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WASHINGTON STATE MATHEMATICS COUNCIL 2000 MIDDLE SCHOOL MATH OLYMPIAD Session II ANSWERS: SEVENTH GRADE NOTE: Take off half-credit
if units were asked for in the question but not provided by the team. |
7 |
Number Sense
1. The
mean is 20. (The 4 #'s are 17, 19, 21, 23. Give 2 points if 4 #'s are given instead of mean.)
2. 143 (Formula
for the nth term
is 3n - 7.)
3. 3 (Note: The cycle is 1-3-9-7.)
4. 24 (Note: 16
multiples of 6 and 12 multiples of 8 less the 4 repeated common multiples of 6 &
8)
5. $30
Measurement
1. 34 (Note: 17 cuts at 2 minutes each.)
2. Wednesday
3. 8
cups or 8
cups
4. 2,464
lbs or 1 ton 464 lbs
5. Thursday,
October 12, at 4:20 a.m. or October 12 at 4:20 a.m.
(Note: 150,000 seconds is 1 day, 17 hours, 40
minutes)
Geometric
Sense
1. 123.6
(if used π button) or 123.8 (if used 3.14 for π) (Answers may include sq. in. label.)
2. 22.5 or 22
3. Any
right triangle with an area of 88 (whose legs multiply to equal 176). Examples are:
4. 304 (Give 2 points for
16 x 19.) (Note: The theater contains 16 rows of 19 seats.)
5. 9
(people)
Probability
& Statistics
1. 30 (5 one-digit numerals and 25 two-digit
numerals)
2. Several
possibilities: e.g., 36, 38, 40, 42, 44, 46 or &nbP 20, 30, 40, 42, 52, 62.
The
two middle numbers must add to 82; the 4 other numbers must add to 164.
3. 1/1,296 or 6/7,776
4. 1/5 or 4/20 or .2 or 20%
5. 96 (60 within-conference games and 36
across-conference games)
Algebraic
Sense
1. 12
2. 20 (20th
place)
3. 6 (ways) (8 cents, 48 cents,
88 cents, 128 cents, 168 cents, and 208cents in 8 cent stamps, with the rest being filled in with 5 cent
stamps)
4. $75
5. 4950
(is the 4-digit number) (Note: 49.50 is the mean of 49 and 50)
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WASHINGTON STATE MATHEMATICS COUNCIL 2000 MIDDLE SCHOOL MATH OLYMPIAD Session II ANSWERS: EIGHTH GRADE NOTE: Take off half-credit
if units were asked for in the question but not provided by the team. |
8 |
Number Sense
1. (a) 1 (Note: day 42)
(b) 6 (Note: days 12, 24, 36, 48, 60,
72) (All 3 girls work out on day 84.)
2. 15
(shots)
3. 1892 (Notes: 442 = 1936; 1936-44=1892)
4. base 3
and base 8 (Notes: base
3 = 64, base 4 = 145, base 5 = 276, base 6 = 469,
base
7 = 736, base 8 = 1089, base 9 =
1,540, base 10 = 2,101)
5. 1 5 15 30 45 51 45 30 15 5 1
1 6 21 50 90 126 141 126 90 50 21 6 1
(Method: Each number in a row is determined by
numbers above it in the previous row. It is the sum of the number directly above it and the two numbers
directly to the left of that
number. If there are no numbers to the
left of that number (or if there is
only 1 number to the left of that number),
then only those 2 (or 1) numbers are summed to get the number in the row
below.)
Measurement
1. 56
yards (Note: 7 yards of length
needed 8 times, filling
the 18' or 216" length by 2'3" width pieces)
2. 400 (hare-leaps)
3. Wednesday
4. 8
cups or 8
cups
5. 14
(groups of rafters) (Note: Groups leaving at 4 a.m. through 5 p.m.)
Geometric
Sense
1. Any
right triangle with an area of 88 (whose legs multiply to equal 176). Examples are:
2. 8,000 (cubes)
3. There
are (at least?) 3 possible answers -- the 7 pointed star at right and the two figures at left:
4. 60 + 6
or 78 or 79 (depending on their calcaultion method)
5. 28 or
28 units
Probability
& Statistics
1. 5/14
or or 10/28 or 20/56 (Give 2 points for 5/28 or 10/56.)
There
are 8 X 7=56 possible ways to choose 2 coins without replacement. Of these 56 ways, there are 20 ways
to get 15 cents:
(2
dime choices for 1st coin) (5 nickel choices for 2nd coin) = 10 choices with
dime 1st,
(5
nickel choices for 1st coin) (2 dimes choices for 2nd coin) = 10 choices with
nickel 1st.
[The 56 possible 2-coin chocies are as
follows. Note that d1 means dime #1, n2 means nickel
#2, etc. The 20 choices that are worth
15 cents are in boldface.]
14 ways with dime first 15 nickel-dime or nickel-quarter ways with nickel first
d1,n1 d2,n1 d1,q n1,d1 n3,d2 n1,q
d1,n2 d2,n2 d2,q n1,d2 n4,d1 n2,q
d1,n3 d2,n3 d1,d2 n2,d1 n4,d2 n3,q
d1,n4 d2,n4 d2,d1 n2,d2 n5,d1 n4,q
d1,n5 d2,n5 n3,d1 n5,d2 n5,q
20
ways with 2 nickels 7 ways with quarter first
n1,n2 n2,n1 n3,n1 n4,n1 n5,n1 q,n1 q,n5
n1,n3 n2,n3 n3,n2 n4,n2 n5,n2 q,n2 q,d1
n1,n4 n2,n4 n3,n4 n4,n3 n5,n3 q,n3 q,d2
n1,n5 n2,n5 n3,n5 n4,n5 n5,n4 q,n4
2. 13
3. (a) 2,073 (items total)
(b) 136 (families had 2 items)
4. Several
possibilities: e.g., 36, 38, 40, 42, 44, 46 or 20, 30, 40, 42, 52, 62.
The
two middle numbers must add to 82; the 4 other numbers must add to 164.
5. 0 (zero) (If 3 men get their hats, the fourth man does too!)
Algebraic
Sense
1. 39
2. $75
3. 61 (day 61)
4. 4950
(is the 4-digit number) (Note: 49.50 is the mean of 49 and 50)
5. 8
(days) (Give 2
points for 8.57 or 
days.)