4. _________How many factors of 1000 can be divided by 20 without a remainder?
5. _________
The square shown is divided into 4 congruent rectangles. If the
perimeter of the square is 144 units, what is the perimeter of one
of the four congruent rectangles?
6. _________
Two integers have a difference of −18 and a sum of 2. What is the product of the
two integers?
7. _________
The median of a set of consecutive odd integers is 138. If the greatest integer in
the set is 145, what is the smallest integer in the set?
8.
_________
Among all three-digit integers from 100 to 400, how many have exactly one digit
that is an 8?
9. _________
Ben and Dan are two of the members on the school’s chess team. In a
tournament against their rival team, Ben played exactly 1 out of every 4
games. Dan, who played more games, played 14 games. What is the largest
number of games the team could have played?
10. ________
Peter Pedals rode his bike a total of 500 miles in five days.
Each day he rode 10 more miles than he had ridden on the
previous day. How many miles did Peter ride on just the fifth
day?
sq in
Outcome
# of Occurrences
1
14
2
5
3
9
4
7
5
7
6
8
%
units
miles
$
factors
integers
games

MATHCOUNTS 2008-2009
24
Warm-Up 2
1. _________
A pattern of equilateral triangles will be made from
matchsticks, as shown. One whole matchstick is used
per side on each triangle. If the pattern is extended
and uses exactly 77 matchsticks, how many triangles
will be formed?
2. _________
The ratio of the length of a rectangular room to its width is 5:3. The perimeter of
the room is 48 feet. What is the area of the room?
3. _________What is the greatest perfect square that is a factor of 7! ?
4. _________
A standard six-sided die with its faces numbered 1 to 6 is rolled once, and a dime
is tossed once. What is the probability of rolling a number less than 3 and tossing a
tail? Express your answer as a common fraction.
5. _________
In a recent survey of 300 students, 152 students had at least one dog,
120 students had at least one cat, and 46 students had at least one cat
and at least one dog. How many of the surveyed students did not
have either a cat or a dog?
6. _________
Alicia’s average score on her five tests is 88 points. The score range for each test
is 0 points to 100 points, inclusive. What is the lowest possible score that Alicia
could have earned on one of the five tests?
7. _________
The numerical value of a particular square’s area is equal to the numerical value of
its perimeter. What is the length of a side of the square?
8.
_________
When converted to be in the same unit of measure, what is the ratio of 4 cm to
1 km? Express your answer as a common fraction.

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