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Unit Vii Data Interpretation
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Percentage Based Data Interpretation – Quiz 3
Percentage Based Data Interpretation Quiz 3 (10 MCQs)
This set of multiple-choice questions evaluates skills in percent change calculation, identifying increases or decreases, and interpreting percentages. It covers basic arithmetic, data interpretation, and the conversion between percentages and decimals. Students will practice breaking down percentages, summing them, and applying formulas to solve problems related to surface area distribution and part-whole relationships.
Quiz Instructions
Select an option to see the correct answer instantly.
1.
Find 78% of 160.
A) 128.4.
B) 124.8.
C) 124.
D) 128.
Show Answer
Correct Answer:
Correct answer is: (B) 124.8.
Exam Relevance:
SAT, GRE, GMAT, CAT
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 78% of 160, we first convert 78% to a decimal by dividing by 100, which gives 0.78. Then, we multiply 160 by 0.78:
\[ 160 \times 0.78 = 124.8 \]
Option Analysis:
Option A:
128.4 is incorrect because it results from a calculation error, possibly due to misplacing the decimal point.
Option B:
124.8 is the correct answer as it results from the accurate calculation of 160 multiplied by 0.78.
Option C:
124 is incorrect because it does not account for the decimal part of the multiplication.
Option D:
128 is incorrect because it results from a calculation error, possibly due to misplacing the decimal point.
2.
In a team there are 240 members(Males and Females). Two-third of them are males. 15% of males are graduate. Remaining males are non-graduate. Three fourth of the females are graduate. Remaining females are non-graduate.1) What is the difference between the number of females who are non-graduate and the number of males who are graduate?
Show Answer
Correct Answer:
Correct answer is: (A) 4.
Exam Relevance:
CAT, GMAT, GRE, Bank PO
Difficulty:
Moderate
Concept notes:
The question involves calculating the number of males and females who are graduates and non-graduates, and then finding the difference between the number of non-graduate females and graduate males.
Common Mistakes:
A common mistake could be misinterpreting the percentages or incorrectly calculating the number of graduates and non-graduates.
Explanations:
1. Total members = 240.
2. Number of males = \(\frac{2}{3} \times 240 = 160\).
3. Number of females = \(240 - 160 = 80\).
4. Number of male graduates = \(15\% \times 160 = 0.15 \times 160 = 24\).
5. Number of male non-graduates = \(160 - 24 = 136\).
6. Number of female graduates = \(\frac{3}{4} \times 80 = 60\).
7. Number of female non-graduates = \(80 - 60 = 20\).
8. Difference between the number of female non-graduates and male graduates = \(20 - 24 = -4\). Since we are asked for the absolute difference, the answer is 4.
Option Analysis:
Option A:
Correct. The difference is 4.
Option B:
Incorrect. The difference is not 5.
Option C:
Incorrect. The difference is not 6.
Option D:
Incorrect. The difference is not 8.
3.
What percent of 20 is 5?
A) 1%.
B) 4%.
C) 25%.
D) 85%.
Show Answer
Correct Answer:
Correct answer is: (C) 25%.
Exam Relevance:
SAT, GRE, GMAT, CAT
Difficulty:
Moderate
Concept notes:
To find what percent of 20 is 5, we use the formula: \(\text{Percentage} = \left(\frac{\text{Part}}{\text{Whole}}\right) \times 100\).
Common Mistakes:
A common mistake is to misinterpret the question and calculate the percentage incorrectly, such as dividing 20 by 5 instead of 5 by 20.
Explanations:
To find what percent of 20 is 5, we use the formula:
\[
\text{Percentage} = \left(\frac{\text{Part}}{\text{Whole}}\right) \times 100
\]
Here, the part is 5 and the whole is 20. Plugging in the values, we get:
\[
\text{Percentage} = \left(\frac{5}{20}\right) \times 100 = 0.25 \times 100 = 25\%
\]
Thus, 5 is 25% of 20.
Option Analysis:
Option A:
1% is incorrect because 1% of 20 is 0.2, not 5.
Option B:
4% is incorrect because 4% of 20 is 0.8, not 5.
Option C:
25% is correct because 25% of 20 is 5.
Option D:
85% is incorrect because 85% of 20 is 17, not 5.
4.
The percent a quantity decreases from its original amount
A) Percent Decrease.
B) Scale Factor.
C) Percent Increase.
D) None of above.
Show Answer
Correct Answer:
Correct answer is: (A) Percent Decrease.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Easy
Concept notes:
Percent decrease is the measure of how much a quantity has reduced in terms of a percentage of its original amount.
Common Mistakes:
A common mistake is confusing percent decrease with percent increase or scale factor. Percent decrease specifically refers to a reduction in quantity.
Explanations:
Percent decrease is the correct term for the percentage by which a quantity has decreased from its original amount. This is calculated by taking the difference between the original amount and the new amount, dividing by the original amount, and then multiplying by 100 to get the percentage.
Option Analysis:
Option A:
Correct. Percent decrease is the measure of how much a quantity has reduced in terms of a percentage of its original amount.
Option B:
Incorrect. Scale factor is a ratio used to scale up or down the size of an object, not a measure of percentage decrease.
Option C:
Incorrect. Percent increase is the measure of how much a quantity has increased in terms of a percentage of its original amount, not a decrease.
Option D:
Incorrect. This option is not applicable as the correct answer is provided in Option A.
5.
At a birthday party 40% of the children had an ice-cream. 150 children attended the party. How many had an ice-cream?
A) 60.
B) 70.
C) 80.
D) 90.
Show Answer
Correct Answer:
Correct answer is: (A) 60.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Easy
Concept notes:
To find the number of children who had an ice-cream, we need to calculate 40% of the total number of children who attended the party.
Common Mistakes:
A common mistake is to misinterpret the percentage or to perform the calculation incorrectly, leading to an incorrect number of children.
Explanations:
To find 40% of 150 children:
1. Convert the percentage to a decimal: 40% = 0.40.
2. Multiply the total number of children by the decimal: 150 * 0.40 = 60.
Therefore, 60 children had an ice-cream.
Option Analysis:
Option A:
Correct. 60 children had an ice-cream.
Option B:
Incorrect. 70 is not the correct number of children who had an ice-cream.
Option C:
Incorrect. 80 is not the correct number of children who had an ice-cream.
Option D:
Incorrect. 90 is not the correct number of children who had an ice-cream.
6.
About 75% of the Earth's surface is covered by water while the remaining surface is covered by land. Find the percentage of land.
A) 30%.
B) 100%.
C) 25%.
D) 20%.
Show Answer
Correct Answer:
Correct answer is: (C) 25%.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Easy
Concept notes:
The question involves basic percentage calculation and understanding of the Earth's surface composition.
Common Mistakes:
A common mistake could be misinterpreting the percentage of water coverage and not correctly calculating the remaining percentage for land.
Explanations:
The Earth's surface is covered by 75% water. To find the percentage of land, subtract the percentage of water from 100%.
100% - 75% = 25%
Thus, the percentage of land is 25%.
Option Analysis:
Option A:
30% is incorrect because it does not account for the correct subtraction from 100%.
Option B:
100% is incorrect because it represents the total surface area, not the land percentage.
Option C:
25% is correct as it accurately represents the remaining percentage after subtracting the water coverage.
Option D:
20% is incorrect because it does not match the correct calculation.
7.
Name the two steps to calculating a percent of a number
A) Cross multiply then divide.
B) Change the decimal to a percent then cross multiply.
C) Change the percent to a decimal then divide.
D) Change the percent to a decimal then multiply.
Show Answer
Correct Answer:
Correct answer is: (D) Change the percent to a decimal then multiply.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Easy
Concept notes:
To calculate a percent of a number, you first convert the percent to a decimal and then multiply the decimal by the number.
Common Mistakes:
A common mistake is to use cross multiplication or to divide instead of multiplying after converting the percent to a decimal.
Explanations:
To find a percent of a number, you first convert the percent to a decimal by dividing by 100. For example, 25% becomes 0.25. Then, you multiply this decimal by the number. For instance, to find 25% of 80, you would calculate 0.25 * 80 = 20.
Option Analysis:
Option A:
Cross multiply then divide is not the correct method for calculating a percent of a number.
Option B:
Changing the decimal to a percent and then cross multiplying is not the correct method for calculating a percent of a number.
Option C:
Changing the percent to a decimal and then dividing is not the correct method for calculating a percent of a number.
Option D:
Changing the percent to a decimal and then multiplying is the correct method for calculating a percent of a number.
8.
A Stationery seller had some Pens, Sharpeners, Erasers & Pencils. He sells 65% of the total units and still has 175 units. Originally, he had:
A) 588 units.
B) 400 units.
C) 272 units.
D) 500 units.
Show Answer
Correct Answer:
Correct answer is: (D) 500 units.
Exam Relevance:
GMAT, GRE, SAT, ACT
Difficulty:
Moderate
Concept notes:
The problem involves calculating the original number of units based on the percentage sold and the remaining units.
Common Mistakes:
A common mistake is to misinterpret the percentage sold and remaining units, leading to incorrect calculations.
Explanations:
Let the original number of units be \( x \).
The seller sells 65% of the total units, so 35% of the units remain.
Given that 35% of the units is 175 units, we can set up the equation:
\[ 0.35x = 175 \]
Solving for \( x \):
\[ x = \frac{175}{0.35} \]
\[ x = 500 \]
Thus, the original number of units is 500.
Option Analysis:
Option A:
588 units is incorrect because it does not satisfy the given condition.
Option B:
400 units is incorrect because it does not satisfy the given condition.
Option C:
272 units is incorrect because it does not satisfy the given condition.
Option D:
500 units is correct because it satisfies the given condition.
9.
How would you find 35% of 24?
A) Find the sum of 25% and 10% of 24.
B) Divide 24 by 35.
C) Subtract 35 and 24.
D) None of above.
Show Answer
Correct Answer:
Correct answer is: (A) Find the sum of 25% and 10% of 24.
Exam Relevance:
SAT, GRE, GMAT, CAT
Difficulty:
Easy
Concept notes:
To find 35% of a number, you can break it down into simpler percentages and add them together.
Common Mistakes:
A common mistake is to directly divide 24 by 35, which does not yield the correct percentage.
Explanations:
To find 35% of 24, we can break it down into 25% and 10% of 24 and then add the results.
25% of 24 is calculated as \( \frac{25}{100} \times 24 = 6 \).
10% of 24 is calculated as \( \frac{10}{100} \times 24 = 2.4 \).
Adding these together, \( 6 + 2.4 = 8.4 \).
Thus, 35% of 24 is 8.4.
Option Analysis:
Option A:
This is the correct approach as it breaks down 35% into 25% and 10%, which are easier to calculate.
Option B:
Dividing 24 by 35 does not give the correct percentage value.
Option C:
Subtracting 35 from 24 is not a valid method for finding a percentage.
Option D:
This is incorrect as Option A is the correct approach.
10.
Penelope spent $ 120 on groceries last week. This week she spent $ 105. Find the percent change and classify as a percent increase or decrease.
A) 12.5% increase.
B) 12.5% decrease.
C) 14.3% increase.
D) 14.3% decrease.
Show Answer
Correct Answer:
Correct answer is: (B) 12.5% decrease.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Moderate
Concept notes:
The concept of percent change involves calculating the difference between two values and expressing that difference as a percentage of the original value. In this case, we need to determine the percent decrease from $120 to $105.
Common Mistakes:
A common mistake is to calculate the percent change incorrectly by using the wrong formula or by not identifying whether it is an increase or decrease.
Explanations:
To find the percent change, we first calculate the difference between the two values:
\[ \text{Difference} = 120 - 105 = 15 \]
Next, we express this difference as a percentage of the original value:
\[ \text{Percent Change} = \left( \frac{15}{120} \right) \times 100 = 12.5\% \]
Since the value decreased from $120 to $105, this is a 12.5% decrease.
Option Analysis:
Option A:
Incorrect because it suggests a 12.5% increase, which is not the case.
Option B:
Correct because it accurately reflects a 12.5% decrease.
Option C:
Incorrect because it suggests a 14.3% increase, which is not the case.
Option D:
Incorrect because it suggests a 14.3% decrease, which is not the case.
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Frequently Asked Questions
What is the purpose of percentage-based data interpretation?
Percentage-based data interpretation helps in understanding the relative size of different parts of a whole, making it easier to compare and analyze data.
How do I calculate a percentage decrease?
To calculate a percentage decrease, subtract the new amount from the original amount, divide the result by the original amount, and then multiply by 100 to get the percentage.
What skills are required for percentage-based data interpretation?
Basic arithmetic skills, such as addition, subtraction, multiplication, and division, are essential, along with the ability to convert percentages to decimals and vice versa.
How can I apply percentage-based data interpretation in real life?
Percentage-based data interpretation can be applied in various real-life scenarios, such as calculating discounts, understanding statistical data, or analyzing financial reports.
What is the significance of the sum of percentages in data interpretation?
The sum of percentages in data interpretation should equal 100%, indicating that all parts of the whole are accounted for, which helps in verifying the accuracy of the data.