Q163 / 270 · NDA 2021 (Phase 2) · Mathematics

Suppose set $A$ consists of first 250 natural numbers that are multiples of 3 and set $B$ consists of first 200 even natural numbers. How many elements does $A \cup B$ have?

  • A
    324
  • B
    364
  • Correct answer
    C
    384
  • D
    400

Solution

$\begin{aligned} & \mathrm{A}=\{3,6,9, \ldots 750\} \\ & n(\mathrm{~A})=250 \\ & \mathrm{~B}=\{2,4,6, \ldots 400\} \\ & n(\mathrm{~B})=200 \\ & \mathrm{~A} \cap \mathrm{~B}=\{6,12, \ldots 396\} \\ & n(\mathrm{~A} \cap \mathrm{~B})=66 \\ & \therefore n(\mathrm{~A} \cup \mathrm{~B})=n(\mathrm{~A})+n(\mathrm{~B})-n(\mathrm{~A} \cap \mathrm{~B}) \\ & =250+200-66=384\end{aligned}$

Hence, the correct answer is option: 'C'.

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