**Facebook Fermat Mathematical Olympiad**)

**A. Warm-up**

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

A) 1

B) 2

C) 3

D) 4

E) 5

Answer : B

A) 16

B) 9

C) 12

D) 10

E) 8

Answer : B

B) 140

C) 150

D) 160

E) 170

Answer : C

4. Tom can cycle at the speed of 20km/h and run at the speed of 12km/h. He takes part in a combined cycling and running race which covers a total distance of 21 km. If he cycles for 45 minutes, how long does it take him to finish the whole race?

A) 20 min

B) 30 min

C) 45 min

D) 60 min

E) 75 min

Answer : E

5. A star is given below. Find the size of the interior angle at vertex A.

A) \(10^o\)

B) \(20^o\)

C) \(30^o\)

D) \(35^o\)

E) \(40^o\)

Answer : C

**B. Speed-up**

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

6. When Peter adds two 2-digit numbers, he fills each of the cells below with one of the digits 0, 1, 2, 3, 4, 5, 6 so that every cell is different. What is the units digit of the sum?

A) 2

B) 3

C) 4

D) 5

E) 6

Answer : D

7. At the weekend, Anna drives to her grandparents’ house. She goes 30km straight, then turns right and kept going for 25km. Then she turns right again and goes 10km straight. Finally, she turns right and goes another 10km. Find the shortest distance between Anna’s house and the grandparent’s house.

A) 25km

B) 75km

C) 35km

D) 15km

E) 55km

Answer : A

8. Based on the pattern below, how many small squares are there in the 50th figure counting from the left?

A) 302

B) 308

C) 312

D) 316

E) None of the above

Answer : A

9. Given three balances below. Find the weight of the heaviest ball.

A) 1.8kg

B) 0.4kg

C) 2.0kg

D) 1.2kg

E) 1.6kg

Answer : E

10. Candace stacked 6 boxes of volume 8cm^3 each to build the figure below. She painted all surfaces of the stair (except the bottom). Find the total unpainted area in cm^2.

A) 72

B) 56

C) 144

D) 76

E) 112

Answer : A

**C. Challenge**

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

11. Two identical equilateral triangles are overlapped to form a star as in the figure below. Find the area of the star given that each triangle has an area of 36cm^2?

A) 60cm^2

B) 72cm^2

C) 54cm^2

D) 48cm^2

E) None of the above

Answer : D

12. A grocery store sold 9 packets with 3, 7, 8, 10, 11, 12, 14, 15, and, 20 eggs respectively. Sofia and Nana bought 4 packets for each person. Given that the number of eggs Nana bought is 2 times the number of Sofia’s eggs. How many eggs are there in the remaining packet?

A) 7

B) 11

C) 10

D) 14

E) 20

Answer : C

13. Straight lines are drawn on 3 faces of a cuboid as in the figure below. An ant is standing at one corner of the cuboid. It wants to reach the sugar cubes but it can only go along the drawn lines or the edges. Given that it always moves in such a way that it gets closer to sugar and farther away from the original spot. How many different ways can it do that?

A) 20

B) 26

C) 24

D) 16

E) 18

Answer : C

14. Given a square paper with a perimeter of 8m. It is placed on a round table such that all vertices lie on the circle. Can you find the area of the table NOT covered by the paper?

A) 8π – 8

B) 32π – 64

C) 4π – 8

D) 2π – 4

E) 4π – 4

Answer : D

15. Father goes from home to the park, then goes to Lucy’s summer camp to take her home. Given that the diagram below represents the father’s distance from home and the average speed of the whole trip is 24km/h. When does father get to Lucy’s camp?

A) 12:30

B) 11:30

C) 12:15

D) 12:15

E) None of the above

Answer : A

**D. Star of hope**

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

16. Four friends need to go through an extremely dark tunnel. Because the tunnel is so small and stuffy, no more than 2 people can go in at the same time. Unfortunately, they have only one candle. Person or people going in the tunnel must carry the candle to see the way. If they go in the tunnel in a pair, they must crawl together at the speed of the slower person. The amount of time they need to pass through the tunnel alone is recorded in the table below.

At least how many minutes does it take all 4 people to pass through that tunnel?

Answer : 20