Berikut ini adalah soal beserta kunci jawaban Fermat Mathematic Olympiad (FMO) 2021 grade 8 (Sc: Edukultur Indonesia)

**A. Warm-up**

**(4 points per question / No points deducted for wrong answers)**

1. Jack has a square piece of paper. He folds it twice along the dashed lines and cuts the paper as in the picture below. How many pieces will he get after opening it?

A) 5

B) 12

C) 7

D) 6

E) 9

Answer : A

2. The librarian found that for every 12 minutes, there is another student entering the library. The students must leave after reading for 90 minutes. At most how many students are still in the library when it is about to closed?

A) 4

B) 5

C) 6

D) 7

E) 8

Answer : E

3. There are 4 friends including Jane, Josh, Jack and Jill. They bought 9 different

shirts listed in the table below. Jane bought 2 shirts with the same price. Josh

bought the top three cheapest items. Jack had to pay 50 USD for all of his

shirts. Find the color and the size of Jill’s shirt.

A) White – L

B) Grey – M

C) Black – S

D) Black – M

E) Grey – L

Answer : D

4. What is the weight of the heaviest object?

A) 0.4 kg

B) 0.8 kg

C) 1.6 kg

D) 1.2 kg

E) 2 kg

Answer : C

5. The diagram shows a quadrilateral *PQRS* in which *PQ* and *QR* have the same length. Also, *PR* bisects *SPQ* and the ratio of *SPR* to PRS is 2:3. Given that *PSR* = 110° . How large is *PQR*?

A) 124º

B) 120º

C) 114º

D) 126º

E) 110º

Answer : A

**B. Speed-up**

**(6 points per question / No points deducted for wrong answers)**

6. Given a table in which three squares have been filled with numbers. The remaining squares need to be filled with numbers so that the sum of each row, each column and each of the two diagonals are the same. Find the number in the cell with question mark.

A) 6

B) 12

C) 8

D) 10

E) 14

Answer : C

7. Given 3 circles externally tangent to each other with center A, B and C. If

*AB* = 7cm; *AC* = 8cm and *BC* = 9cm , what is the total area of these three circles?

A) 29π

B) 48π

C) 24π

D) 50π

E) 194π

Answer : D

8. Each letter is a distinct digit. Find the value of A + P + P + L + E.

A) 11

B) 12

C) 13

D) 14

E) 15

Answer : B

9. Two friends start riding bike at the same time from A but they follow 2 different

paths as the figure below. Since their speed ratio is 3 : 4, they finally meet each other at D which is 2km from C. Find the length of the shorter path from A to D.

A) 28km

B) 16km

C) 8km

D) 6km

E) 12km

Answer : E

10. While reading a book, Wendy reads one page more each day than the preceding day. After 4 days, she has read 150 pages. In exactly 10 days, she finishes the book. How many pages are there in this book?

A) 395

B) 405

C) 375

D) 410

E) 385

Answer : B

**C. Challenge**

**(8 points per question / No points deducted for wrong answers)**

11. Peter is putting 99 apples into boxes of two different sizes. A large box can hold 12 apples while a small box can hold 5 apples. All boxes must be full. How many boxes will he need if this number must be greater than 10?

A) 15

B) 17

C) 12

D) 16

E) 14

Answer : B

12. Oliver did a road trip and passed through 5 paths A, B, C, D, E with a total time of 2 hours. The time and length of each path is recorded in the diagram with equally-spaced lines below. Find his speed on path B given that the whole journey is 75.6km long.

A) 68km/h

B) 64km/h

C) 60km/h

D) 72km/h

E) 54km/h

Answer : C

13. A number is called “lucky” if it is divisible by 2 and all of the digits are different. When swapping the first and the last digit, we get a new number which is still divisible by 2. How many 4-digit “lucky” numbers are there?

A) 1600

B) 1120

C) 672

D) 1080

E) 864

Answer : C

14. Fred wants to put 7 identical cubes into a tank with base 15cm x 10cm and a water level of 4cm. At most how high can the water level reach?

A) 7.8cm

B) 10.8cm

C) 4.8cm

D) 9.8cm

E) 8.8cm

Answer : D

15. Given a square paper with side length 20cm. Andy folded it as the figure below to get a trapezium whose perimeter is 10cm less than the original square. Find the area (in \(cm^2\)) of the trapezium.

A) \(150cm^2\)

B) \(250cm^2\)

C) \(350cm^2\)

D) \(280cm^2\)

E) None of the above

Answer : B

**D. Star of hope**

**(10 points per question/ 10 points deducted for wrong answer)**

In this part, you must write your answer on the answer sheet.

16. A hospital ward has 18 nurses working on three eight-hour shifts a day. During the pandemic, these nurses work on the following conditions:

a. 13 nurses will report on the first shift

b. 8 nurses will report on the second shift

c. 6 nurses will report on the third shift

If each of the nurses must report at least one shift in a day, what is the greatest

possible number of nurses that must report in all three shifts?

Answer : 4