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The area of the region bounded by the curves $y = \left | x-1 \right |

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Manager
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Joined: 11 Dec 2013
Posts: 121
Location: India
GMAT Date: 03-15-2015
WE: Education (Education)
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The area of the region bounded by the curves $y = \left | x-1 \right |  [#permalink]

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New post 28 Jan 2019, 23:40
4
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A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

27% (02:34) correct 73% (02:14) wrong based on 12 sessions

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The area of the region bounded by the curves \(y = \left | x-1 \right |\) and \(y = \left | 3\right | - \left | x \right |\) is _______ sq. units

A) 2
B) 3
C) 4
D) 5
E) 6

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Joined: 09 Mar 2018
Posts: 997
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Re: The area of the region bounded by the curves $y = \left | x-1 \right |  [#permalink]

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New post 29 Jan 2019, 07:15
4d wrote:
The area of the region bounded by the curves \(y = \left | x-1 \right |\) and \(y = \left | 3\right | - \left | x \right |\) is _______ sq. units

A) 2
B) 3
C) 4
D) 5
E) 6


IMO C

y=|x−1| and y=|3|−|x|

Hear me out on this, Just get the boundary values for the two modulus

y=|x−1| => y = x-1 or y = -x+1 and plot on the graph

by finding boundary values at (0,-1), (0,1) and (1,0)

y=|3|−|x| => y = 3-x or y =-3+x

by finding boundary values at (0,-3), (0,3) and (3,0)

When plotted the points it should look like this > >

We will get two triangles, bounded by 1,0 & 0,1 || 3,0 & 0,3

Area of a triangle 1/2 * 3* 3 - 1/2 * 1* 1

9/2 - 1/2

4
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Re: The area of the region bounded by the curves $y = \left | x-1 \right |   [#permalink] 29 Jan 2019, 07:15
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