ISEE Lower Level Quantitative Reasoning Quiz: Graph Interpretation

What this quiz covers

This quiz focuses on Graph Interpretation, 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. 30
2. 55 (correct answer)
3. 65
4. 90

Explanation: The total number of students is 120. Half of 120 is 60. The question states that the soccer section is 'slightly less than half' of the circle. Therefore, the best estimate for the number of students who chose soccer would be a number slightly less than 60. Out of the choices, 55 is the most reasonable estimate.

Question 2

1. 1/5
2. 3/10 (correct answer)
3. 1/3
4. 2/5

Explanation: The total budget amount is extra information not needed to solve the problem. Combine the percentages for Parks and Roads: 20% + 10% = 30%. To convert a percentage to a fraction, place it over 100: 30/100. This fraction simplifies to 3/10.

Question 3

1. 1/8 (correct answer)
2. 1/5
3. 1/4
4. 7/8

Explanation: First, find the total points scored by the first three players: 12 + 15 + 8 = 35. Next, find the points scored by David by subtracting this from the total: 40 - 35 = 5. Finally, create a fraction of David's points over the total points: 5/40. This fraction simplifies to 1/8.

Question 4

1. 20
2. 30
3. 40 (correct answer)
4. 80

Explanation: This is a two-step problem. First, determine the total number of students. If one-fourth (1/4) of the students is 20, then the total number of students is 4 * 20 = 80. Second, find the number of students who chose Science. Science is one-half (1/2) of the total. So, 1/2 of 80 is 40 students.

Question 5

1. 5
2. 40 (correct answer)
3. 50
4. 80

Explanation: First, find the fraction of students in the survey who have a cat. 5 out of 50 students have a cat, which is the fraction 5/50, simplifying to 1/10. To find the expected number in the whole school, multiply this fraction by the total school population: (1/10) * 400 = 40. About 40 students would be expected to have a cat.

Question 6

1. 7/25
2. 1/5
3. 2/5 (correct answer)
4. 3/5

Explanation: The phrase 'at least two siblings' means 2 siblings or more. In this class, 7 students have 2 siblings and 3 students have 3 siblings. The total number of students with at least two siblings is 7 + 3 = 10. The total number of students in the class is 25. So, the fraction is 10/25, which simplifies to 2/5.

Question 7

1. 4 (correct answer)
2. 8
3. 16
4. 24

Explanation: First, find the number of students who play soccer or basketball. Soccer: 1/2 of 32 = 16. Basketball: 1/4 of 32 = 8. Total is 16 + 8 = 24. Find the number of remaining students: 32 - 24 = 8. Of these remaining 8 students, 1/2 play baseball. So, 1/2 of 8 = 4. Four students play baseball.

Question 8

1. 1/4
2. 2/3
3. 1/2
4. 1/3 (correct answer)

Explanation: When you encounter fraction problems involving parts of a whole, you need to identify what represents the "part" and what represents the "total." This question asks what fraction of all items sold were cookies, so cookies are your part and all items combined are your whole. First, find the total number of items sold by adding all categories: 50 cookies + 25 cupcakes + 75 donuts = 150 total items. The fraction of cookies is then $\frac{\text{cookies}}{\text{total items}} = \frac{50}{150}$. To simplify this fraction, divide both numerator and denominator by their greatest common factor, which is 50: $\frac{50}{150} = \frac{1}{3}$. Looking at the wrong answers: Choice (A) gives $\frac{1}{4}$, which you might get if you incorrectly calculated the total as 200 instead of 150. Choice (B) gives $\frac{2}{3}$, which is far too large since cookies represent much less than two-thirds of the sales. Choice (C) gives $\frac{1}{2}$, which you might choose if you compared cookies only to donuts (50 out of 75+50 = 125) rather than to all items. The correct answer is (D) $\frac{1}{3}$ because 50 cookies out of 150 total items simplifies to $\frac{1}{3}$. Study tip: Always double-check that your denominator includes ALL relevant categories when finding fractions of a total. Write out "part/whole" to keep your setup clear, and don't forget to simplify your final fraction.

Question 9

1. 20
2. 30 (correct answer)
3. 40
4. 60

Explanation: First, find the total number of cars that passed in the first two hours (1 PM and 2 PM). This is 20 + 40 = 60 cars. The problem states that the number of cars at 3 PM was half of this total. So, calculate half of 60, which is 60 ÷ 2 = 30. There were 30 cars at 3 PM.

Question 10

1. 1/3
2. 1/2
3. 2/3 (correct answer)
4. 3/4

Explanation: The total number of students is 30. The number of students who chose red is 10. The number of students who chose a color that was not red is the total number of students minus those who chose red: 30 - 10 = 20. The fraction is 20/30, which simplifies to 2/3.

Question 11

1. 10 (correct answer)
2. 20
3. 30
4. 50

Explanation: First, find the number of portraits: 1/3 of 60 is 20. Next, find the number of landscapes: 1/2 of 60 is 30. Together, these are 20 + 30 = 50 paintings. To find the number of still-life paintings, subtract this from the total: 60 - 50 = 10. Alternatively, find the fraction of still-life paintings: 1 - 1/3 - 1/2 = 1 - 5/6 = 1/6. Then, 1/6 of 60 is 10.

Question 12

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

Explanation: First, find the number of students in the debate club by subtracting the others from the total: 48 - (12 + 16 + 8) = 48 - 36 = 12. Next, find the total number of students in the art club or debate club: 8 + 12 = 20. The fraction is 20 out of 48 students, which is 20/48. This fraction simplifies to 5/12.

Question 13

1. 1/10
2. 1/5
3. 1/2
4. 3/10 (correct answer)

Explanation: When you encounter circle graph problems, you're working with parts of a whole, which means you'll need to find fractions or percentages that represent different portions of the total survey group. First, let's identify what we know: 100 total people, with Spring (30), Summer (40), and Fall (20) already given. Since these must add up to 100, Winter must represent the remaining people: $100 - 30 - 40 - 20 = 10$ people chose Winter. The question asks for the fraction representing those who chose Fall OR Winter combined. That's $20 + 10 = 30$ people out of 100 total, which gives us the fraction $\frac{30}{100}$. Simplifying by dividing both numerator and denominator by 10, we get $\frac{3}{10}$. Looking at the wrong answers: Choice A ($\frac{1}{10}$) represents only the Winter group (10 out of 100 people), but ignores the Fall group entirely. Choice B ($\frac{1}{5}$) equals $\frac{20}{100}$, which represents only the Fall group and excludes Winter. Choice C ($\frac{1}{2}$) would mean 50 people chose Fall or Winter, but our calculation shows only 30 people did. The correct answer is D) $\frac{3}{10}$. Study tip: In circle graph problems, always verify that all parts add up to the whole before calculating. When the question asks for combined groups, make sure you're adding all the relevant categories together—don't accidentally calculate just one portion when multiple groups are requested.

Question 14

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

Explanation: To find how many times greater Seaport's rainy days were than Oakhaven's, divide the number of rainy days in Seaport by the number in Oakhaven. Seaport had 120 rainy days and Oakhaven had 30. So, 120 ÷ 30 = 4. Seaport had 4 times the number of rainy days as Oakhaven.

Question 15

1. 10
2. 18
3. 50 (correct answer)
4. 90

Explanation: First, find the number of roses: 6 symbols * 5 flowers/symbol = 30 roses. Then, find the number of tulips: 4 symbols * 5 flowers/symbol = 20 tulips. The total number of roses and tulips is the sum of these two amounts: 30 + 20 = 50 flowers.

Question 16

1. Monday and Tuesday
2. Monday and Thursday
3. Wednesday and Thursday
4. Tuesday and Wednesday (correct answer)

Explanation: When you see a question asking you to find which two values add up to a specific target, you need to systematically check each pair by adding them together. Let's add up each pair of days to see which totals approximately 120: For choice A (Monday and Tuesday): $49 + 78 = 127$. This is close to 120, but let's check the other options to see if there's a better match. For choice B (Monday and Thursday): $49 + 61 = 110$. This is 10 away from 120. For choice C (Wednesday and Thursday): $42 + 61 = 103$. This is 17 away from 120. For choice D (Tuesday and Wednesday): $78 + 42 = 120$. This equals exactly 120! Choice D gives us the exact target of 120, making it the best answer. Choice A is incorrect because 127 is 7 more than 120, which isn't as close as an exact match. Choice B is wrong because 110 is 10 less than the target. Choice C is incorrect because 103 is 17 less than 120, making it the furthest from our target. When solving "approximate total" problems, calculate each possibility and choose the one closest to the target number. However, if you find an exact match like we did here, that's always your best choice. Remember to work systematically through each answer choice rather than stopping at the first one that seems close.

Question 17

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

Explanation: First, find the total amount raised. $100 +$150 + $120 +$130 = $500. The 2nd grade raised$100. The fraction is 100/500. This simplifies to 1/5. Even though the question asks for 'about what fraction', the exact answer is one of the choices.

Question 18

1. 1/2
2. 2/3 (correct answer)
3. 3/2
4. 3/4

Explanation: The question asks for the fraction of fantasy books compared to mystery books. There are 60 fantasy books and 90 mystery books. The fraction is 60/90. To simplify, divide both the numerator and the denominator by their greatest common divisor, which is 30. 60 ÷ 30 = 2, and 90 ÷ 30 = 3. The simplified fraction is 2/3.

Question 19

1. 1/6
2. 1/3
3. 1/4
4. 1/5 (correct answer)

Explanation: When you encounter fraction problems involving data from graphs or tables, you need to identify the part and the whole, then express their relationship as a fraction. First, find the total pages read during the week by adding all five days: 20 + 15 + 25 + 15 + 25 = 100 pages total. Monday's reading was 20 pages, so you need the fraction that represents 20 out of 100, which is $\frac{20}{100}$. Simplify this by dividing both numerator and denominator by their greatest common factor of 20: $\frac{20}{100} = \frac{1}{5}$. This confirms answer choice D is correct. Let's examine why the other choices are wrong. Choice A ($\frac{1}{6}$) would mean Monday represented about 16.7% of the total reading, but $\frac{20}{100} = 20\%$, so this is too small. Choice B ($\frac{1}{3}$) represents about 33.3% of the total, which would require Monday's reading to be about 33 pages instead of 20. Choice C ($\frac{1}{4}$) equals 25%, meaning Monday would need to be 25 pages, not 20. Remember this key strategy: in fraction-of-total problems, always calculate the complete total first, then create your fraction using $\frac{\text{part}}{\text{whole}}$. Don't forget to simplify your final answer by finding the greatest common factor. Many students make errors by rushing to create a fraction without properly calculating the total or by forgetting to reduce their answer to lowest terms.

Question 20

1. 30
2. 60 (correct answer)
3. 120
4. 180

Explanation: To estimate, round the total number of animals to 240. Cows are close to 1/2, so about 1/2 of 240 = 120 cows. Chickens are about 1/4, so about 1/4 of 240 = 60 chickens. The rest are pigs. The fraction for pigs would be 1 - 1/2 - 1/4 = 1/4. So the number of pigs should be about the same as the number of chickens. About 1/4 of 240 is 60. Therefore, 60 is the best estimate for the number of pigs.