From the following options, three options are similar in a certain pattern and one is different from them. Choose the option that is different from the rest.

Appeared in: CGHS SSC - 2018

Explanation

128 is the only number in the set that does not follow the algebraic pattern n3 + n.
The other numbers fit this pattern: 30 = 33 + 3, 68 = 43 + 4, and 222 = 63 + 6.
Alternatively, 128 is a perfect power of 2 (27), while the other numbers are products of multiple distinct prime factors, making it unique.

Option A: This option is incorrect because 222 follows the established pattern n3 + n.
Option C: This option is incorrect because 30 follows the established pattern n3 + n.
Option D: This option is incorrect because 68 follows the established pattern n3 + n.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Odd One Out (Number Classification) as background academic context rather than a clinical decision trigger.
This question assesses logical reasoning and pattern recognition, which are general aptitude skills required in many professional fields, including nursing.
While not a direct clinical question, the analytical skills used to solve it are similar to those needed for interpreting data, identifying trends in vital signs, and recognizing patterns in patient symptoms.
What if the number was 130 instead of 128? In that case, all four numbers would follow the n3 + n pattern (130 = 53 + 5), and a different logic (like powers of 2) would be needed to find an odd one out, or the question would be invalid.

How to Approach the Question

First, examine the given numbers to identify any simple, obvious properties like even/odd, prime/composite, or if they are perfect squares or cubes.
Next, search for a more complex mathematical relationship or pattern that might connect three of the numbers. Common patterns involve arithmetic sequences or algebraic formulas like n2 ± k or n3 ± k.
In this case, test the pattern n3 + n. For n=3, 33+3 = 30. For n=4, 43+4 = 68. For n=6, 63+6 = 222.
Verify if the remaining number fits the pattern. For n=5, 53+5 = 130, which is not 128. This confirms 128 is the outlier.
Consider alternative logics to confirm the answer. Note that 128 is a power of 2 (27), while the others are not, providing a second reason for it being the odd one out.

Concept Tested & Keywords

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Practise the full CGHS SSC - 2018

Attempt every question from this paper in a timed mock, then review the full solution for each one.