24. every 12 minutes, bus a completes a trip from p to x
to s to x to p. every 20 minutes, bus b completes a
trip from q to x to t to x to q. every 28 minutes,
bus c completes a trip from r to x to u to x to
r. at 1:00 p. m. , buses a, b and c depart from p, q e-
#t
and r, respectively, each driving at a constant speed,
and each turning around instantly at the endpoint of its
route. each bus runs until 11:00 p. m. at how many times
r
s
between 5:00 p. m. and 10:00 p. m. will two or more buses
arrive at x at the same time?
(a) 18
(b) 19 (c) 20
(d) 21 (e) 22
25. a sequence of positive integers with 2020 terms is called an ft sequence if each term
after the second is the sum of the previous two terms. for example, if the first two
terms of an ft sequence are 8 and 7, the sequence would begin 8, 7, 15, 22, 37,.
for some positive integer m, there are exactly 2415 ft sequences where the first two
terms are each less than 2m and the number of odd-valued terms is more than twice
the number of even-valued terms. what is the value of m?
(a) 21
(b) 69 (c) 115 (d) 35
(e) 105
