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505-555 (Easy)|   Geometry|      
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What is the width of MN of rectangle MNOP? 31 Jan 2016, 07:22
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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)!

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15% (low)

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83% (00:54) correct 17% (01:00) wrong based on 93 sessions

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What is the width of MN of rectangle MNOP?

(1) OP = x + 4
(2) The area is 48

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D
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What is the width of MN of rectangle MNOP? 31 Jan 2016, 23:48
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Bunuel

What is the width of MN of rectangle MNOP?

(1) OP = x + 4
(2) The area is 48

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option 1: 4x-2=x+4
So x=2

option 2: 8(4x-2)=48
So x=2

Option D
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What is the width of MN of rectangle MNOP? 01 Feb 2016, 07:25
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Bunuel

What is the width of MN of rectangle MNOP?

(1) OP = x + 4
(2) The area is 48

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Question : MN = 4x-2 = ?

Statement 1: OP = x + 4
From Figure, OP = MN (Opposite sides of a rectangle)
i.e. MN = 4x-2 = x+4
i.e. x = 2
i.e. MN = 4*2-2 = 6
SUFFICIENT

Statement 2: The area is 48
Area = (4x-2)*8 = 48
i.e. x = 2
i.e. MN = 4*2-2 = 6
SUFFICIENT

Answer: option D
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What is the width of MN of rectangle MNOP? 01 Feb 2016, 23:18
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Answer should be D.

Option 1

Rectangle: OP=MN Hence, 4x-2=x+4 --->x=2; Sufficient

Option 2

Area of Rectangle = MN*MP = 8*(4x-2) = 48--->x=2; Sufficient
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What is the width of MN of rectangle MNOP? 03 Feb 2016, 01:19
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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

What is the width of MN of rectangle MNOP?

(1) OP = x + 4
(2) The area is 48


In the original condition, there is 1 variable(x), which should match with the number of equations. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
For 1), in 4x-2=x+4, x=2 is derived, which is unique and sufficient.
For 2), in (4x-2)8=48, x=2 is derived, which is unique and sufficient.
Therefore, the answer is D.


-> For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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What is the width of MN of rectangle MNOP? 17 Mar 2023, 10:54
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