A Question is given followed by two Statements I and II. Consider the Question and the Statements. Age of…
A Question is given followed by two Statements I and II. Consider the Question and the Statements. Age of each of P and Q is less than 100 years but more than 10 years. If you interchange the digits of the age of P, the number represents the age of Q.
Question: What is the difference of their ages?
Statement-I: The age of P is greater than the age of Q.
Statement-II: The sum of their ages is 11/6 times their difference.
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
Let P = $10x + y$ and Q = $10y + x$. Statement I alone (P > Q) gives many possibilities, not sufficient. Statement II alone: $P + Q = (11/6)(P - Q)$ gives $11(x+y) = (11/6)(9)(x-y)$, simplifying to $6(x+y) = 9(x-y)$, i.e. $x = 5y$. With single digits, y = 1, x = 5, so P = 51, Q = 15 and the difference is 36 - unique. Hence statement II alone is sufficient, so the answer is that one statement alone suffices but not the other.