Question: The area bounded by the curves |x + y| = 1 and |x - y| = 1 is
- 3
- 4
- 2
- 1
- None
Correct Answer: C
Solution and Explanation:
Approach Solution 1:
|x+y|=1 represents two lines: x+y=1 and x+y=-1 --> y=1-x and y=-1-x. Find the x and y intercept of these lines to plot;
|x-y|=1 represents two lines: x-y=1 and x-y=-1 --> y=x-1 and y=x+1. Find the x and y intercept of these lines to plot;
Notice that these lines are mirror images of each other. Here is a square you get when you plot them:
Notice that the diagonal of this square is equal to 2 (the difference between x intercepts). Area of a square is diagonal^2/2=2^2/2=2.
Approach Solution 2:
Another method to solve is:
X+Y=1
-X-y=1
X-y=1
-X+y=1
Output X= +_ 1
Y=+_1
Plot the values of X and Y on graph, you will see the square
Now using pythagoras theorem to find the diagonal,which will be the side of that square.
= Square root 2
Squaring it will be 2
Approach Solution 3:
(1) Derive all equations
|x + y| = 1
eq1: x + y = 1
eq2: x + y = -1
|x - y| = 1
eq3: x - y = 1
eq4: y - x = 1
(2) Plot your graph using x=0 and y=0.
eq1: 0,1 and 1,0
eq2: 0,-1 and -1,0
eq3: 0-1 and 1,0
eq4: 0,-1 and -1,0
(3) You will recognize a region that is a square with a diagonal of 2
(4) Calculate the area.
diagonal= side*√2
side= 2/√2
side= √2
Area= side^2= √2^2= 2
“The area bounded by the curves |x + y| = 1 and |x - y| = 1 is”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.
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