Number Analogy

A number analogy question presents a pair of numbers with a hidden relationship, then gives you a third number and asks for the fourth. It is written as: 4 : 16 :: 5 : ? The colon means "is related to." Your job is to find the rule that connects 4 to 16, then apply that same rule to 5. Rules include multiplication, squaring, adding a fixed value, doubling, halving, or combining operations.

1. Write down the first pair and try basic operations: add, subtract, multiply, divide, square, cube.
2. State the rule precisely: "The first number is squared to give the second" (4 squared = 16).
3. Apply that rule to the third number: 5 squared = 25.
4. Match 25 against the answer options.
5. If no basic rule fits, try two-step rules: "multiply by 3 then subtract 1."

Example 1: 3 : 9 :: 7 : ?

• Check: 3 x 3 = 9, so the rule is "multiply by 3."
• Apply: 7 x 3 = 21.
• Answer: 21.

Example 2: 6 : 10 :: 11 : ?

• Check: 6 + 4 = 10, so the rule is "add 4."
• Apply: 11 + 4 = 15.
• Answer: 15.
• Trap option: 22 (multiplied by 2 — wrong rule).

• Assuming the rule is always multiplication; always verify with the first pair before applying.
• Two answer options are "close" — e.g. 15 and 16. This is deliberate; one comes from the right rule, one from a slightly wrong operation.
• Missing two-step rules. If single operations fail, try add-then-multiply or square-then-subtract.

1. 5 : 25 :: 8 : ?
2. 12 : 6 :: 20 : ?