🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books

Ratio Based Data Interpretation Quiz 4 (10 MCQs)

This set of multiple-choice questions evaluates ratio interpretation, comparison of quantities, and real-life application. It covers concepts such as ratio calculation, proportional distribution, and total quantity verification. Skills tested include ratio simplification, decimal conversion, and expenditure calculation. Questions involve part-to-part ratios, poodles to total ratio, and savings to expenditure ratio.

Quiz Instructions

Select an option to see the correct answer instantly.

1. Which of the following options is a real life example of a ratio?

Correct Answer: Correct answer is: (B) 4 meatballs: 1 cup of sauce.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Easy

Concept notes: A ratio compares two quantities by division. It shows how much of one quantity corresponds to another.

Common Mistakes: A common mistake is to confuse a ratio with a simple quantity or a single item, such as "12 noodles" or "1 jar of sauce."

Explanations: The correct answer is "4 meatballs: 1 cup of sauce" because it represents a comparison between two quantities. It shows the relationship between the number of meatballs and the amount of sauce, which is a ratio.

Option Analysis:

Option A: This is a single quantity and not a comparison between two quantities.
Option B: This is a ratio because it compares the number of meatballs to the amount of sauce.
Option C: This is a single quantity and not a comparison between two quantities.
Option D: This is a single quantity and not a comparison between two quantities.

2. Which ratio is proportional to the ratio 1/5?

Correct Answer: Correct answer is: (B) 2/10.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Easy

Concept notes: Two ratios are proportional if they can be simplified to the same fraction.

Common Mistakes: A common mistake is to assume that any fraction with a 5 in the denominator is proportional to 1/5, which is not necessarily true.

Explanations: To determine if a ratio is proportional to 1/5, we need to check if it can be simplified to 1/5. The ratio 2/10 can be simplified by dividing both the numerator and the denominator by 2, resulting in 1/5. Therefore, 2/10 is proportional to 1/5.

Option Analysis:

Option A: 2/5 cannot be simplified to 1/5.
Option B: 2/10 simplifies to 1/5, which is proportional to 1/5.
Option C: 5/1 is not proportional to 1/5.
Option D: 15/20 simplifies to 3/4, which is not proportional to 1/5.

3. Tom, Mike and William love collecting stamps.The ratio of their stamps is 4: 2: 3.Tom has 32 stamps.How many stamps does William have?

Correct Answer: Correct answer is: (C) 24.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Moderate

Concept notes: The problem involves understanding and applying ratios to find the number of stamps William has, given the ratio and the number of stamps Tom has.

Common Mistakes: A common mistake is misinterpreting the ratio or incorrectly scaling the ratio to the given number of stamps.

Explanations: The ratio of stamps between Tom, Mike, and William is 4:2:3. This means for every 4 stamps Tom has, William has 3 stamps. Given that Tom has 32 stamps, we can determine the scaling factor by dividing 32 by 4, which is 8. Therefore, William's number of stamps is 3 times the scaling factor, which is 3 * 8 = 24.

Option Analysis:

Option A: 72 is incorrect because it does not match the ratio when scaled correctly.
Option B: 64 is incorrect because it does not match the ratio when scaled correctly.
Option C: 24 is correct because it matches the ratio when scaled correctly.
Option D: 8 is incorrect because it does not match the ratio when scaled correctly.

4. Neelam's annual income is Rs. 288000. Her annual savings amount to Rs. 36000. The ratio of her savings to her expenditure is

Correct Answer: Correct answer is: (B) 1: 7.

Exam Relevance: CAT, GMAT, GRE, SAT

Difficulty: Easy

Concept notes: The ratio of savings to expenditure can be calculated by first determining the expenditure and then forming the ratio with the savings.

Common Mistakes: A common mistake is to confuse the ratio of savings to income instead of savings to expenditure.

Explanations: 1. Calculate the expenditure: Expenditure = Annual Income - Annual Savings Expenditure = 288000 - 36000 = 252000 2. Form the ratio of savings to expenditure: Ratio = Savings : Expenditure Ratio = 36000 : 252000 3. Simplify the ratio: Divide both terms by the greatest common divisor (GCD) of 36000 and 252000, which is 36000. Ratio = 36000/36000 : 252000/36000 Ratio = 1 : 7 Thus, the ratio of her savings to her expenditure is 1: 7.

Option Analysis:

Option A: Incorrect because the ratio 1: 8 does not match the simplified ratio of 1: 7.
Option B: Correct because the simplified ratio of savings to expenditure is 1: 7.
Option C: Incorrect because the ratio 1: 6 does not match the simplified ratio of 1: 7.
Option D: Incorrect because the ratio 1: 5 does not match the simplified ratio of 1: 7.

5. Wilson has 2 black, 3 red, and 5 white toy cars. What is the ratio of red toy cars to all the toy cars?

Correct Answer: Correct answer is: (C) 3:10.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Moderate

Concept notes: The ratio of red toy cars to all the toy cars can be found by dividing the number of red toy cars by the total number of toy cars.

Common Mistakes: A common mistake is to confuse the ratio of red toy cars to white toy cars or black toy cars instead of the total number of toy cars.

Explanations: To find the ratio of red toy cars to all the toy cars, we first need to determine the total number of toy cars. Wilson has 2 black, 3 red, and 5 white toy cars. The total number of toy cars is: \[ 2 + 3 + 5 = 10 \] The number of red toy cars is 3. Therefore, the ratio of red toy cars to all the toy cars is: \[ \frac{3}{10} \] Expressing this as a ratio, we get: \[ 3:10 \] Thus, the correct answer is 3:10.

Option Analysis:

Option A: 3:5 is incorrect because it does not represent the ratio of red toy cars to the total number of toy cars.
Option B: 1:3 is incorrect because it does not represent the ratio of red toy cars to the total number of toy cars.
Option C: 3:10 is correct because it accurately represents the ratio of red toy cars to the total number of toy cars.
Option D: None of the above is incorrect because 3:10 is a valid option.

6. Part-to-Part Ratios: Convert 7:3 to decimal

Correct Answer: Correct answer is: (B) 0.7.

Exam Relevance: GMAT, GRE, SAT, ACT

Difficulty: Easy

Concept notes: In ratio-based data interpretation, converting a ratio to a decimal involves dividing the first part of the ratio by the sum of both parts.

Common Mistakes: A common mistake is to divide the first part by the second part directly, instead of dividing by the sum of both parts.

Explanations: To convert the ratio 7:3 to a decimal, we first find the sum of the parts: 7 + 3 = 10. Then, we divide the first part (7) by the sum (10): 7 ÷ 10 = 0.7.

Option Analysis:

Option A: 0.3 is incorrect because it represents the decimal form of the second part (3) divided by the sum (10), not the first part (7).
Option B: 0.7 is correct because it represents the decimal form of the first part (7) divided by the sum (10).
Option C: 0.14 is incorrect because it does not represent the correct division of the parts.
Option D: 0.42 is incorrect because it does not represent the correct division of the parts.

7. There are 20 girls and 15 boys in a class.(a) What is the ratio of number of girls to the number of boys?(b) What is the ratio of number of girls to the total number of students in the class?

Correct Answer: Correct answer is: (A) 4:3, 4:7.

Exam Relevance: SAT, GRE, GMAT, ACT

Difficulty: Easy

Concept notes: The question involves calculating ratios based on given data. The first part requires finding the ratio of the number of girls to the number of boys, and the second part requires finding the ratio of the number of girls to the total number of students.

Common Mistakes: A common mistake is to misinterpret the total number of students as only the number of girls or boys, rather than the sum of both.

Explanations: To find the ratio of the number of girls to the number of boys: 1. Number of girls = 20 2. Number of boys = 15 3. Ratio of girls to boys = 20:15 4. Simplify the ratio by dividing both numbers by their greatest common divisor (GCD), which is 5. 5. 20 ÷ 5 = 4, 15 ÷ 5 = 3 6. Therefore, the ratio of girls to boys is 4:3. To find the ratio of the number of girls to the total number of students: 1. Total number of students = Number of girls + Number of boys = 20 + 15 = 35 2. Ratio of girls to total students = 20:35 3. Simplify the ratio by dividing both numbers by their GCD, which is 5. 4. 20 ÷ 5 = 4, 35 ÷ 5 = 7 5. Therefore, the ratio of girls to total students is 4:7.

Option Analysis:

Option A: Correct. The ratio of girls to boys is 4:3, and the ratio of girls to total students is 4:7.
Option B: Incorrect. The ratio of girls to boys is not 4:6, and the ratio of girls to total students is not 3:5.
Option C: Incorrect. The ratio of girls to boys is not 6:3, and the ratio of girls to total students is not 67:45.
Option D: Incorrect. The ratio of girls to boys is not 6:8.

8. Changbin bought fruits in the supermarket. He bought bananas, mangoes, and strawberries, in the ratio 2:5:6. How many kilos of each fruit did he buy if the total kilo is 26 kilograms?

Correct Answer: Correct answer is: (C) 4 kg of bananas,10 kg of mangoes,12 kg of strawberries.

Exam Relevance: SAT, GRE, GMAT, CAT

Difficulty: Moderate

Concept notes: In ratio-based data interpretation, the total quantity is divided according to the given ratio. The sum of the parts of the ratio should equal the total quantity.

Common Mistakes: A common mistake is to assume the ratio values directly represent the quantities without scaling them to the total.

Explanations: The ratio of bananas, mangoes, and strawberries is 2:5:6. The sum of the parts of the ratio is 2 + 5 + 6 = 13. The total weight is 26 kg. Each part of the ratio represents \( \frac{26}{13} = 2 \) kg. Therefore, the weight of bananas is \( 2 \times 2 = 4 \) kg, the weight of mangoes is \( 5 \times 2 = 10 \) kg, and the weight of strawberries is \( 6 \times 2 = 12 \) kg.

Option Analysis:

Option A: 2 kg of bananas, 5 kg of mangoes, 6 kg of strawberries. This option does not satisfy the total weight of 26 kg.
Option B: 3 kg of bananas, 10 kg of mangoes, 13 kg of strawberries. This option does not satisfy the ratio 2:5:6.
Option C: 4 kg of bananas, 10 kg of mangoes, 12 kg of strawberries. This option satisfies both the ratio and the total weight.
Option D: 5 kg of bananas, 10 kg of mangoes, 11 kg of strawberries. This option does not satisfy the ratio 2:5:6.

9. Simplify the ratio 75:10, 72:16:32, 140:112

Correct Answer: Correct answer is: (B) 15:2, 9:2:4, 5:4.

Exam Relevance: GMAT, GRE, SAT, ACT

Difficulty: Moderate

Concept notes: To simplify a ratio, divide each term by their greatest common divisor (GCD).

Common Mistakes: A common mistake is to simplify only part of the ratio or to use incorrect GCD values.

Explanations: 1. Simplify 75:10: - GCD of 75 and 10 is 5. - 75 ÷ 5 = 15, 10 ÷ 5 = 2. - Simplified ratio: 15:2. 2. Simplify 72:16:32: - GCD of 72, 16, and 32 is 8. - 72 ÷ 8 = 9, 16 ÷ 8 = 2, 32 ÷ 8 = 4. - Simplified ratio: 9:2:4. 3. Simplify 140:112: - GCD of 140 and 112 is 28. - 140 ÷ 28 = 5, 112 ÷ 28 = 4. - Simplified ratio: 5:4.

Option Analysis:

Option A: Incorrect because the second ratio is not simplified correctly (1:2:3 instead of 9:2:4).
Option B: Correct as it matches the simplified ratios derived from the given values.
Option C: Incorrect because the second ratio is not simplified correctly (6:5:1 instead of 9:2:4).
Option D: Incorrect because the second ratio is not simplified correctly (4:3:5 instead of 9:2:4).

10. There are 44 collies and 56 poodles. Which is the correct ratio for poodles to total number of dogs?

Correct Answer: Correct answer is: (C) 56:100.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Moderate

Concept notes: The ratio of poodles to the total number of dogs is calculated by dividing the number of poodles by the total number of dogs and expressing it as a ratio.

Common Mistakes: A common mistake is to confuse the ratio of poodles to total dogs with the ratio of collies to total dogs or to misinterpret the total number of dogs.

Explanations: To find the ratio of poodles to the total number of dogs, we first calculate the total number of dogs. The total number of dogs is the sum of collies and poodles, which is 44 + 56 = 100. The ratio of poodles to the total number of dogs is then 56:100.

Option Analysis:

Option A: 156:100 is incorrect because the total number of dogs is 100, not 156.
Option B: 44:100 is incorrect because it represents the ratio of collies to the total number of dogs, not poodles.
Option C: 56:100 is correct because it represents the ratio of poodles to the total number of dogs.
Option D: 56 is incorrect because it is not a ratio; it is just the number of poodles.

Frequently Asked Questions

What is a part-to-part ratio?

A part-to-part ratio compares one part of a whole to another part of the same whole. For example, if there are 10 girls and 15 boys in a class, the part-to-part ratio of girls to boys is 10:15, which can be simplified to 2:3.

How do you convert a ratio to decimal form?

To convert a ratio to decimal form, divide the first number by the second number. For example, the ratio 3:4 can be converted to decimal form by dividing 3 by 4, resulting in 0.75.

What is the purpose of simplifying ratios?

Simplifying ratios makes them easier to understand and compare. It involves dividing both parts of the ratio by their greatest common divisor. For example, the ratio 12:18 simplifies to 2:3 by dividing both numbers by 6.

How can ratios be used in real-life situations?

Ratios are used in real-life situations to compare quantities, such as the ratio of poodles to the total number of dogs in a park or the ratio of toy cars to total toys in a collection. They help in making proportional distributions and understanding relationships between different quantities.

What is the difference between a ratio and a proportion?

A ratio compares two quantities, while a proportion compares two ratios. For example, if the ratio of girls to boys is 2

🏠 Back to Homepage 📘 Download PDF Books 📕 Premium PDF Books