SOLUTION: The no. of ordered pairs (x, y) of positive integers such that x+y=90 and their greatest common divisor is 6 equals A) 15. B) 14. C) 8. D) 10

Question 889795: The no. of ordered pairs (x, y) of positive integers such that x+y=90 and their greatest common divisor is 6 equals
A) 15. B) 14. C) 8. D) 10
Answer by JulietG(1812) (Show Source): You can put this solution on YOUR website!
Let's look at products of 6.
6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90
Which pairs equal 90?
6 + 84
12 + 78
18 + 72
66 + 24
60 + 30
54 + 36
48 + 42
Zero is a NEUTRAL integer. I'm only seeing 7 pairs. Ah, but this is a trick question -- there are actually 14. Do you know why?
.
Reverse the numbers for the ordered pair. Not just {6,84} but also {84,6}, etc.
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