2015 Shoreline Math Olympiad
(Answer Key)
Fourth Grade - Individual Test 1
Problem
Number Answer Explanation
1 A
2 A
3 D 100 + 1,000 + 10,000 = 11,100
4 B Possible pairs of factors: 1 & 24, 2 & 12, 3 & 8, 4 & 6. Only 2 + 12 or 14 is listed in choices. 5 B 9 feet = 3 yards; 3 yards x $0.30/yd = $0.90
6 C
7 C 1 quart = 2 pints = 4 cups
8 D Prime numbers between 10 and 20 are 11, 13, 17, 19, therefore 4 prime numbers. 9 B 20 (even #s) – 10 (mult. Of 4s) = 10
10 C 5/2 = 2.5, thus there are 25.
11 C 12 – 8 = 4 more gray tiles in one room; 4 x 10 rooms = 40 more gray tiles.
12 C Area of shaded rectangle: 5 x 6 or 30 sq. cm. Area of ABCD: 8 x 20 or 160 sq. cm. Thus, fractional part: 30/160 or 3/16.
13 D The least common multiple of 3, 4, and 5 is 60. 14 C Coins found: 1 quarter, 2 dimes, 2 nickels.
2015 Shoreline Math Olympiad
(Answer Key)
Fourth Grade - Individual Test 2
Problem
Number Answer Explanation
1 C
2 B
3 B
4 A 15 – (4 x 3) = 3; 3/15 = 1/5
5 C 50 x 40 x 100 = 200,000, thus 5 zeros. 6 D ¼ = 0.25, thus 25 hundredths.
7 C 8 x 20 = 160; 160 + 14 = 174 cents or $1.74.
8 B
9 B Only possible distribution is 5, 5, 6, 6, 7, 7, 7. Thus, the range is 2. 10 B 23 x 47 ≈ 20 x 50 or 1,000
11 A 4 hr./24 hr. or 1/6
12 C Alicia rode for 40 min. (Beth for 20 min.). Thus, she rode for 40/60 or 2/3 of the hour.
13 B
14 C Area of entire rectangle: 4 x 6 or 24 sq. in. Area of “cut out” piece: 1 x 4 or 4 sq. in. The difference is 24 – 4 = 20 sq. in.
2015 Shoreline Math Olympiad
(Answer Key)
Fourth Grade - Team Test 1
Proble m Numb er Answ er Explanation
1 495 Largest three-digit number: 853 Smallest three-digit number: 358 Difference: 853 – 358 or 495
2 403 Apples: 42 lb.
Bananas: 2 x 42 or 84 lb. Cherries: 84 + 62 or 146 lb. Pears: 146 – 15 or 131 lb.
TOTAL Weight: 42 + 84 + 146 + 131 or 403 lb.
3 7
(or 7th,
#7, etc.)
Use “guess and check”. See table below as an example.
Guess of Garth’s positio n Therefore, the
number of students behind him is
The number of
students ahead of him is
10th 15 9
11th 14 10
5th 20 4
7th 18 6
Since 18 is three times 6, Garth’s position is 7th in the line.
4 10 Make an organized list. A possible list is shown below using teams A, B, C, D, and E. There will be 10 matches.
AB >>> team A plays team B AC BC
AD BD CD
AE BE CE DE
cuts per plank to produce these 8 lengths. Thus, the total time for the cuts would be (8 planks x 7 cuts) x 3
minutes or 168 minutes.
6 3 Because packages A and B weigh 7 pounds, package C weighs 11 – 7 or 4 pounds. Since packages A and C weigh a total of 8 pounds, package A weighs 8 – 4 or 4 pounds. Thus package B weighs 7 – 4 or 3 pounds.
7 234 The table shows the dimensions of all of the rectangles that can be made from the 12 tiles and the perimeter of the largest rectangle:
Length
(in tiles) Width (intiles) Perimeter (in no.of tile edges) Perimeter (ininches)
1 12 (1+12)x2=26
edges
26 x 9= 234
in.
2 6 (2+6)x2=16
edges
16 x 9= 144 in.
3 4 (3+4)x2=14
2015 Shoreline Math Olympiad
(Answer Key)
Fourth Grade - Team Test 2
Proble m Numb
er
Answer Explanation
1 1/4 Divide the triangle ADE into 4 equal parts. Triangle ABC is one-fourth of the triangle ADE.
C
2 2 Since the pattern is the repetition of four digits, “2563”, we should look for the largest multiple of 4 that is less than or equal to “61”. It turns out to be “60”, therefore, the 61st digit to the right of the decimal point is the first
digit of the pattern, which is “2”.
3 237 One digit numbers (1 through 9): 9 digits
Two digit numbers (10 through 99): 2 x 90 or 180 digits Three digit numbers (100 through 115): 16 x 3 or 48 digits
Total number of digits: 9 + 180 + 48 or 237 digits.
4 40 Plant 4 shrubs at the corners and 9 between the corners on each side. Thus, 4 + 9 x 4 or 40 shrubs.
A
B
5 1, 3 1 and 3 are NOT possible. The process could be to
remove all multiples of 2 and 5 and check the remaining scores. The table below shows the checks of possible ending scores that are not multiples of 2 or 5.
Possible ending scores that are not multiples of 2
or 5
Combinations of 0, 2 or 5 that produce possible ending scores
1 not possible
3 not possible
7 2 and 5
9 5 and two 2s
11 Three 2s and a 5
13 Four 2s and a 5
17 Three 5s and a 2 or six 2s and a 5 19 Three 5s and two 2s or seven 2s
and a 5
6 20
(blue) 12 (red)
After the blocks were moved, each bucket contains 16 blocks because “each bucket will have the same number of blocks”. Since “4 blocks were moved from the blue bucket to the red bucket,” the result is 16 – 4
or 12 blocks in the red bucket and 16 + 4 or 20 blocks in the blue bucket.
7 2 Let R = radish, A = apple, C = cantaloupe.
Sentence:
1 R R R R R R R R R = A A C
2 R R R R R R R R R = A A (R R R A) >>> Since C = R R
R A
3 R R R R R R = A A A >>> removing 3 Rs from both
sides of equation
2015 Shoreline Math Olympiad
(Answer Key)
Fourth Grade – Mental Math 1
Proble m Numb
er
Answer Explanation
1 90 24/8 = 3; 3 x 60 = 180; 180/2 = 90
2 4 Perfect squares < 20 have odd number of factors; thus 1, 4, 9, 16.
3 500 10 x 100 = 1,000; 1,000/2 = 500
Fourth Grade – Mental Math 2
Proble m Numb
er
Answer Explanation
1 7 $50 - $13 = $37; 37/5 = 7.4; thus 7 five dollar bills.
2 300,000 3 x 100 = 300; 300 x 100 x 10 = 300,000
