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18 Sep 2018, 22:12
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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:
75%
(hard)
Question Stats:
27% (01:55) correct
73%
(02:21)
wrong
based on 11
sessions
History
Date
Time
Result
Not Attempted Yet
If the figure above is a quarter circle and AC is 5, what is the perimeter of the shaded region?
(1) The perimeter of the rectangle ABDF is 14.
(2) AB = 4/5*AF
Attachment:
image009.jpg
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19 Sep 2018, 05:13
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Solution
Given:
- • The radius of the circle = 5
To find:
- • The perimeter of the shaded region
Approach and Working:
Perimeter of the shaded region = length of arc CE + EF + BF +BC
- • Length of arc EC = 2ᴨr/4 = 5ᴨ
• EF = AE – AF = 5 – AF
• FB = AD = 5
• BC = AC – AB = 5 – AB
Thus, the perimeter of the shaded region = 5ᴨ + (5 - AF) + 5 + (5 - AB) = 5ᴨ + 15 – (AB + AF)
Analysing Statement 1
“The perimeter of the rectangle ABDF is 14”
- • Implies, ABDF is a rectangle and 2(AB + AF) = 14
- o AB + AF = 7
Therefore, Statement 1 is sufficient to arrive at a unique answer
Analysing Statement 2
“AB = 4/5 * AF”
- • Perimeter of the shaded region = 5ᴨ + 15 – (AB + AF)
• However, we cannot find the value of AB or AF from the given information
Therefore, Statement 2 is NOT sufficient to arrive at a unique answer
Hence, the correct answer is option A.
Answer: A
19 Sep 2018, 09:20
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EgmatQuantExpert
I think answer is D. because using AB=4/5 AF, we can substitue in AB^2+ AF^2 = 25 and get both AB and AF. and then find the perimeter.
