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Mathematics

Playing with Numbers

Number Operations and Properties
100 pts
40 questions • ~35 min
Aayush Nayak
6-B
Grade 6
YBIS
Home
Read each question carefully and answer to the best of your ability. Show all working for word problems.
1.
True / False The number 10 is a multiple of 5.
1 pt
True
False
Answer: True
2.
True / False Every multiple of 2 is an even number.
1 pt
True
False
Answer: True
3.
True / False The HCF of co-prime numbers 9 and 14 is 3.
1 pt
True
False
Answer: False
4.
True / False Multiplying any number by 1 gives the same number.
1 pt
True
False
Answer: True
5.
True / False The sum of two odd numbers is always odd.
1 pt
True
False
Answer: False
6.
True / False The number 1 is considered a prime number.
1 pt
True
False
Answer: False
7.
True / False The smallest prime number is 2.
1 pt
True
False
Answer: True
8.
True / False Zero is neither positive nor negative.
1 pt
True
False
Answer: True
9.
True / False Multiplying two negative numbers gives a positive product.
1 pt
True
False
Answer: True
10.
True / False A prime number has exactly two distinct factors: 1 and the number itself.
1 pt
True
False
Answer: True
11.
Multiple Choice What is the first step in solving 14 + 8 × 4 + 194 ÷ 7?
2 pts
A. Addition
B. Multiplication
C. Division
D. Subtraction
Answer: C. Division
12.
Multiple Choice Which operation should be performed first according to BODMAS?
2 pts
A. Addition
B. Multiplication
C. Division
D. Brackets
Answer: D. Brackets
13.
Multiple Choice What is the smallest prime number?
2 pts
A. 1
B. 2
C. 3
D. 5
Answer: B. 2
14.
Multiple Choice The HCF of 4 and 15 is:
2 pts
A. 1
B. 2
C. 4
D. None
Answer: A. 1
15.
Multiple Choice Which of the following numbers is divisible by 3?
2 pts
A. 73
B. 137
C. 54
D. 277
Answer: C. 54
16.
Multiple Choice Which number is a perfect number?
2 pts
A. 496
B. 459
C. 495
D. 469
Answer: A. 496
17.
Multiple Choice The 8th prime number minus the 12th prime number equals:
2 pts
A. 30
B. 14
C. 18
D. 28
Answer: B. 14
18.
Multiple Choice If a number is divisible by 90, it must be divisible by:
2 pts
A. 7 and 45
B. 9 and 11
C. 8 and 18
D. 5 and 9
Answer: C. 8 and 18
19.
Multiple Choice Which digit should replace '#' in 90##53 to make it divisible by 11?
2 pts
A. 3
B. 0
C. 1
D. 2
Answer: D. 2
20.
Multiple Choice What is the least number that can replace '*' in 764*52 so it is divisible by 11?
2 pts
A. 3
B. 4
C. 5
D. 6
Answer: A. 3
21.
Fill in the Blank The smallest prime number is _____.
2 pts
Answer: 2
22.
Fill in the Blank A number divisible by 10 ends with _____.
2 pts
Answer: 0
23.
Fill in the Blank To solve 36 ÷ 3 × 4, you should first perform the _____ operation.
2 pts
Answer: division
24.
Fill in the Blank The LCM of 3 and 4 is _____.
2 pts
Answer: 12
25.
Fill in the Blank The HCF of two prime numbers always equals _____.
2 pts
Answer: 1
26.
Fill in the Blank According to BODMAS, _____ should be solved first in the expression 4 + (5 × 3).
2 pts
Answer: brackets
27.
Fill in the Blank The sum of digits rule is used to check divisibility by _____.
2 pts
Answer: 3
28.
Fill in the Blank The number _____ is both a factor of itself and 0.
2 pts
Answer: 1
29.
Fill in the Blank Prime factorisation can be done using either the division method or the _____ method.
2 pts
Answer: factor tree
30.
Fill in the Blank A number divisible by both 5 and 9 is also divisible by _____.
2 pts
Answer: 45
31.
Word Problem If a number is divisible by both 6 and 8, what is the smallest such positive number? Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Find LCM of 6 and 8
Step 2: Prime factors of 6: 2, 3; Prime factors of 8: 2, 2, 2
Step 3: LCM = 2×2×2×3 = 24
Answer: 24
32.
Word Problem A car travels 150 km in 3 hours. What is its average speed? Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Speed = Distance / Time
Step 2: Speed = 150 / 3
Answer: 50 km/h
33.
Word Problem Find the least number of 5-digit divisible by 45. Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: 5-digit number: 10000
Step 2: Prime factors of 45: 3×3×5
Step 3: Least 5-digit = 45 × 223
Answer: 10035
34.
Word Problem A bus stops every 8th block and a tram stops at every 12th block. What is the first block they both stop at? Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Find LCM of 8 and 12
Step 2: Prime factors of 8: 2×2×2; Prime factors of 12: 2×2×3
Step 3: LCM = 2×2×2×3 = 24
Answer: 24
35.
Word Problem If three water tanks hold 5000L, 7500L, and 10000L respectively, what is the maximum container size to drain them exactly?
5 pts
Working:
Answer:
Worked Solution:
Step 1: Find HCF of 5000, 7500, 10000
Step 2: Prime factors of 5000: 2×2×2×5×5×5; Prime factors of 7500: 2×3×5×5×5; Prime factors of 10000: 2×2×2×5×5×5
Step 3: HCF = 5×5×5
Answer: 125
36.
Word Problem In a colony, there are 3 types of events every 4 days, 6 days, and 9 days. What is the first day they all coincide? Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Find LCM of 4, 6, 9
Step 2: Prime factors of 4: 2×2; Prime factors of 6: 2×3; Prime factors of 9: 3×3
Step 3: LCM = 2×2×3×3 = 36
Answer: 36
37.
Word Problem Calculate the number that should be added to 9813 to make it divisible by 5, 8, and 10.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Find LCM of 5, 8, 10
Step 2: Prime factors of 5: 5; Prime factors of 8: 2×2×2; Prime factors of 10: 2×5
Step 3: LCM = 2×2×2×5 = 40
Step 4: Sum = 9813 + x
Step 5: Solve: 9813 + x = multiple of 40
Answer: 27
38.
Word Problem If 764*52 needs to be divisible by 11, what single digit number replaces *? Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Apply divisibility rule of 11: Sum of odd places - sum of even places
Step 2: (7+4+5)-(6+*+2)
Step 3: Solve => 16-(*+8)=0 or multiple of 11
Answer: 3
39.
Word Problem Determine the smallest digit added to 31290876 to make it divisible by 5, 8, and 10. Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Find LCM of 5, 8, and 10
Step 2: LCM = 40
Step 3: Add digit x so that 31290876 + x
Step 4: Find smallest x such that 31290876 + x = multiple of 40
Answer: 4
40.
Word Problem What number should be subtracted from 1002 to make it divisible by 3 and 4? Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Find LCM of 3 and 4
Step 2: Prime factors of 3: 3; Prime factors of 4: 2×2
Step 3: LCM = 2×2×3 = 12
Step 4: Solve 1002 - x = multiple of 12
Answer: 2
40
Total Questions
100
Total Points
~35
Minutes