Determining final direction faced after sequential angular turns
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
The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
The Question can be answered by using either Statement alone
The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
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.
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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