Identify the relationship in a number pair - CogAT Grades 3 Plus

The number pair (63, 21) demonstrates a specific pattern. If the number 84 is the first number in a new pair following the same pattern, what is the second number?
Answer: 28 When you encounter number pattern problems, you need to identify the mathematical relationship between the numbers in the given pair, then apply that same relationship to find the unknown number. Looking at the pair (63, 21), you should test common relationships like addition, subtraction, multiplication, and division. Let's check division: $63 ÷ 21 = 3$ . This means the first number is exactly 3 times the second number, or equivalently, the second number is one-third of the first number. To verify this pattern works for the new pair, apply the same rule: if 84 is the first number, then the second number should be $84 ÷ 3 = 28$ . This confirms that answer choice D (28) is correct. Now let's examine why the other options are wrong. Choice A (12) would create the relationship $84 ÷ 12 = 7$ , which doesn't match our pattern of dividing by 3. Choice B (42) gives us $84 ÷ 42 = 2$ , showing a "divide by 2" pattern instead of "divide by 3." Choice C (21) would mean $84 ÷ 21 = 4$ , creating a "divide by 4" relationship that doesn't match the original pair. For CogAT number pattern questions, always start by testing the most straightforward mathematical operations first: addition, subtraction, multiplication, and division. Once you identify the pattern, double-check by applying it both ways—make sure it works from first number to second number and confirms the relationship you've identified.
The number pair (36, 9) follows a specific pattern. If this same pattern is applied to create the pair (48, ?), what number completes the second pair?
Answer: 12 The relationship is division by 4: 36 ÷ 4 = 9. Applying this to 48: 48 ÷ 4 = 12. Choice B (16) represents division by 3. Choice C (6) represents division by 8. Choice D (24) represents division by 2.
In the pair (15, 45), there is a mathematical relationship. Using this same relationship, what number pairs with 20?
Answer: 60 The relationship is multiplication by 3: 15 × 3 = 45. Applying this to 20: 20 × 3 = 60. Choice B (65) represents adding 45 to 20. Choice C (80) represents multiplication by 4. Choice D (35) represents adding 15 to 20.
Consider the relationship shown in the pair (42, 6). This same relationship connects 35 to which number?
Answer: 5 When you encounter relationship questions like this, you need to identify the mathematical pattern connecting the first pair of numbers, then apply that same relationship to find the missing number. Looking at the pair (42, 6), you should test common mathematical relationships. Let's check division: $42 ÷ 6 = 7$ . This means 42 is 7 times larger than 6, or equivalently, 6 is one-seventh of 42. Now apply this same relationship to 35: $35 ÷ 7 = 5$ . So 35 connects to 5 through the same "divide by 7" relationship. Let's examine why each wrong answer fails. Choice A) 7 would suggest the relationship is subtraction (42 - 6 = 36, but 35 - 7 = 28, not a consistent pattern) or that you confused the divisor with the answer. Choice C) 210 represents multiplication instead of division (35 × 6 = 210), which reverses the intended relationship direction. Choice D) 29 comes from subtraction (35 - 6 = 29), applying the wrong operation entirely. The correct answer is B) 5 because it maintains the consistent mathematical relationship of division by 7. On CogAT relationship questions, always test multiple operations systematically: addition, subtraction, multiplication, and division. Once you identify the pattern in the given pair, apply that exact same operation to the new number. Don't get distracted by answers that use the numbers from the original pair in different ways—focus on replicating the relationship, not reusing the specific numbers.
The number pair (81, 27) demonstrates a pattern. If 60 is the first number in a pair following this same pattern, what would be the second number?
Answer: 20 When you encounter number pattern questions, your goal is to identify the mathematical relationship between the numbers in the given pair, then apply that same relationship to find the missing number. Looking at the pair (81, 27), you need to determine what operation transforms 81 into 27. Let's test division: $81 ÷ 3 = 27$ . This works! The pattern is that the second number equals the first number divided by 3. Now apply this pattern to the new pair starting with 60: $60 ÷ 3 = 20$ . So the second number should be 20, which is choice B. Let's examine why the other answers don't work. Choice A (15) would result from dividing 60 by 4, which doesn't match our pattern of dividing by 3. Choice C (30) comes from dividing 60 by 2, again not matching the established pattern. Choice D (12) would require dividing by 5, which also breaks the pattern we identified from the original pair. The key trap here is assuming different mathematical relationships. Some students might look for subtraction patterns (81 - 54 = 27) or other operations, but division by 3 is the simplest and most consistent pattern that connects 81 to 27. Strategy tip: When solving pattern problems, always test the simplest mathematical operations first (addition, subtraction, multiplication, division). Once you find the pattern, apply it exactly to the new numbers. Double-check by verifying that your identified pattern actually works with the original pair before moving to the new one.
Look at the number pair (12, 48). The operation that transforms 12 into 48 is the same operation that transforms 16 into which number?
Answer: 64 When you encounter questions about number relationships and operations, you need to identify the pattern or rule that connects the first pair of numbers, then apply that same rule to find the missing number in the second pair. Looking at the pair (12, 48), you need to determine what operation transforms 12 into 48. Let's check: $48 ÷ 12 = 4$ . So the operation is "multiply by 4" (or $12 × 4 = 48$ ). Now apply this same operation to 16: $16 × 4 = 64$ . This confirms that D) 64 is correct. Let's examine why the other choices are wrong. Choice A) 80 would result from multiplying 16 by 5 ( $16 × 5 = 80$ ), but 5 isn't the relationship between 12 and 48. Choice B) 52 would come from adding 36 to 16 ( $16 + 36 = 52$ ), and while it's true that $12 + 36 = 48$ , this represents adding a fixed amount rather than applying the multiplicative relationship. Choice C) 32 results from multiplying 16 by 2 ( $16 × 2 = 32$ ), but this ignores the actual relationship in the original pair. The key strategy for these relationship problems is to always test both addition/subtraction and multiplication/division to find the pattern. Check your work by applying the operation you identified in both directions. These CogAT questions often include distractors that result from common computational errors or from applying the wrong type of operation, so double-check that you've identified the correct relationship before solving.
In the number pair (8, 40), there is a relationship between the two numbers. If 11 is the first number in a new pair with the same relationship, what is the second number?
Answer: 55 When you see number pair relationship questions, you need to identify the pattern connecting the first and second numbers, then apply that same rule to the new situation. Looking at the pair (8, 40), let's find the relationship. You could think: "What do I do to 8 to get 40?" One approach is multiplication: $8 \times 5 = 40$ . Another approach is to notice that $8 \times 8 = 64$ , but that's not 40. Let's try addition: $8 + 32 = 40$ . But the multiplication pattern $8 \times 5 = 40$ seems most straightforward. Applying this "multiply by 5" rule to the new pair: $11 \times 5 = 55$ . So if 11 is the first number, the second number should be 55. Looking at the wrong answers: Choice A (51) might tempt you if you mistakenly added 40 to 11, thinking the relationship was "add 40" rather than "multiply by 5." Choice B (43) could result from adding 32 to 11, if you incorrectly identified the relationship as "add 32" from the original pair. Choice D (88) would come from doubling 11, misidentifying the pattern as "multiply by 2" instead of "multiply by 5." The correct answer is C (55). Strategy tip: For number relationship questions, always test your identified pattern by working backwards. If you think the rule is "multiply by 5," check: does $8 \times 5$ actually equal 40? This verification step helps you avoid calculation errors and confirms you've found the right relationship.
In the number pair (18, 54), what operation transforms the first number into the second number? Apply this same relationship to find the missing number in the pair (24, ?).
Answer: 72 The relationship is multiplication by 3: 18 × 3 = 54. Applying this to 24: 24 × 3 = 72. Choice B (42) represents adding 18 to 24. Choice C (78) represents adding 54 to 24. Choice D (96) represents multiplying 24 by 4.
The pair (56, 14) follows a mathematical rule. Using this same rule, what number would pair with 72?
Answer: 18 When you encounter questions about number pairs following a mathematical rule, you need to identify the relationship between the two numbers in the given pair, then apply that same relationship to find the missing number. Looking at the pair (56, 14), you should test different mathematical operations to find the pattern. Let's check division: $56 ÷ 14 = 4$ . This means the first number is exactly 4 times the second number. Let's verify this makes sense: $14 × 4 = 56$ ✓ Now apply this same rule to 72. If 72 is the first number and follows the same pattern, then: $72 ÷ 4 = 18$ . So 72 pairs with 18, making C the correct answer. Let's examine why the other choices are incorrect. Choice A (24) would mean $72 ÷ 24 = 3$ , which doesn't match our rule of dividing by 4. Choice B (36) gives us $72 ÷ 36 = 2$ , again breaking the pattern. Choice D (12) results in $72 ÷ 12 = 6$ , which is also inconsistent with the established rule. These incorrect answers represent common traps: they're all factors of 72, but only 18 maintains the specific relationship established by the original pair. Strategy tip: Always identify the mathematical relationship in the given pair first, then systematically apply it to the new situation. Don't just look for numbers that "seem related" - the relationship must be exact and consistent. Testing your answer by working backwards (like $18 × 4 = 72$ ) helps confirm you've found the right pattern.
Consider the number pair (7, 28). The same relationship that connects these numbers also connects 9 to which number?
Answer: 36 The relationship is multiplication by 4: 7 × 4 = 28. Applying this to 9: 9 × 4 = 36. Choice B (45) represents multiplication by 5. Choice C (32) represents adding 23 (the difference between 28 and 7, but incorrectly applied). Choice D (27) represents multiplication by 3.

Start this quiz