Berikut ini adalah soal beserta kunci jawaban Fermat Mathematic Olympiad (FMO) 2021 (Sc: Halaman facebook FMO)

1. Anna has a circular paper. She folds it twice and cuts along the red line as

instructed below. How many pieces of paper will she get?

A. 3

B. 5

C. 12

D. 8

E. 10

2. Solve the riddle below to find the sum \(A + B\).

A. 233

B. 89

C. 123

D. 165

E. 178

3. Abby and her father turn their back against each other and go

straight for \(20 m\). Then they both turn left and walk for \(15 m\). How many meters are Abby far from her father now?

A. 40m

B. 50m

C. 25m

D. 35m

E. 30m

4. Ashley writes ten expressions on a paper. Ashley asks Tracy to find all expressions whose value is a positive integer. At most how many expressions can Tracy find?

A. 5

B. 6

C. 7

D. 8

E. 9

5. A group of 100 workers wanted to make a 7-floor building. They built the first floor in 1 month. Then, another group of 100 workers came and they worked together. Given that their productivity is the same, in total how many months do they need to complete the building?

A. 4

B. 5

C. 7

D. 8

E. 13

6. The worker uses 12 cubic blocks to build a 2-step flight of stair as the figure below. To prevent it from getting damaged, he covers all the surfaces of the stair with square hard tiles of side length \(15cm\), except for the bottom. Find the total area of the hard tiles needed for this stair in \(m^2\).

A. \(8550 cm^2\)

B. \(2280 cm^2\)

C. \(6750 cm^2\)

D. \(4275 cm^2\)

E. \(4285 cm^2\)

7. There are 40 students in class 7A. Some students must do a survey about the favorite desserts of all students in the class. Their findings are listed below:

Amy: “65% of the class like ice-creams.”

Ben: “Five eights of the class like chocolates.”

Claire: “75% of the class like yogurt.”

Derek: “Two thirds of the class like flan.”

Erik: “60% of the class like cookies.”

Which student must have done the survey wrongly?

A. Amy

B. Ben

C. Claire

D. Derek

E. Erik

8. Six students in class 7C do a medical check. Their heights and weights are recorded in the graph below. Among six friends, Joey is the heaviest and Lucy is the fourth lightest. How many centimeters is Joey higher than Lucy?

A. 0 cm

B. 2 cm

C. 4 cm

D. 8 cm

E. 10 cm

9. The traffic lights at three different road crossings change after every 30 seconds, 45 seconds and 60 seconds. If they all change simultaneously at 08:20 for the first time, then when do they change simultaneously for the fifth time?

A. 08:23

B. 08:32

C. 08:25

D. 08:24

E. 08:35

10. Which cube below can be made from this net?

A.

B.

C.

D.

E.

11. Greg starts with 0 points in a riddle game. For each question, if he answers correctly, his score is added five points. If he doesn’t answer, his score is added three points. If he answers wrongly, his score stays the same. In the end of the game, he gets 89 points. At least how many questions did he receive?

A. 18

B. 19

C. 20

D. 21

E. 22

12. In the will of Mr. Chris, he divides his square piece of land into 5 parts for 5 children. The land given to Betty, Cindy, Dolly and Emma are squares. Only Andy’s land is rectangular with perimeter 560m. Find the perimeter of Mr. Chris’s land.

A. 1400m

B. 1500m

C. 1600m

D. 1800m

E. None of the above

13. Andy and Billy go jogging back and forth from home to the park. They both start at 06:45 from home. Andy walks at the speed 3km/h and Billy runs at the speed 6km/h. After the start, Billy meets Andy for the second time at 07:09. How far is it from home to the park?

A. 600m

B. 900m

C. 1km

D. 1200m

E. None of the above

14. Identical cubes are placed on top of each other to form a solid shape. The top view and the view from one side of the shape are shown below. At most how many cubes does the shape contain?

A. 11

B. 12

C. 13

D. 14

E. None of the above

15. Mulan fills number in a sequence of groups with spiral pattern as below. Find the sum of all numbers in the last column of the \(5^{th}\) group.

A. 509

B. 500

C. 505

D. 504

E. None of the above

16. Seven candidates: Aurora, Brenna, Clara, Donna, Erik, Freya, and Gloria, were invited to an interview. Immediately upon arrival, they were sent to one of three interview rooms: 1, 2 and 3. After the interview, they have the following discussion:

Brenna: “I was the third person to enter Room 1”.

Clara: “I was the last person to enter my room.”

Erik: “I was the only person in my room.”

Freya: “Three people including Aurora were already in the room when I entered.”

Gloria: “I was one among the two candidates taken to Room 2.”

**List all interviewees taken to room 1**.

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