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Percentages Quiz 38 (10 MCQs)

This set of multiple-choice questions evaluates the ability to convert fractions to percentages, understand decimal conversion, and perform basic arithmetic operations. It covers concepts such as finding a fraction of a number, multiplication, and division by 100. The material also includes percentage calculations, including converting decimals to percentages and calculating percentage increases.

Quiz Instructions

Select an option to see the correct answer instantly.

1. What is 82% As a decimal?

Correct Answer: Correct answer is: (D) 0.82.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Easy

Concept notes: To convert a percentage to a decimal, divide the percentage by 100.

Common Mistakes: A common mistake is to think that 82% is 82.0 or 8200, which is incorrect. Remember, percentages are fractions of 100.

Explanations: To convert 82% to a decimal, divide 82 by 100. This gives 0.82.

Option Analysis:

Option A: 8200 is incorrect because it is 82 multiplied by 100, not divided by 100.
Option B: 820 is incorrect because it is 82 multiplied by 10, not divided by 100.
Option C: 0.082 is incorrect because it is 8.2% as a decimal, not 82%.
Option D: 0.82 is correct because it is 82 divided by 100.

2. What is 50% of 88?

Correct Answer: Correct answer is: (D) 44.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Easy

Concept notes: To find 50% of a number, you can divide the number by 2.

Common Mistakes: A common mistake is to misinterpret the percentage, such as calculating 50% as 50 instead of dividing by 2.

Explanations: To find 50% of 88, you can divide 88 by 2. This gives: \[ 88 \div 2 = 44 \] Thus, 50% of 88 is 44.

Option Analysis:

Option A: 58 is incorrect because 58 is not half of 88.
Option B: 46 is incorrect because 46 is not half of 88.
Option C: 42 is incorrect because 42 is not half of 88.
Option D: 44 is correct because 44 is half of 88.

3. How do you express one half as percentages?

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

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Easy

Concept notes: To express one half as a percentage, we convert the fraction 1/2 to a percentage by multiplying by 100.

Common Mistakes: A common mistake is to confuse the fraction 1/2 with other fractions like 1/4 or 3/4, leading to incorrect percentages like 25% or 75%.

Explanations: To convert one half (1/2) to a percentage, we multiply the fraction by 100. This gives us: \[ \frac{1}{2} \times 100 = 50\% \] Thus, one half is 50%.

Option Analysis:

Option A: 100% is incorrect because 100% represents the whole, not one half.
Option B: 25% is incorrect because 25% represents one quarter, not one half.
Option C: 50% is correct because 50% represents one half.
Option D: 75% is incorrect because 75% represents three quarters, not one half.

4. You had $ 24 this week. Next week you hope to have saved $ 30. What is the percent of change?

Correct Answer: Correct answer is: (D) 25%.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Moderate

Concept notes: The concept of percentage change involves calculating the difference between two values and expressing that difference as a percentage of the original value.

Common Mistakes: A common mistake is to confuse the percentage change with the absolute change, which is simply the difference between the two values.

Explanations: To find the percent of change, we first calculate the difference between the next week's amount and this week's amount: \[ 30 - 24 = 6 \] Next, we express this difference as a percentage of the original amount (this week's amount): \[ \frac{6}{24} \times 100 = 25\% \] Thus, the percent of change is 25%.

Option Analysis:

Option A: $6 is the absolute change, not the percentage change.
Option B: $25 is not relevant to the calculation of percentage change.
Option C: 6% is incorrect because it does not reflect the correct percentage change.
Option D: 25% is the correct percentage change.

5. If you scored 18 out of 20 on a test, what percentage did you get?

Correct Answer: Correct answer is: (A) 90%.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Easy

Concept notes: To convert a fraction to 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 find the percentage, we convert the fraction $\frac{18}{20}$ to a percentage by multiplying by 100: \[ \frac{18}{20} \times 100 = 90\% \]

Option Analysis:

Option A: Correct. 90% is the correct percentage for 18 out of 20.
Option B: Incorrect. 80% is not the correct percentage for 18 out of 20.
Option C: Incorrect. 85% is not the correct percentage for 18 out of 20.
Option D: Incorrect. 95% is not the correct percentage for 18 out of 20.

6. The number 0.406 written as a percent is .....

Correct Answer: Correct answer is: (B) 40.6%

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Easy

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

Common Mistakes: A common mistake is to misplace the decimal point when converting from decimal to percentage.

Explanations: To convert 0.406 to a percentage, multiply 0.406 by 100: 0.406 × 100 = 40.6 Thus, 0.406 as a percentage is 40.6%.

Option Analysis:

Option A: 406% is incorrect because it is 10 times larger than the correct value.
Option B: 40.6% is correct because it is the result of multiplying 0.406 by 100.
Option C: 4.06% is incorrect because it is 10 times smaller than the correct value.
Option D: None of the above is incorrect because 40.6% is a valid option.

7. What is 15% of $ 4,800.00?

Correct Answer: Correct answer is: (C) $ 720.00.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Moderate

Concept notes: To find 15% of $4,800.00, we need to calculate the product of 15% and $4,800.00.

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

Explanations: To find 15% of $4,800.00, we first convert 15% to a decimal by dividing by 100, which gives 0.15. Then, we multiply 0.15 by $4,800.00: \[ 0.15 \times 4800 = 720 \] Thus, 15% of $4,800.00 is $720.00.

Option Analysis:

Option A: $7.20 is incorrect because it is too small.
Option B: $72.00 is incorrect because it is also too small.
Option C: $720.00 is correct as calculated.
Option D: $7,200.00 is incorrect because it is too large.

8. What is 40% of 50?

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

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 confuse the percentage with the decimal form, leading to incorrect calculations.

Explanations: To find 40% of 50, convert 40% to its decimal form, which is 0.40. Then, multiply 50 by 0.40: \[ 50 \times 0.40 = 20 \] Thus, 40% of 50 is 20.

Option Analysis:

Option A: 0.4 is the decimal form of 40%, not the result of 40% of 50.
Option B: 20 is the correct result of 40% of 50.
Option C: 40 is the percentage, not the result of 40% of 50.
Option D: 80 is not the result of 40% of 50.

9. Jada's sister earns $ 15 per hour. The store offers her a raise-a 9% increase per hour. After the raise, how much will Jada's sister make per hour?

Correct Answer: Correct answer is: (D) $ 16.35.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Moderate

Concept notes: The concept tested here is the calculation of a percentage increase in a given amount.

Common Mistakes: A common mistake is to add the percentage increase directly to the original amount without converting the percentage to a decimal and then multiplying.

Explanations: To find the new hourly wage after a 9% raise, we first convert the percentage to a decimal by dividing by 100: 9% = 0.09. Next, we calculate the raise amount by multiplying the original hourly wage by the decimal: $15 * 0.09 = $1.35. Finally, we add the raise amount to the original hourly wage: $15 + $1.35 = $16.35.

Option Analysis:

Option A: Incorrect, as $13.65 is less than the original wage and does not account for the raise.
Option B: Incorrect, as $1.35 is the raise amount, not the new hourly wage.
Option C: Incorrect, as $15.00 is the original hourly wage before the raise.
Option D: Correct, as $16.35 is the new hourly wage after a 9% raise.

10. What is 25% of 80?

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

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Easy

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

Common Mistakes: A common mistake is to think that 25% of 80 is 40, which is actually 50% of 80.

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

Option Analysis:

Option A: 30 is incorrect because 30 is not 25% of 80.
Option B: 40 is incorrect because 40 is 50% of 80, not 25%.
Option C: 15 is incorrect because 15 is not 25% of 80.
Option D: 20 is correct because 20 is 25% of 80.

Frequently Asked Questions

What is the difference between a percentage and a decimal?

A percentage is a number expressed as a fraction of 100, while a decimal is a number expressed in the base-10 system. To convert a percentage to a decimal, divide by 100, and to convert a decimal to a percentage, multiply by 100.

How do you calculate a percentage increase?

To calculate a percentage increase, subtract the original value from the new value, divide the result by the original value, and then multiply by 100 to get the percentage increase.

What is the process for converting a fraction to a percentage?

To convert a fraction to a percentage, divide the numerator by the denominator to get a decimal, then multiply the decimal by 100 to convert it to a percentage.

How can you find half of a number?

To find half of a number, divide the number by 2. This is equivalent to multiplying the number by 0.5.

What is the significance of the percent symbol (%)?

The percent symbol (%) indicates that the number preceding it is a fraction of 100. For example, 50% means 50 out of 100 or 0.5 in decimal form.

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