sanju09 wrote:In the rectangular coordinate system, is the point (m, n) farther from the origin than point (p, q)?
(1) mn − pq = 12
(2) p + q = 21.
(1) mn − pq = 12
If p = 10, q = 0, m = 4, n = 3, then distance between (4, 3) and (0, 0) = √(4² + 3²) = 5 and distance between (10, 0) and (0, 0) = √(10² + 0²) = 10. Here, point (p, q) is farther from the origin than point (m, n).
If p = 1, q = 1, m = 1, n = 13, then distance between (1, 13) and (0, 0) = √(1² + 13²) = √170 and distance between (1, 1) and (0, 0) = √(1² + 1²) = √2. Here, point (m, n) is farther from the origin than point (p, q).
No definite answer; NOT sufficient.
(2) p + q = 21
If p = 21, q = 0, m = 4, n = 3, then distance between (4, 3) and (0, 0) = √(4² + 3²) = 5 and distance between (21, 0) and (0, 0) = √(21² + 0²) = 21. Here, point (p, q) is farther from the origin than point (m, n).
If p = 18, q = 3, m = 33, n = 2, then distance between (33, 2) and (0, 0) = √(33² + 2²) = √1093 and distance between (18, 3) and (0, 0) = √(18² + 3²) = √333. Here, point (m, n) is farther from the origin than point (p, q).
No definite answer; NOT sufficient.
Combining (1) and (2), we can take the same examples as in statement 2; again NOT sufficient.
The correct answer is
E.
