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GATE 2017 ME (ME1) – Question 8

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 2 marks · Multiple choice

Let $S_1$ consist of $(x,y)$ satisfying $|x-1|\leq2$, $|y+2|\leq3$. Let $S_2$ satisfy $x-y\geq-2$, $y\geq1$, $x\leq3$. Find the area of $S=S_1\cup S_2$.

  1. 26
  2. 28
  3. 32
  4. 34

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Correct answer: (C) 32

Explanation

The first set is the rectangle $-1\leq x\leq3$, $-5\leq y\leq1$, of area $4(6)=24$. The second is the triangle $1\leq y\leq x+2$ with vertices $(-1,1),(3,1),(3,5)$, of area $4(4)/2=8$. They intersect only on the segment $y=1$, which has zero area. The union area is $24+8=32$, C.

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