Pick the odd one:?

AIIMS Delhi NO - 2018

Reasoning

Hard

Appeared in: AIIMS Delhi NO - 2018

Explanation

The number 196 is the odd one out because it does not follow the 'reverse square' property shared by the other three numbers.
This property states that the square of the reverse of a number's square root must be equal to the reverse of the number itself.
For 196, the square root is 14. The reverse of 14 is 41. The square of 41 is 1681.
The reverse of 196 is 691. Since 1681 is not equal to 691, 196 does not fit the established pattern.

Option A: This option is incorrect because it follows the 'reverse square' pattern. The square root is 11, and its reverse is also 11. The square of 11 is 121, which is the reverse of the original number 121.
Option B: This option is incorrect because it follows the 'reverse square' pattern. The square root is 12, and its reverse is 21. The square of 21 is 441, which is the reverse of the original number 144.
Option C: This option is incorrect because it follows the 'reverse square' pattern. The square root is 13, and its reverse is 31. The square of 31 is 961, which is the reverse of the original number 169.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Logical Reasoning: Identifying the 'Odd One Out' based on mathematical properties as background academic context rather than a clinical decision trigger.
While not a clinical question, this type of logical reasoning assesses analytical and problem-solving skills, which are crucial for nurses.
Nurses use deductive and inductive reasoning daily to assess patient conditions, interpret lab data, and make critical decisions about care.
For example, when a patient's vital signs deviate from their baseline, a nurse must quickly analyze the pattern of changes to identify the underlying cause, similar to finding the 'odd one out' in a set of data.

How to Approach the Question

First, examine all the given numbers to identify any obvious common properties. In this case, all numbers (121, 144, 169, 196) are perfect squares of consecutive integers (11², 12², 13², 14²).
Since a simple property (being a perfect square) applies to all, look for a more complex relationship or a secondary property that links most of the numbers.
Test different logical patterns. One might be palindromes (only 121), but this is a very simple property. A stronger pattern often involves the relationship that makes them a series.
Test the 'reverse square' property, which relates the number to its square root. Calculate if the square of the reversed root equals the reverse of the original number.
Apply this rule to each option systematically: 121 (11² vs 11²), 144 (12² vs 21²), 169 (13² vs 31²), and 196 (14² vs 41²).
Identify the number that fails the test. Here, 196 is the only number where the reverse of the number (691) does not match the square of the reversed root (1681).

Concept Tested & Keywords

Concept Tested: Logical Reasoning: Identifying the 'Odd One Out' based on mathematical properties.
Stem keywords: Pick, odd one
Lead-in keywords: odd one
Negative lead-in flag: false

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