UKMT JMC 2025

25 questions

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UKMT JMC 2025 0/25
1 Algebra · Level 3
What is \(10%\) of \(\dfrac{1}{2}\) of \(20\)?
A
1
B
2
C
5
D
10
E
20
2 Algebra · Level 3
What is the value of \(\dfrac{4444 + 5555}{1111 + 2222}\)?
A
3
B
6.5
C
33
D
333
E
3333
3 Number Theory · Level 3
How many of the following are factors of 2025? 15 25 45 75 225
A
1
B
2
C
3
D
4
E
5
4 Algebra · Level 3
In March 2024, the British runner, Jasmin Paris, became the first woman ever to finish the 100-mile 'Barkley Marathons' in Tennessee. Her finishing time of 59 hours, 58 minutes and 21 seconds meant that she narrowly beat the cut-off time of 60 hours for the event. By how many seconds did Jasmin beat this cut-off time?
A
99
B
109
C
119
D
129
E
139
5 Geometry · Level 3
The diagram shows the square and the equilateral triangle. What is the size of the angle?
question image
A
\(10°\)
B
\(12°\)
C
\(15°\)
D
\(22 \dfrac{1}{2} °\)
E
\(30°\)
6 Algebra · Level 3
Carol and Sandra swim at their local 25 m pool. Sandra always swims 4 lengths in the same amount of time as Carol swims 3 lengths. One Monday morning, Carol swims 36 lengths. How far would Sandra swim in the same time?
A
600 m
B
675 m
C
900 m
D
1200 m
E
1350 m
7 Number Theory · Level 3
What is the difference between the smallest four-digit multiple of 3 and the largest three-digit multiple of 4?
A
3
B
4
C
5
D
6
E
7
8 Algebra · Level 3
The country which, on average, eats the most chocolate per person is Switzerland, with the average person consuming 8.8 kg each year. How many 100 g chocolate bars would this be?
A
8.8
B
88
C
880
D
8800
E
88 000
9 Number Theory · Level 3
All four digits of 2 two-digit numbers are different. What is the smallest possible sum of the two numbers?
A
30
B
33
C
37
D
40
E
42
10 Algebra · Level 3
The length of a turtle is 60 cm plus a third of its length. How long is the turtle?
A
70 cm
B
75 cm
C
85 cm
D
90 cm
E
120 cm
11 Number Theory · Level 3
Three consecutive one-digit positive integers are a square, a cube and a prime (not necessarily in that order). What is the product of the three integers?
A
0
B
6
C
60
D
210
E
504
12 Geometry · Level 3
Two identical squares, \(P Q R S\) and \(T U V W\), overlap to form the 21 cm by 12 cm rectangle \(P Q V W\) shown. What is the area, in \(cm^2\), of the shaded rectangle \(T U R S\)?
question image
A
24
B
36
C
48
D
72
E
96
13 Algebra · Level 3
In a sequence of rectangles, the first has height 10 cm and width 13 cm. Each of the following rectangles is 2 cm higher and 1 cm wider than the previous rectangle in the sequence. How many rectangles in this sequence are also squares?
A
0
B
1
C
2
D
4
E
an infinite number
14 Number Theory · Level 3
Which of these is equal to \(3^3 + 4^3 + 5^3\)?
A
\(6^3\)
B
\(8^3\)
C
\(10^3\)
D
\(12^3\)
E
\(12^9\)
15 Algebra · Level 3
Gill has had a baby girl! Weighing the baby at the clinic was not as much of a problem as when Gill was small, but the only available scales measured in imperial units. Baby weighed 8 pounds 13 ounces. Given that there are 16 ounces in a pound and 1 ounce is equivalent to approximately 28.35 grams, what was the approximate weight, in kilograms, of Gill's baby?
A
3 kg
B
4 kg
C
5 kg
D
6 kg
E
7 kg
16 Algebra · Level 3
What is the sum of \(20%\) of \(40%\) of 60 and \(40%\) of \(60%\) of 80?
A
20
B
20.4
C
24
D
24.4
E
28
17 Counting and Probability · Level 3
The diagram shows three pairs of parallel line segments. Altogether, how many triangles are there in the diagram?
question image
A
4
B
6
C
8
D
10
E
12
18 Number Theory · Level 3
A particular number has exactly nine factors, including 1 and itself. The number has 9 and 12 as factors. What is the number?
A
24
B
36
C
48
D
72
E
144
19 Counting and Probability · Level 3
Ibraheem has 10 cards. Four display the letter P; three display Q; two display R and one displays S. He also has 10 counters. One shows the number 3; two show 1; three show 4 and four show 2. He places one counter on the top of each card so that every pairing is different. Which one of these pairings does he *not* make?
A
P2
B
R4
C
Q1
D
R2
E
S4
20 Geometry · Level 3
\(P\), \(Q\), \(R\) and \(S\) are four points in that order on a straight line; \(P R = 6\) cm, \(Q S = 4\) cm and \(R\) is 1 cm nearer to \(S\) than it is to \(Q\). What is the length of \(P S\)?
A
7 cm
B
7.5 cm
C
8 cm
D
8.5 cm
E
9 cm
21 Geometry · Level 3
In the diagram, \(P Q R S\) and \(J K L M\) are squares. Each corner of \(J K L M\) is one third of the way along an edge of \(P Q R S\). What is the ratio of the area of \(J K L M\) to the area of \(P Q R S\)?
question image
A
\(1 : 2\)
B
\(5 : 9\)
C
\(3 : 5\)
D
\(4 : 7\)
E
\(3 : 4\)
22 Algebra · Level 3
Idil has 12 bags of sweets. Some bags contain 3 mints, 4 toffees and a fudge; some bags contain 4 mints, 5 toffees and 2 fudges; the remaining bags contain 6 mints and 3 fudges. The bags contain 31 toffees in total. In total, how many fudges do the bags contain?
A
22
B
23
C
24
D
25
E
26
23 Algebra · Level 3
The map in the diagram shows three towns and the roads between them. The length of the road between any two towns is a whole number of kilometres. The route from \(P\) to \(R\) via \(Q\) is twice as long as the direct route from \(P\) to \(R\). The route from \(P\) to \(Q\) via \(R\) is three times as long as the direct route from \(P\) to \(Q\). Which of the following could be the length of the route from \(P\) back to \(P\) via \(Q\) and \(R\)?
question image
A
74 km
B
81 km
C
95 km
D
108 km
E
124 km
24 Number Theory · Level 3
When 180 is divided by a positive integer \(N\), the remainder is 5. For how many values of \(N\) is this true?
A
4
B
5
C
6
D
7
E
8
25 Geometry · Level 3
Given a cube, how many equilateral triangles are there whose vertices are three vertices of the cube?
A
1
B
3
C
6
D
8
E
24

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