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Unit Vii Data Interpretation
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Ratio Based Data Interpretation – Quiz 25
Ratio Based Data Interpretation Quiz 25 (10 MCQs)
This set of multiple-choice questions evaluates skills in ratio application, sum calculation, multiplier determination, and data interpretation. Concepts include annual to monthly conversion, income and savings ratio, percentage application, share distribution, and simplifying ratios. Students will practice ratio simplification, finding the greatest common divisor, and interpreting visual data.
Quiz Instructions
Select an option to see the correct answer instantly.
1.
What is the ratio of 100 grams to 250 grams?
A) 2:5.
B) 1:2.5.
C) 4:1.
D) 5:2.
Show Answer
Correct Answer:
Correct answer is: (A) 2:5.
Exam Relevance:
GMAT, GRE, SAT, ACT
Difficulty:
Easy
Concept notes:
The concept of ratio involves comparing two quantities by division. In this case, we need to find the ratio of 100 grams to 250 grams.
Common Mistakes:
A common mistake is to not simplify the ratio correctly. For example, one might incorrectly think the ratio is 100:250 without simplifying it.
Explanations:
To find the ratio of 100 grams to 250 grams, we divide both numbers by their greatest common divisor (GCD). The GCD of 100 and 250 is 50. Dividing both numbers by 50, we get:
\[ \frac{100}{50} : \frac{250}{50} = 2 : 5 \]
Thus, the ratio of 100 grams to 250 grams is 2:5.
Option Analysis:
Option A:
Correct. The ratio 2:5 is the simplified form of 100:250.
Option B:
Incorrect. The ratio 1:2.5 is not in the simplest form and does not match the correct answer.
Option C:
Incorrect. The ratio 4:1 is incorrect as it does not represent the relationship between 100 and 250.
Option D:
Incorrect. The ratio 5:2 is the reverse of the correct answer and does not match the relationship between 100 and 250.
2.
The pet store has 18 dogs toys for sale. 10 toys are frisbees and the rest are bones. What is the ratio of bones to frisbees in simplest form?
A) 5/9.
B) 8/10.
C) 4/5.
D) 18/10.
Show Answer
Correct Answer:
Correct answer is: (C) 4/5.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Moderate
Concept notes:
The question requires calculating the ratio of bones to frisbees and simplifying it to its simplest form.
Common Mistakes:
A common mistake is not simplifying the ratio to its simplest form or miscounting the number of bones.
Explanations:
1. The total number of dog toys is 18.
2. The number of frisbees is 10.
3. The number of bones is 18 - 10 = 8.
4. The ratio of bones to frisbees is 8:10.
5. Simplify the ratio by dividing both numbers by their greatest common divisor, which is 2.
6. 8 ÷ 2 = 4 and 10 ÷ 2 = 5.
7. The simplified ratio is 4:5, which is equivalent to 4/5.
Option Analysis:
Option A:
5/9 is incorrect because it does not represent the simplified ratio of bones to frisbees.
Option B:
8/10 is incorrect because it is not in its simplest form.
Option C:
4/5 is correct because it is the simplified ratio of bones to frisbees.
Option D:
18/10 is incorrect because it does not represent the ratio of bones to frisbees.
3.
Simplify this ratio 8:10:12
A) 1:2:3.
B) 4:5:6.
C) 4:6:5.
D) 4:9:3.
Show Answer
Correct Answer:
Correct answer is: (B) 4:5:6.
Exam Relevance:
SAT, GRE, GMAT, CAT
Difficulty:
Easy
Concept notes:
To simplify a ratio, divide each term by the greatest common divisor (GCD) of all terms.
Common Mistakes:
A common mistake is to simplify each term individually without considering the GCD of all terms.
Explanations:
To simplify the ratio 8:10:12, we first find the GCD of 8, 10, and 12. The GCD of these numbers is 2. We then divide each term by 2:
8 ÷ 2 = 4
10 ÷ 2 = 5
12 ÷ 2 = 6
Thus, the simplified ratio is 4:5:6.
Option Analysis:
Option A:
Incorrect because 1:2:3 is not the simplified form of 8:10:12.
Option B:
Correct because 4:5:6 is the simplified form of 8:10:12.
Option C:
Incorrect because 4:6:5 does not maintain the correct order of the original ratio.
Option D:
Incorrect because 4:9:3 does not simplify the original ratio correctly.
4.
Bob has 16 red cards and 20 green cards. What is the ratio of Bob's red cards to his green cards:
A) 2:3.
B) 3:4.
C) 4:5.
D) 5:6.
Show Answer
Correct Answer:
Correct answer is: (C) 4:5.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Moderate
Concept notes:
The concept of ratio involves comparing two quantities by division. In this case, we need to find the ratio of Bob's red cards to his green cards.
Common Mistakes:
A common mistake is to misinterpret the order of the ratio. The ratio of red cards to green cards should be written as the number of red cards divided by the number of green cards.
Explanations:
To find the ratio of Bob's red cards to his green cards, we start with the given numbers:
- Red cards: 16
- Green cards: 20
The ratio of red cards to green cards is:
\[ \frac{16}{20} \]
To simplify this ratio, we find the greatest common divisor (GCD) of 16 and 20, which is 4. We then divide both the numerator and the denominator by 4:
\[ \frac{16 \div 4}{20 \div 4} = \frac{4}{5} \]
Thus, the simplified ratio of Bob's red cards to his green cards is 4:5.
Option Analysis:
Option A:
2:3 is incorrect because it does not match the simplified ratio of 16:20.
Option B:
3:4 is incorrect because it does not match the simplified ratio of 16:20.
Option C:
4:5 is correct because it matches the simplified ratio of 16:20.
Option D:
5:6 is incorrect because it does not match the simplified ratio of 16:20.
5.
The ratio of income of a person to his savings is 10: 1. If his savings for one year is Rs.6000, what is his income per month?
A) 5200.
B) 6000.
C) 4800.
D) 5000.
Show Answer
Correct Answer:
Correct answer is: (D) 5000.
Exam Relevance:
CAT, GMAT, GRE, Bank PO, SSC CGL
Difficulty:
Moderate
Concept notes:
The question involves understanding the ratio of income to savings and converting annual savings into monthly income.
Common Mistakes:
A common mistake is to directly use the annual savings amount as the monthly income without converting it to a monthly figure.
Explanations:
Given the ratio of income to savings is 10:1, and the annual savings is Rs. 6000. This means the annual income is 10 times the savings, which is 10 * 6000 = Rs. 60000. To find the monthly income, we divide the annual income by 12: 60000 / 12 = Rs. 5000.
Option Analysis:
Option A:
5200 is incorrect because it does not match the calculated monthly income.
Option B:
6000 is incorrect because it represents the annual savings, not the monthly income.
Option C:
4800 is incorrect because it does not match the calculated monthly income.
Option D:
5000 is correct as it matches the calculated monthly income.
6.
Jay and Jake divided the money allowance in the ratio 4:5. If Jake's share is Php 345, find the total money.
A) Php 276.00.
B) Php 285.00.
C) Php 621.00.
D) Php 1,380.
Show Answer
Correct Answer:
Correct answer is: (C) Php 621.00.
Exam Relevance:
SAT, GRE, GMAT, ACT
Difficulty:
Moderate
Concept notes:
In ratio-based data interpretation, the total amount can be found by first determining the individual shares based on the given ratio and then summing them up.
Common Mistakes:
A common mistake is to assume that the given amount (Php 345) is the total amount, rather than one part of the ratio.
Explanations:
1. The ratio of Jay's share to Jake's share is 4:5.
2. Let Jay's share be 4x and Jake's share be 5x.
3. Given that Jake's share is Php 345, we can set up the equation 5x = 345.
4. Solving for x, we get x = 345 / 5 = 69.
5. Now, Jay's share is 4x = 4 * 69 = 276.
6. The total money is the sum of Jay's and Jake's shares: 276 + 345 = 621.
Option Analysis:
Option A:
Incorrect, as Php 276.00 is Jay's share, not the total amount.
Option B:
Incorrect, as Php 285.00 does not match the calculated total.
Option C:
Correct, as Php 621.00 is the total amount when both shares are summed.
Option D:
Incorrect, as Php 1,380 is not the correct total amount.
7.
A bird's eggs are hatching! There are 12 yellow baby birds and 50 red baby birds. What is the ratio of yellow birds to red birds?
A) 12:50.
B) 12:62.
C) 50:12.
D) 50:62.
Show Answer
Correct Answer:
Correct answer is: (A) 12:50.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Easy
Concept notes:
A ratio is a comparison of two quantities by division. In this case, the ratio of yellow birds to red birds is expressed as the number of yellow birds to the number of red birds.
Common Mistakes:
A common mistake is to include the total number of birds in the ratio, which would be incorrect. The ratio should only compare the two specific quantities given.
Explanations:
The number of yellow birds is 12 and the number of red birds is 50. The ratio of yellow birds to red birds is therefore 12:50.
Option Analysis:
Option A:
Correct. The ratio of yellow birds to red birds is 12:50.
Option B:
Incorrect. This option includes the total number of birds (12 + 50 = 62), which is not the correct way to express the ratio.
Option C:
Incorrect. This option reverses the order of the ratio, comparing red birds to yellow birds instead of yellow birds to red birds.
Option D:
Incorrect. This option includes the total number of birds (12 + 50 = 62) and reverses the order of the ratio.
8.
At Toby's school, students wear a uniform. Students can choose from a red shirt or a white shirt. Using the tape diagram, what is the ratio of red shirts worn to white shirts worn?
A) 1 to 4.
B) 1 to 5.
C) 4 to 1.
D) 4 to 5.
Show Answer
Correct Answer:
Correct answer is: (C) 4 to 1.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Moderate
Concept notes:
The ratio of red shirts to white shirts is determined by comparing the number of red shirts to the number of white shirts using the information provided in the tape diagram.
Common Mistakes:
A common mistake is to misinterpret the tape diagram, leading to an incorrect ratio. For example, students might confuse the ratio of red shirts to the total number of shirts instead of the ratio of red shirts to white shirts.
Explanations:
The tape diagram shows that for every 4 red shirts, there is 1 white shirt. Therefore, the ratio of red shirts to white shirts is 4 to 1.
Option Analysis:
Option A:
Incorrect because the ratio 1 to 4 would mean there is 1 red shirt for every 4 white shirts, which is not supported by the tape diagram.
Option B:
Incorrect because the ratio 1 to 5 would mean there is 1 red shirt for every 5 white shirts, which is not supported by the tape diagram.
Option C:
Correct because the tape diagram shows 4 red shirts for every 1 white shirt, giving a ratio of 4 to 1.
Option D:
Incorrect because the ratio 4 to 5 would mean there are 4 red shirts for every 5 white shirts, which is not supported by the tape diagram.
Mnemonic:
R4W1: Remember the ratio of red to white shirts as 4 to 1.
9.
The sum of two numbers is 84 and their ratio is 5:2. Find numbers.
A) 60, 24.
B) 50, 34.
C) 55, 29.
D) 56, 28.
Show Answer
Correct Answer:
Correct answer is: (A) 60, 24.
Exam Relevance:
SAT, GRE, GMAT, CAT
Difficulty:
Easy
Concept notes:
In ratio-based data interpretation, the sum of the parts of the ratio should equal the total sum given. The ratio 5:2 means the numbers can be represented as 5x and 2x, where x is a common multiplier.
Common Mistakes:
A common mistake is to assume the numbers are directly 5 and 2 without considering the multiplier x.
Explanations:
Let the two numbers be 5x and 2x. According to the problem, the sum of these numbers is 84.
\[ 5x + 2x = 84 \]
\[ 7x = 84 \]
\[ x = \frac{84}{7} \]
\[ x = 12 \]
Now, substituting x back into the expressions for the numbers:
\[ 5x = 5 \times 12 = 60 \]
\[ 2x = 2 \times 12 = 24 \]
Thus, the numbers are 60 and 24.
Option Analysis:
Option A:
60, 24. This is the correct answer as derived from the ratio and sum.
Option B:
50, 34. This does not satisfy the ratio 5:2 or the sum 84.
Option C:
55, 29. This does not satisfy the ratio 5:2 or the sum 84.
Option D:
56, 28. This does not satisfy the ratio 5:2 or the sum 84.
10.
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.3)What is the ratio between the total number of males and the number of females who are non-graduate?
A) 4:1.
B) 6:7.
C) 8:1.
D) 3:4.
Show Answer
Correct Answer:
Correct answer is: C
Exam Relevance:
CAT, GMAT, GRE, SAT
Difficulty:
Moderate
Concept notes:
The question involves calculating the ratio between the total number of males and the number of females who are non-graduate based on given percentages and total numbers.
Common Mistakes:
A common mistake could be misinterpreting the percentages and not correctly calculating the number of non-graduate females.
Explanations:
1. Total members = 240
2. Number of males = 2/3 * 240 = 160
3. Number of females = 240 - 160 = 80
4. Number of graduate males = 15% of 160 = 0.15 * 160 = 24
5. Number of non-graduate males = 160 - 24 = 136
6. Number of graduate females = 3/4 * 80 = 60
7. Number of non-graduate females = 80 - 60 = 20
8. Ratio of total males to non-graduate females = 160 : 20 = 8 : 1
Option Analysis:
Option A:
Incorrect because the ratio 4:1 does not match the calculated ratio.
Option B:
Incorrect because the ratio 6:7 does not match the calculated ratio.
Option C:
Correct because the ratio 8:1 matches the calculated ratio.
Option D:
Incorrect because the ratio 3:4 does not match the calculated ratio.
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Frequently Asked Questions
What is the purpose of ratio-based data interpretation?
Ratio-based data interpretation helps in understanding the relationship between different sets of data, making it easier to analyze and compare quantities in various contexts.
How can I apply ratios to solve real-world problems?
Ratios can be applied to solve real-world problems by converting given data into ratios, simplifying them, and using these simplified ratios to make comparisons or predictions about the data.
What is the significance of simplifying ratios?
Simplifying ratios makes the data more manageable and easier to understand, allowing for clearer comparisons and more accurate interpretations of the relationships between different quantities.
How do I use a common multiplier in ratio problems?
A common multiplier is used to adjust ratios so that they can be compared directly. This involves finding a number that, when multiplied by each part of the ratio, makes the ratios equivalent and easier to compare.
What skills are essential for interpreting data using ratios?
Essential skills include the ability to calculate and simplify ratios, understand the relationship between parts and the whole, and apply ratios to solve problems involving comparisons and distributions.