NIMCET 2013 Logical Reasoning Question 76 with Solution

Question 76

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 in the changed setting, which of the following could have been the original setting?

(A) A ON, B ON, C ON

(B) A ON, B OFF, C ON

(C) A OFF, B ON, C OFF

(D) A OFF, B OFF, C ON

View Dynamic Solution & Explanation ▼

Correct Solution: Option B

Step-by-step Solution:

Quick Solution & Analysis

Important Note: Based on a logical step-by-step analysis of the rules, the correct answer appears to be Option B. The answer key in the image marking "Correct: C" seems to be an error. The explanation below shows the correct deduction.

This is a "working backwards" puzzle. We are given the final state and need to find the initial state that would lead to it. The easiest way to solve this is to test each option as a potential "original setting" and apply the forward-moving rules.

Target Final State: "only B is ON" => { A OFF, B ON, C OFF }

Testing the Options

A. If the original setting was {A ON, B ON, C ON}:This matches the condition for Rule (iii). The rule says "change C to OFF".
The result would be {A ON, B ON, C OFF}. (This does not match our target).
B. If the original setting was {A ON, B OFF, C ON}:This state does not match the specific conditions of rules (i), (ii), or (iii). Therefore, it falls under the "catch-all" Rule (iv). The rule says to flip all switches.
- A (ON) flips to OFF.
- B (OFF) flips to ON.
- C (ON) flips to OFF.
The result is {A OFF, B ON, C OFF}. (This is a perfect match for our target state.)
C. If the original setting was {A OFF, B ON, C OFF}:This is an "other situation", so Rule (iv) applies. We flip all switches.
The result would be {A ON, B OFF, C ON}. (This does not match our target).
D. If the original setting was {A OFF, B OFF, C ON}:This is an "other situation", so Rule (iv) applies. We flip all switches.
The result would be {A ON, B ON, C OFF}. (This does not match our target).

Final Answer: The only original setting that results in the changed setting of "only B is ON" is A ON, B OFF, C ON.