Bunuel wrote:

In the rectangle above, the shaded square regions A and B are to be folded along lines PQ and RS respectively onto rectangular region X. What will be the area, in square inches, of the part of A that overlaps with B?

(A) 5

(B) 10

(C) 15

(D) 20

(E) 25

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Great question. A little slippery. The figure and my diagram are not to scale.

The middle portion,

X, is wider than the two squares on the end, though it does not look that way.

1) Find the middle portion's length.

Squares A and B have side length 5 each, total of 10. Rectangle length is 17.

(17 - 10) = 7 = middle region's length

2) Track on where the fold of each square lands (on the diagram, where each square's edge lands is marked in color):

-- When square A is folded over, 7 - 5 = 2 inches remain on the right side of the middle region

So when square B is folded over . . .

B has side length of 5 inches. 2 of those 5 inches will

not overlap with A

-- When square B is folded over, 7 - 5 = 2 inches remain on the left side of the middle region

Exactly as above. A has side length of 5 inches

2 of A's 5 inches in length will

not overlap with B

3) Area, in square inches, of the part of A that overlaps with B (on diagram, gray area)?

Length of overlap: 7 - 2 - 2 = 3

Area of overlap, L = 3, height is 5:

(3 * 5) = 15

ANSWER C

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