A Question is given followed by two Statements I and II. Consider the Question and the Statements. Question:…
A Question is given followed by two Statements I and II. Consider the Question and the Statements.
Question: Is (x+y) an integer?
Statement-I: (2x+y) is an integer.
Statement-II: (x+2y) is an integer.
Which one of the following is correct in respect of the above Question and the Statements?
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
Solution
Statement I alone: $2x + y$ integer does not fix x + y (e.g. x = 1.5, y = 2 gives x+y = 3.5 not integer; x = 1, y = 2 gives x+y = 3 integer). Statement II alone is similarly insufficient. Combining: even with both $2x+y$ and $x+2y$ integers, x+y may not be an integer (e.g. x = 1.33, y = 2.33 makes both integers but x+y = 3.66). Hence the question cannot be answered even using both statements together. (The Insights IAS key lists this as C/D; the Vision IAS marked answer D is used here.)