Apply the same relationship to complete a number analogy - CogAT Grades K 2

1. Find the missing number: $6$ is to $18$ as $9$ is to what?
   Answer: $27$ The relationship is multiply by 3: $6 × 3 = 18$. Following the same pattern, $9 × 3 = 27$. Choice A (18) adds 9, choice B (24) adds 15, and choice D (36) multiplies by 4.
2. Complete the pattern: $8$ is to $2$ as $20$ is to what number?
   Answer: $5$ The relationship is dividing by 4: $8 ÷ 4 = 2$. Following the same pattern, $20 ÷ 4 = 5$. Choice A (4) divides by 5, choice C (10) divides by 2, and choice D (15) subtracts 5.
3. What number makes this analogy complete: $15$ is to $3$ as $25$ is to what?
   Answer: $5$ The relationship is dividing by 5: $15 ÷ 5 = 3$. Following the same pattern, $25 ÷ 5 = 5$. Choice B (10) subtracts 15, choice C (20) subtracts 5, and choice D (30) adds 5.
4. What number fits this pattern: $10$ is to $5$ as $14$ is to what?
   Answer: $7$ When you see "A is to B as C is to what?" questions, you're looking for a relationship or pattern between the first pair of numbers that also applies to the second pair. Let's examine the relationship between $10$ and $5$. Think about what operation connects these numbers: $10 ÷ 2 = 5$, or you could say $10 - 5 = 5$. The key is to find which relationship makes the most sense and then apply it consistently. Looking at division: $10 ÷ 2 = 5$. If we apply this same relationship to $14$, we get $14 ÷ 2 = 7$. This gives us answer choice D) $7$, which is correct. Let's check why the other answers don't work. Choice A) $6$ would mean $14 ÷ 6 = 2.33...$, which doesn't match our $÷2$ pattern. Choice B) $9$ would require $14 ÷ 9 = 1.55...$, again breaking the pattern. Choice C) $8$ gives us $14 ÷ 8 = 1.75$, which also doesn't maintain the relationship we found in the first pair. You might have considered subtraction ($10 - 5 = 5$), but applying this to $14$ would mean $14 - ? = 5$, giving you $9$. However, this creates an inconsistent pattern since the difference changes from $5$ to $5$, while division by $2$ maintains the same operation throughout. For analogy questions like this, always identify the mathematical relationship first, then apply that exact same operation to find your answer.
5. If $12$ is to $6$ as $18$ is to what number?
   Answer: $9$ The relationship is dividing by 2: $12 ÷ 2 = 6$. Following the same pattern, $18 ÷ 2 = 9$. Choice A (6) ignores the second number, choice C (12) subtracts 6, and choice D (36) doubles instead of halving.

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