Question

A man wears gloves of two colours - Red and Green. He has altogether 30 Red Gloves and 10 Green Gloves. Supposing he has to take out Gloves in dark, how many must he take out to be sure that he has a matching pair?

• A. 3
• B. 4
• C. 5
• D. 6

Answer 1

The Correct Option is A

To determine how many gloves the man must take out to ensure he has at least one matching pair, we must consider the worst-case scenario in which every glove picked is of a different color.

Step-by-step Reasoning:

1. The man has two types of gloves: Red and Green.
2. The total number of gloves is not directly important for this problem, since it’s about the worst-case scenario for picking up different colors to ensure a pair.
3. Consider the possibility where he picks one Red Glove and one Green Glove. He still would not have a matching pair as both are of different colors.
4. Thus, the third glove he picks would necessarily be either Red or Green, which means it would have to match one of the two previously picked gloves. This is because there are only two colors available.

Therefore, to ensure that he has at least one matching pair, he must pick out 3 gloves.

The correct choice from the given options is 3.