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In square ABCD, E is a point on side CD.
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30 Apr 2023, 23:13
30 Apr 2023, 23:13
Expert Reply
00:00
Question Stats:
63% (01:02) correct
36% (01:42) wrong based on 22 sessions
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Attachment:
GRE square shaded region.jpg [ 10 KiB | Viewed 2079 times ]
In square ABCD, E is a point on side CD.
Quantity A |
Quantity B |
Area of the shaded region |
Area of the unshaded region |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
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Re: In square ABCD, E is a point on side CD.
[#permalink]
28 May 2023, 01:29
28 May 2023, 01:29
1
Expert Reply
OE
Let us draw a perpendicular from E which intersects AB at F.
GRE square (3).jpg [ 18.61 KiB | Viewed 1884 times ]
Since ABCD is a square, EF divides it into two rectangles BCEF and FEDA.
As we know that a diagonal divides the rectangle into two equal areas.
So, BE being a diagonal of BCEF divides it in two equal regions, say X.
Similarly, AD being a diagonal of FEDA divides it into two equal regions, say Y.
GRe square 2.jpg [ 23.66 KiB | Viewed 1869 times ]
Area of the shaded region X + Y
Area of the unshaded region X + Y
C is the answer
Let us draw a perpendicular from E which intersects AB at F.
Attachment:
GRE square (3).jpg [ 18.61 KiB | Viewed 1884 times ]
Since ABCD is a square, EF divides it into two rectangles BCEF and FEDA.
As we know that a diagonal divides the rectangle into two equal areas.
So, BE being a diagonal of BCEF divides it in two equal regions, say X.
Similarly, AD being a diagonal of FEDA divides it into two equal regions, say Y.
Attachment:
GRe square 2.jpg [ 23.66 KiB | Viewed 1869 times ]
Area of the shaded region X + Y
Area of the unshaded region X + Y
C is the answer
gmatclubot
Re: In square ABCD, E is a point on side CD. [#permalink]
28 May 2023, 01:29
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