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Percentage Applications Quiz 9 (10 MCQs)

This set of multiple-choice questions evaluates understanding of percentage applications, including fraction to percentage conversion, decimal approximation, discount calculation, and cricket statistics. It tests skills in arithmetic operations, problem solving, and sequential percentage calculations, such as compound discounts and tax calculations.

Quiz Instructions

Select an option to see the correct answer instantly.

1. A test has 20 questions. If Peter gets 80% correct, how many questions did Peter get correct?

Correct Answer: Correct answer is: (B) 16 correct.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Easy

Concept notes: To find the number of questions Peter got correct, we need to calculate 80% of the total number of questions.

Common Mistakes: A common mistake is to misinterpret the percentage and calculate incorrectly, such as dividing the total number of questions by 80 instead of multiplying by 0.80.

Explanations: To find the number of questions Peter got correct, we calculate 80% of 20 questions. This is done by multiplying 20 by 0.80: \[ 20 \times 0.80 = 16 \] Thus, Peter got 16 questions correct.

Option Analysis:

Option A: Incorrect. 4 correct is not the correct calculation of 80% of 20 questions.
Option B: Correct. 16 correct is the correct calculation of 80% of 20 questions.
Option C: Incorrect. 4% is not relevant to the problem.
Option D: Incorrect. 25 correct is not possible since there are only 20 questions.

2. Which option is closest to being equivalent to $\frac{1}{3}$

Correct Answer: Correct answer is: (A) 33.3%

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Easy

Concept notes: The concept of converting fractions to percentages is fundamental in percentage applications. The fraction $\frac{1}{3}$ can be converted to a percentage by multiplying by 100.

Common Mistakes: A common mistake is to confuse the decimal representation of $\frac{1}{3}$, which is approximately 0.333, with the percentage form, which is 33.3%.

Explanations: To convert the fraction $\frac{1}{3}$ to a percentage, we multiply by 100: \[ \frac{1}{3} \times 100 = 33.333\ldots \approx 33.3\% \] Thus, 33.3% is the closest option to $\frac{1}{3}$.

Option Analysis:

Option A: 33.3% is the closest to $\frac{1}{3}$.
Option B: 0.3 is the decimal form of $\frac{3}{10}$, not $\frac{1}{3}$.
Option C: 33 is a whole number and not a percentage.
Option D: $\frac{3}{6}$ simplifies to $\frac{1}{2}$, which is 50%.

3. A tax of 15% is added to the marked price of articles. If a purchaser pays $ 552 inclusive of tax, what is the amount of tax paid?

Correct Answer: Correct answer is: (C) $ 72.

Exam Relevance: SAT, GRE, GMAT, ACT

Difficulty: Moderate

Concept notes: The question involves calculating the amount of tax paid when the total price inclusive of tax is given. The tax is a percentage of the marked price, and the total price is the sum of the marked price and the tax.

Common Mistakes: A common mistake is to assume that the tax amount can be directly calculated as 15% of the total price paid, which is incorrect. The tax is 15% of the marked price, not the total price.

Explanations: Let the marked price be $ P $. The tax is 15% of $ P $, so the tax amount is $ 0.15P $. The total price paid is the sum of the marked price and the tax, which is $ P + 0.15P = 1.15P $. Given that the total price paid is $552, we can set up the equation: \[ 1.15P = 552 \] Solving for $ P $: \[ P = \frac{552}{1.15} = 480 \] The tax amount is $ 0.15P $: \[ 0.15 \times 480 = 72 \] Thus, the amount of tax paid is $72.

Option Analysis:

Option A: $ 36.80 is incorrect because it does not match the calculated tax amount.
Option B: $ 40.20 is incorrect because it does not match the calculated tax amount.
Option C: $ 72 is correct as it matches the calculated tax amount.
Option D: $ 82.80 is incorrect because it does not match the calculated tax amount.

4. A baseball jersey is on sale for $ 18.45 and is 40% off the regular price. How much does the jersey cost ORIGINALLY?

Correct Answer: Correct answer is: (B) $ 30.75.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Moderate

Concept notes: The problem involves finding the original price of an item given its sale price and the discount percentage. The key concept is understanding how to reverse the percentage discount to find the original price.

Common Mistakes: A common mistake is to assume the sale price is the original price minus the discount percentage directly, without reversing the calculation.

Explanations: To find the original price, we need to reverse the discount calculation. The sale price is 60% of the original price (since 100% - 40% = 60%). Let $ P $ be the original price. The sale price is given as $18.45, which is 60% of $ P $. Therefore, we can set up the equation: \[ 0.60 \times P = 18.45 \] To solve for $ P $, divide both sides by 0.60: \[ P = \frac{18.45}{0.60} \] \[ P = 30.75 \] Thus, the original price of the jersey is $30.75.

Option Analysis:

Option A: This option suggests the sale price is the original price, which is incorrect.
Option B: This option correctly calculates the original price by reversing the discount.
Option C: This option is much lower than the sale price and does not make sense in the context of the problem.
Option D: This option is higher than the correct original price and does not match the calculation.

5. On average, an adult male's body weight is about 60% water. If an adult male weighs 180 pounds, then what is his "water weight?"

Correct Answer: Correct answer is: (B) 108 pounds.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Easy

Concept notes: The question involves calculating a percentage of a given total weight to find the water weight.

Common Mistakes: A common mistake is to misinterpret the percentage or to perform the calculation incorrectly.

Explanations: To find the water weight, we need to calculate 60% of the total body weight. The total body weight is 180 pounds. Step 1: Convert the percentage to a decimal. 60% = 0.60 Step 2: Multiply the total body weight by the decimal. 180 pounds * 0.60 = 108 pounds Therefore, the water weight is 108 pounds.

Option Analysis:

Option A: 102 pounds is incorrect because it does not match the calculation of 60% of 180 pounds.
Option B: 108 pounds is correct because it matches the calculation of 60% of 180 pounds.
Option C: 112 pounds is incorrect because it does not match the calculation of 60% of 180 pounds.
Option D: 116 pounds is incorrect because it does not match the calculation of 60% of 180 pounds.

6. Dexter has some chocolate.He gives 20% to Annie and eats 40% of what he has left.He puts the remaining 72g into the fridge for later.True or False: Dexter started with 150g of chocolate.

Correct Answer: Correct answer is: A) True.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Moderate

Concept notes: The problem involves applying percentage calculations to determine the initial amount of chocolate Dexter had.

Common Mistakes: A common mistake is to misinterpret the sequence of percentage calculations or to incorrectly apply the percentages to the remaining chocolate.

Explanations: Let's denote the initial amount of chocolate Dexter had as $ x $ grams. 1. Dexter gives 20% of the chocolate to Annie: \[ \text{Chocolate given to Annie} = 0.20x \] \[ \text{Chocolate left} = x - 0.20x = 0.80x \] 2. Dexter eats 40% of the remaining chocolate: \[ \text{Chocolate eaten} = 0.40 \times 0.80x = 0.32x \] \[ \text{Chocolate left after eating} = 0.80x - 0.32x = 0.48x \] 3. The remaining chocolate is 72 grams: \[ 0.48x = 72 \] 4. Solve for $ x $: \[ x = \frac{72}{0.48} = 150 \] Thus, Dexter started with 150 grams of chocolate, confirming the answer is True.

Option Analysis:

Option A: True. This is the correct answer as the calculations show that Dexter started with 150 grams of chocolate.
Option B: False. This is incorrect because the calculations show that Dexter indeed started with 150 grams of chocolate.

7. What is 6% of 125? (Hint: You may want to find what 1% is first.)

Correct Answer: Correct answer is: (D) 7.5.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Easy

Concept notes: To find 6% of 125, first determine 1% of 125, then multiply by 6.

Common Mistakes: A common mistake is to directly multiply 125 by 0.06 without first finding 1%.

Explanations: To find 6% of 125, start by calculating 1% of 125: 1% of 125 = 125 / 100 = 1.25. Next, multiply 1.25 by 6 to get 6% of 125: 1.25 * 6 = 7.5. Thus, 6% of 125 is 7.5.

Option Analysis:

Option A: 1.25 is 1% of 125, not 6%.
Option B: 0.75 is not a correct calculation for 6% of 125.
Option C: 750 is much larger than the correct value.
Option D: 7.5 is the correct value for 6% of 125.

8. A batsman scored 120 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets?

Correct Answer: Correct answer is: (C) 50%.

Exam Relevance: GRE, GMAT, SAT, CAT

Difficulty: Moderate

Concept notes: The question requires calculating the percentage of runs scored by running between the wickets. This involves basic arithmetic and percentage calculation.

Common Mistakes: A common mistake is to incorrectly calculate the total runs scored from boundaries and sixes, leading to an incorrect percentage.

Explanations: First, calculate the total runs scored from boundaries and sixes: - Runs from boundaries: 3 boundaries × 4 runs each = 12 runs - Runs from sixes: 8 sixes × 6 runs each = 48 runs - Total runs from boundaries and sixes: 12 + 48 = 60 runs Next, calculate the runs scored by running between the wickets: - Total runs scored: 120 runs - Runs scored by running: 120 - 60 = 60 runs Finally, calculate the percentage of runs scored by running: - Percentage of runs scored by running: (60 / 120) × 100 = 50% Thus, the batsman made 50% of his total score by running between the wickets.

Option Analysis:

Option A: 40% is incorrect because it does not match the calculated percentage.
Option B: 45% is incorrect because it does not match the calculated percentage.
Option C: 50% is correct as it matches the calculated percentage.
Option D: 60% is incorrect because it does not match the calculated percentage.

Mnemonic: Runs from boundaries and sixes, subtract from total, divide by total, multiply by 100.

9. A video game is on sale for 12% off the regular price of $ 60. What is the sale price of the video game?

Correct Answer: Correct answer is: (A) $ 52.80.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Easy

Concept notes: The concept involves calculating the sale price after a discount is applied to the regular price.

Common Mistakes: A common mistake is to calculate the discount amount and subtract it from the regular price incorrectly.

Explanations: To find the sale price, first calculate the discount amount by multiplying the regular price by the discount percentage. The regular price is $60 and the discount is 12%. 1. Calculate the discount amount: \[ \text{Discount amount} = 60 \times \frac{12}{100} = 60 \times 0.12 = 7.20 \] 2. Subtract the discount amount from the regular price to get the sale price: \[ \text{Sale price} = 60 - 7.20 = 52.80 \] Thus, the sale price of the video game is $52.80.

Option Analysis:

Option A: Correct. The sale price after a 12% discount is $52.80.
Option B: Incorrect. This option does not account for the correct discount calculation.
Option C: Incorrect. This option represents the price if the discount were added to the original price, which is not the case.
Option D: Incorrect. This option represents the discount amount, not the sale price.

10. There is a discount of 20% on a table of $ 1000. If you are a member, there is a further discount 30% on the remaining value. What is the total discount?

Correct Answer: Correct answer is: (A) $ 440.

Exam Relevance: SAT, ACT, GMAT, GRE

Difficulty: Moderate

Concept notes: The question involves applying successive percentage discounts to a given amount. The first discount is applied to the original price, and the second discount is applied to the reduced price after the first discount.

Common Mistakes: A common mistake is to add the two discounts together (20% + 30% = 50%) and apply a single 50% discount to the original price, which would be incorrect.

Explanations: 1. Calculate the first discount: 20% of $1000. \[ 0.20 \times 1000 = 200 \] The price after the first discount is: \[ 1000 - 200 = 800 \] 2. Calculate the second discount: 30% of $800. \[ 0.30 \times 800 = 240 \] The price after the second discount is: \[ 800 - 240 = 560 \] 3. The total discount is the difference between the original price and the final price: \[ 1000 - 560 = 440 \]

Option Analysis:

Option A: Correct. The total discount is $440.
Option B: Incorrect. This would be the result if only the first discount was applied.
Option C: Incorrect. This would be the result if the discounts were added together and applied as a single discount.
Option D: Incorrect. This is not a valid calculation based on the given discounts.

Frequently Asked Questions

What is the purpose of learning percentage applications?

Learning percentage applications helps in understanding how percentages are used in everyday situations, such as calculating discounts, tax, and other financial transactions.

How do I convert a fraction to a percentage?

To convert a fraction to a percentage, divide the numerator by the denominator, then multiply the result by 100. For example, 1/4 as a percentage is 25%.

What is a compound discount?

A compound discount involves applying multiple percentage discounts sequentially to a price, resulting in a final sale price that is less than the original price.

How can I calculate the total price including tax?

To calculate the total price including tax, multiply the original price by the tax rate, then add the result to the original price.

What is the difference between a percentage discount and a sequential discount?

A percentage discount applies a single percentage reduction to the original price, while a sequential discount applies multiple percentage reductions one after another.

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