Identify the relationship in a number pair - CogAT Grades K 2

Look at this number pair: $8, 12$ . Now look at this number pair: $5, ?$ . If both pairs follow the same rule, what number goes in the place of the question mark?
Answer: $9$ The rule is add 4. In the first pair: 8 + 4 = 12. So for the second pair: 5 + 4 = 9. Choice B (10) comes from adding 5 instead of 4. Choice C (7) comes from adding 2. Choice D (1) comes from subtracting 4 instead of adding.
Look at the number pair $4, 16$ . If you use the same rule with the number $6$ , what number would you get?
Answer: $24$ The rule is multiply by 4. In the pair 4, 16: 4 × 4 = 16. Applying this rule to 6: 6 × 4 = 24. Choice A (10) comes from adding 4. Choice B (12) comes from multiplying by 2. Choice C (18) comes from adding 12 or multiplying by 3.
The number pair $6, 2$ follows a rule. Which other number pair follows the same rule?
Answer: $9, 3$ The rule is divide by 3. In the pair 6, 2: 6 ÷ 3 = 2. Choice A follows the same rule: 9 ÷ 3 = 3. Choice B gives 8 ÷ 4 = 2 (different rule). Choice C gives 4 ÷ 2 = 2 (different rule). Choice D reverses the original relationship.
Tom makes number pairs using a secret rule. He shows you: $7, 21$ and $9, 27$ . If his next first number is $5$ , what will his second number be?
Answer: $15$ Tom's rule is multiply by 3. In 7, 21: 7×3=21. In 9, 27: 9×3=27. For 5: 5×3=15. Choice A (12) comes from adding 7. Choice C (18) might come from confusing the rule as adding 11 then 18. Choice D (20) comes from multiplying by 4.
In these number pairs, one pair does NOT follow the same rule as the others: $2, 8$ , $3, 12$ , $5, 20$ , $4, 12$ . Which pair is different?
Answer: $4, 12$ Three pairs follow the rule 'multiply by 4': 2×4=8, 3×4=12, and 5×4=20. The pair 4, 12 follows the rule 'multiply by 3' (4×3=12), making it different. Students might choose other options by incorrectly identifying the main pattern.
The number pair $12, 4$ uses the same rule as $18, 6$ . Which number would make this pair follow the same rule: $21, ?$
Answer: $7$ The rule is divide by 3. In 12, 4: 12÷3=4. In 18, 6: 18÷3=6. For 21, ?: 21÷3=7. Choice A (6) comes from subtracting 15. Choice C (8) comes from subtracting 13. Choice D (9) comes from dividing by approximately 2.3.
4 is to 10 as 7 is to ?
Answer: 16 Double the first number and add 2: 4 x 2 + 2 = 10. Applying the same rule to 7 gives 7 x 2 + 2 = 16. The tempting wrong answer is 14, which only doubles 7 but leaves out the extra +2 the pattern requires.
Look at this pattern in number pairs: $1, 4$ , $2, 5$ , $3, 6$ . What number pair comes next?
Answer: $4, 7$ The pattern shows that each first number increases by 1 (1, 2, 3, so next is 4) and the rule for each pair is 'add 3' (1+3=4, 2+3=5, 3+3=6). So the next pair is 4, 7 (4+3=7). Choice B applies a different rule. Choices C and D start with wrong first numbers.
5 is to 11 as 7 is to ?
Answer: 15 Double the first number and add 1: 5 times 2 is 10 plus 1 is 11. Apply the same rule to 7: 7 times 2 is 14 plus 1 is 15. The tempting wrong answer is 14 because it only doubles the number and forgets the extra 1.
In the number pair $15, 10$ , what happens to get from the first number to the second number?
Answer: Subtract $5$ To get from 15 to 10, you subtract 5 because 15 - 5 = 10. Choice A (add 5) would give 15 + 5 = 20. Choice C (add 10) would give 15 + 10 = 25. Choice D (subtract 10) would give 15 - 10 = 5.
Look at these number pairs: $3, 6$ and $7, 14$ . What is the same rule for both pairs?
Answer: Times $2$ The rule is multiply by 2 (times 2). For the first pair: 3 × 2 = 6. For the second pair: 7 × 2 = 14. Choice A (add 3) works for the first pair but not the second (7 + 3 = 10, not 14). Choice B (add 4) doesn't work for either pair. Choice D (times 3) gives 3 × 3 = 9, not 6.

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