Data sufficiency - inequality p vs q
Question
Question: Is p greater than q? Statement-1: p × q is greater than zero. Statement-2: p² is greater than q². Which one of the following is correct in respect of the above Question and the Statements?
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 independently for the query "Is p > q?" :
Statement 1: pq > 0. This means p and q share the same mathematical sign (both positive or both negative). It tells us nothing about their relative magnitudes (e.g., could be 3 > 2 or 2 < 3). Insufficient.
Statement 2: p² > q² \implies |p| > |q|. This tells us the absolute value of p is larger, but handles signs ambiguously:
Since both outcomes are possible, Statement 2 alone is insufficient .
Combine both statements: Even when combined, p and q can still be both positive (3 > 2 \rightarrow Yes) or both negative (-3 < -2 \rightarrow No)[cite: 4021, 4022]. The sign ambiguity persists, making the question completely unanswerable.
Answer: (d).
Question details
Year
2023
Paper
CSAT
Question
Q56
Section
Data Interpretation & Sufficiency
Sub-topic
Data Sufficiency
Type
Data sufficiency
Difficulty
Medium
Source hint
Data sufficiency
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