There are 30 socks in a drawer...

[BTGmoderatorLU]

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

The OA is B.

Can any explain in detail this DS question please? Thanks.

[Jay@ManhattanReview]

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

The OA is B.

Can any explain in detail this DS question please? Thanks.

So, we have 60% of 30 = 18 socks of red color and 12 socks of blue color.

Case 1: The first sock is red and the second sock is red. The number of socks to be taken out = 2.

Case 2: The first sock is blue and the second sock is blue. The number of socks to be taken out = 2.

Case 3: The first sock is red, the second sock is blue, and whatever color the third sock is, we either get two socks of the red color or the blue color. We are certain that the socks are of the same color. The minimum number of socks to be taken out = 3.

Since only in Case 3, we are certain that at least two socks of the same color have been chosen, the correct answer is 3.

The correct answer: B

Hope this helps!

-Jay

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[Scott@TargetTestPrep]

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

The OA is B.

Can any explain in detail this DS question please? Thanks.

We see that 30 x 0.6 = 18 socks are red, and 12 are blue.

In order to be certain that two socks of the same color are chosen, we need to choose at least 3 socks. For example, if we first select a red, then we could select a blue, and then in the third selection, regardless of whether we have selected a red or blue sock, we now have a pair.

Answer: B