In a certain sock drawer, there are 4 pairs of black socks, 3 pairs of gray socks and 2 pairs of orange socks. If socks

[V VJesus12]

In a certain sock drawer, there are 4 pairs of black socks, 3 pairs of gray socks and 2 pairs of orange socks. If socks are removed at random without replacement, what is the minimum number of socks that must be removed in order to ensure that two socks of the same color have been removed?

A. 4
B. 7
C. 9
D. 10
E. 11

[spoiler]OA=A[/spoiler]

Source: Magoosh

[S shekki]

it's an easy one. consider the worst case scenario, that everytime we pick a sock, it's a unique colour. so, it will happen for only the first 3 times. the first 3 socks picked can be of any random individual colour. however the 4th sock has to belong to one of the 3 colours as we dont have any other colour option. hence OA 4

[Brent@GMATPrepNow]

In a certain sock drawer, there are 4 pairs of black socks, 3 pairs of gray socks and 2 pairs of orange socks. If socks are removed at random without replacement, what is the minimum number of socks that must be removed in order to ensure that two socks of the same color have been removed?

A. 4
B. 7
C. 9
D. 10
E. 11

[spoiler]OA=A[/spoiler]

Source: Magoosh

If we remove 1 black sock, 1 gray sock, and 1 orange sock, then we still don't have a matching sock. So, we can select 3 socks WITHOUT having a matching pair.
However, if we pick ANY sock for our fourth sock, that sock MUST match one of the first 3 socks selected.

Answer: A

Cheers,
Brent

[Scott@TargetTestPrep]

In a certain sock drawer, there are 4 pairs of black socks, 3 pairs of gray socks and 2 pairs of orange socks. If socks are removed at random without replacement, what is the minimum number of socks that must be removed in order to ensure that two socks of the same color have been removed?

A. 4
B. 7
C. 9
D. 10
E. 11

[spoiler]OA=A[/spoiler]

Solution:

We can remove 1 black, 1 gray, and 1 orange sock first. The next sock selection of any color would ensure that at least one pair of socks of the same color has been removed.

Answer: A

[Scott@TargetTestPrep]

In a certain sock drawer, there are 4 pairs of black socks, 3 pairs of gray socks and 2 pairs of orange socks. If socks are removed at random without replacement, what is the minimum number of socks that must be removed in order to ensure that two socks of the same color have been removed?

A. 4
B. 7
C. 9
D. 10
E. 11

[spoiler]OA=A[/spoiler]

Solution:

We can remove 1 black, 1 gray, and 1 orange sock first. The next sock selection of any color would ensure that at least one pair of socks of the same color has been removed.

Answer: A