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16 Jun 2020, 06:52
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
65% (02:27) correct
35%
(02:52)
wrong
based on 99
sessions
History
Date
Time
Result
Not Attempted Yet
What fraction of the square ABCD above, where AE = EB, is shaded?
A. 1/6
B. 1/5
C. 1/4
D. 1/3
E. 1/2
Are You Up For the Challenge: 700 Level Questions
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2020-06-16_1748.png [ 38.12 KiB | Viewed 6937 times ]
16 Jun 2020, 23:46
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I want to share a simple solution WHICH DOES NOT INVOLVE MAKING ANY SKETCH/DIAGRAM, but a tiny little imagination.
The shaded area is ‘less than triangle ADC’ therefore less than ½ of area of square.
Imagine diagonal line joining Point D and B. Let us say the point of intersection of two diagonals is O.
Now, the shaded area is ‘more than triangle DOC’ therefore more than ¼ of area of square.
Out of 5 options, how many options have value between ½ and ¼ ? Just 1/3.
The shaded area is ‘less than triangle ADC’ therefore less than ½ of area of square.
Imagine diagonal line joining Point D and B. Let us say the point of intersection of two diagonals is O.
Now, the shaded area is ‘more than triangle DOC’ therefore more than ¼ of area of square.
Out of 5 options, how many options have value between ½ and ¼ ? Just 1/3.
General Discussion
16 Jun 2020, 07:17
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Bunuel
Answer: Option D
Please check the attachment for explanation. Check the video solution for step-by-step solution (The solution shows the uninformed first attempt at question)
Attachments
Screenshot 2020-06-16 at 7.46.26 PM.png [ 681.48 KiB | Viewed 6576 times ]
16 Jun 2020, 08:08
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Let AC and DE meet at O. So, triangle AOE and triangle COD are similar.
=> Sides and corresponding heights will be in the same ratio.
Say, COD height h1, AOE height h2. => AE/CD = h2/h1 => h2/h1 = 1/2
But, h1+h2 = AD = CD => h2 = (2/3) * CD
Area of triangle COD = 0.5 * h2 * CD = 0.5 * (2/3)*CD * CD = (1/3) * CD^2 = 1/3 * Area of square
Ratio= 1/3
=> Sides and corresponding heights will be in the same ratio.
Say, COD height h1, AOE height h2. => AE/CD = h2/h1 => h2/h1 = 1/2
But, h1+h2 = AD = CD => h2 = (2/3) * CD
Area of triangle COD = 0.5 * h2 * CD = 0.5 * (2/3)*CD * CD = (1/3) * CD^2 = 1/3 * Area of square
Ratio= 1/3
