Question: Is (p + q - r) greater than (p - q + r), where p, q and r are integers? Statement-1: (p - q) is…

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?
  1. The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone.
  2. The Question can be answered by using either Statement alone.
  3. The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
  4. The Question cannot be answered even by using both the Statements together.

Solution

The question reduces to: is $(p+q-r) > (p-q+r)$, i.e. is $2q > 2r$, i.e. is $q > r$? Statement 1 gives $p > q$ — no info on q vs r. Statement 2 gives $p < r$ — no info on q vs r. Together: $q < p$ and $p < r$, so $q < r$, giving a definite answer. Both statements together are needed.

Asked in: CSAT 2023

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