Data sufficiency - (p+q)^2-4pq positive
Question
A question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option. Question: Is (p+q)² - 4pq, where p, q are natural numbers, positive ? Statement I: p < q Statement II: p > q 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 can be answered even without using any of the Statements.
Explanation
Expand the given algebraic expression: (p+q)² - 4pq = p² + 2pq + q² - 4pq = (p-q)². Since p and q are natural numbers, the square of their difference is always non-negative (\ge 0). To be strictly positive (⟨MATH⟩> 0⟨/MATH⟩), we only need to ensure that ⟨MATH⟩p \ne q⟨/MATH⟩. Statement I states p < q, guaranteeing p \ne q. Sufficient. Statement II states p > q, also guaranteeing p \ne q. Sufficient.
Answer: (b).
Question details
Year
2025
Paper
CSAT
Question
Q54
Section
Data Interpretation & Sufficiency
Sub-topic
Data Sufficiency
Type
Data sufficiency
Difficulty
Hard
Source hint
Data sufficiency
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