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JMC 2015 Challenge

1. Which of the following calculations gives the largest answer?

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A:
1 − 2 + 3 + 4
B:
1 + 2 − 3 + 4
C:
1 + 2 + 3 − 4
D:
1 + 2 − 3 − 4
E:
1 − 2 − 3 + 4

2. It has just turned 22:22.

‍
How many minutes are there until midnight?

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A:
178
B:
138
C:
128
D:
108
E:
98

What is the value of

‍

A:
1
B:
8
C:
678
D:
823
E:
12 359

4. In this partly completed pyramid, each rectangle is to be filled with the sum of the two numbers in the rectangles immediately below it.

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What number should replace x?

‍

A:
3
B:
4
C:
5
D:
7
E:
12

5.

What is that number?

‍

A:
24
B:
36
C:
48
D:
60
E:
72

6. What is the value of x in this triangle?

‍

‍

A:
45
B:
50
C:
55
D:
60
E:
65

7. The result of the calculation 123 456 789 × 8 is almost the same as 987 654 321 except that two of the digits are in a different order.

What is the sum of these two digits?

A:
3
B:
7
C:
9
D:
15
E:
17

8. Which of the following has the same remainder when it is divided by 2 as when it is divided by 3?

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A:
3
B:
5
C:
7
D:
9
E:
11

9. According to a newspaper report, “A 63-year-old man has rowed around the world without leaving his living room.” He clocked up 25 048 miles on a rowing machine that he received for his 50th birthday.

Roughly how many miles per year has he rowed since he was given the machine?

A:
200
B:
500
C:
1000
D:
2000
E:
4000

10.

What is the largest value of all the expressions that can be obtained in this way?

‍

A:
10
B:
14
C:
15
D:
24
E:
25

11. What is the smallest prime number that is the sum of three different prime numbers?

A:
11
B:
15
C:
17
D:
19
E:
23

12. A fish weighs the total of 2 kg plus a third of its own weight.

What is the weight of the fish in kg?

‍

A:
2 1/3
B:
3
C:
4
D:
6
E:
8

13. In the figure shown, each line joining two numbers is to be labelled with the sum of the two numbers that are at its end points.


How many of these labels are multiples of 3?

A:
10
B:
9
C:
8
D:
7
E:
6

14. Digits on a calculator are expressed by a number of horizontal and vertical illuminated bars.

‍

‍

The digits and the bars which represent them are shown in the diagram.

‍

How many digits are both prime and represented by a prime number of illuminated bars?

‍

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

15. Which of the following is divisible by all of the integers from 1 to 10 inclusive?

A:
23 × 34
B:
34 × 45
C:
45 × 56
D:
56 × 67
E:
67 × 78
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