Question

A group of 200 people are chosen randomly at a conference. Later, it was found that 120 of them like blue pens and 140 like green pens while 70 like both green and blue pens. Determine the number of people thus chosen who like neither green nor blue pens?

• A. 20
• B. 12
• C. 10
• D. 25
• E. 27

Hint:

Use inclusion-exclusion: $n(A \cup (b) = n((a) + n((b) - n(A \cap (b)$.

Answer 1

The Correct Option is C

Step 1: Total = 200. Like blue = 120, like green = 140, like both = 70.
Step 2: Like blue or green = $120 + 140 - 70 = 190$.
Step 3: Like neither = $200 - 190 = 10$.
Step 4: Final Answer: 10.