This question tests the ability to identify number pattern rules at the ISEE Lower Level. Understanding number patterns involves recognizing sequences that are governed by specific mathematical rules, such as arithmetic or geometric progressions. In this sequence, the numbers 4, 8, 16, 32 follow a pattern where each number is multiplied by 2 (4×2=8, 8×2=16, 16×2=32). Choice C (64) is correct because it accurately applies the rule of multiplying by 2, making the next number 32×2=64. Choice A (36) incorrectly adds 4 instead of multiplying, while choice D (96) multiplies by 3 instead of 2. To help students, teach them to recognize geometric sequences where each term is a constant multiple of the previous term and to double-check their calculations.

We need to find a rule that works for every pair of corresponding numbers (2 and 5, 4 and 9, 6 and 13, etc.). Let's test the rules. Rule A: 2 + 3 = 5, but 4 + 3 = 7, not 9. Rule C: 2 × 3 - 1 = 5, but 4 × 3 - 1 = 11, not 9. Rule D: 2 x 2 - 3 = 1, not 5. Rule B works for all pairs: 2 × 2 + 1 = 5; 4 × 2 + 1 = 9; 6 × 2 + 1 = 13. This is the correct rule.

This question tests the ability to identify number pattern rules at the ISEE Lower Level. Understanding number patterns involves recognizing sequences that are governed by specific mathematical rules, such as arithmetic or geometric progressions. In this sequence, the numbers 20, 16, 12, 8, 4 follow a pattern where each number decreases by 4 (20-4=16, 16-4=12, 12-4=8, 8-4=4). Choice B is correct because it accurately describes the rule of subtracting 4 each time. Choice A (Add 4) is incorrect because the sequence is decreasing, not increasing, a common error when students don't pay attention to the direction of change. To help students, teach them to notice whether sequences are increasing or decreasing and to verify that the operation produces each subsequent number in the sequence.

This question tests the ability to identify number pattern rules at the ISEE Lower Level. Understanding number patterns involves recognizing sequences that are governed by specific mathematical rules, such as arithmetic or geometric progressions. In this sequence, the numbers 6, 10, 14, 18 follow a pattern where each number increases by 4 (6+4=10, 10+4=14, 14+4=18). Choice B (22) is correct because it accurately describes the rule of adding 4, making the next number 18+4=22. Choice A (20) is incorrect because it adds only 2 instead of 4, while choices C (24) and D (26) add too much. To help students, teach them to find the difference between consecutive terms and verify that this difference remains constant throughout the sequence.

This question tests the ability to identify number pattern rules at the ISEE Lower Level. Understanding number patterns involves recognizing sequences that are governed by specific mathematical rules, such as arithmetic or geometric progressions. In this sequence, the numbers 3, 6, 12, 24, 48 follow a pattern where each number is multiplied by 2 (3×2=6, 6×2=12, 12×2=24, 24×2=48). Choice B is correct because it accurately describes the rule of multiplying by 2 each time. Choice A (Add 3) is incorrect because the differences between consecutive terms are not constant (6-3=3, but 12-6=6), a common error when students only check the first difference. To help students, teach them to check if the ratio between consecutive terms is constant for multiplicative patterns and to verify the rule works for all given numbers.

To find the original number, we must work backward from the output using inverse operations. The opposite of 'subtracts 7' is 'adds 7'. The opposite of 'multiplies by 4' is 'divides by 4'. Start with the output, 33. First, add 7: 33 + 7 = 40. Then, divide by 4: 40 ÷ 4 = 10. The original number was 10.

Let's look at the amount subtracted at each step. From 200 to 190, we subtract 10. From 190 to 181, we subtract 9. From 181 to 173, we subtract 8. From 173 to 166, we subtract 7. The amount being subtracted is decreasing by 1 each time (10, 9, 8, 7, ...).

The rule must work for all given pairs. Let's test some possible rules. An 'add 7' rule works for the first pair (3 + 7 = 10), but not the second (5 + 7 = 12, not 16). A 'multiply by 2, add 4' rule works for the first pair (3 × 2 + 4 = 10), but not the second (5 × 2 + 4 = 14, not 16). The correct rule is 'multiply by 3, then add 1'. Let's check: 3 × 3 + 1 = 10; 5 × 3 + 1 = 16; 8 × 3 + 1 = 25. The rule works for all pairs. Applying this rule to the new input: 10 × 3 + 1 = 31.

First, find the rule. An increase of 3 stars (from 5 to 8) results in an increase of 9 points (from 17 to 26). This means each star is worth 9 ÷ 3 = 3 points. The rule is 'multiply the number of stars by 3, and then add or subtract a constant'. Let's check with 5 stars: 5 × 3 = 15. To get to 17, we must add 2. So the rule is 'multiply by 3, then add 2'. Let's check with 8 stars: 8 × 3 + 2 = 24 + 2 = 26. The rule works. For 10 stars: 10 × 3 + 2 = 30 + 2 = 32 points.

To find the rule, look at the difference between consecutive numbers. From 5 to 6, the difference is +1. From 6 to 8, the difference is +2. From 8 to 11, the difference is +3. The rule is to add a number that increases by 1 each time. The sequence is: Term 1: 5; Term 2: 5+1=6; Term 3: 6+2=8; Term 4: 8+3=11. To find the seventh term, we continue the pattern: Term 5: 11+4=15; Term 6: 15+5=20; Term 7: 20+6=26.