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Unit V Mathematical Reasoning And Aptitude
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Percentages – Quiz 37
Percentages Quiz 37 (10 MCQs)
This set of multiple-choice questions evaluates skills in percentage calculation, decimal conversion, and basic arithmetic. Concepts covered include decimal to percentage conversion, multiplication, division, and applying percentage discounts. Students will demonstrate their ability to solve problems involving percentage values, sales tax, and total cost calculations.
Quiz Instructions
Select an option to see the correct answer instantly.
1.
A St. Louis Cardinals hat costs $ 18. If there is 8% sales tax, what is the total cost of the hat including tax?
A) $ 1.44.
B) $ 22.74.
C) $ 21.36.
D) $ 19.44.
Show Answer
Correct Answer:
Correct answer is: (D) $ 19.44.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Easy
Concept notes:
The question involves calculating the total cost of an item including sales tax, which is a straightforward application of percentages.
Common Mistakes:
A common mistake is to add the tax amount directly to the original price without calculating the tax correctly.
Explanations:
To find the total cost of the hat including tax, follow these steps:
1. Calculate the sales tax amount: \( 18 \times 0.08 = 1.44 \).
2. Add the sales tax to the original price: \( 18 + 1.44 = 19.44 \).
Thus, the total cost of the hat including tax is $19.44.
Option Analysis:
Option A:
$1.44 is the amount of sales tax, not the total cost.
Option B:
$22.74 is incorrect as it does not match the correct calculation.
Option C:
$21.36 is incorrect as it does not match the correct calculation.
Option D:
$19.44 is the correct total cost including tax.
2.
What is value of 5% of 200
A) 5.
B) 10.
C) 50.
D) 100.
Show Answer
Correct Answer:
Correct answer is: (B) 10.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Easy
Concept notes:
To find 5% of 200, we need to calculate the fraction of 200 that corresponds to 5%.
Common Mistakes:
A common mistake is to misinterpret the percentage as a whole number, leading to incorrect calculations.
Explanations:
To find 5% of 200, we use the formula:
\[ \text{Percentage} = \left( \frac{\text{Percentage Value}}{100} \right) \times \text{Total Value} \]
\[ 5\% \text{ of } 200 = \left( \frac{5}{100} \right) \times 200 \]
\[ = 0.05 \times 200 \]
\[ = 10 \]
Option Analysis:
Option A:
5 is incorrect because it is the result of 2.5% of 200, not 5%.
Option B:
10 is correct because it is the result of 5% of 200.
Option C:
50 is incorrect because it is the result of 25% of 200, not 5%.
Option D:
100 is incorrect because it is the result of 50% of 200, not 5%.
3.
What is 50% of 78?
A) 36.
B) 38.
C) 39.
D) 40.
Show Answer
Correct Answer:
Correct answer is: (C) 39.
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 or to perform the wrong arithmetic operation.
Explanations:
To find 50% of 78, we divide 78 by 2:
\[ 78 \div 2 = 39 \]
Thus, 50% of 78 is 39.
Option Analysis:
Option A:
36 is incorrect because 36 is not half of 78.
Option B:
38 is incorrect because 38 is not half of 78.
Option C:
39 is correct because 39 is half of 78.
Option D:
40 is incorrect because 40 is not half of 78.
4.
What is the equivalent percent to 0.08?
A) 0.08%.
B) 8%.
C) 80%.
D) 800%.
Show Answer
Correct Answer:
Correct answer is: (B) 8%.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Easy
Concept notes:
To convert a decimal to a percentage, multiply the decimal by 100.
Common Mistakes:
A common mistake is to think that 0.08 is 0.08% or 80%, which are incorrect.
Explanations:
To convert 0.08 to a percentage, multiply 0.08 by 100. This gives 8%. Therefore, 0.08 is equivalent to 8%.
Option Analysis:
Option A:
0.08% is incorrect because it is not the correct conversion of 0.08 to a percentage.
Option B:
8% is the correct conversion of 0.08 to a percentage.
Option C:
80% is incorrect because it is not the correct conversion of 0.08 to a percentage.
Option D:
800% is incorrect because it is not the correct conversion of 0.08 to a percentage.
5.
What is 12% of 144?
A) 18.30.
B) 17.28.
C) 12.56.
D) 19.45.
Show Answer
Correct Answer:
Correct answer is: (B) 17.28.
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 use the wrong decimal form.
Explanations:
To find 12% of 144, convert 12% to its decimal form, which is 0.12. Then, multiply 144 by 0.12:
\[ 144 \times 0.12 = 17.28 \]
Option Analysis:
Option A:
18.30 is incorrect because it is not the result of 144 multiplied by 0.12.
Option B:
17.28 is correct because it is the result of 144 multiplied by 0.12.
Option C:
12.56 is incorrect because it is not the result of 144 multiplied by 0.12.
Option D:
19.45 is incorrect because it is not the result of 144 multiplied by 0.12.
6.
Which is the decimal for 23.4%?
A) 0.0234.
B) 0.234.
C) 2.34.
D) 23.4.
Show Answer
Correct Answer:
Correct answer is: (B) 0.234.
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 misplace the decimal point, leading to incorrect conversion.
Explanations:
To convert 23.4% to a decimal, divide 23.4 by 100. This results in 0.234.
Option Analysis:
Option A:
0.0234 is incorrect because it places the decimal point one place too far to the left.
Option B:
0.234 is correct because it correctly places the decimal point two places to the left of 23.4.
Option C:
2.34 is incorrect because it places the decimal point one place too far to the right.
Option D:
23.4 is incorrect because it does not convert the percentage to a decimal at all.
7.
Mr. Thiele ordered a $ 10 burger. When he went to pay, the restaurant marked down the burger 22%. How much did he pay after the markdown? (a)
A) $ 7.80.
B) $ 2.20.
C) $ 12.20.
D) $ 17.80Tags7.4.D.
Show Answer
Correct Answer:
Correct answer is: (A) $ 7.80.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Easy
Concept notes:
The concept tested here is the calculation of a percentage discount on a given amount.
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 amount Mr. Thiele paid after the markdown, we need to calculate the discount and subtract it from the original price.
1. Calculate the discount amount: 22% of $10.
\[
\text{Discount} = 10 \times \frac{22}{100} = 10 \times 0.22 = 2.20
\]
2. Subtract the discount from the original price:
\[
\text{Final Price} = 10 - 2.20 = 7.80
\]
Thus, Mr. Thiele paid $7.80 after the markdown.
Option Analysis:
Option A:
Correct. The final price after the markdown is $7.80.
Option B:
Incorrect. This is the discount amount, not the final price.
Option C:
Incorrect. This is the original price plus the discount amount, which is not the final price.
Option D:
Incorrect. This is an incorrect calculation and does not represent the final price.
8.
What is 0.56 written as a percent?
A) 56%.
B) 5%.
C) 6%.
D) 5.6%.
Show Answer
Correct Answer:
Correct answer is: (A) 56%.
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 misinterpret the decimal as a percentage without multiplying by 100.
Explanations:
To convert 0.56 to a percentage, multiply 0.56 by 100. This gives 56%. Therefore, 0.56 written as a percent is 56%.
Option Analysis:
Option A:
Correct. 0.56 multiplied by 100 is 56%.
Option B:
Incorrect. 0.56 multiplied by 100 is not 5%.
Option C:
Incorrect. 0.56 multiplied by 100 is not 6%.
Option D:
Incorrect. 0.56 multiplied by 100 is not 5.6%.
9.
If Manuel deposits 25% of $ 130 into a savings account, what is the amount of his deposit?
A) $ 5.20.
B) $ 25.00.
C) $ 32.50.
D) $ 97.50.
Show Answer
Correct Answer:
Correct answer is: (C) $ 32.50.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Moderate
Concept notes:
To find 25% of $130, we need to calculate the fraction of the total amount that corresponds to 25%.
Common Mistakes:
A common mistake is to misinterpret the percentage as a whole number or to use an incorrect decimal conversion.
Explanations:
To find 25% of $130, we first convert 25% to a decimal by dividing by 100, which gives 0.25. Then, we multiply $130 by 0.25:
\[ 130 \times 0.25 = 32.50 \]
Thus, the amount of his deposit is $32.50.
Option Analysis:
Option A:
$5.20 is incorrect because it is too small.
Option B:
$25.00 is incorrect because it does not account for the correct percentage calculation.
Option C:
$32.50 is correct as it is the result of the correct percentage calculation.
Option D:
$97.50 is incorrect because it is too large.
10.
A local hardware store sold 12% of its hammers on Saturday. If the hardware store sold 9 hammers on Saturday, how many did the store have in stock to begin with?
A) 65.
B) 75.
C) 98.
D) 108.
Show Answer
Correct Answer:
Correct answer is: (B) 75.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Moderate
Concept notes:
The problem involves finding the original quantity when a percentage of it is known. This requires understanding how to convert a percentage into a fraction and then solving for the original quantity.
Common Mistakes:
A common mistake is to misinterpret the percentage as a direct multiplication factor without converting it into a fraction or decimal first.
Explanations:
To find the original number of hammers, we start with the given information that 12% of the hammers equals 9. We can set up the equation:
\[ 0.12 \times \text{Total Hammers} = 9 \]
To solve for the total number of hammers, we divide both sides by 0.12:
\[ \text{Total Hammers} = \frac{9}{0.12} \]
\[ \text{Total Hammers} = 75 \]
Thus, the store originally had 75 hammers in stock.
Option Analysis:
Option A:
65 is incorrect because 12% of 65 is not 9.
Option B:
75 is correct because 12% of 75 is 9.
Option C:
98 is incorrect because 12% of 98 is not 9.
Option D:
108 is incorrect because 12% of 108 is not 9.
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Frequently Asked Questions
What is the process of converting a decimal to a percentage?
To convert a decimal to a percentage, multiply the decimal by 100 and add the percent symbol (%).
How do you calculate a percentage discount?
To calculate a percentage discount, multiply the original price by the discount percentage and then subtract the result from the original price.
What is the purpose of learning about percentages in mathematical reasoning?
Learning about percentages helps in understanding proportions, calculating discounts, and analyzing data in various real-world scenarios.
How can you convert a percentage to a decimal?
To convert a percentage to a decimal, divide the percentage by 100 and remove the percent symbol (%).
What is the significance of the percent symbol (%) in mathematical calculations?
The percent symbol (%) indicates that the number preceding it is a fraction of 100, used to express proportions or ratios in a standardized way.