A Question is given followed by two Statement I and II. Consider the Question and the Statements. A person…
A Question is given followed by two Statement I and II. Consider the Question and the Statements. A person buys three articles p, q and r for Rs 50. The price of the article q is Rs 16 which is the least.
Question: What is the price of the article p?
Statement-I: The cost of p is not more than that of r.
Statement-II: The cost of r is not more than that of p.
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
Since $p + q + r = 50$ and $q = 16$, we have $p + r = 34$. Statement I alone ($p \le r$) is not sufficient; Statement II alone ($r \le p$) is not sufficient. Combining, $p \le r$ and $r \le p$ gives $p = r$, so $p = r = 17$. Hence both statements together are required.