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Percentage Applications Quiz 18 (10 MCQs)

This set of multiple-choice questions evaluates skills in decimal conversion, percent notation, multiplication, and basic arithmetic. It covers concepts such as decimal to percent conversion, fraction to percentage, and percentage applications, including discount and tax calculations. The questions test the ability to perform intermediate steps, solve equations, and apply percentage calculations in various contexts.

Quiz Instructions

Select an option to see the correct answer instantly.

1. Joey wants to collect 20 coins from foreign countries. If he has 3 coins so far, what percent of his collection is complete?

Correct Answer: Correct answer is: (B) 15%.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Easy

Concept notes: To find the percentage of Joey's collection that is complete, we need to calculate the ratio of the number of coins he has to the total number of coins he wants to collect, and then convert this ratio to a percentage.

Common Mistakes: A common mistake is to misinterpret the ratio or to perform the calculation incorrectly, leading to an incorrect percentage.

Explanations: To find the percentage of Joey's collection that is complete, we use the formula: \[ \text{Percentage Complete} = \left( \frac{\text{Number of Coins Collected}}{\text{Total Number of Coins Desired}} \right) \times 100 \] Substituting the given values: \[ \text{Percentage Complete} = \left( \frac{3}{20} \right) \times 100 \] First, calculate the fraction: \[ \frac{3}{20} = 0.15 \] Next, convert the fraction to a percentage: \[ 0.15 \times 100 = 15\% \] Thus, Joey has completed 15% of his collection.

Option Analysis:

Option A: 7% is incorrect because it does not match the calculated percentage.
Option B: 15% is correct as it matches the calculated percentage.
Option C: 20% is incorrect because it does not match the calculated percentage.
Option D: 85% is incorrect because it does not match the calculated percentage.

2. How much will you pay for a $ 10.99 book with 8.9% sales tax added on top?

Correct Answer: Correct answer is: (C) $ 11.97.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Moderate

Concept notes: To find the total cost of a book with sales tax, you need to calculate the tax amount and add it to the original price.

Common Mistakes: A common mistake is to add the tax percentage directly to the original price without converting it to a decimal and calculating the actual tax amount.

Explanations: 1. Calculate the tax amount: - Sales tax rate = 8.9% - Convert the percentage to a decimal: 8.9% = 0.089 - Calculate the tax amount: $10.99 * 0.089 = $0.97711 2. Add the tax amount to the original price: - Total cost = $10.99 + $0.97711 = $11.96711 3. Round the total cost to the nearest cent: - Total cost = $11.97

Option Analysis:

Option A: $0.98 is the tax amount, not the total cost.
Option B: $10.97 is less than the original price, which is incorrect.
Option C: $11.97 is the correct total cost after adding the tax.
Option D: $0.89 is not the correct tax amount or total cost.

3. Samantha's pink scarf was on sale for $ 25. It had been reduced by 45%. What was the original cost of the scarf?

Correct Answer: Correct answer is: (A) $ 45.45.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Moderate

Concept notes: The problem involves calculating the original price of an item given its sale price and the percentage discount.

Common Mistakes: A common mistake is to incorrectly apply the percentage discount to the sale price instead of solving for the original price.

Explanations: To find the original cost of the scarf, we need to determine the price before the 45% discount was applied. Let $ x $ be the original price. The sale price is given as $25, which is 55% of the original price (since 100% - 45% = 55%). We can set up the equation: \[ 0.55x = 25 \] To solve for $ x $, divide both sides by 0.55: \[ x = \frac{25}{0.55} \] \[ x = 45.45 \] Thus, the original cost of the scarf is $45.45.

Option Analysis:

Option A: Correct. The original price is $45.45.
Option B: Incorrect. This value does not match the calculation.
Option C: Incorrect. This value does not match the calculation.
Option D: Incorrect. This value does not match the calculation.

4. On a 50 question test, Danielle answered 78% of the questions correctly. How many questions did she get wrong?

Correct Answer: Correct answer is: (B) 11.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Easy

Concept notes: The concept involves calculating the number of questions answered incorrectly based on the percentage of questions answered correctly.

Common Mistakes: A common mistake is to directly calculate 78% of 50 and assume that is the number of questions answered incorrectly, rather than calculating the number of questions answered correctly and then finding the difference from the total.

Explanations: First, calculate the number of questions answered correctly: \[ 78\% \text{ of } 50 = \frac{78}{100} \times 50 = 39 \] Next, subtract the number of correct answers from the total number of questions to find the number of incorrect answers: \[ 50 - 39 = 11 \] Thus, Danielle got 11 questions wrong.

Option Analysis:

Option A: 39 is the number of questions answered correctly, not the number of questions answered incorrectly.
Option B: 11 is the correct number of questions answered incorrectly.
Option C: 28 is not the correct number of questions answered incorrectly.
Option D: 78 is the percentage of questions answered correctly, not the number of questions answered incorrectly.

5. True or False. 0.72 is less than 7/12.

Correct Answer: Correct answer is: B) False.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Easy

Concept notes: To compare 0.72 and 7/12, we need to convert both to the same form, either both as decimals or both as fractions.

Common Mistakes: A common mistake is to assume that 0.72 is less than 7/12 without converting them to the same form for accurate comparison.

Explanations: First, convert 7/12 to a decimal. To do this, divide 7 by 12: \[ 7 \div 12 = 0.5833\overline{3} \] Now, compare 0.72 and 0.5833\overline{3}: \[ 0.72 > 0.5833\overline{3} \] Therefore, 0.72 is greater than 7/12, making the statement "0.72 is less than 7/12" false.

Option Analysis:

Option A: This option is incorrect because 0.72 is not less than 7/12.
Option B: This option is correct because 0.72 is greater than 7/12.

6. Express the $\frac{4}{20}$

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

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Easy

Concept notes: To express a fraction as a percentage, multiply the fraction by 100.

Common Mistakes: A common mistake is to misinterpret the fraction and not multiply by 100 correctly.

Explanations: To convert the fraction $\frac{4}{20}$ to a percentage, we multiply it by 100: \[ \frac{4}{20} \times 100 = 20\% \]

Option Analysis:

Option A: 25% is incorrect because $\frac{4}{20} \times 100 = 20\%$.
Option B: 20% is correct because $\frac{4}{20} \times 100 = 20\%$.
Option C: 50% is incorrect because $\frac{4}{20} \times 100 = 20\%$.
Option D: 24% is incorrect because $\frac{4}{20} \times 100 = 20\%$.

7. Write each decimal as a percent: 0.22

Correct Answer: Correct answer is: (C) 22%

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Easy

Concept notes: To convert a decimal to a percent, multiply the decimal by 100 and add the percent symbol (%).

Common Mistakes: A common mistake is to misplace the decimal point when converting, leading to incorrect percentages.

Explanations: To convert the decimal 0.22 to a percent, multiply 0.22 by 100. This gives 22%. Therefore, 0.22 as a percent is 22%.

Option Analysis:

Option A: 220% is incorrect because it is 10 times the correct value.
Option B: 22.2% is incorrect because it is not the correct conversion of 0.22.
Option C: 22% is correct because 0.22 multiplied by 100 equals 22%.
Option D: 2.2% is incorrect because it is 10 times smaller than the correct value.

8. You have to create 28 name badges for senior citizens as a community service. If you complete 75% of these on Monday, how many do you have left to complete?

Correct Answer: Correct answer is: (A) 7.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Easy

Concept notes: The question involves calculating a percentage of a total and then determining the remaining quantity.

Common Mistakes: A common mistake would be to calculate the percentage incorrectly or to misinterpret the question and calculate the number completed instead of the number remaining.

Explanations: To find out how many name badges are completed on Monday, calculate 75% of 28: \[ 75\% \text{ of } 28 = \frac{75}{100} \times 28 = 0.75 \times 28 = 21 \] So, 21 name badges are completed on Monday. To find the number of name badges left to complete: \[ 28 - 21 = 7 \] Therefore, 7 name badges are left to complete.

Option Analysis:

Option A: Correct. 7 name badges are left to complete.
Option B: Incorrect. 35 is not the correct number of name badges left to complete.
Option C: Incorrect. 21 is the number of name badges completed, not the number left to complete.
Option D: Incorrect. 47 is not the correct number of name badges left to complete.

9. What number is 2% of 35?

Correct Answer: Correct answer is: (C) .7.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Easy

Concept notes: To find 2% of 35, we need to calculate the fraction of 35 that corresponds to 2%.

Common Mistakes: A common mistake is to misinterpret the percentage as a whole number or to incorrectly place the decimal point.

Explanations: To find 2% of 35, we first convert the percentage to a decimal by dividing by 100: \[ 2\% = \frac{2}{100} = 0.02 \] Next, we multiply 35 by 0.02: \[ 35 \times 0.02 = 0.7 \] Thus, 2% of 35 is 0.7.

Option Analysis:

Option A: 7 is incorrect because it is 10 times larger than the correct value.
Option B: 0.057 is incorrect because it is much smaller than the correct value.
Option C: 0.7 is the correct value as calculated.
Option D: 0.007 is incorrect because it is much smaller than the correct value.

10. What is 5% of 120? Hint: Find 10% first, then cut in half (divide by 2).

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

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Easy

Concept notes: To find 5% of a number, first find 10% and then divide by 2.

Common Mistakes: A common mistake is to directly calculate 5% without using the 10% as an intermediate step, leading to potential calculation errors.

Explanations: To find 5% of 120, first calculate 10% of 120: 10% of 120 = 120 * 0.10 = 12. Next, divide this result by 2 to get 5%: 12 / 2 = 6. Thus, 5% of 120 is 6.

Option Analysis:

Option A: 12 is incorrect because it is 10% of 120, not 5%.
Option B: 24 is incorrect because it is twice the correct answer, 12, which is 10% of 120.
Option C: 6 is correct because it is half of 12, which is 10% of 120.
Option D: 100 is incorrect because it is not related to the calculation of 5% of 120.

Frequently Asked Questions

What is the purpose of learning percentage applications?

Learning percentage applications helps in understanding how to calculate discounts, taxes, and other real-life scenarios involving percentages, enhancing practical math skills.

How do you 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 the difference between a percentage discount and sales tax?

A percentage discount reduces the price of an item, while sales tax adds to the price. Both are calculated as a percentage of the original price but serve different purposes in financial transactions.

How can I check if my percentage calculation is correct?

To verify a percentage calculation, you can convert the percentage back to a decimal and multiply it by the original value to see if you get the calculated amount. For example, 20% of 50 should be 10.

What skills are necessary to solve percentage application problems?

Basic arithmetic skills, including multiplication, division, and understanding of decimals and fractions, are essential for solving percentage application problems effectively.

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