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26 Sep 2017, 23:22
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C
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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
Attachment:
2017-09-27_1015_001.png [ 5.88 KiB | Viewed 2335 times ]
27 Sep 2017, 07:53
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Bunuel
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
Attachment:
2017-09-27_1015_001.png
The answer is C
when the Square A overlaps rectangle PR then the length of the region not overlapped is 2.
Similarly the length of the region not overlapped by B is 2 so the area overlapped will have length 3 so the area would be 3*5=15
27 Sep 2017, 12:00
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Bunuel
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
Attachment:
The attachment 2017-09-27_1015_001.png is no longer available
Attachment:
trifold.png [ 9.28 KiB | Viewed 1964 times ]
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
