A Question is given followed by two Statements I and II. Consider the Question and the Statements. P, Q, R…
A Question is given followed by two Statements I and II. Consider the Question and the Statements. P, Q, R and S appeared in a test.
Question: Has P scored more marks than Q?
Statement-I: The sum of the marks scored by P and Q is equal to the sum of the marks scored by R and S.
Statement-II: The sum of the marks scored by P and S is more than the sum of the marks scored by Q and R.
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 ($P + Q = R + S$) does not tell whether P > Q. Statement II alone ($P + S > Q + R$) also does not. Combining: from I, $P - Q = R - S$; from II, $P - Q > R - S$ - this combination still does not definitely establish whether P scored more than Q. Hence the question cannot be answered even using both statements together.