Question

Which option has all four parts, that belong to the disc shown on the left? 

• A. A
• B. B
• C. C
• D. D

Hint:

In division and arrangement problems, carefully compare each piece to determine which options contain all the required parts.

Answer 1

The Correct Option is A

A quick way to check this is to see if the four pieces click back together into the original disc, edge to edge.

1. Option A: Lining up the straight edges of these four pieces closes them into one complete circle with no gap or overlap. The outer curved edges trace one continuous boundary too.
2. Option B: One straight edge in this set is a different length than its matching neighbor needs to be. The pieces cannot be pushed together without leaving a sliver of space.
3. Option C: Two of the pieces here have straight edges that do not meet at the same angle as the rest. Trying to close this set into a circle leaves an overlap.
4. Option D: A piece in this group has an outer curve that bulges more than the others. The reassembled boundary would not form a smooth single circle.

Only the pieces in option A close edge to edge into one smooth disc with no gaps or overlaps.

the correct answer is Option A.

Answer 2

Another check is whether the four pieces, together, account for exactly the full area of the original disc, no more and no less.

1. Option A: The four pieces here are proportioned as quarters of the same disc. Adding their areas together accounts for the whole disc, with nothing left over and nothing doubled up.
2. Option B: One piece in this set is larger than its counterpart from the original disc. The total area of these four pieces would exceed the area of the original disc.
3. Option C: Two of the pieces here are thinner than their true counterparts. The combined area of this set falls short of the original disc's full area.
4. Option D: A piece in this group duplicates a slice already covered by another piece. The total area double counts part of the disc.

Since the four pieces in option A add up to exactly the disc's full area with no overlap or shortfall, that is the correct set.

the correct answer is Option A.