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PriyankaPalit7
Joined: 28 May 2018
Last visit: 13 Jan 2020
Posts: 117
Own Kudos:
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Location: India
Schools: ISB '21 (A)
GMAT 1: 640 Q45 V35
GMAT 2: 670 Q45 V37
GMAT 3: 730 Q50 V40
04 May 2019, 00:03
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
52% (02:25) correct
48%
(02:34)
wrong
based on 79
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The figure above shows two right triangles ΔPSR and ΔPRQ that share a common side PR, which measures 5 units. If QR = 4PS, what is the area of the quadrilateral PQRS?
(1) The area of ΔPSR is 6 square units
(2) The area of ΔPRQ is 30 square units
(1) The area of ΔPSR is 6 square units
(2) The area of ΔPRQ is 30 square units
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04 May 2019, 00:14
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PriyankaPalit7
Let, PS = x
i.e. QR = 4x
Question: Area of PQRS = ?
Statement 1: The area of ΔPSR is 6 square units
Let, RS = y
i.e Area of the Triangle PSR \(= (1/2)x*y = 6\)
i.e. \(x*y = 12\)
and \(x^2 + y^2 = 5^2\)
Solving the above two equations we will get INTERCHANGEABLE SOLUTIONS of x and y
i.e. first solution (x, y) = (3, 4)
i.e. Second solution (x, y) = (4, 3)
Hence, we get multiple values for side QR which may be 3*4 pr 4*4 hence rendering different area of PQRS therefore
NOT SUFFICIENT
Statement 2: The area of ΔPRQ is 30 square units
i.e. \((1/2)5*QR = 30\)
i.e. \(QR = 12\)
i.e. \(PS = 12/4 = 3\)
i.e. Area of ΔPSR = (1/2)*3*4 = 6
i.e. PQRS = 30+6 = 36
Hence we get unique area of PQRS therefore
SUFFICIENT
Answer: Option B
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