Classification (numbers): Split each 4-digit number into its first two digits and last two digits. Identify the number in which both halves share a special property that the others do not.

Difficulty: Medium

Correct Answer: 3216

Explanation:


Introduction / Context:
Number classification often depends on embedded patterns when a number is split into parts. Here, each 4-digit number can be read as two 2-digit numbers (first two digits and last two digits). We check for a distinctive common property across the halves.



Given Data / Assumptions:

  • Options: 3216, 2338, 3205, 2015.
  • Interpret each as XYZW → (XY) and (ZW).
  • Target property to investigate: powers of 2 among 2-digit numbers.


Concept / Approach:
Powers of 2 within two digits are 16, 32, 64. We check whether each half belongs to this set. If both halves are powers of 2, that number is special compared to the others.



Step-by-Step Solution:

3216 → 32 and 16: both are powers of 2 (32=2^5, 16=2^4).2338 → 23 (not a power of 2), 38 (not a power of 2).3205 → 32 (power of 2), 05 (5, not a power of 2).2015 → 20 (not), 15 (not).


Verification / Alternative check:
You could test divisibility by repeatedly halving the number. 32 and 16 successively half to 1 without remainder; others do not.



Why Other Options Are Wrong:

2338 has neither half as a power of 2.3205 has only one half (32) as a power of 2.2015 has neither half as a power of 2.


Common Pitfalls:
Misreading 05 as 0 or overlooking leading zero formatting. Treat 05 as 5 for the property check.



Final Answer:
3216

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