NIMCET 2013 Logical Reasoning Question 75 with Solution

Question 75

Logical Reasoning Puzzles Easy

Direction: Questions are based on the following: There are three switches A, B and C which can be in ON/OFF position. Their settings change as per the following rules: i) If A is the only switch as ON, change B to ON. ii) If A and B are only switches as ON, change C to ON. iii) If all three switches are ON, change C to OFF. iv) For all other situations, all switches in ON are changed to OFF and all switches in OFF are changed to ON If only B is ON, the changed setting will be:

(A) A ON, B ON, C ON

(B) A ON, B ON, C OFF

(C) A ON, B OFF, C ON

(D) A OFF, B OFF, C ON

View Dynamic Solution & Explanation ▼

Correct Solution: Option C

Step-by-step Solution:

Quick Solution

This is a rule-based logic puzzle. The key is to identify the starting configuration of the switches and then find which of the four rules applies to that exact situation.

1. Identify the Initial State and Find the Correct Rule

The problem asks for the outcome when the initial state is: "If only B is ON".
This means the starting configuration is: A is OFF, B is ON, and C is OFF.

Now, we must check the list of rules to see which one matches this state:

Rule: "If A is the only switch as ON..."
This condition (A ON, B OFF, C OFF) does not match our initial state.
Rule: "If A and B are only switches as ON..."
This condition (A ON, B ON, C OFF) does not match our initial state.
Rule: "If all three switches are ON..."
This condition (A ON, B ON, C ON) does not match our initial state.
Rule: "For all other situations..."
Since none of the specific conditions in rules (i), (ii), or (iii) were met, our state falls into the category of "all other situations". This is the rule we must apply.

2. Apply the Rule to Find the Final State

- Since our initial state falls under the condition for Rule (iv), we must follow its instruction.
- The instruction is: "all switches in ON are changed to OFF and all switches in OFF are changed to ON". This means we must flip the state of every switch.

- We start with {A OFF, B ON, C OFF} and apply the change:

A changes from OFF to ON.
B changes from ON to OFF.
C changes from OFF to ON.

Final Answer: The changed setting will be A ON, B OFF, C ON.