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23 Jul 2015, 03:10
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
80% (01:16) correct
20%
(01:28)
wrong
based on 147
sessions
History
Date
Time
Result
Not Attempted Yet
Is the area of the top of a rectangular pool larger than 1000 square feet?
(1) The pool's top measures 50 feet diagonally.
(2) One side of the pool's top measures 25 feet.
Kudos for a correct solution.
(1) The pool's top measures 50 feet diagonally.
(2) One side of the pool's top measures 25 feet.
Kudos for a correct solution.
23 Jul 2015, 03:21
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Bunuel
Let, Length of Pool = L
Width of Pool = W
i.e. ARea of Pool = L*B
Question : Is L*B > 1000?
Statement 1: The pool's top measures 50 feet diagonally.
Diagonal = 50
Case-1: L=48, B=14, Area = 672 i.e. Less than 1000
Case-2: L=\(25\sqrt{2}\), B=\(25\sqrt{2}\), \(Area_{Max} = 1250\) i.e. Greater than 1000
CONCEPT: Area of a rectangle for a given Diagonal will be Maximum when the sides of Rectangle are taken equal
NOT SUFFICIENT
Statement 2: One side of the pool's top measures 25 feet.
Second side can be very long or very short. Hence
NOT SUFFICIENT
Combining the two statements:
L^2 + B^2 = 50^2 and L=25
i.e. B can be calculated and the area will be exactly calculated which can definitely be compared with 1000. Hence,
SUFFICIENT
Answer; option C
ENGRTOMBA2018
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Concentration: Finance, Strategy
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23 Jul 2015, 04:18
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Bunuel
Is l*b > 1000 ft^2?
Per statement 1, diag = 50 feet ---> the sides of the rectangle can be 30, 40 feet resp. Thus area = 30*40 = 1200 ft^2 . "Yes"
But if , \(b=10\) ---> \(l = 20\sqrt{6}\) ---->\(l*b = 10*20\sqrt{6}\) = \(200 \sqrt{6}\) < 1000. Thus "No". This statement is not sufficient.
Per statement 2, b =25. Without l, we can not find the area. Thus this statement is not sufficient.
COmbining, we get diag = 50, b =25 ---> \(l = \sqrt{1875}\).
You do not have to calculate the area but only need to know that you will get 1 unique value for the area that will either be a "yes" for >1000 or a definite "no" for >1000.
Either way, both statements are sufficient when combined and hence C is the correct answer.
