Let A, B, C, D, E be five numbers such that A is greater than C, D is smaller than B, C is greater than B, and A is smaller than E. Which is the smallest number among all?

Appeared in: CGHS SSC - 2018

Explanation

The problem requires ordering five numbers based on a set of relative comparisons.
By translating the given statements into inequalities (A > C, C > B, B > D, E > A), we can link them together.
Combining A > C and C > B gives A > C > B.
Adding B > D to this chain results in A > C > B > D.
The final piece of information, E > A, places E at the beginning of the sequence, making the full order E > A > C > B > D.
In this final sequence, D is clearly the smallest number.

Option A: The statement 'A is greater than C' (A > C) and 'C is greater than B' (C > B) shows that C is larger than at least one other number (B).
Option C: The statement 'C is greater than B' (C > B) and 'D is smaller than B' (B > D) directly shows that B is larger than D.
Option D: The statement 'A is greater than C' (A > C) directly proves that A is not the smallest, as it is larger than C.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Logical Reasoning and Ordering as background academic context rather than a clinical decision trigger.
This question tests logical reasoning and analytical skills, which are fundamental for nurses.
Nurses use similar deductive reasoning to prioritize patient care, interpret sequences of changing vital signs, and troubleshoot equipment by systematically eliminating possibilities.
For example, if a patient's blood pressure is dropping (A > B), and their heart rate is increasing (C > D), a nurse must quickly synthesize these data points to identify potential causes like hypovolemia.

How to Approach the Question

First, carefully read all the conditions and translate them from words into mathematical symbols (e.g., 'greater than' becomes '>', 'smaller than' becomes '<').
Look for a common element that can link two or more conditions. Here, 'C' links 'A' and 'B' (A > C and C > B).
Build a chain of relationships by combining the inequalities step-by-step (A > C > B).
Continue to add the remaining conditions (B > D and E > A) to extend the chain until all elements are included.
Once the complete order is established (E > A > C > B > D), read the question again to identify what is being asked (smallest, largest, middle).
Select the option that matches your conclusion from the ordered chain.

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.