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Unit Vii Data Interpretation
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Percentage Based Data Interpretation – Quiz 49
Percentage Based Data Interpretation Quiz 49 (10 MCQs)
This set of multiple-choice questions evaluates skills in percentage calculation, area interpretation, ratio conversion, and data interpretation. It covers concepts such as base value, discount amount, percentage decrease, and weight proportion. Students will practice logical deduction, equation setup, and numerical computation to solve problems involving percentages, decimals, and arithmetic operations.
Quiz Instructions
Select an option to see the correct answer instantly.
1.
It rained 10% of the 30 days last month. On how many days did it NOT rain?
A) 3 days.
B) 10 days.
C) 15 days.
D) 27 days.
Show Answer
Correct Answer:
Correct answer is: (D) 27 days.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Easy
Concept notes:
To find the number of days it did not rain, we first need to determine the number of days it rained. Given that it rained 10% of the 30 days, we can calculate the number of rainy days and then subtract this from the total number of days to find the number of days it did not rain.
Common Mistakes:
A common mistake is to directly assume the number of rainy days without performing the percentage calculation, leading to incorrect results.
Explanations:
1. Calculate the number of rainy days: \( 10\% \) of 30 days is \( \frac{10}{100} \times 30 = 3 \) days.
2. Subtract the number of rainy days from the total number of days: \( 30 - 3 = 27 \) days.
Thus, it did not rain on 27 days.
Option Analysis:
Option A:
3 days. This is the number of rainy days, not the number of days it did not rain.
Option B:
10 days. This is not the correct calculation of the number of days it did not rain.
Option C:
15 days. This is not the correct calculation of the number of days it did not rain.
Option D:
27 days. This is the correct number of days it did not rain.
2.
A coin contains 9 grams of nickel, and 16 grams of copper. Its total weight is 25 grams.What percentage of the metal in the coin is copper?
A) 64%.
B) 6%.
C) 14%.
D) 36%.
E) 156%.
Show Answer
Correct Answer:
Correct answer is: (A) 64%.
Exam Relevance:
SAT, GRE, GMAT, ACT
Difficulty:
Easy
Concept notes:
To find the percentage of copper in the coin, we need to calculate the proportion of copper in the total weight of the coin and then convert it to a percentage.
Common Mistakes:
A common mistake is to confuse the weight of copper with the total weight of the coin, leading to incorrect percentage calculations.
Explanations:
1. The total weight of the coin is 25 grams.
2. The weight of copper in the coin is 16 grams.
3. To find the percentage of copper, we use the formula:
\[
\text{Percentage of copper} = \left( \frac{\text{Weight of copper}}{\text{Total weight of the coin}} \right) \times 100
\]
4. Substituting the values:
\[
\text{Percentage of copper} = \left( \frac{16}{25} \right) \times 100 = 0.64 \times 100 = 64\%
\]
Option Analysis:
Option A:
Correct. The percentage of copper in the coin is 64%.
Option B:
Incorrect. 6% is not the correct percentage of copper.
Option C:
Incorrect. 14% is not the correct percentage of copper.
Option D:
Incorrect. 36% is not the correct percentage of copper.
Option E:
Incorrect. 156% is not the correct percentage of copper.
3.
Paula found a sweatshirt that costs $ 76. The sweatshirt is on sale for 25% off the original price. What is the amount of the discount on this sweatshirt?
A) $ 19.
B) $ 95.
C) $ 57.
D) $ 51.
Show Answer
Correct Answer:
Correct answer is: (A) $ 19.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Easy
Concept notes:
The concept involves calculating the discount amount based on a given percentage off the original price.
Common Mistakes:
A common mistake is to calculate the final price after the discount instead of the discount amount itself.
Explanations:
To find the discount amount, we need to calculate 25% of the original price of the sweatshirt. The original price is $76.
1. Convert the percentage to a decimal: 25% = 0.25.
2. Multiply the original price by the decimal: $76 × 0.25 = $19.
Thus, the discount amount is $19.
Option Analysis:
Option A:
Correct. The discount amount is $19.
Option B:
Incorrect. This is not the discount amount but a higher value.
Option C:
Incorrect. This is not the discount amount but a lower value.
Option D:
Incorrect. This is not the discount amount but a lower value.
4.
On Business Day, after 2 hours P6A sold 36% of their cookies. They found out they still had 128 cookies left to sell. How many cookies did they have in the beginning of Business Day?
A) 100.
B) 150.
C) 180.
D) 200.
Show Answer
Correct Answer:
Correct answer is: (D) 200.
Exam Relevance:
SAT, ACT, GMAT, GRE
Difficulty:
Moderate
Concept notes:
The problem involves calculating the initial quantity of cookies based on the percentage sold and the remaining quantity.
Common Mistakes:
A common mistake is to misinterpret the percentage sold and remaining, leading to incorrect calculations.
Explanations:
Let the initial number of cookies be \( x \).
After 2 hours, 36% of the cookies were sold, which means 64% of the cookies were left. According to the problem, 64% of the initial cookies is equal to 128 cookies.
We can set up the equation:
\[ 0.64x = 128 \]
To find \( x \), we solve for \( x \):
\[ x = \frac{128}{0.64} \]
\[ x = 200 \]
Thus, the initial number of cookies is 200.
Option Analysis:
Option A:
100 is incorrect because 64% of 100 is 64, not 128.
Option B:
150 is incorrect because 64% of 150 is 96, not 128.
Option C:
180 is incorrect because 64% of 180 is 115.2, not 128.
Option D:
200 is correct because 64% of 200 is 128.
5.
What is the percent of the shaded portion of the figure?
A) 20%.
B) 80%.
C) 60%.
D) 70%.
Show Answer
Correct Answer:
Correct answer is: (C) 60%.
Exam Relevance:
SAT, GRE, GMAT, ACT
Difficulty:
Moderate
Concept notes:
In percentage based data interpretation, the shaded portion of a figure is calculated by determining the ratio of the shaded area to the total area and then converting this ratio to a percentage.
Common Mistakes:
A common mistake is to misinterpret the shaded area or the total area, leading to incorrect calculations.
Explanations:
To determine the percent of the shaded portion, we need to calculate the ratio of the shaded area to the total area and then convert this ratio to a percentage. If the shaded area is 60% of the total area, then the correct answer is 60%. This means that the shaded portion covers 60% of the total area of the figure.
Option Analysis:
Option A:
20% is incorrect because it does not match the given shaded portion.
Option B:
80% is incorrect because it does not match the given shaded portion.
Option C:
60% is correct as it matches the given shaded portion.
Option D:
70% is incorrect because it does not match the given shaded portion.
6.
Last year, there were 60 schools participated in Springfield Cup. This year, there is a 15% decrease in the numbers of schools participating Springfield Cup. How many schools participated in Springfield Cup this year?
A) 9.
B) 51.
C) 12.
D) 69.
Show Answer
Correct Answer:
Correct answer is: (B) 51.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Moderate
Concept notes:
The question involves calculating a percentage decrease and applying it to find the new number of schools participating in the Springfield Cup.
Common Mistakes:
A common mistake is to misinterpret the percentage decrease and incorrectly calculate the new number of schools.
Explanations:
1. Start with the original number of schools: 60.
2. Calculate the 15% decrease: \( 60 \times 0.15 = 9 \).
3. Subtract the decrease from the original number: \( 60 - 9 = 51 \).
Thus, the number of schools participating this year is 51.
Option Analysis:
Option A:
9 is the amount of the decrease, not the final number of schools.
Option B:
51 is the correct number of schools after a 15% decrease.
Option C:
12 is not the correct number of schools after a 15% decrease.
Option D:
69 is not the correct number of schools after a 15% decrease.
7.
Bill is in a class of 15 boys and 35 girls. 40% of the students in the class take the bus to school. How many students do not take the bus to school?
A) 15.
B) 20.
C) 30.
D) 35.
Show Answer
Correct Answer:
Correct answer is: (C) 30.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Moderate
Concept notes:
The question involves calculating the number of students who do not take the bus based on the given percentage.
Common Mistakes:
A common mistake is to misinterpret the percentage and calculate the number of students who take the bus instead of those who do not.
Explanations:
1. Calculate the total number of students in the class: 15 boys + 35 girls = 50 students.
2. Determine the number of students who take the bus: 40% of 50 students = 0.40 * 50 = 20 students.
3. Calculate the number of students who do not take the bus: 50 students - 20 students = 30 students.
Option Analysis:
Option A:
15 is incorrect because it does not match the calculated number of students who do not take the bus.
Option B:
20 is incorrect because it represents the number of students who take the bus, not those who do not.
Option C:
30 is correct because it matches the calculated number of students who do not take the bus.
Option D:
35 is incorrect because it does not match the calculated number of students who do not take the bus.
8.
Which percent equation matches the following:What percent of 80 is 90?
A) $90\cdot x\ =\ 80$.
B) $80\cdot x\ =\ 90$.
C) $90\cdot80\ =\ x$.
D) None of above.
Show Answer
Correct Answer:
Correct answer is: (B) $80\cdot x\ =\ 90$.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Moderate
Concept notes:
The question asks what percent of 80 is 90. This can be translated into the equation \(80 \cdot x = 90\), where \(x\) represents the unknown percentage.
Common Mistakes:
A common mistake is to misinterpret the question and set up the equation incorrectly, such as \(90 \cdot x = 80\), which would be incorrect.
Explanations:
To find what percent of 80 is 90, we need to set up the equation where 80 is multiplied by the unknown percentage \(x\) to equal 90. This translates to \(80 \cdot x = 90\). Solving for \(x\) will give us the percentage.
Option Analysis:
Option A:
This equation \(90 \cdot x = 80\) is incorrect because it suggests 90 is the base value, which is not the case. The base value is 80.
Option B:
This equation \(80 \cdot x = 90\) correctly represents the problem, where 80 is the base value and \(x\) is the unknown percentage.
Option C:
This equation \(90 \cdot 80 = x\) is incorrect because it suggests multiplying 90 and 80 to find the percentage, which does not align with the problem statement.
Option D:
This option is incorrect because one of the provided equations does match the problem statement.
9.
What is 16% of 60?
A) 9.6.
B) 12.
C) .096.
D) 26.7.
Show Answer
Correct Answer:
Correct answer is: (A) 9.6.
Exam Relevance:
SAT, GRE, GMAT, ACT
Difficulty:
Easy
Concept notes:
To find a percentage of a number, multiply the number by the percentage (expressed as a decimal).
Common Mistakes:
A common mistake is to misinterpret the percentage as a whole number or to forget to convert the percentage to a decimal.
Explanations:
To find 16% of 60, convert 16% to a decimal by dividing by 100, which gives 0.16. Then, multiply 60 by 0.16:
\[ 60 \times 0.16 = 9.6 \]
Option Analysis:
Option A:
9.6 is the correct answer.
Option B:
12 is incorrect because it is the result of 20% of 60, not 16%.
Option C:
0.096 is incorrect because it is the result of 0.16% of 60, not 16%.
Option D:
26.7 is incorrect because it is not a valid result for 16% of 60.
10.
Find 72% of 123
A) 8.856.
B) 88.56.
C) 885.6.
D) 8856.
Show Answer
Correct Answer:
Correct answer is: (B) 88.56.
Exam Relevance:
SAT, GRE, GMAT, ACT
Difficulty:
Easy
Concept notes:
To find a percentage of a number, multiply the number by the percentage (expressed as a decimal).
Common Mistakes:
A common mistake is to misplace the decimal point when converting the percentage to a decimal.
Explanations:
To find 72% of 123, we first convert 72% to a decimal by dividing by 100, which gives 0.72. Then, we multiply 123 by 0.72:
\[ 123 \times 0.72 = 88.56 \]
Option Analysis:
Option A:
8.856 is incorrect because it is too small. The decimal point is misplaced.
Option B:
88.56 is correct as it is the result of the calculation.
Option C:
885.6 is incorrect because it is too large. The decimal point is misplaced.
Option D:
8856 is incorrect because it is much too large. The decimal point is misplaced.
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Frequently Asked Questions
What is the purpose of percentage-based data interpretation?
Percentage-based data interpretation helps in understanding and comparing data by expressing it as a percentage of a base value, making it easier to analyze trends and proportions.
How can I 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 formula to calculate the discount amount?
The discount amount can be calculated by multiplying the original price by the percentage discount. For example, a 20% discount on a $100 item would be $20.
How do I calculate the remaining quantity after a percentage decrease?
To find the remaining quantity after a percentage decrease, subtract the percentage decrease from 100%, then multiply the result by the initial quantity. For example, a 30% decrease on 100 units leaves 70 units.
What skills are essential for solving percentage-based data interpretation problems?
Essential skills include understanding percentage equations, multiplication, and the ability to convert between percentages and decimals, as well as interpreting data from tables or graphs.