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JMC 2022 Challenge cont...

16. The diagram shows a seven-sided polygon, π‘ƒπ‘„π‘…π‘†π‘‡π‘ˆπ‘‰. It is formed from two equilateral triangles π‘ƒπ‘„π‘Š and π‘†π‘‡π‘ˆ of side-length 5 cm and 8 cm respectively. The two triangles overlap in an equilateral triangle of side-length 2 cm.

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What is the perimeter of π‘ƒπ‘„π‘…π‘†π‘‡π‘ˆπ‘‰?

A:
27 cm
B:
30 cm
C:
33 cm
D:
36 cm
E:
39 cm

17. Amrita and Beatrix play a game in which each player starts with 10 counters. In each round of thegame, one player wins and is given 3 counters; and her opponent has 1 counter removed. At the endof the game, Amrita and Beatrix have 40 counters and 16 counters respectively.How many rounds of the game did Amrita win?

A:
10
B:
11
C:
12
D:
13
E:
14

18. The diagram shows a parallelogram.

What is the value of 𝑦?

A:
22
B:
24
C:
25
D:
28
E:
30

19. At the start of the day I had three times as many apples as pears. By the end of the day, after eating five apples but no pears, I had twice as many pears as apples.

How many pieces of fruit did I have at the start of the day?

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A:
4
B:
8
C:
12
D:
16
E:
20

20. During a particularly troublesome lesson, the following conversation occurs:

Pam: "I always tell the truth."

Quentin: "Pam is lying."

Roger: "Both Pam and Quentin are lying."

Susan: "Everyone is lying."

Terry: "Everyone is telling the truth."

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How many people are telling the truth?

A:
0
B:
1
C:
2
D:
3
E:
4

21. Two lists of numbers are as shown below.

Jenny decided she would move one number from List S to List T and one number from List T to List S so that the sum of the numbers in the new List S is equal to the sum of the numbers in the new List T. In how many ways could she do this?

A:
1
B:
2
C:
3
D:
4
E:
5

22. A triangular pyramid with vertices 𝑇, π‘ˆ, 𝑉 and 𝑄 is removed from the solid cube shown.

How many edges does the remaining solid have?

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A:
4
B:
6
C:
8
D:
10
E:
12

23. The price of a train ticket increased by 5% and then decreased by 20% in a special offer. It was then Β£4 less expensive than its original price.

What was the original price of the ticket?

‍

A:
Β£8.60
B:
Β£13
C:
Β£20.40
D:
Β£25
E:
Β£26.40

24. Flori’s Flower shop contains fewer than 150 flowers. All the flowers are purple, yellow, red or white.The ratio of purple flowers to yellow flowers is 1 : 2, the ratio of yellow flowers to red flowers is 3 : 4and the ratio of red flowers to white flowers is 5 : 6.

How many flowers are there in Flori’s shop?

A:
133
B:
136
C:
139
D:
142
E:
145

25. In the number pyramid shown, each cell above the bottom row contains the sum of the numbers in the two cells immediately below it. The sum of the numbers in the bottom row is 17.

What is the central number of the bottom row?

A:
2
B:
3
C:
4
D:
5
E:
6
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