REMT 2011 – MATHEMATICAL LOGISTICS
5:50 AM
Muhammad Yusuf
, Posted in
1. The difference between two
numbers is 45, and the difference between their squares is 3000. What is the
sum of these numbers?
2. Eight people are going to
participate in a tug-of-war match; they have to be divided up into two
four-person teams. In how may different way can this be done?
3. If the expression (x + y + z)10 is expanded, and
all like terms combined, how many terms will the simplified expression contain?
4. What is the smallest perfect
square greater than one million?
5. How many rectangles are there
in this figure?
6. If I toss a fair coin six
times in a row, what is the probability that it will come up heads at least
five out of the six times?
7. How many distinct 10-letter
sequences can be made using the letters of the word
BOOKKEEPER?
8. What rational number,
expressed as a fraction in lowest terms, does the sum 0.7 + 0.72 +
0.73 + 0.74 + … become arbitrarily close to?
9. I was able to cycle up a long
hill at a rate of 18 miles per hour. I came back down the same way at 36 miles
per hour. What was my average speed, in miles per hour, for this ride?
10. A coffee distributor has on
hand 150 pounds of light-roasted coffee that costs $8 per pound. How many
pounds of dark-roasted coffee costing $12 per pound should be mixed with it to
get a medium blend costing $9.50 per pound?
11. A 500-gallon water tank has
two outlet valves. One valve can empty the entire tank in 60 minutes. The other
valve can do the same in 40 minutes. How many minutes will it take to empty the
entire tank if both valves are used?
12. What is the only value of K for which the system
Kx – 3y = 17
5x + 2y = 3
fails to have a solution?
13. If the expression (x + y + z)10 is expanded, and
all like terms combined, how many terms will the simplified expression contain?
14. A certain type of combination
lock has a combination consisting of a sequence of three integers in the range
from 1 to 25. The first and third integers could be either the same as or
different from each other, but the second integer must be different from both
the first integer and the third integer. How many possible combinations are
there for this type of lock?
15. A flower arrangement contains
60 flowers; some of these flowers have 5 petals, and the rest have 8 petals.
Altogether there are 420 petals in the arrangement. How many 5-petaled flowers
are there?
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