ISEE Lower Level Quantitative Reasoning Quiz: Ratios In Context

What this quiz covers

This quiz focuses on Ratios In Context, giving you a quick way to practice the rules, question types, and explanations that matter most for ISEE Lower Level Quantitative Reasoning.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

Question 1

1. The ratio of orange juice to the total punch is 3 to 2.
2. There is more cranberry juice than orange juice.
3. The ratio of cranberry juice to orange juice is 3 to 2.
4. For every 5 cups of punch, 3 cups are orange juice. (correct answer)

Explanation: The ratio of orange juice to cranberry juice is 3 to 2. The total parts of the mixture are 3 + 2 = 5 parts. This means the ratio of orange juice to the total punch is 3 to 5. Statement D correctly expresses this relationship: out of 5 cups of total punch, 3 cups are orange juice.

Question 2

1. 9 to 12
2. 3 to 4 (correct answer)
3. 4 to 3
4. 18 to 24

Explanation: The ratio of cows to sheep is 36 to 48. To find the simplest form, find the greatest common factor (GCF) of 36 and 48. The GCF is 12. Divide both numbers by 12: 36 ÷ 12 = 3 and 48 ÷ 12 = 4. The simplest ratio is 3 to 4.

Question 3

1. 3 to 4
2. 4 to 7
3. 3 to 7 (correct answer)
4. 12 to 28

Explanation: First, find the number of boys: 28 total students - 16 girls = 12 boys. The ratio of boys to the total number of students is 12 to 28. To simplify, find the greatest common factor of 12 and 28, which is 4. Divide both numbers by 4: 12 ÷ 4 = 3 and 28 ÷ 4 = 7. The simplified ratio is 3 to 7.

Question 4

1. 3 to 4
2. 1 to 2 (correct answer)
3. 3 to 6
4. 12 to 24

Explanation: First, find the total number of fruits: 8 apples + 12 bananas + 4 oranges = 24 fruits. The ratio of bananas to the total number of fruits is 12 to 24. To simplify, divide both numbers by their greatest common factor, which is 12. 12 ÷ 12 = 1 and 24 ÷ 12 = 2. The simplified ratio is 1 to 2.

Question 5

1. 2 to 3 (correct answer)
2. 3 to 2
3. 2 to 5
4. 3 to 5

Explanation: First, find the number of cats: 30 total animals - 18 dogs = 12 cats. The ratio of cats to dogs is 12 to 18. The greatest common factor of 12 and 18 is 6. Simplify the ratio by dividing both numbers by 6: 12 ÷ 6 = 2 and 18 ÷ 6 = 3. The ratio is 2 to 3.

Question 6

1. 6 to 5 (correct answer)
2. 5 to 6
3. 1 to 1
4. 6 to 11

Explanation: The question provides the number of sides for each shape. A hexagon has 6 sides and a pentagon has 5 sides. The ratio of the number of sides of a hexagon to the number of sides of a pentagon is 6 to 5. This ratio is already in its simplest form because 6 and 5 have no common factors other than 1.

Question 7

1. 13 to 25
2. 12 to 13
3. 4 to 9
4. 13 to 12 (correct answer)

Explanation: When you encounter ratio problems, you need to carefully identify what groups you're comparing and count each group accurately. Let's organize the given information: There are 10 rose bushes (4 red, 6 not red) and 15 tulip plants (9 red, 6 not red). You need the ratio of red flowers to non-red flowers. First, count the red flowers: 4 red roses + 9 red tulips = 13 red flowers total. Next, count the non-red flowers: 6 non-red roses + 6 non-red tulips = 12 non-red flowers total. Therefore, the ratio of red flowers to non-red flowers is 13 to 12. Looking at the wrong answers: Choice A (13 to 25) incorrectly compares red flowers to the total number of plants instead of just the non-red flowers. Choice B (12 to 13) reverses the ratio by putting non-red flowers first instead of red flowers first. Choice C (4 to 9) only compares red roses to red tulips, completely ignoring the non-red flowers that should be in the denominator. Study tip: In ratio problems, always double-check that you're comparing the right groups in the right order. Write down what each part of your ratio represents before calculating, and make sure your categories don't overlap and account for all items mentioned in the problem.

Question 8

1. 1 to 3 (correct answer)
2. 1 to 2
3. 10 to 20
4. 10 to 30

Explanation: First, find the total number of books: 10 + 14 + 6 = 30 books. The ratio of books on the first shelf to the total number of books is 10 to 30. To simplify, divide both numbers by their greatest common factor, 10. 10 ÷ 10 = 1 and 30 ÷ 10 = 3. The simplified ratio is 1 to 3.

Question 9

1. 1 to 2
2. 2 to 1 (correct answer)
3. 2 to 3
4. 16 to 8

Explanation: First, find the number of children wearing hats: 24 children × (1/3) = 8 children. Next, find the number of children not wearing hats: 24 total - 8 with hats = 16 children. The ratio of children not wearing hats to children wearing hats is 16 to 8. To simplify, divide both numbers by their greatest common factor, 8. 16 ÷ 8 = 2 and 8 ÷ 8 = 1. The ratio is 2 to 1.

Question 10

1. 1 to 2
2. 2 to 3
3. 1 to 3 (correct answer)
4. 30 to 90

Explanation: First, find the time for the credits: 90 total minutes - 60 minutes of story = 30 minutes of credits. The ratio of credit time to total time is 30 to 90. To simplify, divide both numbers by their greatest common factor, 30. 30 ÷ 30 = 1 and 90 ÷ 30 = 3. The simplified ratio is 1 to 3.

Question 11

1. 5 to 1 (correct answer)
2. 1 to 5
3. 5 to 6
4. 25 to 30

Explanation: First, identify the blocks with straight sides (squares and triangles) and curved sides (circles). Number of blocks with straight sides = 15 + 10 = 25. Number of blocks with curved sides = 5. The ratio of blocks with straight sides to blocks with curved sides is 25 to 5. To simplify, divide both numbers by their greatest common factor, 5. 25 ÷ 5 = 5 and 5 ÷ 5 = 1. The simplified ratio is 5 to 1.

Question 12

1. 1 to 7
2. 6 to 7 (correct answer)
3. 6 to 10
4. 30 to 50

Explanation: First, find the number of parked cars that are not red: 35 total parked cars - 5 red cars = 30 non-red cars. The question asks for the ratio of non-red cars to the total number of parked cars, which is 35. The number of spaces (50) is extra information. The ratio is 30 to 35. The greatest common factor of 30 and 35 is 5. Simplify: 30 ÷ 5 = 6 and 35 ÷ 5 = 7. The ratio is 6 to 7.

Question 13

1. 1 to 1 (correct answer)
2. 1 to 2
3. 5 to 7
4. 6 to 12

Explanation: First, count the vowels and consonants in QUANTITATIVE. The word has 12 letters total. Vowels (A, E, I, O, U) are: U, A, I, A, I, E (6 vowels). Consonants are: Q, N, T, T, T, V (6 consonants). The ratio of vowels to consonants is 6 to 6. To simplify, divide both numbers by their greatest common factor, 6. 6 ÷ 6 = 1. The simplified ratio is 1 to 1.

Question 14

1. 2 to 3 (correct answer)
2. 3 to 4
3. 2 to 9
4. 3 to 2

Explanation: First, find the number of percussion players: 45 total members - (20 brass + 15 woodwind) = 45 - 35 = 10 percussion players. The number of hours practiced is extra information not needed to solve the problem. The ratio of percussion players to woodwind players is 10 to 15. The greatest common factor of 10 and 15 is 5. Simplify by dividing both by 5: 10 ÷ 5 = 2 and 15 ÷ 5 = 3. The ratio is 2 to 3.

Question 15

1. 3 to 4
2. 4 to 1
3. 36 to 12
4. 3 to 1 (correct answer)

Explanation: When you encounter ratio problems, you need to carefully identify what quantities are being compared and make sure you express them in the correct order. First, let's find how many cookies Sarah started with and what she did with them. Sarah baked 4 dozen cookies, which equals $4 \times 12 = 48$ cookies total. She gave away 12 cookies to her friend, so she kept $48 - 12 = 36$ cookies for herself. The question asks for the ratio of cookies she kept to cookies she gave away. This means we want: kept : given away = 36 : 12. To simplify this ratio, we divide both numbers by their greatest common factor, which is 12. So $36 ÷ 12 = 3$ and $12 ÷ 12 = 1$, giving us the ratio 3 to 1. Looking at the wrong answers: Choice A (3 to 4) might come from confusing the relationship between the parts, but neither 3 nor 4 represents the correct quantities here. Choice B (4 to 1) could result from incorrectly thinking about the dozens (4) rather than the actual cookies kept (36). Choice C (36 to 12) shows the correct numbers but fails to simplify the ratio to its lowest terms. Remember that ratios should always be expressed in their simplest form unless the problem specifically asks otherwise. Also, pay close attention to the order requested in the question - "A to B" means A comes first in your ratio, which affects your final answer.

Question 16

1. 2 to 3 (correct answer)
2. 3 to 2
3. 2 to 5
4. 12 to 18

Explanation: The ratio of red marbles to blue marbles is 12 to 18. To simplify the ratio, find the greatest common factor of 12 and 18, which is 6. Divide both numbers by 6: 12 ÷ 6 = 2 and 18 ÷ 6 = 3. So, the simplified ratio is 2 to 3.

Question 17

1. 7 to 3
2. 3 to 10
3. 7 to 10 (correct answer)
4. 14 to 6

Explanation: First, find the total number of games played: 14 wins + 6 losses = 20 games. The ratio of games won to total games played is 14 to 20. The greatest common factor of 14 and 20 is 2. Simplify by dividing both numbers by 2: 14 ÷ 2 = 7 and 20 ÷ 2 = 10. The ratio is 7 to 10.

Question 18

1. 3 to 2
2. 2 to 3
3. 3 to 5 (correct answer)
4. 60 to 100

Explanation: First, calculate the total value of the dimes and quarters. A dime is worth 10 cents, so 6 dimes = 6 × 10 = 60 cents. A quarter is worth 25 cents, so 4 quarters = 4 × 25 = 100 cents. The ratio of the value of dimes to the value of quarters is 60 to 100. The greatest common factor of 60 and 100 is 20. Simplify the ratio: 60 ÷ 20 = 3 and 100 ÷ 20 = 5. The simplified ratio is 3 to 5.

Question 19

1. 3 to 5
2. 5 to 8
3. 3 to 8 (correct answer)
4. 15 to 25

Explanation: First, find the total number of vehicles: 25 sedans + 15 SUVs = 40 vehicles. The ratio of SUVs to the total number of vehicles is 15 to 40. The greatest common factor of 15 and 40 is 5. Simplify the ratio by dividing both numbers by 5: 15 ÷ 5 = 3 and 40 ÷ 5 = 8. The ratio is 3 to 8.

Question 20

1. For every 2 students, there must be 15 chaperones.
2. There are 13 more students than chaperones in every group.
3. Out of every 17 people on the trip, 2 are chaperones. (correct answer)
4. There must be exactly 15 students and 2 chaperones on the trip.

Explanation: The ratio 2 to 15 means for every 2 chaperones, there are 15 students. This forms a group of 2 + 15 = 17 people. Therefore, within any group of 17 people that maintains this ratio, 2 will be chaperones and 15 will be students. Choice A reverses the ratio. Choice B is only true for the base unit (15-2=13), not for multiples (e.g., 4 chaperones and 30 students have a difference of 26). Choice D confuses the ratio with the exact number of people required.