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# In the figure above, LMNO and GHJK are rectangles where GH = 1/2 LM an

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Math Expert
Joined: 02 Sep 2009
Posts: 46048
In the figure above, LMNO and GHJK are rectangles where GH = 1/2 LM an [#permalink]

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26 Sep 2017, 00:22
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Question Stats:

81% (00:38) correct 19% (00:39) wrong based on 26 sessions

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In the figure above, LMNO and GHJK are rectangles where GH = 1/2 LM and HJ = 1/2 MN. What fraction of the region bounded by LMNO is NOT shaded?

(A) 1/4
(B) 1/3
(C) 1/2
(D) 2/3
(E) 3/4

Attachment:

2017-09-26_1116_001.png [ 8.46 KiB | Viewed 632 times ]

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In the figure above, LMNO and GHJK are rectangles where GH = 1/2 LM an [#permalink]

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26 Sep 2017, 00:37

Lets assume values for LM and MN.
LM = 40, MN = 30. Area of this rectangle is 1200

GH =$$\frac{1}{2}LM = 20$$ and $$MN = \frac{1}{2}$$MN to be 15, the area of which is 300

Therefore, the area of LMNO that is not shaded is 1200-300 = 900

Fraction not shaded is $$\frac{900}{1200}(\frac{3}{4})$$ of LMNO(Option E)
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In the figure above, LMNO and GHJK are rectangles where GH = 1/2 LM an [#permalink]

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26 Sep 2017, 13:08
Bunuel wrote:

In the figure above, LMNO and GHJK are rectangles where GH = 1/2 LM and HJ = 1/2 MN. What fraction of the region bounded by LMNO is NOT shaded?

(A) 1/4
(B) 1/3
(C) 1/2
(D) 2/3
(E) 3/4

Attachment:
2017-09-26_1116_001.png

Let
LM = x
MN = y

GH = $$\frac{1}{2}x$$
HJ = $$\frac{1}{2}y$$

$$\frac{1}{2}x$$ * $$\frac{1}{2}y$$ = $$\frac{1}{4}$$(xy)

Area of large rectangle: (xy)

What fraction of the region (area) bounded by LMNO is NOT shaded?

Area$$_{large}$$-Area$$_{shaded}$$=Area$$_{unshaded}$$

$$1(xy) -\frac{1}{4}(xy)$$ = $$\frac{3}{4}(xy)$$

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In the figure above, LMNO and GHJK are rectangles where GH = 1/2 LM an   [#permalink] 26 Sep 2017, 13:08
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