2014-11-14 09:00:49

10 < xy < 30
x + y < 9

If x and y are positive integers that satisfy the above conditionals where x > y, what is one possible value of x - y ?

The correct answer is 4, 2, 1
Explanation: The best way to do this is to guess and check on the numbers. Start with the second rule, that x + y < 9, and make a list of possible values, remembering that x has to be greater than y:

(x, y) = (7, 1), (6, 2), (6, 1), (5, 3), (5, 2), (5, 1), (4, 3), (4, 2), (4, 1), (3, 2), (3, 1), (2, 1)

Next, see which of those pairs would create a product between 10 and 30:

(7, 1): 7 x 1 = 7: No
(6, 2): 6 x 2 = 12: Yes
(6, 1) : 6 x 1 = 6: No
(5, 3): 5 x 3 = 15: Yes
(5, 2): 5 x 2 = 10: No
(5, 1): 5 x 1 = 5: No
(4, 3): 4 x 3 = 12: Yes
(4, 2): 4 x 2 = 8: No
(4, 1): 4 x 1 = 4: No
(3, 2): 3 x 2 = 6: No
(3, 1): 3 x 1 = 3: No
(2, 1): 2 x 1 = 2: No

Thus, three pairs work: (6, 2), (5, 3), and (4, 3).

The question asks for x - y, and x - y could thus equal 4, 2, or 1. Any one of those would be acceptable.