Data sufficiency - inequality (p+q-r) vs (p-q+r)
Question
Question: Is (p + q - r) greater than (p - q + r), where p, q and r are integers? Statement-1: (p - q) is positive. Statement-2: (p - r) is negative. 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
Simplify the core question inequality by moving all variables to one side [cite: 3989, 4002]: Is p + q - r > p - q + r ? Subtract p from both sides and combine like terms [cite: 3989, 4002]: Is 2q > 2r \implies Is ⟨MATH⟩q > r⟨/MATH⟩ ?
Now evaluate the data statements based on this simplified target query (micros{q > r}): Statement 1: p - q > 0 \implies p > q. This provides no information about r. Insufficient .
Statement 2: p - r < 0 \implies p < r. This provides no information about q. Insufficient .
Combine both statements: From Statement 1 we have q < p, and from Statement 2 we have p < r. Linking these inequalities yields: q < p < r \implies q < r.
This definitively answers the core question with a firm NO (since q is strictly less than r, not greater)[cite: 3989, 4002]. Because we can formulate a definitive answer, the data is sufficient when combined.
Answer: (c).
Question details
Year
2023
Paper
CSAT
Question
Q57
Section
Data Interpretation & Sufficiency
Sub-topic
Data Sufficiency
Type
Data sufficiency
Difficulty
Medium
Source hint
Data sufficiency
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