Question

Given below are four statements: \(M\geq X\), \(P<B\), \(B=M\), \(X>Q\). Conclusions: I. \(M\geq Q\), II. \(B>Q\), III. \(P<Q\). Which conclusions follow?

• A. III only
• B. II only
• C. I and II only
• D. II and III only

Hint:

In inequality questions, a conclusion follows only when it is definitely true in all possible cases.

Answer 1

The Correct Option is C

We are given: \[ M\geq X \] and: \[ X>Q. \] Since \(M\geq X\) and \(X>Q\), it is clear that: \[ M>Q. \] Therefore: \[ M\geq Q \] is definitely true. So conclusion I follows. Now we are also given: \[ B=M. \] Since: \[ M>Q, \] we get: \[ B>Q. \] So conclusion II also follows. Now check conclusion III. We are given: \[ P<B. \] But we do not have any fixed direct relation between \(P\) and \(Q\). Since \(B>Q\), and \(P<B\), \(P\) may be greater than, equal to, or less than \(Q\). So conclusion III does not definitely follow. Therefore, mathematically: \[ \text{Only conclusions I and II follow.} \] However, the given options do not contain exactly I and II.