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16 is related to 225 following a certain logic. Following the same logic, 7 is related to 99. To which of the following 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 тАУ 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.)
155
159
158
150
155
Observe that the relationship is (x-1)2 - 1. Calculate square of (n-1) and subtract 1 to get the target number.
Observe that the relationship is (x-1)2 - 1. Calculate square of (n-1) and subtract 1 to get the target number.
Analyze the first pattern
For 16: (16 - 1) = 15. Then 15 squared is 225. The logic is (n-1)2 = result.
Verify the second pattern
For 7: (7 - 1) = 6. Then 6 squared is 36. However, the question states 7 is related to 99. Re-evaluating: 16 squared is 256, 256 - 31 = 225. 7 squared is 49, 492 = 98, 98 + 1 = 99. Logic is inconsistent. Let's try (nn) - 31 for 16 and (nn2) + 1 for 7. Actually, the pattern is: (1614)+1 = 225; (714)+1 = 99. The multiplier is 14.
Apply pattern to 11
Using the multiplier logic: (11 * 14) + 1 = 154 + 1 = 155. This matches Option A.
B: 159 is incorrect as it does not follow the (n * 14) + 1 calculation. C: 158 is incorrect as it deviates from the derived formula. D: 150 is incorrect as it does not satisfy the established constant multiplier relationship.
A is correct because the pattern follows the formula (n * 14) + 1, where 16 * 14 + 1 = 225, 7 * 14 + 1 = 99, and 11 * 14 + 1 = 155.
If a simple square logic fails, test for linear functions like (n * k) + c to find hidden constant relationships.
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