2 is related to 9 following a certain logic. Following the same logic, 7 is…
2025
2 is related to 9 following a certain logic. Following the same logic, 7 is related to 64. To which of the given options is 11 related, following the same logic?
(Note: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g., 13 — Operations on 13 such as adding/subtracting/multiplying to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
- A.
121
- B.
144
- C.
100
- D.
169
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Correct answer: B
In a number-based analogy, the same arithmetic rule that connects the first number of a given pair to its related number must first be identified from the example pair(s), and then applied without change to the new number. Since the question requires operations on the whole number only (no digit-splitting), the rule must work through arithmetic operations - such as addition, multiplication, or squaring - applied to the number as a whole.
Test the given pair 2 -> 9: adding 1 to the number and then squaring the result gives (2 + 1)2 = 32 = 9, which matches.
Confirm the same rule on the second given pair, 7 -> 64: (7 + 1)2 = 82 = 64, which also matches - confirming that the rule "add 1, then square" holds consistently across both example pairs.
Apply the confirmed rule to 11: (11 + 1)2 = 122 = 144.
Cross-check by testing a simpler rule: squaring the number directly with no offset (n2) gives 22 = 4 and 72 = 49, neither of which matches 9 or 64, so a zero-offset square is ruled out. The "add 1, then square" rule is a consistent pattern that fits both given example pairs simultaneously, which supports applying it to 11 to obtain the value 144 under the same logic.
Hence, following the same logic, 11 is related to 144.