Mathematics Test No. 1
LCM • HCF • Fractions • Word Problems • BODMAS
1
Three buses leave at intervals of 15, 20 and 30 minutes.
LCM of 15, 20 and 30 = 60
So, they will leave together again after 60 minutes.
Answer: 60 minutes
So, they will leave together again after 60 minutes.
Answer: 60 minutes
2
Chocolates are packed in groups of 6, 10 and 15, with 3 chocolates left each time.
LCM of 6, 10 and 15 = 30
Required number = 30 + 3 = 33
Answer: 33 chocolates
Required number = 30 + 3 = 33
Answer: 33 chocolates
3
Find the smallest number leaving remainder 5 when divided by 8, 12 and 18.
LCM of 8, 12 and 18 = 72
Required number = 72 + 5 = 77
Answer: 77
Required number = 72 + 5 = 77
Answer: 77
4
Find the smallest number that leaves remainders 3, 6 and 8 when divided by 8, 11 and 13 respectively.
We need:
N ≡ 3 (mod 8)
N ≡ 6 (mod 11)
N ≡ 8 (mod 13)
The smallest number satisfying all three conditions is 1139.
Answer: 1139
N ≡ 3 (mod 8)
N ≡ 6 (mod 11)
N ≡ 8 (mod 13)
The smallest number satisfying all three conditions is 1139.
Answer: 1139
5
Find the smallest 4-digit number divisible by 8, 10, 12 and 20.
LCM = 120
Smallest 4-digit multiple = 120 × 9 = 1080
Answer: 1080
Smallest 4-digit multiple = 120 × 9 = 1080
Answer: 1080
6
Find the greatest 4-digit number divisible by 10, 16, 20 and 40.
LCM = 80
Greatest 4-digit multiple = 80 × 124 = 9920
Answer: 9920
Greatest 4-digit multiple = 80 × 124 = 9920
Answer: 9920
7
There are 96 pencils, 144 erasers and 192 sharpeners. Find the greatest number of identical kits that can be made.
HCF of 96, 144 and 192 = 48
Therefore, greatest number of identical kits = 48.
Answer: 48 kits
Therefore, greatest number of identical kits = 48.
Answer: 48 kits
8
Find the greatest number that divides 148, 196 and 244 leaving the same remainder.
196 − 148 = 48
244 − 196 = 48
HCF(48, 48) = 48
Answer: 48
244 − 196 = 48
HCF(48, 48) = 48
Answer: 48
9
Find the greatest number that divides 43, 68 and 93 leaving remainders 3, 4 and 5 respectively.
43 − 3 = 40
68 − 4 = 64
93 − 5 = 88
HCF of 40, 64 and 88 = 8
Check:
43 ÷ 8 → remainder 3
68 ÷ 8 → remainder 4
93 ÷ 8 → remainder 5
Answer: 8
68 − 4 = 64
93 − 5 = 88
HCF of 40, 64 and 88 = 8
Check:
43 ÷ 8 → remainder 3
68 ÷ 8 → remainder 4
93 ÷ 8 → remainder 5
Answer: 8
10
Find the greatest number that divides 152, 200 and 248 leaving remainder 8 each time.
152 − 8 = 144
200 − 8 = 192
248 − 8 = 240
HCF(144, 192, 240) = 48
Answer: 48
200 − 8 = 192
248 − 8 = 240
HCF(144, 192, 240) = 48
Answer: 48
11
2 7/10 + 13/15 + 11/30 = ?
LCM of 10, 15 and 30 = 30
2 7/10 = 67/30
13/15 = 26/30
11/30 = 11/30
67/30 + 26/30 + 11/30 = 104/30
= 52/15
= 3 7/15
Answer: 3 7/15
2 7/10 = 67/30
13/15 = 26/30
11/30 = 11/30
67/30 + 26/30 + 11/30 = 104/30
= 52/15
= 3 7/15
Answer: 3 7/15
12
2 7/12 − 4/15 = ?
2 7/12 = 31/12
LCM of 12 and 15 = 60
31/12 = 155/60
4/15 = 16/60
155/60 − 16/60 = 139/60
= 2 19/60
Answer: 2 19/60
LCM of 12 and 15 = 60
31/12 = 155/60
4/15 = 16/60
155/60 − 16/60 = 139/60
= 2 19/60
Answer: 2 19/60
13
16/21 × 35/24 × 18/25 × 15/12 = ?
After cancelling common factors:
= 1
Answer: 1
= 1
Answer: 1
14
72/91 × 65/36 × 42/25 × 15/28 = ?
After cancellation:
= 9/7
= 1 2/7
Answer: 1 2/7
= 9/7
= 1 2/7
Answer: 1 2/7
15
18/25 ÷ 27/35 = ?
Change division to multiplication:
18/25 × 35/27
= 2/5 × 7/3
= 14/15
Answer: 14/15
18/25 × 35/27
= 2/5 × 7/3
= 14/15
Answer: 14/15
16
2 1/3 − 7/12 + 5/18 = ?
2 1/3 = 7/3
LCM of 3, 12 and 18 = 36
7/3 = 84/36
7/12 = 21/36
5/18 = 10/36
84/36 − 21/36 + 10/36 = 73/36
= 2 1/36
Answer: 2 1/36
LCM of 3, 12 and 18 = 36
7/3 = 84/36
7/12 = 21/36
5/18 = 10/36
84/36 − 21/36 + 10/36 = 73/36
= 2 1/36
Answer: 2 1/36
17
Vaishnavi has 2 3/4 litres of juice and adds 1 5/6 litres more. How much juice does she have altogether?
2 3/4 = 11/4
1 5/6 = 11/6
LCM = 12
11/4 = 33/12
11/6 = 22/12
33/12 + 22/12 = 55/12
= 4 7/12 litres
Answer: 4 7/12 litres
1 5/6 = 11/6
LCM = 12
11/4 = 33/12
11/6 = 22/12
33/12 + 22/12 = 55/12
= 4 7/12 litres
Answer: 4 7/12 litres
18
A container has 5 7/8 litres of liquid. If 2 5/12 litres and 1 1/6 litres are used, how much remains?
5 7/8 = 47/8
2 5/12 = 29/12
1 1/6 = 7/6
LCM = 24
47/8 = 141/24
29/12 = 58/24
7/6 = 28/24
141/24 − 58/24 − 28/24 = 55/24
= 2 7/24 litres
Answer: 2 7/24 litres
2 5/12 = 29/12
1 1/6 = 7/6
LCM = 24
47/8 = 141/24
29/12 = 58/24
7/6 = 28/24
141/24 − 58/24 − 28/24 = 55/24
= 2 7/24 litres
Answer: 2 7/24 litres
19
Each section needs 2 1/4 litres of paint. How much paint is needed for 5 sections?
2 1/4 = 9/4
9/4 × 5 = 45/4
= 11 1/4 litres
Answer: 11 1/4 litres
9/4 × 5 = 45/4
= 11 1/4 litres
Answer: 11 1/4 litres
20
A ribbon is 12 1/2 metres long. How many complete decorations of 1 1/4 metres can be made?
12 1/2 = 25/2
1 1/4 = 5/4
25/2 ÷ 5/4
= 25/2 × 4/5
= 10
Answer: 10 complete decorations
1 1/4 = 5/4
25/2 ÷ 5/4
= 25/2 × 4/5
= 10
Answer: 10 complete decorations
21
Vaishnavi has 7/8 litre of juice and uses 1/4 litre. How much juice is left?
1/4 = 2/8
7/8 − 2/8 = 5/8
Answer: 5/8 litre
7/8 − 2/8 = 5/8
Answer: 5/8 litre
22
[36 ÷ (3 + 3)] × {8 − (5 − 2)} = ?
[36 ÷ 6] × {8 − 3}
= 6 × 5
= 30
Answer: 30
= 6 × 5
= 30
Answer: 30
23
300 ÷ {5 × [2 + (7 − 4)]} + 2 of [12 − {3 × (2 + 1)}] = ?
300 ÷ {5 × [2 + 3]} + 2 of [12 − {3 × 3}]
= 300 ÷ (5 × 5) + 2 of (12 − 9)
= 300 ÷ 25 + 2 × 3
= 12 + 6
= 18
Answer: 18
= 300 ÷ (5 × 5) + 2 of (12 − 9)
= 300 ÷ 25 + 2 × 3
= 12 + 6
= 18
Answer: 18