REMT 2017
MATHEMATICAL
REASONING
ANSWERS
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LAST NAME
FIRST NAME
GRADE
2017G2
1.
My sock drawer has six red socks and four blue socks. If I grab two socks out of this
drawer at random, what is the probability that I will get a matching pair?
2.
How many distinct 8-letter sequences can be made using the letters in the word
PARALLEL?
3.
What is the last digit of the number 20172017 ?
4.
A box with 100 matches weighs 50 grams. The same box with 50 matches weighs 36
grams. How many grams does the box weigh?
5.
Lou completed a morning bike ride of 36 miles in a time of one hour and 15 minutes.
In the afternoon, Lou took a second ride of 44 miles, which took one hour and 45
minutes. What was Lou's average speed, in miles per hour, for the two rides?
2017G3
6.
A group of five students, two juniors and three seniors, are to be selected to serve on
the School Spirit Committee. These students will be selected from among the five
juniors and seven seniors who volunteered. In how many ways could this committee
be selected?
7.
In the expansion of (x+y+z)10, how many terms are there in which the factor z does
not appear?
8.
If ab = 10, bc = 18, and ca = 20, what is the value of abc ?
9.
The hands of a clock coincide at noon. How many minutes must elapse (exactly)
before they coincide again?
10.
There are a total of 81 foreign language students in a high school where they offer
Spanish, French, and German. There are 21 students who take at least 2 languages at
once. If there are 55 Spanish students, 28 French students, and 24 German students,
how many students take all three languages at once?
2017G4
11.
A ribbon, 0.1 millimeters thick and 25 meters long, is tightly wrapped onto a spool,
giving a roll of diameter 10 centimeters. What is the diameter, in centimeters, to
three significant figures, of the spool?
12.
During a total eclipse of the sun, the apparent diameter of the sun and the moon, as
seen from the earth, are equal. If the distance to the moon is 240,000 miles, and the
distance to the sun is 93,000,000 miles, what is the ratio of the volume of the sun to
the volume of the moon? Express your answer to two significant figures.
13.
Regular gas sells for $3.00 a gallon, and High Octane gas sells for $3.25 a gallon. How
many gallons of High Octane should I add to 4 gallons of Regular to get a mixture
that would cost $3.15 a gallon?
14.
How many feet high is a pole that is 15 feet shorter than a tree that is three times as
high as the pole?
15.
An ichthyologist wishes to count the number of fish in a pond. She puts out a net and
catches 30 fish; these are tagged and returned to the pond. The next day she puts
out another net and this time catches 40 fish, two of which have tags. What is the
best estimate for the number of fish in the pond?