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
- There are deers and peacocks in a zoo. By counting heads they are 80. The number of their legs is 200. How many peacocks are there?
- A certain number of horses and an equal number of men are going somewhere. Half of the owners are on their horses' back while the remaining ones are walking along leading their horses. If the number of legs walking on the ground is 70, how many horses are there?
- A, B, C, D and E play a game of cards. A says to B, "If you give me three cards, you will have as many as E has and if I give you three cards, you will have as many as D has". A and B together have 10 cards more than what D and E together have. If B has two cards more than what C has and the total number of cards be 133, how many cards does B have?
- A player holds 13 cards of four suits, of which seven are black and six are red. There are twice as many diamonds as spades and twice as many hearts as diamonds. How many clubs does he hold?
There are fourteen teams playing in a tournament. If every team plays one match with every other team, how many matches will be played in the tournament?
