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Q5859/80Q60
Q59·CSAT · Prelims 2024

Determining final direction faced after sequential angular turns

ReasoningDirection & DistanceFactual singleMedium

Question

A Question is given followed by two Statements I and II. Consider the Question and the Statements. Question: What are the values of m and n, where m and n are natural numbers? Statement-I: m + n > mn and m > n Statement-II: The product of m and n is 24.

Options

a

The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone

b

The Question can be answered by using either Statement alone

c

The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone

Answer
d

The Question cannot be answered even by using both the Statements together

Explanation

Evaluate each statement for data sufficiency:

Statement I gives m + n > mn alongside m > n. For natural numbers, the inequality m + n > mn is highly restrictive and is only satisfied if at least one number is 1. Given m > n, this forces n = 1, making m + 1 > m, which holds true for any m \ge 2. Because m could be any integer from 2 to infinity, Statement I alone is insufficient.

Statement II states mn = 24. Multiple integer sets fit this rule: (24,1), (12,2), (8,3), (6,4). Insufficient.

Combining both statements: Statement I demands n = 1. Substitute this into Statement II: m × 1 = 24 \implies m = 24. This provides a unique solution: m = 24 and n = 1. Both statements are required together.

For natural numbers, the inequality x+y > xy functions as a structural trap that automatically forces the smaller variable to equal 1.

Answer: (c).

Question details

Year

2024

Paper

CSAT

Question

Q59

Section

Logical & Analytical Reasoning

Sub-topic

Direction & Distance

Type

Factual single

Difficulty

Medium

Source hint

Direction sense calculation

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