NIMCET 2015 — Reasoning PYQ

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Question

NIMCET 2015 — Reasoning PYQ

NIMCET | Reasoning | 2015

A drawer contains 10 black and 10 brown socks which are all mixed up. What is the smallest number of socks to be taken from the drawer to decided without seeing them, to be sure that there is atleast one pair of socks of the same colour ?

Choose the correct answer:

Explanation

1. Identify the "Colors" (Holes):

There are only $2$ colors available in the drawer:

Black
Brown

2. Analyze the Worst-Case Scenario:

If you pick $1$ sock, it could be either black or brown.
If you pick $2$ socks, the worst-case is that you get one of each color ( $1$ Black and $1$ Brown). In this case, you do not have a pair yet.

3. The Deciding Pick:

When you pick the $3^{rd}$ sock, it must be either black or brown.
If it is Black, it forms a pair with the first black sock.
If it is Brown, it forms a pair with the first brown sock.

Mathematical Representation:

If there are $n$ colors, the minimum number of items $k$ required to ensure at least one pair is:

k = n + 1

In this case, $n = 2$ (Black and Brown):

k = 2 + 1 = 3

Even though there are $20$ socks in total, you only need to pick $3$ to guarantee a matching pair.

Correct Option: (c) 3