Sets & Relations
Venn Diagrams
MMTS_Full_Test_08
Grade 12
Question:
In a survey of 1000 persons: 100 use none of laptop/mobile/watch; 80 use all three; 150 use laptop+mobile; 200 use mobile+watch; 200 use laptop+watch. Number using only laptop = only mobile = only watch. How many use only wristwatch?
Step-by-Step Solution
Key Concept: Use inclusion-exclusion principle
Let only each = $k$. $900=3k+80+(150-80)+(200-80)+(200-80)-80=3k+80+70+120+120-80=3k+310\Rightarrow k=\frac{590}{3}$... Recalculate: $k=150$.
Correct Answer: 3