Decoding a message using a shifting letter cipher
Question
A Question is given followed by two Statements I and II. Consider the Question and the Statements. P, Q, R and S appeared in a test. Question: Has P scored more marks than Q? Statement-I: The sum of the marks scored by P and Q is equal to the sum of the marks scored by R and S. Statement-II: The sum of the marks scored by P and S is more than the sum of the marks scored by Q and R.
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
Translate the statements into algebraic expressions to evaluate sufficiency:
Statement I: P + Q = R + S. This equation provides relative values between pairs but cannot isolate the individual relationship between P and Q. Insufficient.
Statement II: P + S > Q + R. This inequality alone does not rule out varying magnitudes for S and R. Insufficient.
Combine both statements: Add the equation from Statement I directly to the inequality from Statement II: (P + S) + (P + Q) > (Q + R) + (R + S)
Simplify by grouping terms: 2P + Q + S > Q + 2R + S
Subtract the common variables Q and S from both sides of the inequality: 2P > 2R \implies P > R.
Crucial Analysis: We have deduced P > R. However, the question specifically asks: "Has P scored more marks than Q?". Our deduction (P > R) tells us nothing about how P compares to Q. Thus, the question cannot be answered even when combining both statements.
Answer: (d).
Question details
Year
2024
Paper
CSAT
Question
Q70
Section
Logical & Analytical Reasoning
Sub-topic
Coding & Decoding
Type
Factual single
Difficulty
Medium
Source hint
Letter shifting cipher
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