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Percentages Quiz 20 (10 MCQs)

This set of multiple-choice questions evaluates skills in discount calculation, percentage application, and equation solving. It covers concepts such as marked price, selling price, decimal conversion, and percentage to decimal conversion. Students will practice division by 100, fraction simplification, and multiplication to solve problems related to new price calculation, savings goals, and remaining amount needed.

Quiz Instructions

Select an option to see the correct answer instantly.

1. You have set a goal to save $ 300 by the end of the year. If you have already saved 52% of your goal, how much more money do you need to save by the end of the year?

Correct Answer: Correct answer is: (D) $ 144.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Moderate

Concept notes: The question involves calculating the remaining amount needed to reach a savings goal based on a percentage already saved.

Common Mistakes: A common mistake is to calculate the amount already saved and subtract it from the goal without correctly determining the remaining percentage.

Explanations: 1. Calculate the amount already saved: 52% of $300. \[ 0.52 \times 300 = 156 \] 2. Subtract the amount already saved from the total goal to find the remaining amount needed. \[ 300 - 156 = 144 \] Thus, the amount still needed to save is $144.

Option Analysis:

Option A: $156 is the amount already saved, not the remaining amount needed.
Option B: $154 is incorrect as it does not match the calculation of the remaining amount.
Option C: $146 is incorrect as it does not match the calculation of the remaining amount.
Option D: $144 is the correct remaining amount needed to reach the goal.

2. Change 247% to a decimal

Correct Answer: Correct answer is: (B) 2.47.

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 move the decimal point two places to the left without understanding the division by 100.

Explanations: To convert 247% to a decimal, divide 247 by 100. This results in 2.47.

Option Analysis:

Option A: 24.7 is incorrect because it represents moving the decimal point one place to the left instead of two.
Option B: 2.47 is correct because it is the result of dividing 247 by 100.
Option C: 0.247 is incorrect because it represents moving the decimal point three places to the left instead of two.
Option D: 0.0247 is incorrect because it represents moving the decimal point four places to the left instead of two.

3. Calculate 20% of 70

Correct Answer: Correct answer is: (B) 14.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Easy

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

Common Mistakes: A common mistake is to forget to divide by 100 after multiplying, leading to an incorrect result.

Explanations: To calculate 20% of 70, we use the formula: \[ \text{Percentage of a number} = \left( \frac{\text{Percentage}}{100} \right) \times \text{Number} \] \[ 20\% \text{ of } 70 = \left( \frac{20}{100} \right) \times 70 \] \[ = 0.2 \times 70 \] \[ = 14 \]

Option Analysis:

Option A: 12 is incorrect because it does not match the calculation.
Option B: 14 is correct as it matches the calculation.
Option C: 16 is incorrect because it does not match the calculation.
Option D: 18 is incorrect because it does not match the calculation.

4. Calculate the percent increase. Round to the nearest percent.Original: 45New: 92

Correct Answer: Correct answer is: (C) 104%.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Moderate

Concept notes: The percent increase is calculated by finding the difference between the new and original values, dividing by the original value, and then multiplying by 100 to convert to a percentage.

Common Mistakes: A common mistake is to calculate the percent increase by dividing the new value by the original value and then subtracting 1, which would give an incorrect result.

Explanations: To calculate the percent increase, follow these steps: 1. Find the difference between the new and original values: 92 - 45 = 47. 2. Divide the difference by the original value: 47 / 45 ≈ 1.0444. 3. Multiply by 100 to convert to a percentage: 1.0444 * 100 ≈ 104.44. 4. Round to the nearest percent: 104%. Thus, the percent increase is 104%.

Option Analysis:

Option A: 51% is incorrect because it does not account for the full increase from 45 to 92.
Option B: 1.04% is incorrect because it is a very small percentage and does not reflect the actual increase.
Option C: 104% is correct as it accurately reflects the percent increase from 45 to 92.
Option D: .51 is incorrect because it is not a percentage and does not reflect the actual increase.

5. A shopkeeper allows a discount of 15% on the marked price of an article. If the selling price is Rs. 170, what was the marked price?

Correct Answer: Correct answer is: (B) Rs. 200.

Exam Relevance: CAT, GMAT, GRE, SAT

Difficulty: Moderate

Concept notes: The concept involves understanding the relationship between the marked price, discount, and selling price. The selling price is the marked price minus the discount.

Common Mistakes: A common mistake is to incorrectly calculate the discount or to confuse the marked price with the selling price.

Explanations: Let the marked price be $ M $. The discount is 15%, so the selling price is $ M - 0.15M = 0.85M $. Given the selling price is Rs. 170, we can set up the equation: \[ 0.85M = 170 \] Solving for $ M $: \[ M = \frac{170}{0.85} = 200 \] Thus, the marked price is Rs. 200.

Option Analysis:

Option A: Rs. 190 is incorrect because it does not satisfy the equation $ 0.85M = 170 $.
Option B: Rs. 200 is correct as it satisfies the equation $ 0.85M = 170 $.
Option C: Rs. 210 is incorrect because it does not satisfy the equation $ 0.85M = 170 $.
Option D: Rs. 220 is incorrect because it does not satisfy the equation $ 0.85M = 170 $.

Mnemonic: Discounted Price = Marked Price * (1 - Discount Rate)

6. Cann Electronics has all of their electronics on sale for 20% off. If a computer originally cost $ 1,050, what is the new price?

Correct Answer: Correct answer is: (B) $ 840.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Moderate

Concept notes: The concept tested here is the application of percentage discounts to find the new price of an item.

Common Mistakes: A common mistake is to calculate the discount amount and subtract it from the original price incorrectly, or to add the discount amount to the original price instead of subtracting it.

Explanations: To find the new price after a 20% discount, first calculate the discount amount by multiplying the original price by 20% (0.20). Then, subtract the discount amount from the original price. 1. Calculate the discount amount: $ 1050 \times 0.20 = 210 $ 2. Subtract the discount amount from the original price: $ 1050 - 210 = 840 $ Thus, the new price is $840.

Option Analysis:

Option A: $210 is the discount amount, not the new price.
Option B: $840 is the correct new price after applying the 20% discount.
Option C: $787 is incorrect; it does not match the calculation of the new price after the discount.
Option D: $1,260 is incorrect; it is the result of adding the discount amount to the original price, which is not the correct method.

7. Write the percent as a decimal. 4.3%

Correct Answer: Correct answer is: (C) .043.

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 simply place a decimal point in front of the percentage number without dividing by 100.

Explanations: To convert 4.3% to a decimal, divide 4.3 by 100. This results in 0.043.

Option Analysis:

Option A: 4.3 is incorrect because it does not represent the decimal form of 4.3%.
Option B: .43 is incorrect because it is the result of moving the decimal point one place to the left, not two.
Option C: .043 is correct because it is the result of dividing 4.3 by 100.
Option D: 4300 is incorrect because it is the result of multiplying 4.3 by 1000, not dividing by 100.

8. WHAT PERCENT?!

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

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Moderate

Concept notes: The question asks for a specific percentage, and the correct answer is 25%. Understanding percentages involves converting fractions or ratios into a form that represents parts per hundred.

Common Mistakes: A common mistake is misinterpreting the question or confusing the percentage with other given options. It is important to carefully read the question and ensure the correct percentage is identified.

Explanations: The question asks for a specific percentage, and the correct answer is 25%. This means that the value in question represents 25 parts out of 100. To verify, one can check if the given context or problem setup aligns with this percentage.

Option Analysis:

Option A: 20% is incorrect as it does not match the given context or problem setup.
Option B: 22% is incorrect as it does not match the given context or problem setup.
Option C: 25% is correct as it matches the given context or problem setup.
Option D: 28% is incorrect as it does not match the given context or problem setup.

9. What percent of 190 equals 19?

Correct Answer: Correct answer is: (C) 10 %.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Moderate

Concept notes: To find what percent of 190 equals 19, we need to set up the equation and solve for the percentage.

Common Mistakes: A common mistake is to misinterpret the problem and calculate the percentage incorrectly, such as dividing 190 by 19 instead of finding the percentage of 190 that equals 19.

Explanations: To find what percent of 190 equals 19, we set up the equation: \[ \text{Percentage} \times 190 = 19 \] Let $ x $ be the percentage. Then: \[ x \times 190 = 19 \] To solve for $ x $, divide both sides by 190: \[ x = \frac{19}{190} \] Simplify the fraction: \[ x = \frac{19 \div 19}{190 \div 19} = \frac{1}{10} = 0.1 \] Convert the decimal to a percentage: \[ 0.1 \times 100 = 10\% \] Thus, 10% of 190 equals 19.

Option Analysis:

Option A: 0.1% is incorrect because it is too small.
Option B: 1% is incorrect because it is too small.
Option C: 10% is correct as calculated.
Option D: 19% is incorrect because it is too large.

10. What is 125% of 84?

Correct Answer: Correct answer is: (A) 105.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Easy

Concept notes: To find 125% of a number, you multiply the number by 1.25.

Common Mistakes: A common mistake is to think that 125% means 125 times the number, which would be incorrect. 125% is equivalent to 1.25 in decimal form.

Explanations: To find 125% of 84, we multiply 84 by 1.25: \[ 84 \times 1.25 = 105 \]

Option Analysis:

Option A: Correct. 125% of 84 is 105.
Option B: Incorrect. 188.5 is not the correct result of 125% of 84.
Option C: Incorrect. 473.4 is not the correct result of 125% of 84.
Option D: Incorrect. 356.7 is not the correct result of 125% of 84.

Frequently Asked Questions

What is a percentage?

A percentage is a way of expressing a number as a fraction of 100. It is often used to represent proportions or ratios in a more understandable format.

How do you 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 marked price and selling price?

The marked price is the price of an item before any discount is applied, while the selling price is the price after any discounts have been applied.

How do you calculate a percentage discount?

To calculate a percentage discount, multiply the original price by the discount percentage and then divide by 100. Subtract this amount from the original price to get the discounted price.

What is the purpose of learning about percentages?

Understanding percentages is crucial for various real-life applications, such as calculating discounts, interest rates, and statistical data, which helps in making informed decisions.

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