ISEE Upper Level Quantitative Reasoning Quiz: Comparing Rational Numbers

What this quiz covers

This quiz focuses on Comparing Rational Numbers, giving you a quick way to practice the rules, question types, and explanations that matter most for ISEE Upper 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. Anna, Ben, Carol
2. Ben, Anna, Carol (correct answer)
3. Carol, Ben, Anna
4. Ben, Carol, Anna

Question 2

1. Cars, because $\frac{5}{12} = 0.41\overline{6}$ which is the smallest value
2. Public transit, because $41.\overline{6}\% = 0.41\overline{6}$ which is the smallest value
3. Walking, because $0.41\overline{7}$ is the largest value, indicating the question asks for least preferred
4. Cars and public transit are tied for least preferred, both less than walking (correct answer)

Question 3

1. Machine A, because $\frac{3}{8} = 0.375$ which exceeds the other rates
2. Machine B, because $37.6\% = 0.376$ which exceeds the other rates (correct answer)
3. Machine C, because $0.374$ is the largest value when compared directly
4. Machines A and C are tied with the highest rate, both exceeding Machine B

Question 4

1. First year, because $\frac{1}{16}$ converts to the highest decimal rate
2. Second year, because $6.3\%$ converts to the highest decimal rate (correct answer)
3. Third year, because $0.0624$ is already in decimal form and is largest
4. Second and third years are tied for the highest interest rate

Question 5

1. $x > y$ because fractions are generally larger than percentages under 50%
2. $x < y$ because $43.\overline{3}\% = \frac{13}{30}$ when converted to a fraction
3. $x = y$ because both expressions represent the same rational number (correct answer)
4. $x < y$ because $\frac{13}{30} \approx 0.433$ while $43.\overline{3}\% \approx 0.434$

Question 6

1. Math, because $\frac{3}{7}$ is the largest value when compared to the others
2. Science, because $42.9\%$ is greater than both $\frac{3}{7}$ and $0.428$ (correct answer)
3. English, because $0.428$ is smaller than the others, indicating a measurement error
4. Science and English are tied, since $42.9\% = 0.429$ and both exceed $\frac{3}{7}$

Question 7

1. Store X, because $\frac{1}{8} = 0.125$ which is the smallest decimal value
2. Store Z, because $0.124 < 0.125 < 0.126$ when all discounts are compared (correct answer)
3. Store Y, because $12.6\% = 0.126$ which is greater than the other discounts
4. Store X and Z offer equal discounts, both smaller than Store Y's discount

Question 8

1. The reasoning is correct; $\frac{9}{20} = 45\%$ which is greater than $44.9\%$
2. Fractions and percentages cannot be compared without converting to a common form
3. The statement about fractions and percentages is false, and $\frac{9}{20} > 44.9\%$ (correct answer)
4. The comparison is correct but the general rule about fractions and percentages is invalid

Question 9

1. Alpha, because $\frac{2}{5} = 0.4$ which is the highest percentage of votes
2. Gamma, because $0.402 > 0.4 > 0.398$ when all votes are compared (correct answer)
3. Beta, because $39.8\%$ represents the largest share of votes cast
4. Alpha and Gamma tied, since $\frac{2}{5}$ and $0.402$ are approximately equal

Question 10

1. The athlete with $\frac{14}{25}$ has the best performance at exactly $56\%$
2. The athlete with $55.9\%$ has the best performance as it exceeds the others
3. The athlete with $0.56\overline{1}$ has the best performance as it represents the highest rate (correct answer)
4. All three athletes have essentially identical performance rates within measurement error

Question 11

1. Yes, because $\frac{4}{7} ≈ 0.571$ and $57\% = 0.57$, so $0.571 > 0.57$
2. Yes, because $\frac{4}{7} = 0.\overline{571428}$ and this repeating decimal is greater than $0.57$ (correct answer)
3. No, because $0.\overline{571428} ≠ \frac{4}{7}$ so the premise is incorrect
4. No, because even if $0.\overline{571428} = \frac{4}{7}$, we have $57\% > \frac{4}{7}$

Question 12

1. Monday, because $\frac{7}{20} = 0.35$ which is the highest probability
2. Tuesday, because $35.2\% = 0.352$ which is the highest probability (correct answer)
3. Wednesday, because $0.348$ represents the highest probability value
4. Monday and Wednesday have equal probability, both higher than Tuesday

Question 13

1. $0.4\overline{583} < \frac{11}{24} < 45.8\%$
2. $45.8\% < 0.4\overline{583} < \frac{11}{24}$
3. $45.8\% < \frac{11}{24} < 0.4\overline{583}$ (correct answer)
4. $\frac{11}{24} < 45.8\% < 0.4\overline{583}$

Question 14

1. $\frac{3}{8} < 37\% < \frac{5}{12}$
2. $37\% < \frac{3}{8} < \frac{5}{12}$ (correct answer)
3. $\frac{5}{12} < 37\% < \frac{3}{8}$
4. $\frac{5}{12} < \frac{3}{8} < 37\%$

Question 15

1. Yes, because $0.58\overline{3} > 0.58$ and $58\% = 0.58$ (correct answer)
2. No, because $58\% = 0.583$ which is greater than $0.58\overline{3}$
3. No, because the student made an error; $\frac{7}{12} = 0.583$ exactly
4. Yes, because $58.\overline{3}\% = \frac{7}{12}$ so $\frac{7}{12} > 58\%$

Question 16

1. $79.5\%$, $\frac{4}{5}$, $0.802$ (correct answer)
2. $\frac{4}{5}$, $79.5\%$, $0.802$
3. $79.5\%$, $0.802$, $\frac{4}{5}$
4. $0.802$, $\frac{4}{5}$, $79.5\%$

Question 17

1. The student should compare $\frac{7}{15}$ to $0.47$ instead of $0.4\overline{7}$ for accuracy
2. Converting $\frac{7}{15}$ to decimal form gives $0.4\overline{6}$, which is less than $0.4\overline{7}$ (correct answer)
3. The comparison should be made after converting both numbers to percentage form
4. The student correctly identified that $\frac{7}{15} > 0.4\overline{7}$ but used flawed reasoning

Question 18

1. All three measurements represent different amounts needed for the recipe
2. All three measurements represent exactly the same amount needed for the recipe (correct answer)
3. The flour and sugar measurements are equal, but butter requires a different amount
4. The sugar and butter measurements are equal, but flour requires a different amount