calculation shows a 20% decrease, not 25%.
Option B: 20% is correct as calculated above.
Option C: 15% is incorrect because the calculation shows a 20% decrease, not 15%.
Option D: 10% is incorrect because the calculation shows a 20% decrease, not 10%.

2. What is 5% of 24? Hint: Use 10% of 24

Correct Answer: Correct answer is: (C) 1.2.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Easy

Concept notes: To find 5% of a number, you can first find 10% of the number and then take half of that value.

Common Mistakes: A common mistake is to directly calculate 5% without using the hint provided, which can be more time-consuming.

Explanations: To find 5% of 24, we can use the hint to find 10% of 24 first. 10% of 24 is calculated as: \[ 10\% \times 24 = \frac{10}{100} \times 24 = 2.4 \] Next, we take half of 2.4 to find 5%: \[ \frac{2.4}{2} = 1.2 \] Thus, 5% of 24 is 1.2.

Option Analysis:

Option A: 2.4 is 10% of 24, not 5%.
Option B: 0.24 is not the correct value for 5% of 24.
Option C: 1.2 is the correct value for 5% of 24.
Option D: 4.8 is not the correct value for 5% of 24.

3. Find 25% of 80.

Correct Answer: Correct answer is: (A) 20.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Easy

Concept notes: To find 25% of a number, multiply the number by 0.25.

Common Mistakes: A common mistake is to confuse 25% with 25, leading to incorrect calculations.

Explanations: To find 25% of 80, we multiply 80 by 0.25: \[ 80 \times 0.25 = 20 \]

Option Analysis:

Option A: Correct. 25% of 80 is 20.
Option B: Incorrect. 80 is the original number, not the result of 25% of 80.
Option C: Incorrect. 48 is not the result of 25% of 80.
Option D: Incorrect. 95 is not the result of 25% of 80.

4. A new car cost $ 34 800 three years ago. The book value of the car has depreciated at a reducing balance rate of 25%, 20% and 10% respectively each year since then.The current book value of the car, to the nearest dollar, is:

Correct Answer: Correct answer is: (A) $ 18 792.

Exam Relevance: SAT, ACT, GMAT, GRE

Difficulty: Moderate

Concept notes: The question involves calculating the book value of a car using a reducing balance depreciation method. The reducing balance method applies a fixed percentage to the remaining value of the asset each year.

Common Mistakes: A common mistake is to apply the depreciation rates to the original value of the car each year instead of the remaining value after each depreciation.

Explanations: 1. Initial cost of the car: $34,800. 2. Depreciation in the first year: 25% of $34,800 = 0.25 * $34,800 = $8,700. 3. Remaining value after the first year: $34,800 - $8,700 = $26,100. 4. Depreciation in the second year: 20% of $26,100 = 0.20 * $26,100 = $5,220. 5. Remaining value after the second year: $26,100 - $5,220 = $20,880. 6. Depreciation in the third year: 10% of $20,880 = 0.10 * $20,880 = $2,088. 7. Remaining value after the third year: $20,880 - $2,088 = $18,792. Thus, the current book value of the car is $18,792.

Option Analysis:

Option A: Correct. The calculated value matches the provided answer.
Option B: Incorrect. This value does not match the calculated depreciation.
Option C: Incorrect. This value does not match the calculated depreciation.
Option D: Incorrect. This value does not match the calculated depreciation.
Option E: Incorrect. This value does not match the calculated depreciation.

5. An item costing Rs 200 is being sold at 10%. If the price is further reduced by 5%, the selling price will be

Correct Answer: Correct answer is: (B) Rs 171.

Exam Relevance: GMAT, GRE, CAT, SAT

Difficulty: Moderate

Concept notes: The question involves applying successive percentage reductions to an initial price.

Common Mistakes: A common mistake is to apply the second percentage reduction to the original price instead of the reduced price.

Explanations: 1. The initial price of the item is Rs 200. 2. The first reduction is 10%, so the price after the first reduction is: \[ 200 \times (1 - 0.10) = 200 \times 0.90 = 180 \] 3. The second reduction is 5%, so the price after the second reduction is: \[ 180 \times (1 - 0.05) = 180 \times 0.95 = 171 \] 4. Therefore, the final selling price is Rs 171.

Option Analysis:

Option A: Incorrect, as the price after two reductions is not Rs 170.
Option B: Correct, as the price after two reductions is Rs 171.
Option C: Incorrect, as the price after two reductions is not Rs 175.
Option D: Incorrect, as the price after two reductions is not Rs 179.

6. If 20% of a number is 50, what is the number?

Correct Answer: Correct answer is: (B) 250.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Easy

Concept notes: The concept involves finding the original number when a percentage of it is known.

Common Mistakes: A common mistake is to assume that 20% of the number is 50, so the number must be 50 * 5 = 250 without verifying the calculation.

Explanations: To find the original number, we use the formula: \[ \text{Original Number} = \frac{\text{Given Percentage Value}}{\text{Percentage}} \times 100 \] Given that 20% of the number is 50, we can substitute the values: \[ \text{Original Number} = \frac{50}{20} \times 100 = 250 \] Thus, the original number is 250.

Option Analysis:

Option A: 150 is incorrect because 20% of 150 is 30, not 50.
Option B: 250 is correct because 20% of 250 is 50.
Option C: 100 is incorrect because 20% of 100 is 20, not 50.
Option D: None of the above is incorrect because 250 is a valid option.

7. What is 23% of 62?

Correct Answer: Correct answer is: (A) 14.26.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Easy

Concept notes: To find a percentage of a number, multiply the number by the percentage in decimal form.

Common Mistakes: A common mistake is to misinterpret the percentage as a whole number or to forget to convert the percentage to a decimal.

Explanations: To find 23% of 62, first convert 23% to a decimal by dividing by 100: 23 / 100 = 0.23. Then, multiply 62 by 0.23: 62 * 0.23 = 14.26.

Option Analysis:

Option A: Correct. 14.26 is the result of 23% of 62.
Option B: Incorrect. 142.6 is too large and results from a calculation error, possibly by not converting the percentage to a decimal.
Option C: Incorrect. 0.1426 is too small and results from a calculation error, possibly by misinterpreting the percentage as a decimal without multiplying by the number.
Option D: Incorrect. 76 is not related to the calculation of 23% of 62.

8. Tauqeer Rauf spent $ 210 on school supplies and books. This amount was 30% of his savings. How much was his savings?

Correct Answer: Correct answer is: (A) $ 700.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Moderate

Concept notes: The problem involves finding the total savings given a percentage and the corresponding amount spent.

Common Mistakes: A common mistake is to assume that $210 is the total savings and not a percentage of it.

Explanations: To find the total savings, we need to determine what amount $210 represents 30% of. We can set up the equation: \[ 0.30 \times \text{Total Savings} = 210 \] To solve for the Total Savings, we divide both sides by 0.30: \[ \text{Total Savings} = \frac{210}{0.30} \] \[ \text{Total Savings} = 700 \] Thus, the total savings is $700.

Option Analysis:

Option A: Correct. $700 is the total savings.
Option B: Incorrect. $63 is not the total savings.
Option C: Incorrect. $630 is not the total savings.
Option D: Incorrect. $763 is not the total savings.

9. What is 75% of $ 8.00?

Correct Answer: Correct answer is: (A) 6.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Easy

Concept notes: To find 75% of a number, multiply the number by 0.75.

Common Mistakes: A common mistake is to misinterpret the percentage as a fraction or to use an incorrect decimal equivalent.

Explanations: To find 75% of $8.00, we multiply 8.00 by 0.75: \[ 8.00 \times 0.75 = 6.00 \] Thus, 75% of $8.00 is $6.00.

Option Analysis:

Option A: Correct. 75% of $8.00 is $6.00.
Option B: Incorrect. 56.8 is not the correct result of 75% of $8.00.
Option C: Incorrect. 83 is not the correct result of 75% of $8.00.
Option D: Incorrect. 88 is not the correct result of 75% of $8.00.

10. Calculate the 65% of 500

Correct Answer: Correct answer is: (A) 325.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Easy

Concept notes: To find a percentage of a number, multiply the number by the percentage and then divide by 100.

Common Mistakes: A common mistake is to forget to divide by 100 after multiplying the number by the percentage.

Explanations: To calculate 65% of 500, follow these steps: 1. Multiply 500 by 65: $ 500 \times 65 = 32500 $. 2. Divide the result by 100: $ \frac{32500}{100} = 325 $. Thus, 65% of 500 is 325.

Option Analysis:

Option A: Correct. 325 is the correct answer.
Option B: Incorrect. 32.5 is not the correct answer.
Option C: Incorrect. 50 is not the correct answer.
Option D: Incorrect. None of the above is not applicable since 325 is the correct answer.

Frequently Asked Questions

What is the purpose of learning percentage applications?

Learning percentage applications helps in understanding how percentages are used in real-life scenarios such as calculating discounts, interest rates, and asset depreciation.

How can I convert a percentage to a decimal?

To convert a percentage to a decimal, divide the percentage by 100. For example, 25% becomes 0.25 when converted to a decimal.

What is the difference between percentage increase and percentage decrease?

Percentage increase refers to the amount of increase in a quantity expressed as a percentage of the original amount, while percentage decrease refers to the amount of decrease in a quantity expressed as a percentage of the original amount.

How do I calculate the final selling price after a discount?

To calculate the final selling price after a discount, subtract the discount amount from the original price. The discount amount is the original price multiplied by the discount percentage.

What is reducing balance depreciation?

Reducing balance depreciation is a method of calculating the depreciation of an asset where the depreciation rate is applied to the asset's book value at the beginning of each period.

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