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# If AD = 3x, AE = 5x, EB = y and DC = 5y, what is the ratio of the area

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Joined: 02 Sep 2009
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If AD = 3x, AE = 5x, EB = y and DC = 5y, what is the ratio of the area  [#permalink]

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21 Aug 2018, 06:03
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Difficulty:

15% (low)

Question Stats:

91% (01:28) correct 9% (02:31) wrong based on 41 sessions

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If AD = 3x, AE = 5x, EB = y and DC = 5y, what is the ratio of the area of triangle DEC to the area of rectangle ABCD ?

Note: Figure not drawn to scale

A. 2:7
B. 1:3
C. 2:5
D. 1:2
E. 3:5

Attachment:

GMAT_PS_Magoosh_15.png [ 3.18 KiB | Viewed 896 times ]

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Re: If AD = 3x, AE = 5x, EB = y and DC = 5y, what is the ratio of the area  [#permalink]

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21 Aug 2018, 06:17
Area of triangle DEC = 1/2*AD*DC ( AD will be the height of the triangle)
DEC = 1/2*5Y*3X = 15XY/2

Now area of rectangle ABCD = AD*DC = 5Y*3X = 15XY

The ratio becomes 15XY/2 : 15XY
Which is equal to 1:2

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Re: If AD = 3x, AE = 5x, EB = y and DC = 5y, what is the ratio of the area  [#permalink]

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21 Aug 2018, 23:05

Solution

Given:
• In the given figure, AD = 3x, AE = 5x, EB = y and DC = 5y

To find:
• The ratio of the area of triangle DEC to the area of rectangle ABCD

Approach and Working:
• The area of the triangle DEC = ½ x DC x AD = ½ x 5y x 3x
• The area of the rectangle ABCD = DC x AD= 5y x 3x
• Hence, the ratio = (½ x 5y x 3x): (5y x 3x) = ½: 1 = 1: 2

Hence, the correct answer is option D.

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Re: If AD = 3x, AE = 5x, EB = y and DC = 5y, what is the ratio of the area   [#permalink] 21 Aug 2018, 23:05
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