METHOD
1: Make a chart: Make
a table that compares sentence 2 against sentence
3 for the interval between 50 and 90.
There are 68 songs on the player.
METHOD
2: Use a simpler problem: A multiple
of 6 is one more than a multiple of 5 immediately
following a common multiple. Following 0, 5 is one
less than 6. Following 30, 35 is one less than 36.
Following 60, 65 is one less than 66. This is between
60 and 90, so 3 more than the multiple is 68, the
same as 2 more than the multiple of 6. The number
of songs is 68.
METHOD
3: Find a pattern: 3 more than
a multiple of 5 ends in 3 or 8. However, 2 more
than a multiple of 6 is an even number, so the number
of songs ends in 8: 58, 68, 78, or 88. Only 68 is
3 more than a multiple of 5 and also 2 more than
a multiple of 6.
(Notice that the least common multiple of 5 and
6 is 30 and that all the numbers satisfying sentences
2 and 3 are 8, 38, 68, 98, 128, and so on.)
