🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books

Ratio Based Data Interpretation Quiz 40 (10 MCQs)

This set of multiple-choice questions evaluates skills in ratio manipulation, algebraic equations, cross-multiplication, and proportion solving. It covers concepts such as ratio calculation, simplification, and interpretation, including unit conversion from grams to kilograms and millilitres to litres. Students will practice solving linear equations, identifying equivalent ratios, and applying the greatest common divisor for ratio reduction.

Quiz Instructions

Select an option to see the correct answer instantly.

1. Ratio of 350 g to 3 kg is

Correct Answer: Correct answer is: (C) 7: 60.

Exam Relevance: GRE, GMAT, SAT, ACT

Difficulty: Moderate

Concept notes: To find the ratio of 350 grams to 3 kilograms, we need to convert both quantities to the same unit. Since 1 kilogram equals 1000 grams, 3 kilograms is equal to 3000 grams. The ratio of 350 grams to 3000 grams can then be simplified.

Common Mistakes: A common mistake is to forget to convert the units to the same measurement before calculating the ratio. Another mistake is not simplifying the ratio to its lowest terms.

Explanations: First, convert 3 kilograms to grams: 3 kg = 3000 g. Now, the ratio of 350 g to 3000 g is calculated as follows: \[ \frac{350}{3000} = \frac{35}{300} = \frac{7}{60} \] Thus, the ratio of 350 g to 3 kg is 7:60.

Option Analysis:

Option A: 116: 1 is incorrect because it does not represent the simplified ratio of 350 g to 3000 g.
Option B: 60: 7 is incorrect because it reverses the correct ratio.
Option C: 7: 60 is the correct ratio after simplifying 350 g to 3000 g.
Option D: None is incorrect because the correct ratio is provided in Option C.

2. Two numbers are in ratio of 21: 26. If 8 is added in each, the new numbers are in ratio of 5: 6. Find the ratio of numbers, if 6 is subtracted from each number?

Correct Answer: Correct answer is: (A) 18: 23.

Exam Relevance: CAT, GMAT, GRE, SAT

Difficulty: Moderate

Concept notes: The problem involves finding the ratio of two numbers after performing arithmetic operations on them, based on given initial and new ratios.

Common Mistakes: A common mistake is to incorrectly set up the equations or misinterpret the given ratios, leading to incorrect values for the original numbers.

Explanations: Let the two numbers be \(21x\) and \(26x\). According to the problem, when 8 is added to each number, the new ratio is 5:6. Therefore, we can write the equation: \[ \frac{21x + 8}{26x + 8} = \frac{5}{6} \] Cross-multiplying gives: \[ 6(21x + 8) = 5(26x + 8) \] Expanding both sides: \[ 126x + 48 = 130x + 40 \] Rearranging terms to isolate \(x\): \[ 126x + 48 - 130x = 40 \] \[ -4x + 48 = 40 \] \[ -4x = 40 - 48 \] \[ -4x = -8 \] \[ x = 2 \] Thus, the original numbers are \(21x = 21 \times 2 = 42\) and \(26x = 26 \times 2 = 52\). Now, we need to find the ratio of these numbers when 6 is subtracted from each: \[ 42 - 6 = 36 \quad \text{and} \quad 52 - 6 = 46 \] The new ratio is: \[ \frac{36}{46} = \frac{18}{23} \] Therefore, the ratio of the numbers when 6 is subtracted from each is 18:23.

Option Analysis:

Option A: Correct. The ratio is 18:23.
Option B: Incorrect. The ratio is not 19:25.
Option C: Incorrect. The ratio is not 6:7.
Option D: Incorrect. The ratio is not 9:16.

3. Ella has 5 balloons. Taylor has 7 balloons. Write the ratio of Ella's balloons to Taylor's balloons.

Correct Answer: Correct answer is: (B) 5:7.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Easy

Concept notes: A ratio compares two quantities by division. In this case, the ratio of Ella's balloons to Taylor's balloons is expressed as the number of Ella's balloons to the number of Taylor's balloons.

Common Mistakes: A common mistake is to reverse the order of the ratio, writing Taylor's balloons to Ella's balloons instead of Ella's balloons to Taylor's balloons.

Explanations: The ratio of Ella's balloons to Taylor's balloons is written as the number of Ella's balloons (5) to the number of Taylor's balloons (7). Therefore, the correct ratio is 5:7.

Option Analysis:

Option A: Incorrect because it reverses the order of the ratio, writing Taylor's balloons to Ella's balloons instead of Ella's balloons to Taylor's balloons.
Option B: Correct because it correctly represents the ratio of Ella's balloons to Taylor's balloons as 5:7.
Option C: Incorrect because it does not represent the correct ratio of Ella's balloons to Taylor's balloons.
Option D: Incorrect because it does not represent the correct ratio of Ella's balloons to Taylor's balloons.

Mnemonic: Ella's 5, Taylor's 7, remember the order.

4. Sam and Ryan share some coins in the ratio 4: 9.Ryan gets 65 more coins than Sam. How many coins does Ryan get?

Correct Answer: Correct answer is: (B) 117.

Exam Relevance: GMAT, GRE, SAT, ACT

Difficulty: Moderate

Concept notes: In ratio-based data interpretation, the given ratio represents the distribution of items between two or more parties. Here, the ratio 4:9 indicates that for every 4 parts Sam gets, Ryan gets 9 parts. The difference in the number of parts (9 - 4 = 5 parts) corresponds to the 65 more coins Ryan gets.

Common Mistakes: A common mistake is to directly assume the ratio values as the actual number of coins without considering the difference in parts.

Explanations: 1. Let the number of coins Sam gets be 4x and the number of coins Ryan gets be 9x. 2. According to the problem, Ryan gets 65 more coins than Sam: 9x - 4x = 65. 3. Simplify the equation: 5x = 65. 4. Solve for x: x = 65 / 5 = 13. 5. Calculate the number of coins Ryan gets: 9x = 9 * 13 = 117.

Option Analysis:

Option A: 146.25 is incorrect because it does not match the integer solution derived from the ratio and difference.
Option B: 117 is correct as it matches the solution derived from the ratio and difference.
Option C: 169 is incorrect because it does not match the integer solution derived from the ratio and difference.
Option D: 52 is incorrect because it does not match the integer solution derived from the ratio and difference.

5. Ratio of 500ml to 2 litres is:

Correct Answer: Correct answer is: (A) 1:4.

Exam Relevance: SAT, GRE, GMAT, Competitive Exams

Difficulty: Easy

Concept notes: To find the ratio of 500ml to 2 litres, we need to convert both quantities to the same unit and then simplify the ratio.

Common Mistakes: A common mistake is to forget to convert litres to millilitres or vice versa, leading to an incorrect ratio.

Explanations: First, convert 2 litres to millilitres. Since 1 litre = 1000 millilitres, 2 litres = 2000 millilitres. Now, the ratio of 500ml to 2000ml is 500:2000. Simplify this ratio by dividing both terms by 500, resulting in 1:4.

Option Analysis:

Option A: Correct. The simplified ratio of 500ml to 2000ml is 1:4.
Option B: Incorrect. The ratio 1:6 is not correct after simplification.
Option C: Incorrect. The ratio 1:2 is not correct after simplification.
Option D: Incorrect. The ratio 1:3 is not correct after simplification.

6. Which ratio is equal to 15:20?

Correct Answer: Correct answer is: (C) 21:28.

Exam Relevance: SAT, GRE, GMAT, ACT

Difficulty: Moderate

Concept notes: To determine if two ratios are equal, we need to check if they can be simplified to the same form. This involves finding the greatest common divisor (GCD) of the terms in each ratio and simplifying them.

Common Mistakes: A common mistake is to assume that ratios with similar numbers are equal without simplifying them. For example, 15:20 and 18:25 might appear similar but are not equal when simplified.

Explanations: To check if 15:20 is equal to 21:28, we simplify both ratios: 1. Simplify 15:20: - The GCD of 15 and 20 is 5. - Dividing both terms by 5, we get 15/5 : 20/5 = 3:4. 2. Simplify 21:28: - The GCD of 21 and 28 is 7. - Dividing both terms by 7, we get 21/7 : 28/7 = 3:4. Since both ratios simplify to 3:4, they are equal.

Option Analysis:

Option A: 5:10 simplifies to 1:2, which is not equal to 3:4.
Option B: 18:25 cannot be simplified further and does not equal 3:4.
Option C: 21:28 simplifies to 3:4, which is equal to 15:20.
Option D: 24:30 simplifies to 4:5, which is not equal to 3:4.

7. The ratio of P and Q is 3:5. If P = 27, find Q.

Correct Answer: Correct answer is: (C) 45.

Exam Relevance: SAT, GRE, GMAT, CAT

Difficulty: Easy

Concept notes: The concept of ratio involves comparing two quantities by division. Here, the ratio of P to Q is given as 3:5, meaning for every 3 units of P, there are 5 units of Q.

Common Mistakes: A common mistake is to misinterpret the ratio and incorrectly calculate the value of Q. For example, some might divide 27 by 3 and then multiply by 5, which would be incorrect.

Explanations: Given the ratio P:Q = 3:5 and P = 27, we can set up the proportion: \[ \frac{P}{Q} = \frac{3}{5} \] Substituting P = 27: \[ \frac{27}{Q} = \frac{3}{5} \] To find Q, we cross-multiply: \[ 27 \times 5 = 3 \times Q \] \[ 135 = 3Q \] Solving for Q: \[ Q = \frac{135}{3} = 45 \] Thus, Q = 45.

Option Analysis:

Option A: 35 is incorrect because it does not satisfy the given ratio when P = 27.
Option B: 41 is incorrect because it does not satisfy the given ratio when P = 27.
Option C: 45 is correct because it satisfies the given ratio when P = 27.
Option D: 50 is incorrect because it does not satisfy the given ratio when P = 27.

8. In a class there are 30 boys and 12 girls. Find the ratio of number of boys to number of girls.

Correct Answer: Correct answer is: (B) 5: 2.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Easy

Concept notes: The ratio of the number of boys to the number of girls is found by dividing the number of boys by the number of girls and simplifying the fraction.

Common Mistakes: A common mistake is to confuse the order of the ratio, putting the number of girls first instead of the number of boys.

Explanations: To find the ratio of the number of boys to the number of girls, we divide the number of boys by the number of girls. Here, the number of boys is 30 and the number of girls is 12. The ratio is calculated as follows: \[ \text{Ratio} = \frac{30}{12} = \frac{30 \div 6}{12 \div 6} = \frac{5}{2} \] Thus, the ratio of the number of boys to the number of girls is 5:2.

Option Analysis:

Option A: 2: 5 is incorrect because it reverses the order of the ratio.
Option B: 5: 2 is correct as it correctly represents the ratio of boys to girls.
Option C: 3: 4 is incorrect because it does not simplify the ratio correctly.
Option D: None of the above is incorrect because 5: 2 is a valid option.

9. A class has 15 boys and 20 girls. What is the boy:girl ratio in simplest form?

Correct Answer: Correct answer is: (C) 3:4.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Moderate

Concept notes: The boy:girl ratio is found by dividing the number of boys by the number of girls and simplifying the fraction to its simplest form.

Common Mistakes: A common mistake is to not simplify the ratio to its simplest form, leading to an incorrect answer.

Explanations: To find the boy:girl ratio, we start with the numbers given: 15 boys and 20 girls. The ratio is 15:20. To simplify this ratio, we find the greatest common divisor (GCD) of 15 and 20, which is 5. We then divide both numbers by 5: 15 ÷ 5 = 3 20 ÷ 5 = 4 Thus, the simplified ratio is 3:4.

Option Analysis:

Option A: 4 to 5 is incorrect because it does not represent the simplified form of the given ratio.
Option B: 10 to 13 is incorrect because it does not represent the simplified form of the given ratio.
Option C: 3:4 is the correct answer as it is the simplified form of the given ratio.
Option D: 3:5 is incorrect because it does not represent the simplified form of the given ratio.

10. Avery counts cars and trucks on a road trip. She counts 22 trucks and 45 cars. What is the ratio the number of cars to trucks?

Correct Answer: Correct answer is: (B) 45:22.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Easy

Concept notes: A ratio compares two quantities by division. In this case, the ratio of the number of cars to trucks is calculated by dividing the number of cars by the number of trucks.

Common Mistakes: A common mistake is to confuse the order of the ratio. The question asks for the ratio of cars to trucks, not trucks to cars.

Explanations: The number of cars is 45 and the number of trucks is 22. The ratio of cars to trucks is therefore 45:22. This means for every 45 cars, there are 22 trucks.

Option Analysis:

Option A: Incorrect because it represents the total number of vehicles (cars and trucks) to the number of trucks, which is not the required ratio.
Option B: Correct because it represents the ratio of the number of cars to the number of trucks.
Option C: Incorrect because it represents the total number of vehicles (cars and trucks) to the number of trucks, which is not the required ratio.
Option D: Incorrect because it represents the ratio of the number of trucks to the number of cars, which is the reverse of what is required.

Frequently Asked Questions

What is the purpose of ratio-based data interpretation?

Ratio-based data interpretation helps in understanding the relationship between different quantities and making comparisons, which is essential for analyzing and solving real-world problems.

How can I simplify a ratio?

To simplify a ratio, find the greatest common divisor of the numbers in the ratio and divide each number by this divisor. This process reduces the ratio to its simplest form.

What is the significance of cross multiplication in ratio problems?

Cross multiplication is a method used to solve proportion problems by equating the product of the means to the product of the extremes, which helps in finding unknown values in a ratio.

How do I convert a ratio from grams to kilograms?

To convert a ratio from grams to kilograms, divide each part of the ratio by 1000, since there are 1000 grams in a kilogram. This conversion maintains the ratio's proportionality.

What skills are necessary for solving ratio distribution problems?

Skills necessary for solving ratio distribution problems include understanding equivalent ratios, performing arithmetic operations, and applying the concept of proportion to distribute quantities accurately.

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