ISEE Lower Level Quantitative Reasoning Quiz
Practice Input Output Rules in ISEE Lower Level Quantitative Reasoning with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.
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A number pattern is generated by a rule. The first number in the pattern (Input 1) is 7. The second number (Input 2) is 11. The third number (Input 3) is 15. If the pattern continues, what is the rule to find the number for any input position?
This quiz focuses on Input Output Rules, giving you a quick way to practice the rules, question types, and explanations that matter most for ISEE Lower Level Quantitative Reasoning.
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.
A number pattern is generated by a rule. The first number in the pattern (Input 1) is 7. The second number (Input 2) is 11. The third number (Input 3) is 15. If the pattern continues, what is the rule to find the number for any input position?
Explanation: The numbers are 7, 11, 15. The numbers are increasing by 4 each time. This means the rule involves multiplying the input position by 4. Let's test this for Input 1: 1 * 4 = 4. To get to the output of 7, we must add 3. So the rule is: Multiply the input position by 4, then add 3. Let's check for Input 2: 2 * 4 + 3 = 8 + 3 = 11. It works. Let's check for Input 3: 3 * 4 + 3 = 12 + 3 = 15. It works. Therefore, Choice B is correct. The other choices fail on at least one of the pairs.
A machine processes numbers using a consistent two-step rule. An input of 10 results in an output of 7. An input of 16 results in an output of 10. If a number is put into the machine and the output is 13, what was the input?
Explanation: First, find the rule. The input increases by 6 (16 - 10), and the output increases by 3 (10 - 7). This means the input is multiplied by 1/2 (or divided by 2). Let's test this. For an input of 10: 10 ÷ 2 = 5. To get to the output of 7, we must add 2. The rule is: Divide by 2, then add 2. Let's check with the second pair: 16 ÷ 2 + 2 = 8 + 2 = 10. It works. To find the input for an output of 13, we must reverse the rule: subtract 2, then multiply by 2. 13 - 2 = 11. 11 * 2 = 22. The input was 22.
In a video game, the points for collecting gems follow a rule. Collecting 4 gems gives 25 points, and collecting 6 gems gives 35 points. How many points would a player get for collecting 10 gems?
Explanation: First, find the rule. The number of gems increases by 2 (6 - 4), and the points increase by 10 (35 - 25). This means each gem is worth 5 points (10 ÷ 2 = 5). Let's test this. For 4 gems: 4 * 5 = 20. To get to 25 points, there must be a 5-point bonus. The rule is: Multiply the number of gems by 5, then add 5. Let's check with 6 gems: 6 * 5 + 5 = 30 + 5 = 35. It works. Now apply the rule to 10 gems: 10 * 5 + 5 = 50 + 5 = 55.
A baker uses a rule to determine the number of chocolate chips to add to cookies. For 2 cookies, she uses 15 chips. For 5 cookies, she uses 33 chips. Following this rule, how many chips would she use for 4 cookies?
Explanation: First, find the rule. The number of cookies increases by 3 (5 - 2), and the number of chips increases by 18 (33 - 15). This means each cookie gets 18 ÷ 3 = 6 chips. For 2 cookies, this is 2 * 6 = 12 chips. Since she uses 15 chips, there must be an extra 3 chips added to every batch. The rule is: Multiply the number of cookies by 6, then add 3. Let's check with 5 cookies: 5 * 6 + 3 = 30 + 3 = 33. It works. Now apply the rule to 4 cookies: 4 * 6 + 3 = 24 + 3 = 27.
A function machine changes numbers according to a rule. If the input is 3, the output is 13. If the input is 5, the output is 21. Following the same rule, what will the output be if the input is 8?
Explanation: First, find the rule. The input increases by 2 (from 3 to 5), and the output increases by 8 (from 13 to 21). This means the rule involves multiplying by 4 (8 ÷ 2 = 4). Let's test this. For an input of 3: 3 * 4 = 12. To get to the output of 13, we must add 1. So the rule is: Multiply by 4, then add 1. Let's check with the second pair: 5 * 4 + 1 = 20 + 1 = 21. It works. Now apply the rule to the new input, 8: 8 * 4 + 1 = 32 + 1 = 33.
The temperature of an experiment changes based on a rule. At 2 minutes, the temperature is 19 degrees. At 5 minutes, the temperature is 34 degrees. If the pattern continues, what was the temperature at 0 minutes (the start)?
Explanation: When you see a temperature changing over time with a consistent pattern, you're dealing with a linear relationship. The key is finding how much the temperature changes per minute, then working backward to the starting point. First, calculate the rate of change. From 2 minutes to 5 minutes (a 3-minute span), the temperature went from 19 degrees to 34 degrees. That's an increase of 34−19=15 degrees over 3 minutes, so the rate is 15÷3=5 degrees per minute. Now work backward from any known point. Using the 2-minute mark: if the temperature was 19 degrees at 2 minutes, and it increases by 5 degrees each minute, then 2 minutes earlier (at 0 minutes) it would have been 19−(2×5)=19−10=9 degrees. Let's check why the other answers are wrong. Choice A (4 degrees) would mean the temperature increased by 15 degrees in just 2 minutes, giving a rate of 7.5 degrees per minute—but this doesn't match the 5-degree rate we calculated. Choice B (5 degrees) would create a rate of 7 degrees per minute from 0 to 2 minutes, again inconsistent with our pattern. Choice C (14 degrees) would mean only a 5-degree increase in 2 minutes (2.5 degrees per minute), which contradicts the 15-degree increase we observed from minutes 2 to 5. For linear pattern problems, always find the rate first, then use it consistently to work forward or backward. Double-check by verifying your answer produces the same rate throughout the problem.
A machine has an input and an output. The following pairs were recorded: (4, 9) and (10, 21). Which rule does the machine follow?
Explanation: When you encounter a function machine problem, you need to find the mathematical rule that transforms each input into its corresponding output. Test each given rule against both data points to see which one works consistently. Let's check answer choice D) Multiply the input by 2, then add 1. For the first pair (4, 9): 4×2+1=8+1=9 ✓. For the second pair (10, 21): 10×2+1=20+1=21 ✓. This rule works perfectly for both pairs. Now let's see why the other options fail. Choice A) Add 5 to the input gives us 4+5=9 (correct for the first pair) but 10+5=15 (should be 21, so this fails). Choice B) Multiply by 3, then subtract 3 produces 4×3−3=12−3=9 (correct) but 10×3−3=30−3=27 (should be 21, so this fails). Choice C) Multiply by 1, then add 5 gives us 4×1+5=9 (correct) but 10×1+5=15 (should be 21, so this fails). The key strategy for function machine problems is to always test your suspected rule against every given data point. A single correct result isn't enough—the rule must work for all pairs. Start by testing the simpler operations first, but don't assume the first rule that works for one pair is automatically correct.
A rule is used to change a number. The number 10 is changed to 4. The number 25 is changed to 19. Following this rule, what number would be changed to 34?
Explanation: Let's determine the rule. The input changes from 10 to 25 (an increase of 15), and the output changes from 4 to 19 (an increase of 15). This means the rule is simply to subtract a constant number. To get from 10 to 4, we subtract 6. The rule is: Subtract 6. Let's check: 25 - 6 = 19. It works. To find the input that gives an output of 34, we must reverse the rule, which means adding 6. 34 + 6 = 40. The input was 40.
A number machine follows the rule 'multiply by 3, then subtract 5'. If the output is 28, what was the input?
Explanation: To find the input when given the output, we must perform the inverse (opposite) operations in the reverse order. The reverse of 'subtract 5' is 'add 5'. The reverse of 'multiply by 3' is 'divide by 3'. So, we start with the output 28, add 5, and then divide by 3. 28 + 5 = 33. 33 ÷ 3 = 11. The input was 11. We can check this: (11 * 3) - 5 = 33 - 5 = 28.
The input/output pairs (3, 11) and (7, 27) are generated by a machine. What is the output for an input of 5?
Explanation: First, find the rule. The input increases by 4 (7 - 3), and the output increases by 16 (27 - 11). This means the rule involves multiplying the input by 4 (16 ÷ 4 = 4). For an input of 3: 3 * 4 = 12. To get to the output of 11, we must subtract 1. The rule is: Multiply by 4, then subtract 1. Let's check with the second pair: 7 * 4 - 1 = 28 - 1 = 27. It works. Now, apply the rule to an input of 5: 5 * 4 - 1 = 20 - 1 = 19.
A number machine follows a two-step rule. When the input is 4, the output is 14. When the input is 7, the output is 23. What is the rule?
Explanation: The rule must work for both pairs. Let's test the choices. For C: Input 4 -> 4 * 3 + 2 = 12 + 2 = 14. This works. Input 7 -> 7 * 3 + 2 = 21 + 2 = 23. This also works. Therefore, this is the correct rule. Choice A works for the first pair (4 + 10 = 14) but not the second (7 + 10 = 17, not 23). Choice B works for the first pair (4 * 2 + 6 = 14) but not the second (7 * 2 + 6 = 20, not 23). Choice D works for the first pair (4 * 4 - 2 = 14) but not the second (7 * 4 - 2 = 26, not 23).
A pattern machine operates on a two-part rule. An input of 20 results in an output of 9. An input of 30 results in an output of 14. What is the rule?
Explanation: The correct rule must work for both given pairs. Let's test Choice A. Input 20 -> 20 ÷ 2 - 1 = 10 - 1 = 9. This works. Input 30 -> 30 ÷ 2 - 1 = 15 - 1 = 14. This also works. Therefore, Choice A is the correct rule. Choice B works for the first pair (20 - 11 = 9) but not the second (30 - 11 = 19, not 14). Choice C works for the first pair (20 ÷ 5 + 5 = 9) but not the second (30 ÷ 5 + 5 = 11, not 14). Choice D does not work for the first pair (20 ÷ 4 + 4 = 9).
A 'secret code' machine follows a two-step rule. When the input is 8, the output is 20. When the input is 12, the output is 32. What will the output be when the input is 5?
Explanation: First, find the rule. The input increases by 4 (12 - 8), and the output increases by 12 (32 - 20). This means the rule involves multiplying by 3 (12 ÷ 4 = 3). Let's test this. Input 8 -> 8 * 3 = 24. To get to the output of 20, we must subtract 4. The rule is: Multiply by 3, then subtract 4. Let's check with the second pair: 12 * 3 - 4 = 36 - 4 = 32. It works. Now apply the rule to the new input, 5: 5 * 3 - 4 = 15 - 4 = 11.
A plant's height is measured each week. After 2 weeks, it was 17 cm tall. After 4 weeks, it was 27 cm tall. Assuming the plant grows at a constant rate and following the same rule, how tall was the plant after 1 week?
Explanation: This is a linear growth problem where you need to find a pattern in how the plant grows over time. When you see "constant rate" and measurements at different time points, think about finding the rate of change and working backwards. First, let's find the plant's growth rate. From week 2 to week 4 (a 2-week period), the plant grew from 17 cm to 27 cm. That's 27−17=10 cm of growth over 2 weeks, so the rate is 10÷2=5 cm per week. Now we can work backwards from week 2. If the plant was 17 cm tall after 2 weeks and grows 5 cm per week, then after 1 week it must have been 17−5=12 cm tall. Let's check why the other answers are wrong. Choice A (5 cm) is actually the growth rate per week, not the height after 1 week—this is a common trap where students confuse the rate with the actual measurement. Choice B (7 cm) might come from incorrectly calculating the growth rate or making arithmetic errors. Choice C (15 cm) could result from subtracting 2 cm instead of 5 cm, perhaps by confusing the time intervals. When tackling constant rate problems, always identify what's changing (height), find the rate of change between known points, then use that rate to work forward or backward to find unknown values. Double-check by verifying your answer maintains the same rate throughout all given points.
The table below shows the relationship between two numbers, x and y. If x is 3, y is 10. If x is 6, y is 19. If x is 9, y is 28. Which equation describes the rule?
Explanation: The rule must work for all three pairs. Let's test Choice D. For x=3: y = 3(3) + 1 = 9 + 1 = 10. This works. For x=6: y = 3(6) + 1 = 18 + 1 = 19. This works. For x=9: y = 3(9) + 1 = 27 + 1 = 28. This works. Therefore, Choice D is the correct rule. Choice A works only for the first pair. Choice B works only for the first pair. Choice C works only for the first pair.
An old machine works according to a rule. An input of 15 gives an output of 8. An input of 21 gives an output of 10. What output would an input of 33 produce?
Explanation: First, find the rule. The input increases by 6 (21 - 15), and the output increases by 2 (10 - 8). This suggests the rule involves multiplying by 2/6, which simplifies to 1/3 (or dividing by 3). Let's test this. Input 15 -> 15 ÷ 3 = 5. To get to the output of 8, we add 3. The rule is: Divide by 3, then add 3. Let's check the second pair: 21 ÷ 3 + 3 = 7 + 3 = 10. It works. Now apply the rule to the new input, 33: 33 ÷ 3 + 3 = 11 + 3 = 14.
A 'Rule Master' machine follows a rule. Input 5 gives Output 22. Input 9 gives Output 38. Which of the following inputs would result in an output of 50?
Explanation: First, find the rule. The input increases by 4 (9 - 5), and the output increases by 16 (38 - 22). This means the rule involves multiplying by 4 (16 ÷ 4 = 4). Let's test this. Input 5 -> 5 * 4 = 20. To get to 22, we add 2. The rule is: Multiply by 4, then add 2. Let's check: 9 * 4 + 2 = 36 + 2 = 38. The rule is correct. To find the input for an output of 50, we reverse the rule: subtract 2, then divide by 4. 50 - 2 = 48. 48 ÷ 4 = 12. The input was 12.
The cost to rent a canoe is based on a fixed fee plus an hourly rate. It costs 23fora3−hourrentaland33 for a 5-hour rental. What is the rule to find the total cost for a given number of hours?
Explanation: The difference in time is 2 hours (5 - 3), and the difference in cost is 10(33 - 23).Thismeansthehourlyrateis10 ÷ 2 = 5perhour.Fora3−hourrental,thecostfromthehourlyrateis3∗5 = 15.Sincethetotalcostis23, the fixed fee must be 23−15 = 8.Theruleis:Multiplythenumberofhoursby5andadd8.Let′scheckwiththe5−hourrental:5∗5 + 8=25 + 8=33. The rule is correct.
A robot follows a two-step command sequence. When given the number 6, it produces 29. When given the number 10, it produces 49. If the robot produces 39, what number was it given?
Explanation: First, find the rule. The input increases by 4 (10 - 6), and the output increases by 20 (49 - 29). This means the rule involves multiplying by 5 (20 ÷ 4 = 5). Let's test this. Input 6 -> 6 * 5 = 30. To get to 29, we subtract 1. The rule is: Multiply by 5, then subtract 1. Let's check: 10 * 5 - 1 = 50 - 1 = 49. The rule is correct. To find the input for an output of 39, we reverse the rule: add 1, then divide by 5. 39 + 1 = 40. 40 ÷ 5 = 8. The input was 8.