The second number in the given number-pairs is obtained by performing certain mathematical operation(s) on the first number. The same operation(s) is/are followed in all the number-pairs, except one. Find that odd number-pair. (NOTE: The relation should be found without breaking down the numbers into its constituent digits)

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Step 1: Analyze the pairs to find a consistent operation.

Check pair 1: 18 : 306
Try multiplication: 18 * 17 = 306 (since 18 * 17 = 306)

Check pair 3: 25 : 650
Try multiplication: 25 * 26 = 650

Check pair 4: 23 : 552
Try multiplication: 23 * 24 = 552

Step 2: Check pair 2: 13 : 182
Try multiplication: 13 * 14 = 182

Step 3: Observe the pattern in multipliers:
For 18, multiplier is 17 (one less than 18)
For 25, multiplier is 26 (one more than 25)
For 23, multiplier is 24 (one more than 23)
For 13, multiplier is 14 (one more than 13)

Step 4: The pattern is inconsistent for pair 1 (multiplier is 17, which is less than 18), but pairs 2, 3, and 4 have multiplier one more than the first number.

Step 5: However, pair 1's multiplier is less by 1, pair 2, 3, 4 multipliers are greater by 1.

Step 6: Since the question states the same operation is followed except one pair, the odd pair is the one that does not follow the pattern of multiplying the first number by (number + 1).

Pairs 2, 3, and 4 follow: second number = first number * (first number + 1)
Pair 1 does not follow this.

Therefore, the odd pair is 18 : 306.

Rechecking calculations:
18 * 19 = 342 (not 306)
18 * 17 = 306

So pair 1 is the odd one out.

Correction: The odd pair is 18 : 306, not 13 : 182.

Final conclusion:
Pairs 2, 3, 4 follow second number = first number * (first number + 1)
Pair 1 does not.

Hence, the odd pair is 18 : 306.

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