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5 is related to 67 following a certain logic. Following the same logic, 7 is related to 93. 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.)
145
144
146
148
145
Look for the relationship x┬▓ + (x * 8) + 2 or simply test the pattern n(n+8) + 2.
Look for the relationship x┬▓ + (x * 8) + 2 or simply test the pattern n(n+8) + 2.
Analyze the relationship for 5
If we take x = 5, the logic is 5 * (5 + 8) + 2 = 5 * 13 + 2 = 65 + 2 = 67.
Verify the relationship for 7
If we take x = 7, the logic follows 7 * (7 + 8) + 2 = 7 * 15 + 2 = 105 + 2 = 107. Since 107 is not 93, let us check another logic: 5 * 13 + 2 = 67 and 7 * 13 + 2 = 91 + 2 = 93. The multiplier is fixed at 13 and offset is +2.
Apply logic to 11
Using the identified formula (x * 13) + 2, for 11 we get (11 * 13) + 2 = 143 + 2 = 145.
B: 144 is incorrect as it does not satisfy the formula (11 * 13 + 2). C: 146 is incorrect as it exceeds the calculated result by 1. D: 148 is incorrect as it exceeds the calculated result by 3.
A is correct because the logic follows the pattern (n * 13) + 2, which for n = 11 results in 11 * 13 + 2 = 145.
When number analogies do not fit squares or cubes, always check for linear relationships like (n * constant) +/- offset before moving to complex powers.
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