Select the option that is related to the third number on the same basis as the second number is related o the first number.

126:147:: 138:?

Appeared in: DSSSB - 28 August 2019 (Shift-1)

Explanation

The relationship between the numbers in the analogy is based on a consistent ratio.
In the first pair, 126 and 147 share a common divisor of 21, establishing a 6:7 ratio (126 = 6 × 21; 147 = 7 × 21).
To find the missing number, the same 6:7 ratio must be applied to 138.
First, a new multiplier is found by dividing 138 by 6, which equals 23.
Finally, this new multiplier is applied to the second part of the ratio: 7 × 23 = 161.

Option A: This option does not follow the 6:7 ratio established by the first pair of numbers.
Option C: This number does not result from applying the 6:7 ratio with the multiplier (23) derived from 138.
Option D: This number does not fit the 6:7 pattern. If 156 were the answer, the ratio would be 138:156, which simplifies to 23:26, not 6:7.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Number Analogy and Ratios as background academic context rather than a clinical decision trigger.
While this is a general intelligence question, the underlying skill of logical and proportional reasoning is crucial in nursing.
Nurses use proportional reasoning (ratios) daily for critical tasks like calculating medication dosages, titrating intravenous (IV) drips based on patient weight and desired dose, and converting between different units of measurement (e.g., mg to mcg).
Strong reasoning skills help nurses to quickly identify patterns and anomalies in patient data, leading to better clinical decision-making and improved patient safety.

How to Approach the Question

First, identify the question type as a number analogy, formatted as A:B :: C:?. The goal is to find the rule that links A to B and apply it to C.
Examine the first pair, 126 and 147. Test for simple relationships like addition or subtraction (147 - 126 = 21). Applying this to the second pair gives 138 + 21 = 159, which is not an option.
Next, consider a multiplicative or ratio-based relationship. Find the greatest common divisor (GCD) of 126 and 147, which is 21.
Express the first pair as a ratio using the GCD: 126 = 6 × 21 and 147 = 7 × 21. This confirms a 6:7 ratio.
Apply this 6:7 ratio to the second pair, where 138 corresponds to the '6' part.
Calculate the new multiplier by dividing 138 by 6, which gives 23.

Concept Tested & Keywords

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Practise the full DSSSB - 28 August 2019 (Shift-1)

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