smo 2019 gr 5 mental math #1...4. mango lox needs a rectangular box to hold 2,400 cubic centimeters...

2019 Shoreline Math Olympiad Fifth Grade – Mental Math Test #1

Question #1: What is one-third of 39?

Question #2: A puppy blanket costs 38 cents. A kitten blanket costs 83 cents.

What would it cost to buy 3 puppy blankets and 3 kitten blankets? Write your answer in terms of dollars and cents.

Question #3: If there are 8 ounces in a cup, and 16 cups in a gallon, how many

ounces are in 5 gallons?

2019 Shoreline Math Olympiad Fifth Grade – Mental Math Test #2

Question #1: One giraffe burps every 30 seconds. Another giraffe burps every

40 seconds. If they burp simultaneously at 1:37 PM, what time is it the next time they burp simultaneously? Be sure to include AM or PM in your answer.

Question #2: How many whole numbers have exactly two digits? Question #3: The perimeter of a rectangle is 4.5 inches. If the rectangle is 1

inch long, what is its area in square inches? Write your answer as a decimal number.

– PLEASE TURN OVER – (page 1 of 2)

2019 Shoreline Math Olympiad Fifth Grade – Individual Test #1

1. Which of the following is not equal to 32 x 450? A. 1 x 14400 B. 320 x 45 C. 8 x 900 D. 5 x (1000 + 1880)

2. Moley the bright green moldwarp counts moles on his legs and tail. He finds 9985 on the first leg, 9992 on the second, 9996 on the third, and 9978 on the fourth. How many must he have on his tail, if he has 50,000 overall?

A. 10049 B. 9959 C. 10009 D. 9909

3. The circus that just came to town has 75 ceremonial elephants, 165 spinning spiders, 255 arguing ants, and 345

dancing worms. If elephants have 4 legs each, spiders have 8 legs each, ants have 6 legs each, and worms have no legs, how many total legs are in the circus?

A. 840 B. 300 C. 3150 D. 1620 4. Three different 2-digit whole numbers have a sum of 34. The product of the three numbers must be A. 1430 B. 1452 C. 1716 D. cannot be determined from the information given 5. A “perfect square number” is the result of multiplying a whole number by itself. For example, 25 and 81 are

perfect square numbers because 5 × 5 = 25 and 9 × 9 = 81. What is the sum of all perfect square numbers greater than 25 and less than 81?

A. 85 B. 100 C. 114 D. 149 6. To bake a baby cookie, you need 1 () teaspoons of flour and 1.3 chocolate chips. If Sanza uses 10 teaspoons of

flour and 10 chocolate chips to bake as many whole baby cookies as possible, what ingredient amounts are left over?

A. 1 () teaspoons of flour and 1.3 chocolate chips B. *) teaspoons of flour and 0.9 chocolate chips

C. no flour and 0.25 chocolate chips D. () teaspoons of flour and 0.3 chocolate chips 7. There are 12 inches in a foot, 3 feet in a yard, 22 yards in a chain, 10 chains in a furlong, and 8 furlongs in a mile.

Which of the following is not equivalent to one mile? A. 80 chains B. 8 furlongs C. 176 yards D. 5280 feet 8. Rose builds a rectangular prism by gluing together 1001 wooden cubes, each of which is 1 inch x 1 inch x 1

inch. Which of these choices could be one of the dimensions of the prism? A. 17 inches B. 77 inches C. 90 inches D. 101 inches

(page 2 of 2 - 2019 SMO 5th grade individual test #1)

9. Pointy goes to school on the coordinate plane. Pointy’s classroom is at (7,5) and the library is at (7,8). From the

library, the distance to the classroom and the distance to the gym are the same. Where could the gym be? A. (10,5) B. (7,2) C. (8,5) D. (4,8) 10. Which of the following expressions is equivalent to +, −

./?

A. *( −

,) B. )0 −

*(* C. (12 −

(*(* D. () −

(,

11. Two Unbeetable Beets and a Sleek Leek cost 58 cents. Two Sleek Leeks and an Unbeetable Beet cost 47 cents.

What is the cost of one Sleek Leek and one Unbeetable Beet? A. 105 cents B. 50 cents C. 35 cents D. 11 cents 12. The sum of two consecutive multiples of 3 is A. always odd B. always even C. odd in all cases except one D. even in all cases except one

13. Twenty-four very tiny chairs are arranged, evenly spaced, around a round table. In clockwise order, the chairs

are labeled “#1,” “#2,” etc. through “#24.” Which of the following sets of chairs could form the vertices of an equilateral triangle?

A. #2, #12, #22 B. #11, #3, #19 C. #16, #12, #8 D. #1, #8, #15 14. Xin has a favorite number. If Xin starts with 8, subtracts her magic number, and then multiplies the result by her

magic number, the final result is 15. Xin’s magic number must be

A. 3 B. 5 C. 8 D. cannot be determined from the information given

15. Otto started from home at 1:00 PM and drove exactly 20 minutes at a constant speed to the grocery store. He

spent exactly 10 minutes shopping for tomatoes. Then Otto drove back home – in fact, he was in such a hurry to make tomato juice that he drove back home twice as fast as he had driven to the store. What time did he arrive back at home?

A. 1:35 PM B. 1:40 PM C. 2:10 PM D. 1:50 PM

END OF TEST! YOU MAY KEEP THIS COPY WHEN FINISHED


9. What are the coordinates of the point that is halfway between (1,7) and (8,28)? A. (4,14) B. (3,21) C. (3.5, 14.5) D. (4.5, 17.5) 10. Which of the following expressions is equivalent to 18.25 × ( − 292? A. 9 × ( + 9 × ( − 136 − 166 B. 2 ×(9.725 × ( − 146)

C. 18 × ( + 0.25 × ( − (18 × 16 − 4) D. 73 ×(( − 16) ÷ 4 11. You can trade two Unbeetable Beets for a Sleek Leek and 58 cents. You can also trade two Sleek Leeks for an

Unbeetable Beet and 13 cents. What is the cost of one Sleek Leek and one Unbeetable Beet? A. 28 cents B. 43 cents C. 45 cents D. 71 cents 12. The sum of two consecutive multiples of 3 is A. always odd B. always even C. odd in all cases except one D. even in all cases except one

13. In how many distinct ways can the letters “GEESE” be arranged? A. 5 B. 20 C. 40 D. 60 14. Xiao has a favorite number. If Xiao starts with 8, subtracts his magic number, and then multiplies the result by

his magic number, the final result is 15. Xiao’s magic number must be

A. 3 B. 5 C. 8 D. cannot be determined from the information given

15. Otto drove east 10 miles at 30 miles per hour to go to the grocery store. He spent 10 minutes shopping for

tomatoes. Then he drove west 20 miles at 60 miles per hour, to his job as a tomato juice squeezer. Which of the following graphs correctly shows Otto’s distance from home as a function of time?

A. B. C. D.


5

10

20 40 60

distance from home (mi)

time (min)

5

10

20 40 60


time (min)

5

10

20 40 60


time (min)

5

10

20 40 60


time (min)

X along a

straight line ?

v I -

Reese arrange

I

-


2019 Shoreline Math Olympiad Fifth Grade – Individual Test #2

1. There are 32 ounces in a quart. How many quarts does the 9280-ounce HydroBlaster water bottle hold?

A. 280 B. 290 C. 300 D. 310

2. There is only one value that can go in the blank to make the equation 7 ×__ = 132 correct. Which of the

following numbers is closest to that value? A. 19 B. 12 C. 16 D. 9 3. If there are 3 teaspoons in a tablespoon, and 7 tablespoons in a toadspoon, then 8 toadspoons are equivalent to A. 24 tablespoons B. 21 teaspoons C. 56 teaspoons D. 168 teaspoons 4. Mango Lox needs a rectangular box to hold 2,400 cubic centimeters of tangled socks. Which of the following

box sizes will exactly contain his socks, with no space left over?

A. 20 cm x 40 cm x 3 cm B. 8 cm x 30 cm x 20 cm C. 24 cm x 100 cm x ))* cm D. 2.4 cm x 10 cm x 10 cm

5. February 1, 2019, was a Friday. What is the sum of all the dates in February 2019 that were Thursdays? A. 28 B. 45 C. 46 D. 70

6. Right now, Frances is 24 years old and Sam is 8 years old. In how many years will Frances’s age be twice Sam’s age?

A. 8 B. 12 C. 16 D. 24 7. Three consecutive whole numbers add up to 153. What is the product of the three whole numbers? A. 5852 B. 124950 C. 132600 D. 140556 8. Which of the following statements is false? A. every square is also a rhombus B. a rhombus cannot be a rectangle C. some parallelograms are also rectangles D. a trapezoid may have 3 congruent sides


[DRAFT] 2019 Shoreline Math Olympiad Fifth Grade – Individual Test #2

1. There are 128 ounces in a gallon. How many gallons does the 896-ounce HydroBlaster water bottle hold?

A. 6 B. 7 C. 8 D. 9 2. If 7 × H = 132, what is the value of H, rounded to the nearest whole number? A. 9 B. 12 C. 16 D. 19 3. If there are 3 teaspoons in a tablespoon, and 7 tablespoons in a toadspoon, then 8 toadspoons are equivalent to A. 56 tablespons B. 21 teaspoons C. 24 toadspoons D. 168 teaspoons 4. If ) = 11, then ) + ) × ) = A. 110 B. 121 C. 132 D. 242 5. February 1, 2019, was a Friday. What is the sum of all the day numbers in February 2018 that were Thursdays? A. 36 B. 45 C. 46 D. 75

6. If Sam is 3 years younger than Frances, how many years older than Sam will Frances be in 10 years? A. 3 B. 4 C. 7 D. 10 7. Three consecutive whole numbers add up to 153. What is the largest of the three whole numbers? A. 43 B. 51 C. 52 D. 61 8. The area of this right triangle is A. 40 B. 60 C. 68 D. 120

928

7 7.5X

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will exactly containhis socks with no

space leftover ?

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9. The product of the digits in the quotient of 999,999 ÷ 7 is A. 0 B. 280 C. 2240 D. 142,857 10. The ones digit of the product of twelve 12’s (that is, 12 × 12 × 12 × 12 × 12 × 12 × 12 × 12 × 12 × 12 × 12

× 12) is A. 6 B. 4 C. 8 D. 2 11. Shonda calculates (1 + 2) × (3 + 4) × (5 + 6) and gets the correct answer. Her friend Pat writes the same

expression, removes the parentheses, and calculates that result. Which of the following statements is true? A. Shonda’s result equals Pat’s result B. Shonda’s result is 160 more than Pat’s result C. Shonda’s result is 7 times Pat’s result D. Shonda’s result is less than Pat’s result 12. In the decimal multiplication equation A.B×A.B=WH.EE, each letter represents a different

non-zero digit. Which of the following numbers could A.B represent? A. 3.8 B. 4.2 C. 5.6 D. 6.2 13. Which of the following numbers is a multiple of both 6 and 14? A. 240 B. 252 C. 266 D. 280 14. After I cut my birthday cake into 8 identical slices, I cut half of those 8 slices in half. Then I take all the slices I

now have, and I cut half of those in half. After all this cutting, how many slices of cake are there? A. 16 B. 18 C. 24 D. 32 15. A square piece of paper is folded in half in one direction, then the other, and then a straight, 45-degree angle

cut is made at the corner where the two fold lines meet. The cut-off corner is then discarded. When the paper is unfolded, how many lines of symmetry will the paper (including the cut) have?

A. 0 B. 1 C. 2 D. 4



9. The product of the digits of the result of 999,999 ÷ 7 is A. 0 B. 280 C. 2240 D. 142,857 10. If you were to multiply 12 12’s together (12 to the 12th power), the ones digit of the result would be A. 2 B. 4 C. 6 D. 8 11. Shonda calculates (1 + 2) × (3 + 4) × (5 + 6) and gets the correct answer. Her friend Pat writes the same

expression, removes the parentheses, and calculates that result. Which of the following statements is true? A. Shonda’s result equals Pat’s result B. Shonda’s result is 160 more than Pat’s result C. Shonda’s result is 7 times Pat’s result D. Shonda’s result is less than Pat’s result 12. If 3 = 11, 4 = 14, and 5 = 17, then 5 × (4 − 3) + 3 = A. 4 × 4 − 3 +5 B. 4 × 4 + 3 +5 C. 4 ×5 +4 − 3 D. 4 ×5 +4 + 3 13. Marta tries to make a 2 x 2 “magic square” where both rows, both columns, and both diagonals all have the

same sum. Constructing this type of magic square is A. impossible B. possible, but only if all 4 numbers in the square are equal C. possible, but only if it has at least one 0 (zero) D. possible, but not with whole numbers 14. At Pip’s pizzeria, you can have pepperoni, mushrooms, or peppers sprinkled on your pizza. You can also have

any combination of those mixed together, or none at all. How many different pizzas can you get at Pip’s? A. 3 B. 4 C. 6 D. 8 15. A square is folded in half in one direction, then the other, and then a straight, 45-degree angle cut is made at the

corner where the two fold lines meet. When the paper is unfolded, how many lines of symmetry will the paper (including the cut) have?

A. 0 B. 1 C. 2 D. 4


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2019 Shoreline Math Olympiad Fifth Grade – Team Test #1

1. Continue the pattern in the boxes shown. What number should go in box A?

2. If this arithmetic sequence is continued, what number should go in the box? Express your answer as a reduced

(simplified) fraction.

!"#$ , !"%$ , !""$ , ☐

3. Horatio wants to make two piles of coins: one worth 34 cents (to pay for a tiny salad) and one worth 66 cents (to

pay for a tiny latte). If he may only use pennies, nickels, dimes, quarters, and half-dollars, what is the least number of coins he will need to make the two piles?

4. At Kellstein Middle School, which has 130 students overall, 70 students are on the megabasketball team and 65

students are in the microglee club. If 12 students participate in both activities, how many participate in neither?

(page 2 of 2 - 2019 SMO 5th grade team test #1)

5. One lap around the Shoreline Speedway track is 360 meters. Ameena and Imran both start driving clockwise

around the track at the same place and time. While they both travel at constant speeds, Ameena is slightly faster, driving 24 meters for every 19 meters that Imran drives. Eventually, Ameena will “lap” Imran and their cars will meet again somewhere on the track. When that happens, how many meters has Imran traveled?

6. Shaila is bringing her pet dinosaurs for Take Your Extinct Reptile to School Day. This pie chart shows how many of

her dinosaurs are in each category. If she has 15 velociraptors, how many pet dinosaurs does Shaila bring in all? 7. On the new social network SnapFace, every member was a friend of every other member, until Fluffles

unfriended Gooeygoo, leaving 44 total friendships remaining on the network. How many people are members of SnapFace? Note: A friendship between two people, A and B, means that A is a friend of B and B is a friend of A.



5. Imran and Ameena both drove the same 10-mile road, starting at the same time. Amena drove four times as

fast as Imran and arrived 15 minutes sooner. How fast did Imran drive, in miles per hour? 6. Shaila is bringing her pet dinosaurs for Take Your Extinct Reptile to School Day. This pie chart shows how many of

her dinosaurs are in each category. If she has 39 velociraptors, how many pet dinosaurs does Shaila bring in all? 7. On the new social network SnapFace, every member was a friend of every other member, until Fluffles

unfriended Gooeygoo, leaving 44 total friendships remaining on the network. How many people are members of SnapFace? Note: A friendship between two people, A and B, means that A is a friend of B and B is a friend of A.



5. Berta works twice as fast as Albert. Carla works twice as fast as Berta. Darla works twice as fast as Carla. If

Darla can do a job in exactly one hour, how many minutes would it take them all to do the same job if they split up the labor and start and finish simultaneously?

6. Bobby is bringing his pet dinosaurs for Take Your Extinct Reptile to School Day. This pie chart shows how many of

his dinosaurs are in each category. If he has 39 velociraptors, how many pet dinosaurs does he bring in all? 7. On the new social network SnapFace, everyone is a friend of everyone else, until Fluffy unfriends Curly, leaving 44

friendships remaining. How many people are members of SnapFace? Note: A friendship between two people, A and B, means that A is a friend of B and B is a friend of A.


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2019 Shoreline Math Olympiad Fifth Grade – Team Test #2

1. Bongo Cat wants to expand his drum collection by picking up a new drum kit. To pick up the drum kit, he must

travel on the grid lines shown, starting at the northwest (top-left) corner and ending at the southeast (bottom-right) corner. He must travel only in the southward or eastward direction, but he may turn at any intersection. How many different paths can Bongo Cat take?

2. Farmer Fran wants to build a rectangular pen, using 42 meters of fencing, where each side of the pen will have a

whole number length (in meters). What is the maximum area in square meters that Fran can enclose with her pen?

3. A magic square is a grid where all rows, columns, and diagonals have the same sum. Ileana made a 4 x 4 magic

square using the counting numbers 1 through 16, then erased six of the numbers until it looked like the diagram below. What is the sum of the numbers that Ileana erased from the shaded squares?

4 14 15

9 12

5 8

2 3 13


[DRAFT] 2019 Shoreline Math Olympiad Fifth Grade – Team Test #2

1. There are two clocks on the shelf; each one chimes when the minute hand hits 12. One clock is accurate, but the

other one gains 5 minutes every hour. If both clocks are set to 12:00 now, how many hours will elapse until the next time they chime simultaneously?

2. An astronomer at the observatory shines her laser at a reflector on the moon. If the beam travels to the moon,

reflects back, and returns to the observatory 2.5 seconds later, what is the distance between the reflector and the observatory as a number of megameters? Assume that the speed of light is 300,000 km per second.

3. How many 2-digit numbers have a ones digit that is greater than the tens digit? 4. The friendly Martians are trying to build Earth clocks. It isn’t going well. At 5pm on Monday, they set their 12-

hour (analog) clock correctly, but it loses 3 minutes every hour (so 1 hour later it says 5:57 instead of the correct 6:00). The next time their clock shows the correct time, what day of the week will it be?

North

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but to pick up his new set,he must travel

travel, southward or eastward only , on the

grid lines shown . How many pathscan Bongo Cat take ?

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4. In the early morning of April 1st, the baby shark is swimming 200 m below the ocean surface. It then rises 50 m

to sing that day, and that night, it sinks 30 m to sleep. If it continues to rise 50 m every day and sink 30 m every night after that, on what day of April does the baby shark first reach the ocean surface (depth of 0 m)?

5. Penelope writes all the 3-digit numbers that can be formed using each of the digits {0, 1, 2} exactly once. What is

the sum of all the numbers she writes? Note that a number cannot have 0 as its left-most digit. 6. Sammi gave !" of her birthday cupcake to Roux and another !" of her birthday cupcake to Mabel. Roux and Mabel

complained that Sammi had the biggest share. So Sammi gave 1.27 ounces more to Roux and gave 1.94 ounces more to Mabel. Finally Sammi ate the 7.93 ounces she had left. How many ounces were in Sammi’s original birthday cupcake? Answer as a decimal.

7. The friendly Martians are trying to build Earth clocks. It isn’t going well. At 5:00 PM on Monday, they set their

12-hour clock correctly to show 5:00. But their clock loses 10 minutes every hour (so 1 hour later it says 5:50 instead of the correct 6:00). The next time the Martians’ clock shows the correct time, what day of the week will it be? Note: 12-hour clocks only show hour and minute, not AM or PM.


2019 Shoreline Math Olympiad (Answer Key)

Fifth Grade – Mental Math 1

Problem Number

Answer Explanation

1 13 39 ÷ 3 = 13.

2 [$] 3.63 3 × 0.38 + 3 × 0.83 = 3 × (0.38 + 0.83) = 3 × 1.21 = 3.63.

3 640 [oz | ounces] There are several ways to do the multiplication, but mentally the easiest is probably 8 × 16 × 5 = 8 × 80 = 640.

Fifth Grade – Mental Math 2

Problem Number

Answer Explanation

1 1:39 PM Next simultaneous burp is LCM(30,40) = 120 seconds, or 2 minutes, after the first one at 1:37. Note: “PM” is required, per the problem.

2 90 [numbers |

[whole numbers] The numbers 10 through 99 have 2 digits each, so count up 1 through 99 and then remove 1 through 9. 99 − 9 = 90.

3 1.25 [sq in

| square inches | in2]

The length + width is 4.5 ÷ 2 = 2.25 inches. With a length of 1 inch, the width must be 2.25 − 1 = 1.25 inches and the area is 1 × 1.25 = 1.25 square inches. Note: specifying units “in” or “inches” – a length but not an area – is incorrect.


Fifth Grade - Individual Test 1

Problem Number

Answer Explanation

1 C 32 × 450 = 8 × 4 × 450 = 8 × 1800, not 8 × 900 as choice C suggests.

2 A On Moley’s legs there are 9985 + 9992 + 9996 + 9978 = (10000 − 15) + (10000 − 8) +(10000 − 4) + (10000 − 22) = 40000 − 49 moles total. If Moley has 50,000 total, we need to add 49 to get to 40,000, then another 10,000 to reach 50,000. In all, there must be 10,000 +49 = 10,049 moles on his tail.

3 C Total number of legs is (75 × 4) + (165 × 8) + (255 × 6) + (345 × 0) = 300 + 1320 +1530 + 0 = 3150.

4 A The three whole numbers must be 10, 11, 13. 10 × 11 × 13 = 1430.

5 D 25 = 5 × 5 and 81 = 9 × 9. So the perfect square numbers in between are 6 × 6 = 36, 7 ×7 = 49, 8 × 8 = 64. The sum of these is 36 + 49 + 64 = 149.

6 B

1 89< 1.3, so the flour will run out before the chocolate chips. How many cookies can Sanza

make? 1 cookie will require 1 89 teaspoons of flour, 2 will require 2 ;

9, and so on; continuing the

pattern shows that 7 whole cookies are possible, leaving 10 − 7 × 1 89= 10 − 7 × <

9= ;

9

teaspoons of flour and 10 − 7 × 1.3 = 0.9 chocolate chips.

7 C One mile is 8 furlongs, 8 × 10 = 80 chains, or 80 × 22 = 1760 yards (not 176 yards).

8 B Out of the numbers 17, 77, 90, and 101, only 77 is a factor of 1001. 1001 ÷ 17 = 58R14 (A), 1001 ÷ 77 = 13 (B), 1001 ÷ 90 = 11R11 (C), 1001 ÷ 101 = 9R92 (D).

9 D The gym must be exactly 3 units away from the library, like the classroom is. With (A) it’s 3 units below and 3 right, with (B) it’s 6 units below, with (C) it’s 3 units below and 1 right, and with (D) it’s 3 units left. Only (D) is exactly 3 units away from the library.

10 D The answer choices evaluate to ;9 (A),

>;<

(B), 8? (C), and

88;

(D), respectively. And ><− @

A= 8

8;.

11 C If you make both purchases, you find that 3 beets and 3 leeks cost 58 + 47 = 105 cents. This is 3 times the purchase that the problem asks for. Therefore 1 beet and 1 leek cost 105 ÷ 3 = 35 cents.

12 A Consecutive multiples of 3 are either odd & even or even & odd, so their sum must be odd.

13 B #3 is 8 chairs away (7 chairs between them) from #11, which is 8 chairs from #19, which in turn is 8 chairs from #3.

14 D Both 3 and 5 work. No unique answer can be determined without more information.

15 B Otto arrives at the store in 20 minutes, shops another 10 minutes, and returns home in 10 minutes (half the time he spent on the road before). 20 + 10 + 10 = 40 minutes after 1:00 PM is 1:40 PM.


Fifth Grade - Individual Test 2

Problem Number

Answer Explanation

1 B 9280 ÷ 32 = 290.

2 A 132 ÷ 7 = 18 A@≈ 19 (rounded to the nearest whole number). Or, try each choice and find that

7 × 19 = 133 comes closest to 132.

3 D 3 × 7 × 8 = 21 × 8 = 168.

4 A 2400 = 20 × 40 × 3. None of the other products yields 2400.

5 D The 1st was a Friday, so the 8th was as well, and the 7th must have been the first Thursday. February has 28 or 29 days, so the Thursdays were the 7th, 14th, 21st, 28th. Add these day numbers: 7 + 14 + 21 + 28 = 70.

6 A Try each choice. In 8 years (A), Frances will be 24 + 8 = 32 and Sam will be 8 + 8 = 16, making Frances’s age twice Sam’s.

7 C 153 ÷ 3 = 51, so we know the middle number is 51. In fact the numbers are 50, 51, 52. (Check: 50 + 51 + 52 = 153. ✓) Now find the product: 50 × 51 × 52 = 2600 × 51 = 132600.

8 B A rhombus can be a rectangle (if it’s a square), so B is false. Regarding the other choices: (A) squares are rhombuses because they have 4 congruent sides; (C) parallelograms are rectangles if their adjacent sides are perpendicular; (D) a trapezoid can have 3 congruent sides as long as 2 of those 3 are the non-parallel pair of sides.

9 C 999,999 ÷ 7 = 142,857. Multiply the digits: 1 × 4 × 2 × 8 × 5 × 7 = 8 × 40 × 7 = 2240.

10 A We’re only looking at the ones digit, so this is like multiplying 12 2’s together. 2 × 2 =4, 4 × 2 = 8, 8 × 2 = 16, 16 × 2 = 32, 32 × 2 = 64, 64 × 2 = 128, and so on. The ones digit will repeat in a pattern: 2, 4, 8, 6, 2, 4, 8, 6, …. The 12th item in this sequence is 6.

11 C Shonda’s result is (1 + 2) × (3 + 4) × (5 + 6) = 3 × 7 × 11 = 231. Pat’s result is 1 + 2 × 3 +4 × 5 + 6 = 1 + 6 + 20 + 6 = 33. [Note order of operations: multiplication before addition.] Shonda’s result is greater than Pat’s, so (A) and (D) don’t apply. The difference between the results is not 160. And indeed, 231 = 7 × 33.

12 D 3.8 × 3.8 = 14.44 (A); 4.2 × 4.2 = 17.64 (B); 5.6 × 5.6 = 31.36 (C); and 6.2 × 6.2 = 38.44 (D) Only (D) fits the WH.EE pattern (W = 3,H = 8, E = 4). Note: (D) doesn’t work because we need H ≠ E.

13 B By dividing, we find that 240 (A) is not a multiple of 14 [240 ÷ 14 = 17R2], and 266 (C) and 280 (D) are not multiples of 6 [266 ÷ 6 = 44R2, 280 ÷ 6 = 46R4].

14 B First step: 4 slices are cut in half (to make 8) and 4 are left intact: 8 + 4 = 12. Second step: 6

slices are cut in half (to make 12) and 6 are left intact: 12 + 6 = 18. Shortcut: 4 × 9;× 9;= 18.

15 D The resulting paper will be the original square with a diagonal square inside, centered and tilted at 45°. This is symmetrical horizontally, vertically, and along both diagonals.

2019 Shoreline Math Olympiad

(Answer Key)

Fifth Grade - Team Test 1 Problem Number

Answer Explanation

1 4096

Each box is the sum of two other boxes: The one to the left, and the one diagonally below-left. Fill in the rows from bottom to top. The bottom row will have 0; next row up will have 0, 0; then 0, 0, 0; then 24, 24, 24, 24; then 60, 84, 108, 132, 156; then 50, 110, 194, 302, 434, 590; then 15, 65, 175, 369, 671, 1105, 1695; and finally the top row will have 1, 16, 81, 256, 625, 1296, 2401, 4096. [Note that the pattern in the top row is 1<, 2<, 3<, …. For box A, 8< = 4096.]

2 JKJL

If we place all the fractions over a common denominator, we see that the arithmetic

sequence begins as follows: <A8;M

, A?8;M

, ?;8;M

, … So the number in the box must be 88>8;M

= ;9;<

.

3 10 The 34-cent pile can be formed from 1 quarter, 1 nickel, and 4 pennies (6 coins). The 66-cent pile can be formed from 1 half-dollar, 1 dime, 1 nickel, and 1 penny (4 coins). 6 +4 = 10. [Note that if this were only one combined pile of 100 cents, we could use 2 coins (both half-dollars).]

4 7

[students]

One approach is to make a table: Megabasketball? Yes No

Microglee? Yes 12 65 − 12 = 53 No 70 − 12 = 58 ?

All 4 boxes must add up to the total of 130 students at the school. Thus, the missing number is ?= 130 − 12 − 53 − 58 = 7. [This problem can also be solved with a Venn diagram.]

5 1368 [m |

meters]

When Imran has driven 19 m, Ameena has covered 24 m and is 24 − 19 = 5 m ahead. When Imran has driven 38 m, Ameena has covered 48 m and is 48 − 38 = 10 m ahead. For every 19 m Imran covers, Ameena’s lead grows 5 m. When Ameena laps Imran, her lead is 360 m, which is 72 × 5; so Imran has covered 72 × 19 = 1368 m.

6 180

[dinosaurs] The 15 velociraptors represent 1 − 8

;− 8

<− 8

A= 8;

8;− A

8;− 9

8;− ;

8;= 8

8; of the total. So the

total must be 15 ÷ 88;= 15 × 12 = 180.

7 10

[people | members]

Before Fluffles unfriended Gooeygoo, there were 45 friendships. How many network members would be needed for 45 friendships? If there were only 2 members, there would be 1 friendship between them. Every additional member added needs to befriend all the members already there, so with 3 members there are 1 + 2 = 3 friendships, with 4 members there are 1 + 2 + 3 = 6 friendships, and so on. Continuing the pattern, we find that 10 members would have 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45 friendships, which is the correct amount.


Fifth Grade - Team Test 2

Problem Number

Answer Explanation

1 20

[paths]

Bongo Cat must go east exactly 3 times and south exactly 3 times. List the possibilities for the first 2 moves; then for each of those, count up how many ways to perform the final 4 moves. E represents one eastward segment and S represents one southward segment.

If the first 2 moves are …

… the final 4 moves can be … … so # of possibilities

is EE

(east twice) ESSS, SESS, SSES, SSSE

(final east can be any of the 4 moves) 4

SS (south twice)

EEES, EESE, ESEE, SEEE (final south can be any of the 4 moves)

4

ES (east then south)

EESS, ESES, ESSE, SEES, SESE, SSEE (final 2 easts can be #1&2, #1&3, #1&4,

#2&3, #2&4, or #3&4 of the four) 6

SE (south then east)

[same as above] 6

Now add: 4 + 4 + 6 + 6 = 20.

2 110

[m | meters]

The length + width of the pen will be 42 ÷ 2 = 21 meters. So in meters, the pen could be 1 x 20 (for an area of 20 sq m), 2 x 19 (38 sq m), 3 x 18 (54 sq m), 4 x 17 (68 sq m), 5 x 16 (80 sq m), 6 x 15 (90 sq m), 7 x 14 (98 sq m), 8 x 13 (104 sq m), 9 x 12 (108 sq m), or 10 x 11 (110 sq m). The maximum area is 110 sq m.

3 [sum =] 34 The missing numbers are 1, 6, 7, 10, 11, 16. The top row sum is 33 plus the top-right box; the bottom row sum is 18 plus the bottom-left box. To make them equal, we must put the 1 at top-right and 16 at bottom-left. The sum of the remaining numbers is 6 +7 + 10 + 11 = 34.

4 [April] 9[th]

On April 1st, the baby shark rises from 200 m deep to 150 m, then sinks to 180 m. On April 2nd, it rises to 130 m and sinks to 160 m. On successive nights, it sinks to 140 m (April 3rd), 120 m (4th), 100 m (5th), 80 m (6th), 60 m (7th). On the 8th, the baby shark rises to 10 m and sinks to 40 m. That’s less than 50 m deep, so on the 9th, the baby shark rises to the surface.

5 633 Four numbers are possible, two starting with “1” and two starting with “2.” 102 +120 + 201 + 210 = 633.

6 22.28

[oz | ounces]

After Sammi gave out 8< of the cupcake to each friend, and before her second round of

giving, Sammi had 7.93 + 1.27 + 1.94 = 11.14 ounces for herself, and the other two

friends combined had 8; of the cupcake. Thus Sammi’s 11.14 ounces represents the

other half, and 11.14 × 2 = 22.28 ounces represents the entire cupcake.

7 Thursday

In 6 hours of real time, the Martians’ clock loses 1 hour. So in one day (24 hours of real time) it loses 4 hours. In exactly 3 days it loses 12 hours and shows the correct 12-hour time again. And 3 days after Monday is a Thursday. Or: The clock will show the correct time once it has lost 12 hours, or 720 minutes. This happens after 720 ÷ 10 = 72 hours, which is 72 ÷ 24 = 3 days after Monday, which is Thursday.

smo 2019 gr 5 mental math #1...4. mango lox needs a rectangular box to hold 2,400 cubic centimeters...

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