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Unit V Mathematical Reasoning And Aptitude
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Percentage Applications – Quiz 12
Percentage Applications Quiz 12 (10 MCQs)
This set of multiple-choice questions evaluates understanding of percentage applications, including fraction to percentage conversion, fee calculation, and commission calculations. It covers concepts such as commission percentage, fixed salary, tax addition, and discount application. The material also tests skills in basic arithmetic, multiplication, and rounding to the nearest cent.
Quiz Instructions
Select an option to see the correct answer instantly.
1.
A TV is regularly priced at $ 600, but it is on sale for 20% off. What's the sale price?
A) $ 320.
B) $ 500.
C) $ 480.
D) $ 720.
Show Answer
Correct Answer:
Correct answer is: (C) $ 480.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Moderate
Concept notes:
The concept involves calculating the sale price after a percentage discount is applied to the original price.
Common Mistakes:
A common mistake is to calculate the discount amount and subtract it from the original price incorrectly, leading to an incorrect sale price.
Explanations:
To find the sale price, first calculate the discount amount by multiplying the original price by the discount percentage. The original price is $600, and the discount is 20%. The discount amount is calculated as follows:
\[ \text{Discount Amount} = 600 \times \frac{20}{100} = 600 \times 0.20 = 120 \]
Next, subtract the discount amount from the original price to get the sale price:
\[ \text{Sale Price} = 600 - 120 = 480 \]
Thus, the sale price is $480.
Option Analysis:
Option A:
$320 is incorrect because it does not reflect the correct calculation of the discount and the resulting sale price.
Option B:
$500 is incorrect because it does not reflect the correct calculation of the discount and the resulting sale price.
Option C:
$480 is correct because it accurately reflects the sale price after applying the 20% discount.
Option D:
$720 is incorrect because it does not reflect the correct calculation of the discount and the resulting sale price.
2.
You want to buy a shirt. The original price was $ 27, and the sale says 25% off. How much will pay for the shirt?
A) 0.25.
B) 33.75.
C) 6.75.
D) 20.25.
Show Answer
Correct Answer:
Correct answer is: (D) 20.25.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Easy
Concept notes:
To find the sale price of an item, you need to calculate the discount and subtract it from the original price.
Common Mistakes:
A common mistake is to calculate the discount and add it to the original price instead of subtracting it.
Explanations:
1. Calculate the discount amount: 25% of $27.
2. Convert the percentage to a decimal: 25% = 0.25.
3. Multiply the original price by the decimal: $27 * 0.25 = $6.75.
4. Subtract the discount from the original price: $27 - $6.75 = $20.25.
Option Analysis:
Option A:
0.25 is the decimal form of 25%, but it is not the final price.
Option B:
33.75 is incorrect because it is greater than the original price, which is not possible with a discount.
Option C:
6.75 is the discount amount, not the final price.
Option D:
20.25 is the correct final price after applying the 25% discount.
3.
It is known that the gross weight of 3 sacks is 300 kg. If the tare is 1.5%, the net is .....
A) 290,5 kg.
B) 295,5 kg.
C) 295 kg.
D) 297,5 kg.
Show Answer
Correct Answer:
Correct answer is: (B) 295,5 kg.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Moderate
Concept notes:
The tare is the weight of the container or packaging, and the net weight is the weight of the contents alone. The tare is given as a percentage of the gross weight.
Common Mistakes:
A common mistake is to incorrectly calculate the net weight by subtracting the tare percentage directly from the gross weight without converting the percentage to a decimal.
Explanations:
1. The gross weight of the 3 sacks is 300 kg.
2. The tare is 1.5% of the gross weight.
3. Convert the tare percentage to a decimal: 1.5% = 0.015.
4. Calculate the tare weight: 300 kg * 0.015 = 4.5 kg.
5. Subtract the tare weight from the gross weight to find the net weight: 300 kg - 4.5 kg = 295.5 kg.
Option Analysis:
Option A:
290.5 kg is incorrect because it does not account for the correct tare weight calculation.
Option B:
295.5 kg is correct as it accurately reflects the net weight after subtracting the tare weight.
Option C:
295 kg is incorrect because it does not account for the full tare weight calculation.
Option D:
297.5 kg is incorrect because it does not correctly subtract the tare weight from the gross weight.
4.
Write 3/5 as a percent.
A) 3%.
B) 30%.
C) 5%.
D) 60%.
Show Answer
Correct Answer:
Correct answer is: (D) 60%.
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 think that 3/5 is 30% because 3 is 30% of 10. However, the correct method is to multiply the fraction by 100.
Explanations:
To convert the fraction 3/5 to a percentage, multiply it by 100:
\[
\frac{3}{5} \times 100 = 60\%
\]
Option Analysis:
Option A:
3% is incorrect because it does not represent the fraction 3/5 when converted to a percentage.
Option B:
30% is incorrect because it is a common mistake to think that 3 is 30% of 10, but the correct method is to multiply the fraction by 100.
Option C:
5% is incorrect because it does not represent the fraction 3/5 when converted to a percentage.
Option D:
60% is correct because multiplying 3/5 by 100 gives 60%.
5.
Randy gets fixed salary of $ 2000 per month and a commission of 2% on sales. If his total sales are $ 30,000 for the month, find his total salary for the month.
A) $ 2,600.
B) $ 2,000.
C) $ 32,000.
D) $ 2,040.
Show Answer
Correct Answer:
Correct answer is: (A) $ 2,600.
Exam Relevance:
SAT, ACT, GMAT, GRE
Difficulty:
Easy
Concept notes:
The question involves calculating a total salary based on a fixed salary and a commission percentage applied to sales.
Common Mistakes:
A common mistake is to forget to add the fixed salary to the commission earned, or to miscalculate the commission percentage.
Explanations:
1. Randy's fixed salary is $2000.
2. The commission is 2% of his total sales.
3. His total sales are $30,000.
4. Calculate the commission: 2% of $30,000 = 0.02 * $30,000 = $600.
5. Add the commission to the fixed salary: $2000 + $600 = $2600.
Option Analysis:
Option A:
Correct. Randy's total salary is $2600.
Option B:
Incorrect. This is only the fixed salary, not including the commission.
Option C:
Incorrect. This is the total sales amount, not the salary.
Option D:
Incorrect. This is an incorrect calculation of the total salary.
6.
What is 50% of 120?
A) 50.
B) 60.
C) 70.
D) 80.
Show Answer
Correct Answer:
Correct answer is: (B) 60.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Easy
Concept notes:
To find 50% of a number, you multiply the number by 0.5.
Common Mistakes:
A common mistake is to think that 50% of a number is half of the number, but it is important to perform the multiplication to ensure accuracy.
Explanations:
To find 50% of 120, we multiply 120 by 0.5:
\[ 120 \times 0.5 = 60 \]
Option Analysis:
Option A:
50 is incorrect because 50% of 120 is not 50.
Option B:
60 is correct because 120 multiplied by 0.5 equals 60.
Option C:
70 is incorrect because 50% of 120 is not 70.
Option D:
80 is incorrect because 50% of 120 is not 80.
7.
Jimmy sold a book for 69.95 on Cheggs.com. He had to pay a 8% fee for selling the book. How much was Jimmy's fee?
A) $ 5.59.
B) $ 5.60.
C) $ 64.35.
D) $ 75.55.
Show Answer
Correct Answer:
Correct answer is: (B) $ 5.60.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Easy
Concept notes:
The concept involves calculating a percentage of a given amount. Here, we need to find 8% of the selling price of the book.
Common Mistakes:
A common mistake is to misinterpret the percentage calculation, such as adding the percentage to the original amount instead of finding the fee.
Explanations:
To find the fee, we calculate 8% of $69.95. The formula to find a percentage of a number is:
\[ \text{Fee} = \text{Selling Price} \times \left(\frac{\text{Percentage}}{100}\right) \]
\[ \text{Fee} = 69.95 \times \left(\frac{8}{100}\right) \]
\[ \text{Fee} = 69.95 \times 0.08 \]
\[ \text{Fee} = 5.596 \]
Rounding to the nearest cent, the fee is $5.60.
Option Analysis:
Option A:
$5.59 is incorrect because it does not round to the nearest cent correctly.
Option B:
$5.60 is the correct answer as it is the rounded value of the calculated fee.
Option C:
$64.35 is incorrect because it is not the fee but a different amount.
Option D:
$75.55 is incorrect because it is not the fee but a different amount.
8.
You work at a Nordstrom's make-up counter. You earn 20% commission on anything you sell. This week you sold $ 2,000 worth of make-up. How much commission will you earn this week?
A) $ 2,400.
B) $ 400.
C) $ 20.
D) $ 2,020.
E) $ 4,000.
Show Answer
Correct Answer:
Correct answer is: (B) $ 400.
Exam Relevance:
SAT, ACT, GMAT, GRE
Difficulty:
Easy
Concept notes:
The concept tested here is the application of percentage to calculate commission.
Common Mistakes:
A common mistake is to misinterpret the percentage or to perform incorrect arithmetic operations.
Explanations:
To find the commission, we need to calculate 20% of $2,000.
1. Convert the percentage to a decimal: 20% = 0.20
2. Multiply the total sales by the decimal: $2,000 * 0.20 = $400
Thus, the commission earned is $400.
Option Analysis:
Option A:
Incorrect. This option represents the total sales plus the commission, which is not the correct calculation.
Option B:
Correct. This option represents the correct commission amount.
Option C:
Incorrect. This option represents a very small fraction of the correct commission amount.
Option D:
Incorrect. This option represents the total sales plus a small fraction of the commission, which is not the correct calculation.
Option E:
Incorrect. This option represents double the total sales, which is not the correct calculation.
9.
How much does a customer pay for an article marked at $ 50.00 if a tax of 18% is charged?
A) $ 41.00.
B) $ 59.00.
C) $ 68.00.
D) $ 32.00.
Show Answer
Correct Answer:
Correct answer is: (B) $ 59.00.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Easy
Concept notes:
The concept involves calculating the final price of an item after adding a tax percentage to the marked price.
Common Mistakes:
A common mistake is to subtract the tax from the marked price instead of adding it.
Explanations:
To find the final price after adding an 18% tax to a marked price of $50.00, follow these steps:
1. Calculate the tax amount: \( 18\% \) of $50.00.
2. Convert the percentage to a decimal: \( 18\% = 0.18 \).
3. Multiply the marked price by the decimal: \( 50.00 \times 0.18 = 9.00 \).
4. Add the tax amount to the marked price: \( 50.00 + 9.00 = 59.00 \).
Thus, the final price is $59.00.
Option Analysis:
Option A:
Incorrect, as $41.00 is less than the marked price, indicating a subtraction rather than an addition of tax.
Option B:
Correct, as $59.00 is the result of adding 18% tax to the marked price of $50.00.
Option C:
Incorrect, as $68.00 is too high and does not match the correct calculation.
Option D:
Incorrect, as $32.00 is significantly less than the marked price and does not reflect the addition of tax.
10.
In order to qualify for the year-end tennis tournament, Sam must win at least 60 percent of his matches this year. To date, Sam has won 14 of his 18 matches. Of Sam's 13 matches remaining in the year, what is the least number that he must win in order to qualify for the year-end tournament?
A) 4.
B) 5.
C) 6.
D) 7.
E) 8.
Show Answer
Correct Answer:
Correct answer is: (B) 5.
Exam Relevance:
SAT, ACT, GMAT, GRE
Difficulty:
Moderate
Concept notes:
To qualify for the year-end tennis tournament, Sam must win at least 60% of his matches this year. We need to determine the minimum number of matches he must win out of his remaining 13 matches to achieve this goal.
Common Mistakes:
A common mistake is to assume that winning 60% of the remaining matches is sufficient, without considering the total number of matches played.
Explanations:
1. Calculate the total number of matches Sam will play this year: 18 (already played) + 13 (remaining) = 31 matches.
2. Determine the number of matches Sam needs to win to achieve 60%: 0.60 * 31 = 18.6, which rounds up to 19 matches.
3. Sam has already won 14 matches, so he needs to win 19 - 14 = 5 more matches out of the remaining 13 matches to qualify.
Option Analysis:
Option A:
4 matches are insufficient because 14 + 4 = 18 matches, which is less than 19 required matches.
Option B:
5 matches are sufficient because 14 + 5 = 19 matches, which meets the requirement.
Option C:
6 matches are more than necessary, but still correct as it exceeds the minimum requirement.
Option D:
7 matches are more than necessary, but still correct as it exceeds the minimum requirement.
Option E:
8 matches are more than necessary, but still correct as it exceeds the minimum requirement.
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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, taxes, and commissions.
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 difference between net weight and tare weight?
Net weight refers to the weight of the product alone, while tare weight is the weight of the packaging or container, excluding the product.
How do you calculate the final price after applying a discount?
To calculate the final price after a discount, subtract the discount amount from the original price. The discount amount is the original price multiplied by the discount percentage.
What is the significance of finding half of a number in percentage terms?
Finding half of a number in percentage terms means calculating 50% of that number, which is useful in various applications such as splitting costs or determining midpoints.