REMT 2014
MATHEMATICAL
LOGISTICS
ANSWERS
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LAST NAME
FIRST NAME
GRADE
2014H2
1.
Six years ago, John was twice as old as Mary. In four years, Mary will be two-thirds
as old as John. How old is Mary now?
2.
If f(x+1) = x2+1, what is f(x+2) ?
3.
What is the smallest positive integer n with the property that
2n+3n > 1,000,000,000 ?
4.
Four couples are to be seated in a row of eight seats. In how many ways can they be
seated if each couple is to be seated together?
5.
A right triangle has sides of length c, c2, and c3, where c is a real number with
0 < c < 1. What is the value of c ?
2014H3
6.
Let f(x) = x3 – 3x2 + 3x – 9 . Find the value of x for which f -1(x) = 0 .
7.
M and N are real numbers such that when 5x4 + 4x3 + 3x2 + Mx + N is divided by
x2 + 1, the remainder is 0. What is the value of M-N ?
8.
Evaluate the sum 20142 – 20132 + 20122 – 20112 + … + 42 – 32 + 22 – 12 .
9.
Tom can whitewash a fence in 8 hours. Tom and Becky, working together, can do the
job in 3 hours, but it takes Becky and Huck, working together, 4 hours. How many
hours will it take Huck, working alone, to whitewash this fence?
10.
The algebra equation at right comes from a math book on
the planet Altair Four, where the inhabitants do all their
arithmetic in base eight. What is the solution to this
equation, in base eight?
21x – 67 = 7x + 113
2014H4
11.
In a survey, a group of 150 people were asked whether they like chocolate ice cream
and whether they like strawberry ice cream. Of these people 96 said they like
chocolate, 78 said they like strawberry, and 49 said they like both. What is the
probability that a randomly selected person from this group likes neither chocolate
nor strawberry?
12.
A cylindrical water tank is 100 inches in diameter. If 5000 gallons of water are
poured into the tank, how many inches deep, to the nearest inch, will the water be in
the tank? Note: one gallon is 231 cubic inches.
13.
If x#y = x+y+xy, what is the value of 3#4#5?
14.
Expand the expression (x+y+z)10 and collect all like terms. Then remove all terms
that contain an explicit factor of y. What is the sum of all the coefficients of the
remaining terms?
15.
A chemist has a 1-liter beaker that is 3/4 filled with fluid X, and a second 1-liter
beaker that is 2/3 filled with fluid Y. The chemist pours as much as possible of the
fluid Y into the first beaker, thoroughly stirs the mixture, and then pours as much as
possible of this mixture into the second beaker. How many liters of fluid Y are now
in the second beaker?