If rectangles of area pq are placed at opposite positions in a square of side p+q, how many such rectangles will be present?

Correct answer: 2

The direct answer is C: 2. Divide each side of the square of side p+q into parts p and q. The square then contains four regions: a p-by-p square with area p², a q-by-q square with area q², and two rectangles, each measuring p by q and therefore having area pq. These two rectangles lie in opposite, or diagonal, positions. Option A counts only one of them and misses its matching rectangle. Option B has no basis in the four-part decomposition. Option D counts all four regions, not only the rectangles with area pq. The identity (p+q)² = p² + 2pq + q² gives the same result: the coefficient 2 before pq tells us that there are two pq rectangles. A useful memory cue is that the middle term in a square of a sum comes from two equal cross-rectangles.