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JMC 2014 Challenge

1. What is ( 999 − 99 + 9 ) ÷ 9 ?

‍

A:
91
B:
99
C:
100
D:
101
E:
109

2. How many minutes are there in 1/12 of a day?

‍

A:
240
B:
120
C:
60
D:
30
E:
15

3. In my row in the theatre the seats are numbered consecutively from T1 to T50. I am sitting in seat T17 and you are sitting in seat T39.

How many seats are there between us?

‍

A:
23
B:
22
C:
21
D:
20
E:
19

4. The number 987 654 321 is multiplied by 9.

‍
How many times does the digit 8 occur in the result?

‍

A:
1
B:
2
C:
3
D:
4
E:
9

5. What is the difference between the smallest 4-digit number and the largest 3-digit number ?

‍

A:
1
B:
10
C:
100
D:
1000
E:
9899

The diagram shows a square divided into strips of equal width.

‍

Three strips are black and two are grey.

What fraction of the perimeter of the square is grey?

A:
$\frac{1}{5}$
B:
$\frac{1}{4}$
C:
$\frac{4}{25}$
D:
$\frac{1}{3}$
E:
$\frac{2}{5}$

7. What is 2014 − 4102?

‍

A:
−2012
B:
−2088
C:
−2092
D:
−2098
E:
−2112

8. How many prime numbers are there in the list

‍
1, 12, 123, 1234, 12 345, 123 456 ?

‍

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

9. Triangles XYZ and PQR are drawn on a square grid.

What fraction of the area of triangle XY Z is the area of triangle PQR?

‍

A:
$\frac{1}{4}$
B:
$\frac{7}{18}$
C:
$\frac{1}{2}$
D:
$\frac{5}{18}$
E:
$\frac{1}{3}$

10. An equilateral triangle is surrounded by three squares, as shown.

‍

‍

‍

What is the value of x?

‍

A:
15
B:
18
C:
24
D:
30
E:
36

11. The first two terms of a sequence are 1 and 2.

Each of the following terms in the sequence is the sum of all the terms which come before it in the sequence.

Which of these is not a term in the sequence?

‍

A:
6
B:
24
C:
48
D:
72
E:
96

12. In this subtraction, P, Q, R, S and T represent single digits.

‍

What is the value of P + Q + R + S + T ?

A:
30
B:
29
C:
28
D:
27
E:
26

13. A rectangle is split into triangles by drawing in its diagonals.

‍

What is the ratio of the area of triangle P to the area of triangle Q?

A:
1 : 1
B:
1 : 2
C:
2 : 1
D:
2 : 3
E:
the ratio depends on the lengths of the sides of the rectangle

14. Which of these is equal to one million millimetres?

‍

A:
1 metre
B:
10 metres
C:
100 metres
D:
1 kilometre
E:
10 kilometres

15. The diagram shows a rectangular envelope made by folding (and gluing) a single sheet of paper.

‍

What could the original unfolded sheet of paper look like?

(The dashed lines are the fold lines.)

‍

A:
B:
C:
D:
E:
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