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# 2018 Shoreline Math Olympiad Fourth Grade · A. an isosceles triangle B. a right triangle C. an...

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2018 Shoreline Math Olympiad Fourth Grade – Mental Math Test #1 Question #1: Annie is second in the lunch line and Ernie is eighth. How many people are in line between them? Question #2: If it is 9:30am right now, what time will it be in 7 hours and 40 minutes? Be sure to include am or pm in your answer. Question #9: A marching band is arranged in rows of 12. There are 5 rows of brass players, 3 rows of woodwind players, and 1 row of drummers. How many people in all are in the marching band? 2018 Shoreline Math Olympiad Fourth Grade – Mental Math Test #2 Question #1: What is the difference between the 4 th multiple of 3 and the 13 th multiple of 3? Question #2: Hayley’s dump truck can hold 20 tons of gravel at one time. If she wants to transport 390 tons of gravel from the quarry to the work site, what is the fewest number of deliveries she can make? Question #3: What is the difference between the largest number and the smallest number, in the following set of 7 numbers: [8, 3, 12, 5, 6, 1, 7]?
Transcript

Question #1: Annie is second in the lunch line and Ernie is eighth. How many

people are in line between them? Question #2: If it is 9:30am right now, what time will it be in 7 hours and 40

Question #9: A marching band is arranged in rows of 12. There are 5 rows of

brass players, 3 rows of woodwind players, and 1 row of drummers. How many people in all are in the marching band?

Question #1: What is the difference between the 4th multiple of 3 and the 13th

multiple of 3? Question #2: Hayley’s dump truck can hold 20 tons of gravel at one time. If she

wants to transport 390 tons of gravel from the quarry to the work site, what is the fewest number of deliveries she can make?

Question #3: What is the difference between the largest number and the

smallest number, in the following set of 7 numbers: [8, 3, 12, 5, 6, 1, 7]?

1. Last week, 555 people bought the latest bestseller, “Off the Cliff” by Hugo First, at a cost of \$12 each. How

much money was earned by the book’s sales last week? A. \$6000 B. \$6600 C. \$6660 D. \$6666 2. The reading team WordHerd made this bar chart to show the number of pages each

A. 419 B. 806 C. 1184 D. 1445 3. The dolphin exhibit has 2 orcas, 15 bottlenose, and 17 spinners. What fraction of the dolphins are not orcas?

A. 2

34 B.

32

2 C.

16

17 D.

15

17

4. If one angle of a triangle measures 100°, the triangle could not be A. an isosceles triangle B. a right triangle C. an obtuse triangle D. a scalene triangle 5. What is the smallest number of Tuesdays that any month of the year could have? A. 3 B. 4 C. 5 D. 6

6. Mrs. Givens is the best! She begins the day with an empty classroom and 36 candy bars. She hands out 1 candy bar to the first student who walks into the classroom, then 2 to the second student, 3 to the third, and so on until she runs out. How many students get candy bars from Mrs. Givens?

Yom Yom!

A. 8 B. 10 C. 12 D. 14

7. Which of the following fractions is equivalent to the mixed number 31

4 ?

A. 3

4 B.

12

4 C.

13

3 D.

26

8

8. The “Calc You Later” is a lazy device that takes 20 seconds to perform an addition and 80 seconds to perform a

multiplication. How many minutes will the “Calc You Later” take to perform 18 additions and 12 multiplications? A. 6 B. 12 C. 22 D. 32 9. Marshawn leaves his old home in Seattle and drives 800 miles to his new home in Oakland. If he left Seattle at

9:00 am and traveled 60 miles each hour, at what time does he arrive? A. 5:00 pm B. 9:00 pm C. 10:20 pm D. 10:30 pm 10. The first 5 multiples of 12 are 12, 24, 36, 48, 60. What is the 17th multiple of 12? A. 51 B. 96 C. 144 D. 204 11. A dime is worth \$0.10. Therefore, a \$100 bill is worth the same amount of money as Am I too thin?

A. 10 dimes B. 100 dimes C. 1,000 dimes D. 10,000 dimes

12. To make a loaf of banana bread, you need 1

4 teaspoon of salt and

3

4 cup of brown sugar. With the same recipe,

making 7 loaves of bread would require

A. 13

4 teaspoons of salt and 5

1

4 cups of brown sugar B. 7 teaspoons of salt and 3 cups of brown sugar

C. 51

4 teaspoons of salt and 1

3

4 cups of brown sugar D. 2 teaspoons of salt and 6 cups of brown sugar

13. If each small square has an area of 1, what is the total area of this figure? A. 6 B. 7 C. 8 D. 9 14. If two mystery numbers have a sum of 10 and a difference of 4, what is the value of the larger mystery number? A. 3 B. 6 C. 7 D. 8 15. One owl hoots every 8 minutes, and another hoots every 12 minutes. If they both hoot simultaneously at

9:50pm, what is the next time they hoot simultaneously? A. 9:58pm B. 10:14pm C. 10:10pm D. 11:26pm

END OF TEST! YOU MAY KEEP THIS COPY WHEN FINISHED

1. If there are 12 junkinches in a junkfoot, and 3 junkfeet in a junkyard, how many junkinches are in 10 junkyards? A. 30 B. 36 C. 120 D. 360 2. Two consecutive whole numbers, whose product is 132, have a sum of A. 11 B. 23 C. 33 D. cannot be determined with the information given 3. Which of the following lists is arranged from least to greatest?

A. 1

4, 0.24,

1

5, 0.3 B.

1

4,

1

5, 0.24, 0.3 C. 0.3, 0.24,

1

5,

1

4 D.

1

5, 0.24,

1

4, 0.3

4. A taxi driver charges 50¢ for the first mile and 15¢ for each 1

8 mile after that. How much does a 4-mile ride cost?

Where

to bub? A. \$2.00 B. \$3.60 C. \$4.10 D. \$4.80

5. 17

12 +

19

12 =

A. 11

2 B. 3 C. 24 D. 36

6. If Rachel has a \$10 bill and buys as many brownies as possible at \$1.10 each, she will get A. 8 brownies and \$1.20 in change B. 9 brownies and no change

C. 9 brownies and \$0.10 in change D. 10 brownies and \$1.00 in change 7. The product of two consecutive whole numbers is A. always even B. always odd

C. even in exactly one case, otherwise odd D. odd in exactly one case, otherwise even 8. Firestar the cat walked from the forest to the beach in 2 hours. On the way back, the walk took 3 times as long

because he was enjoying the sunset and sipping his latte. What is the total time Firestar took for the round trip? A. 120 minutes B. 240 minutes C. 360 minutes D. 480 minutes

9. There are 5280 feet in one mile and 3 feet in one yard. How many yards are in one mile? A. 880 B. 1000 C. 1760 D. 15840 10. How many hours are in two weeks? A. 48 B. 168 C. 236 D. 336 11. How many different squares are in the grid shown? A. 9 B. 10 C. 13 D. 14 12. Against the Houston Texans, Russell Wilson’s passes gained 452 yards on 41 pass attempts. If 15 passes were

not caught, on average, about how many yards were gained for each pass that was caught? A. 30 B. 26 C. 17 D. 11 13. Evander cuts his circular broccoli pie into 15 identical slices that look like the figure

shown here. What is the measure of angle A? A. 18° B. 24° C. 30° D. 36° 14. If Patty is 98.7 cm tall and Matty is 68.9 cm tall, how much taller is Patty than Matty? A. 29.8 cm B. 32.8 cm C. 27.2 cm D. 39.6 cm 15. Based on this pie chart, which describes the zoo’s 200 hyenas, how many laughing hyenas live at the zoo?

A. 35 B. 40 C. 50 D. 70

Actually, I didn’t

think it was that funny.

END OF TEST! YOU MAY KEEP THIS COPY WHEN FINISHED

𝟕

𝟐𝟎

𝟏

𝟒

𝟐

𝟓

1. When 4 junior wizards sit in a row of 4 chairs, Harry won’t sit next to Draco but Ron must sit next to Hermione,

with her to his right. If Draco sits on the left end, who sits on the right end? Expelliseatmus!

2. A dollar bill is 43 Greenies thick. If there are 10,000 Greenies in a Chasie, and 12 Chasies in a Chunkie, how

many dollar bills would you need to make a stack 1 Chunkie high? Assume that stacked bills rest tightly against each other and round your answer to the nearest whole number.

3. Annabeth uses her celestial bronze knife to cut a 100-ounce cake into 5 identical slices. Percy eats one slice and

Thalia eats another. Then Annabeth cuts one of the remaining slices into 5 identical small pieces and eats 3 of those small pieces. How many ounces of the cake have not been eaten?

4. At the Mightee Dog hot dog factory, giant hot dogs measuring 15 feet in length need to be cut into 9-inch

lengths. If there are 6 giant hot dogs and it takes 4 seconds to make 1 cut, how many seconds will it take to complete all of the cuts?

5. If a scoop of ice cream is 1

4 cup, how many scoops are needed to serve 17 cups of ice cream?

6. Three whole numbers have a product of 480. If one of those numbers is 2, what is the least possible sum the

three whole numbers could have? 7. This is a map of downtown Univille. All traffic must move in the direction shown by the arrows. How many

paths are there from point A to point B?

END OF TEST! YOU MAY KEEP THIS COPY WHEN FINISHED

1. Thuy is filling in a 3 x 3 square with the set of whole numbers 1 through 9 so that every row and column have

the same sum. When Thuy finishes, what number will be in the box marked “X”?

2. Find the perimeter of this “plus” figure. Assume all angles are right angles.

Nice.

3. How many different rectangles of any size are in the figure shown?

4. A world-class sprinter races a total distance of 200 meters, traveling 10 meters in every second. A world class

printer prints 120 pages in each minute. If the sprinter and the printer started and finished at the same time, how many pages did the printer print in all?

2 4

X

6 8

5. The principality of Monthree Carlo uses 1-dollar, 3-dollar, 9-dollar, 27-dollar, and 81-dollar bills. Using this

system, what is the fewest number of bills that a Monthree Carlan would need in order to make a pile worth exactly 200 dollars?

6. My 3 brothers are all teenagers with the same birth date, though they were all born on different years. The sum

of their ages is 53. When my oldest brother is 39, how old will my youngest brother be? 7. If you write out the result of 2000 × 2000 × 2000 × 2000 × 2000 × 2000 × 2000, how many digits would it

have?

END OF TEST! YOU MAY KEEP THIS COPY WHEN FINISHED 2018 Shoreline Math Olympiad

Fourth Grade - Individual Test 1

Problem Number

1 C 12 × 555 = 𝟔𝟔𝟔𝟎

2 B Highest bars are 387 and 419. 387 + 419 = 𝟖𝟎𝟔.

3 C Of the 34 dolphins total, 32 are not orcas. 32

34=

𝟏𝟔

𝟏𝟕

4 B 100° > 90°. Thus it is an obtuse triangle, and cannot be a right triangle.

5 B If the 7th of a month is a Tuesday, so are the 14th, 21st, 28th: 4 total. The next Tuesday would be the 35th, but no month has 35 days.

6 A Continue adding counting numbers and you’ll find that 1 + 2 + 3 + 4 + 5 + 6 + 7 + 𝟖 = 36.

7 D 4 × 3 + 1 = 13, so 31

4 is equivalent to

13

4, and

13

2

2=

𝟐𝟔

𝟖.

8 C The operations take (20 × 18) + (80 × 12) = 1320 seconds. 1320 ÷ 60 = 𝟐𝟐. Or could use estimation; 1 minute for 3 additions = 6 min. and a bit over 15 minutes for multiplications which is a bit over 21; 22 is the only choice that is close.

9 C 800 ÷ 60 = 13 R20. So Marshawn takes 13 hours 20 minutes. After 12 hours, it is 9:00pm; after another 1 hour 20 minutes, it is 10:20pm.

10 D 17 × 12 = 𝟐𝟎𝟒.

11 C 100

0.10=

1000

1= 𝟏𝟎𝟎𝟎. Or, \$100 is worth 10 × 100 = 𝟏𝟎𝟎𝟎 dimes.

12 A 7 ×

1

4= 1

3

4 and 7 ×

3

4= 5

1

4. So we need 𝟏

𝟑

𝟒 teaspoons of salt and 𝟓

𝟏

𝟒 cups of brown sugar.

(Note: C is the same as A but with ingredients reversed, and is therefore incorrect.)

13 C First count the squares; there are 8 of them. Area is 8 × 1 = 𝟖.

14 C Add various pairs of numbers with difference 4: 1 + 5 = 6, 2 + 6 = 8, 3 + 𝟕 = 10 ✓. Or

use the shortcut 10+4

2=

14

2= 𝟕. (Smaller number is

10−4

2=

6

2= 3.)

15 B Least common multiple of 8 and 12 is 24. 24 minutes after 9:50 is 10:14 pm.

Fourth Grade - Individual Test 2

Problem Number

1 D 3 × 12 = 36 junkinches in a junkfoot. 10 × 36 = 𝟑𝟔𝟎.

2 B Try multiplying pairs of consecutive whole numbers; and since 132 > 100 we cannot have two one-digit numbers. So start with 9 and 10: 9 × 10 = 90, 10 × 11 = 110,

11 × 12 = 132 ✓. Now add: 11 + 12 = 𝟐𝟑.

3 D Convert all to decimals:

1

4= 0.25,

1

5= 0.2.

1

5<

1

4. So the correct order is

𝟏

𝟓 , 𝟎. 𝟐𝟒,

𝟏

𝟒, 𝟎. 𝟑

4 C After the first mile (50¢), there are 4 − 1 = 3 miles left; and those 3 miles have 3 ÷

1

8= 24

intervals costing 15¢ each. 0.50 + (24 × 0.15) = 0.50 + 3.60 = 𝟒. 𝟏𝟎.

5 B 17

12+

19

12=

36

12= 𝟑.

6 C Rachel pays 1000¢ for brownies costing 110¢ each. 1000 ÷ 110 = 9 R10. She will get 9 brownies and 10¢ (\$0.10) in change.

7 A If two numbers are consecutive, one will be even and another will be odd. The product of an even number and an odd number is always even.

8 D Forest to beach takes 2 hours, and way back takes 2 × 3 = 6 hours. The round trip takes 2 + 6 = 8 hours, or 8 × 60 = 𝟒𝟖𝟎 minutes.

9 C Each yard is 3 feet, so there are 5280 ÷ 3 = 𝟏𝟕𝟔𝟎 yards in one mile.

10 D 7 days in a week; 14 total days (2 x 7); 24 hours in a day; 24 x 14 = 336.

11 D

There are 9 1x1 squares, 4 2x2 squares, and 1 3x3 square (the entire figure). 9 + 4 + 1 =𝟏𝟒. Here are the 14 squares:

12 C 452 ÷ (41 − 15) = 452 ÷ 26 = 17.38 which is about 17.

13 B 360 ÷ 15 = 𝟐𝟒 degrees per slice.

14 A Patty is taller by 98.7 − 68.9 = 𝟐𝟗. 𝟖 cm. Can also get this answer by approximation.

15 D Laughing hyenas represent 35% of the 200 hyenas, from the pie chart.

(35%) × 200 =35

100× 200 = 35 × 2 = 70.

Fourth Grade - Team Test 1

Problem Number

1 Harry Number the seats 1-4 from left to right. Draco sits in #1. Ron & Hermione must occupy #2 & 3 or #3 & 4. But if they occupy #3 & 4, then Harry would be in #2 next to Draco, which cannot happen; therefore Ron & Hermione are in #2 & 3, leaving Harry in seat #4.

2 2791 12 x 10,000 = 120,000 Greenies needed; 120,000/43 = 2790.7; so you need 2791 to get 1 Chunkie high.

3 48 Each original slice is 100 ÷ 5 = 20 ounces. Each small piece from the final cuts is 20 ÷ 5 =4 ounces. (2 × 20) + (3 × 4) = 52 ounces are eaten, leaving 48 ounces of cake uneaten.

4 456 Each giant hot dog is 15 feet = 180 inches (15 x 12); for 9 inch pieces each giant hot dog makes 20 9-inch pieces 19 cuts for each giant hot dog; 19 x 6 = 114 cuts; 114 x 4 = 456 seconds.

5 68 4 scoops = 1 cup; 4 x 17cups = 68 scoops.

6 33

Let’s call the 3 whole numbers A, B, and C, in ascending order (that is, C ≥ B ≥ A). We know that 2 × B × C = 480, so B × C = 240; make a table of some possible values.

A B C sum

2 1 240 243

2 2 120 124

2 4 60 66

2 6 40 48

2 10 24 36

2 12 20 34

2 15 16 33

7 9

• If we go up and to the right from A, we can either stay at the top level or return to the middle (2 paths). Similarly, if we go down and to the right from A, there are 2 paths.

• If we go directly right from A, then up at the next intersection, we can stay up or return down (2 paths). Similarly, if we go right then down, there are 2 paths.

• If we go directly right from A and stay in the middle level, that is 1 path.

• (2 + 2) + (2 + 2) + 1 = 𝟗.

Fourth Grade - Team Test 2

Problem Number

1 3

When all the squares are filled in, the sum of all 3 columns will be the sum of all the numbers in the box, which is 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45. That makes each column’s sum equal to 45 ÷ 3 = 15. So 4 + X + 8 = 15, which means X = 𝟑.

2 42 There are 6 segments of length 3 and 6 segments of length 4. (6 × 3) + (6 × 4) = 18 + 24 = 𝟒𝟐.

3 18

Make a table of the number of rectangles, by size.

# of rectangles 1 column wide 2 columns wide 3 columns wide

1 row tall 6 4 2

2 rows tall 3 2 1

6 + 4 + 2 + 3 + 2 + 1 = 𝟏𝟖. Note: There is a shortcut. The rectangular grid is 3 x 2, so we can simply calculate (3 + 2 + 1) × (2 + 1) = 𝟏𝟖.

4 40 The sprinter finishes in 200 ÷ 10 = 20 seconds. In those 20 seconds, which is

1

3 of a

minute, the printer will print 1

3× 120 = 𝟒𝟎 pages.

5 6

To use the fewest bills, make the bills used as large as possible. Start with the 81-dollar bills: 200 ÷ 81 = 2 R38. So we use 2 81-dollar bills and have 38 dollars left to make with smaller bills. Now use the 27-dollar bills: 38 ÷ 27 = 1 R11 (1 bill, 11 dollars remaining). Then the 9-dollar bills: 11 ÷ 9 = 1 R2 (1 bill, 2 dollars remaining). The remaining 2 dollars must be made with 2 1-dollar bills. Total number of bills is 2 + 1 + 1 + 2 = 𝟔.

6 36

The highest sum of three different “teen” numbers is 17 + 18 + 19 = 54. To get 53, we

must subtract 1 from one of these numbers (addends) but keep the other two intact; the

only way to do that is to se 16 + 18 + 19 = 53. Therefore, the oldest is 19, the youngest is

16 (3 years younger), and when the oldest is 39 the youngest will be 39 − 3 = 𝟑𝟔.

7 24

2000 × 2000 × 2000 × 2000 × 2000 × 2000 × 2000 = (2 × 2 × 2 × 2 × 2 × 2 × 2) × (1000 × 1000 × 1000 × 1000 × 1000 × 1000 × 1000) which is 128 followed by 21 zeros, for 24 digits in all. Or, on many calculators the result of this calculation will read 1.28E23, which means 1.28 with the decimal point shifted 23 places to the right, for a total of 24 digits to the left of the decimal point.

Fourth Grade – Mental Math 1

Problem Number

1 5 Person #3, 4, 5, 6, 7 => 5 of them. Or, 7 people are in front of Ernie, including Annie and the 1 person in front of her: 7 − 1 − 1 = 𝟓.

2 5:10pm

In 3 hours it will be 12:30pm (half hour after noon), then in another 4 hours it will be 4:30pm, then in another 40 minutes is will be 5:10pm. Or, 9: 30am +7 hours and 40 minutes = 17: 10am = 5: 10pm (subtract 12 from the hour, add 12 hours by going am to pm).

3 108 There are 5 + 3 + 1 = 9 rows, each with 12 people. 9 × 12 = 𝟏𝟎𝟖.

Fourth Grade – Mental Math 2

Problem Number

1 27 (3 x 13) – (3 x 4) = 39 – 12 = 27

2 20

390 ÷ 20 = 19 𝑟10. So she must make 19 deliveries full, plus 1 more delivery partially full, or 19 + 1 = 𝟐𝟎 deliveries total.

3 11 Largest number is 12 and smallest number is 1. 12 − 1 = 𝟏𝟏.

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