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Unit V Mathematical Reasoning And Aptitude
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Percentage Applications – Quiz 6
Percentage Applications Quiz 6 (10 MCQs)
This set of multiple-choice questions evaluates skills in interest rate conversion, percentage increase, multiplier interpretation, fraction conversion, and percentage calculations. It covers arithmetic operations, data interpretation, and problem-solving techniques, including sales tax and tip calculations. Students will practice rounding decimals, determining original numbers, and solving for total quantities.
Quiz Instructions
Select an option to see the correct answer instantly.
1.
Which store sells at least 65 wristbands daily 25% of the time?
A) Store A.
B) Store B.
C) Both.
D) You can't tell.
Show Answer
Correct Answer:
Correct answer is: (B) Store B.
Exam Relevance:
SAT, ACT, GMAT, GRE
Difficulty:
Moderate
Concept notes:
The question involves understanding percentages and interpreting data to determine which store meets a specific criterion.
Common Mistakes:
A common mistake would be to misinterpret the percentage or to confuse the data for Store A and Store B.
Explanations:
To determine which store sells at least 65 wristbands daily 25% of the time, we need to analyze the given data. The problem states that Store B sells at least 65 wristbands daily 25% of the time. This means that 25% of the days, Store B meets or exceeds the 65 wristband threshold. Therefore, Store B is the correct answer.
Option Analysis:
Option A:
Store A does not meet the criterion of selling at least 65 wristbands daily 25% of the time.
Option B:
Store B meets the criterion of selling at least 65 wristbands daily 25% of the time.
Option C:
Both stores do not meet the criterion as only Store B does.
Option D:
The data provided is sufficient to determine the correct answer, so you can tell which store meets the criterion.
2.
If 7/3% of a number is 42, then the number is
A) 9800.
B) 8.
C) 1800.
D) 180.
Show Answer
Correct Answer:
Correct answer is: (C) 1800.
Exam Relevance:
SAT, GRE, GMAT, ACT
Difficulty:
Moderate
Concept notes:
The question involves finding the original number when a percentage of it is given. The key concept is to use the formula: Original Number = (Given Value / Percentage) * 100.
Common Mistakes:
A common mistake is to misinterpret the percentage as a whole number, leading to incorrect calculations.
Explanations:
To find the original number, we use the formula: Original Number = (Given Value / Percentage) * 100. Here, the given value is 42 and the percentage is 7/3%. First, convert 7/3% to a decimal: 7/3% = 7/3 * 1/100 = 7/300. Now, apply the formula: Original Number = (42 / (7/300)) * 100 = 42 * (300/7) = 42 * 42.8571 = 1800.
Option Analysis:
Option A:
9800 is incorrect because it does not satisfy the given percentage condition.
Option B:
8 is incorrect because it is much smaller than the correct value.
Option C:
1800 is correct as it satisfies the given percentage condition.
Option D:
180 is incorrect because it is much smaller than the correct value.
3.
Valerie answered 28 problems on her test correctly. If Valerie correctly answered 80% of the problems on the test, then how many problems were on the test?
A) 22 problems.
B) 25 problems.
C) 35 problems.
D) 36 problems.
Show Answer
Correct Answer:
Correct answer is: (C) 35 problems.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Moderate
Concept notes:
The problem involves finding the total number of problems on a test given the number of correctly answered problems and the percentage of correctly answered problems.
Common Mistakes:
A common mistake is to misinterpret the percentage and incorrectly calculate the total number of problems.
Explanations:
To find the total number of problems on the test, we can set up the following equation based on the given information:
Let \( x \) be the total number of problems on the test.
Valerie correctly answered 28 problems, which is 80% of the total number of problems.
Thus, we can write the equation:
\[ 0.80x = 28 \]
To solve for \( x \), we divide both sides of the equation by 0.80:
\[ x = \frac{28}{0.80} \]
\[ x = 35 \]
Therefore, the total number of problems on the test is 35.
Option Analysis:
Option A:
22 problems. This is incorrect because 22 problems would not yield 28 correct answers at 80%.
Option B:
25 problems. This is incorrect because 25 problems would not yield 28 correct answers at 80%.
Option C:
35 problems. This is correct because 35 problems at 80% correctly answered equals 28 problems.
Option D:
36 problems. This is incorrect because 36 problems would not yield 28 correct answers at 80%.
4.
The holiday store is having a sale this weekend! During the sale, they sell 48 Christmas trees, which is 60% of the trees they have at the store. How many trees did they have at the store before the sale?
A) 48 trees.
B) 80 trees.
C) 32 trees.
D) 25 trees.
Show Answer
Correct Answer:
Correct answer is: (B) 80 trees.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Moderate
Concept notes:
The problem involves finding the total number of trees based on a given percentage. The key concept is understanding how to use percentages to find the original quantity.
Common Mistakes:
A common mistake is to assume that the number of trees sold (48) is the total number of trees, without considering the percentage given.
Explanations:
To find the total number of trees, we need to determine what 100% represents given that 48 trees represent 60% of the total. We can set up the equation:
\[ 48 = 0.60 \times \text{Total Trees} \]
To solve for the total number of trees, we divide both sides by 0.60:
\[ \text{Total Trees} = \frac{48}{0.60} \]
\[ \text{Total Trees} = 80 \]
Thus, the store originally had 80 trees.
Option Analysis:
Option A:
48 trees is incorrect because it only represents 60% of the total trees, not the total number of trees.
Option B:
80 trees is correct as it represents the total number of trees before the sale.
Option C:
32 trees is incorrect because it does not match the calculation based on the given percentage.
Option D:
25 trees is incorrect because it does not match the calculation based on the given percentage.
5.
Fernando had to pay $ 1.40 in sales tax when purchasing a shirt. If that tax rate is 7%, how much did the shirt cost?
A) $ 17.
B) $ 18.
C) $ 19.
D) $ 20.
Show Answer
Correct Answer:
Correct answer is: D) $ 20.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Moderate
Concept notes:
The problem involves calculating the original price of an item given the sales tax amount and the tax rate. The formula to find the original price is: Original Price = Sales Tax Amount / Tax Rate.
Common Mistakes:
A common mistake is to misinterpret the tax rate as a decimal or to incorrectly apply the formula, leading to an incorrect calculation of the original price.
Explanations:
To find the original price of the shirt, we use the formula: Original Price = Sales Tax Amount / Tax Rate. Given the sales tax amount is $1.40 and the tax rate is 7%, we first convert the tax rate to a decimal: 7% = 0.07. Then, we substitute the values into the formula: Original Price = $1.40 / 0.07 = $20. Therefore, the original price of the shirt is $20.
Option Analysis:
Option A:
$17 is incorrect because it does not satisfy the equation when the tax rate is applied.
Option B:
$18 is incorrect because it does not satisfy the equation when the tax rate is applied.
Option C:
$19 is incorrect because it does not satisfy the equation when the tax rate is applied.
Option D:
$20 is correct because it satisfies the equation when the tax rate is applied.
6.
Write $\frac{2}{3}$
A) 2.3%.
B) 66.6%.
C) 6%.
D) 23%.
Show Answer
Correct Answer:
Correct answer is: (B) 66.6%
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Moderate
Concept notes:
To convert a fraction to a percentage, multiply the fraction by 100.
Common Mistakes:
A common mistake is to misinterpret the fraction as a decimal and then convert it to a percentage, leading to incorrect answers.
Explanations:
To convert the fraction \(\frac{2}{3}\) to a percentage, we multiply it by 100:
\[
\frac{2}{3} \times 100 = \frac{200}{3} \approx 66.67\%
\]
Rounding to one decimal place, we get 66.6%.
Option Analysis:
Option A:
2.3% is incorrect because it does not represent the correct conversion of \(\frac{2}{3}\) to a percentage.
Option B:
66.6% is the correct answer as it accurately represents the conversion of \(\frac{2}{3}\) to a percentage.
Option C:
6% is incorrect because it is a much smaller value than the correct conversion of \(\frac{2}{3}\).
Option D:
23% is incorrect because it does not represent the correct conversion of \(\frac{2}{3}\) to a percentage.
7.
What is the rate of interest if R=1.1? (a)
A) 5%.
B) 8%.
C) 10%.
D) 12%.
Show Answer
Correct Answer:
Correct answer is: (C) 10%.
Exam Relevance:
GMAT, GRE, SAT, ACT
Difficulty:
Moderate
Concept notes:
The rate of interest can be determined from the given multiplier R, which represents the factor by which the principal amount increases after one period. In percentage applications, R is often expressed as 1 + (rate of interest / 100).
Common Mistakes:
A common mistake is to confuse the multiplier R with the interest rate directly, without converting it to a percentage.
Explanations:
Given R = 1.1, we can express this as:
\[ R = 1 + \frac{\text{rate of interest}}{100} \]
\[ 1.1 = 1 + \frac{\text{rate of interest}}{100} \]
Subtract 1 from both sides:
\[ 0.1 = \frac{\text{rate of interest}}{100} \]
Multiply both sides by 100:
\[ \text{rate of interest} = 0.1 \times 100 = 10\% \]
Option Analysis:
Option A:
5% is incorrect because it does not match the calculation from the given R value.
Option B:
8% is incorrect because it does not match the calculation from the given R value.
Option C:
10% is correct as it matches the calculation from the given R value.
Option D:
12% is incorrect because it does not match the calculation from the given R value.
8.
A group of friends went to lunch. The bill, before sales tax and tip, was $ 37.50. A sales tax of 8% was added. The group also tipped 18% on the amount after the sales tax was added. What was the total amount of money that the group paid for the lunch?
A) $ 47.79.
B) $ 40.50.
C) $ 3.00.
D) $ 63.50.
Show Answer
Correct Answer:
Correct answer is: (A) $ 47.79.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Moderate
Concept notes:
The problem involves calculating the total cost of a meal including sales tax and tip. The sales tax is applied to the original bill, and the tip is calculated on the total after tax.
Common Mistakes:
A common mistake is to calculate the tip on the original bill amount instead of the total after tax.
Explanations:
1. Calculate the sales tax:
Sales tax = 8% of $37.50 = 0.08 * $37.50 = $3.00.
2. Add the sales tax to the original bill:
Total after tax = $37.50 + $3.00 = $40.50.
3. Calculate the tip:
Tip = 18% of $40.50 = 0.18 * $40.50 = $7.29.
4. Add the tip to the total after tax:
Total amount paid = $40.50 + $7.29 = $47.79.
Option Analysis:
Option A:
Correct. The total amount paid is $47.79.
Option B:
Incorrect. This is the total after tax but before tip.
Option C:
Incorrect. This is the amount of sales tax only.
Option D:
Incorrect. This is an incorrect total amount.
9.
Which of the following is 20% of 200?
A) 20.
B) 30.
C) 40.
D) 100.
Show Answer
Correct Answer:
Correct answer is: (C) 40.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Easy
Concept notes:
To find 20% of 200, we need to calculate 20% of the number 200.
Common Mistakes:
A common mistake is to misinterpret the percentage or to perform incorrect arithmetic operations.
Explanations:
To find 20% of 200, we use the formula:
\[ \text{Percentage} = \left( \frac{\text{Percentage Value}}{100} \right) \times \text{Total Value} \]
\[ 20\% \text{ of } 200 = \left( \frac{20}{100} \right) \times 200 \]
\[ = 0.2 \times 200 \]
\[ = 40 \]
Option Analysis:
Option A:
20 is incorrect because it is not the result of 20% of 200.
Option B:
30 is incorrect because it is not the result of 20% of 200.
Option C:
40 is correct because it is the result of 20% of 200.
Option D:
100 is incorrect because it is not the result of 20% of 200.
10.
A pair of sandals costs $ 10.50. There is a 7% sales tax. What is the total cost of the sandals?
A) $ .74.
B) $ 10.50.
C) $ 12.78.
D) $ 11.24.
Show Answer
Correct Answer:
Correct answer is: (D) $ 11.24.
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 common application of percentages.
Common Mistakes:
A common mistake is to add the sales tax amount directly to the original price without calculating the tax correctly.
Explanations:
To find the total cost of the sandals including the 7% sales tax, follow these steps:
1. Calculate the sales tax amount: \( 10.50 \times 0.07 = 0.735 \).
2. Add the sales tax to the original price: \( 10.50 + 0.735 = 11.235 \).
3. Round the total to the nearest cent: \( 11.24 \).
Thus, the total cost of the sandals is $11.24.
Option Analysis:
Option A:
$0.74 is the incorrect amount of sales tax, not the total cost.
Option B:
$10.50 is the original price without tax.
Option C:
$12.78 is an incorrect total cost, likely due to a calculation error.
Option D:
$11.24 is the correct total cost including the 7% sales tax.
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Frequently Asked Questions
What is the purpose of learning percentage applications?
Learning percentage applications helps in understanding how percentages are used in real-life scenarios such as calculating discounts, interest rates, and sales tax.
How do you convert a fraction to a percentage?
To convert a fraction to a percentage, divide the numerator by the denominator and then multiply the result by 100.
What is the role of the multiplier R in percentage calculations?
The multiplier R is used to adjust the original value by a certain percentage, often seen in interest rate calculations or sales tax computations.
How can percentage applications be used in sales analysis?
Percentage applications can help in analyzing sales data by calculating growth rates, market share, and profit margins, providing insights into business performance.
What skills are necessary for solving percentage problems?
Skills such as arithmetic operations, equation setup, and data interpretation are essential for effectively solving percentage problems.