The second number in each number pair is obtained by performing certain operation(s) on the first number, and the same operation(…

Question

The second number in each number pair is obtained by performing certain operation(s) on the first number, and the same operation(s) apply to all pairs except one. Find that odd number pair. (Operations must be on the whole numbers, without breaking the digits.)

1. A. 34 : 44 (Correct answer)
2. B. 23 : 25
3. C. 35 : 36
4. D. 13 : 16

Correct Answer

Option A — 34 : 44

Detailed Solution & Explanation

The correct answer is 34 : 44.

Key Points

• In three pairs the second number is the next perfect square at or above the first: 23→25 (5²), 35→36 (6²), 13→16 (4²).
• For 34 the next perfect square is 36, not 44, so 34 : 44 does not fit.

Additional Information

• When pairs look unrelated, test the standard families in order: perfect squares, cubes, next prime, and ± a constant.
• Squares worth recognising instantly: 16, 25, 36, 49, 64, 81, 100, 121, 144.
• Here the rule is *the next perfect square at or above the first number*, and 34 → 36 breaks only because 44 is offered instead.