There is a question followed by two statements I and II : Question : If x and y are integers, can we find |x-y| uniquely? I. x2 + y2 = 25 II. x2 - y2 = 7 Which one of the following options is correct?
The question cannot be answered even using any of the statements
Statement I: \(x^2+y^2=25\) has integer solutions (x, y) = (0, ±5), (±5, 0), (±3, ±4), (±4, ±3). These give |x − y| values such as 5, 1 and 7 depending on which pair is taken, so the value is not unique. Statement I alone is insufficient.
Statement II: \(x^2-y^2=7\), i.e., \((x-y)(x+y)=7\). The integer factor pairs of 7 give (x, y) = (4, 3), (4, −3), (−4, 3), (−4, −3), yielding |x − y| equal to either 1 or 7 depending on the pair. Statement II alone is also insufficient.
Combining both: solving \(x^2+y^2=25\) and \(x^2-y^2=7\) together gives \(x^2=16,\ y^2=9\), so x = ±4 and y = ±3. All four sign combinations satisfy both equations simultaneously (since only the squares are fixed), giving |x − y| equal to 1 for (4, 3) or (−4, −3), and 7 for (4, −3) or (−4, 3).
Even together, the two statements do not pin down a unique value of |x − y|. Hence, the question cannot be answered even using both statements together.
Similar Questions
P, Q, R and S are four places. To travel from P to R, one travels via Q and to travel from P to S, one travels via both Q and R. Between P and Q, there are 3 routes; between Q and R, there are 4 routes; and between R and S, there are 5 routes. The time taken to travel through these routes is exhibited on the following chart in hours for a specific vehicle :
Routes Between P and Q Between Q and R Between R and S 1 2 1 2 2 3 1.5 2 3 4 2 2.5 4 - 2 3 5 - - 3.5 How many possible routes are there if the journey takes exactly 7 hours?
Important Questions from Quant Based Puzzle
A number is subtracted from 4 times of it and then, the number obtained is added to its (the resultant’s) next number. If this gives the answer as 91, what was the original number?
When twice of a number added to 3 is multiplied by 5 and added to the number itself, it gives 158. What is the square of that number?
In a class of 72 students, the number of boys is twice the number of girls. Find the number of boys.
Two years ago, T was twice as old as P. P is thrice as old as R. In five years, P will be 29. What is the present age of T?
When a number is added to its multiple of 5 and its square, the sum of these three numbers is 91. Find the number.
