EBITDA wrote:
There are 30 socks in a drawer. 60% of the socks are red and the rest are blue. What is the minimum number of socks that must be taken from the drawer without looking in order to be certain that at least two socks of the same colour have been chosen?
A) 2
B) 3
C) 14
D) 16
E) 20
Please explain in detail your answer so that everyone can follow it.
60% of 30 = 18.
So, there are 18 red socks and there are 12 blue socks.
Check out this possible cases once we have selected TWO socks:
case a: 2 red socks, in which case we have a pair of matching socks. DONE!
case b: 2 blue socks, in which case we have a pair of matching socks. DONE!
case c: 1 red sock and 1 blue sock. No matching socks, so we're not done yet.
Since the first 2 cases result in a pair of matching socks, let's focus on case 3 and what happens when we select a 3rd sock.
If we have 1 red sock and 1 blue sock, then the next sock we select will EITHER match the red sock OR match the blue sock.
In both cases, we are guaranteed to have a pair of matching socks.
So, selecting 3 socks guarantees that we have a pair of matching socks.
Answer:
_________________
Test confidently with gmatprepnow.com