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Q74·CSAT · Prelims 2024

Calculating the new average after altering specific terms in a set

NumericalAveragesFactual single● Medium

Question

A Main Statement is followed by four Statements labelled P, Q, R and S. Choose the ordered pair of the Statements where the first Statement implies the second, and the two Statements are logically consistent with the Main Statement . Main Statement: Pradeep becomes either a Director or a Producer . Statement P: Pradeep is a Director . Statement Q: Pradeep is a Producer . Statement R: Pradeep is not a Director . Statement S: Pradeep is not a Producer.

Options

a

SP only

b

RQ only

c

Both SP and RQ

Answer
d

Neither SP nor RQ

Explanation

The main logical premise is structured as a disjunction: "A or B (D \lor P)". In standard formal propositional logic, a standard "either/or" condition establishes that if one option is explicitly negated, the alternative option must be true (Disjunctive Syllogism).

Let's analyze the pairs provided:

Pair `SP` means Statement S implies Statement P. Statement S indicates "Pradeep is not a Producer" (\neg P). If he is not a producer, he must be a Director, which matches Statement P (D). This is valid logic.
Pair `RQ` means Statement R implies Statement Q. Statement R indicates "Pradeep is not a Director" (\neg D). If he is not a director, he must be a Producer, which matches Statement Q (P). This is also valid logic.

Since both directional sequences represent sound disjunctive logic deductions, option (c) is correct.

For logic gates of the form "Either A or B", the valid deduction path is always \neg A \implies B or \neg B \implies A.

Answer: (c).

Question details

Year

2024

Paper

CSAT

Question

Q74

Section

Numerical Ability

Sub-topic

Averages

Type

Factual single

Difficulty

Medium

Source hint

Average manipulation

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