StudentAayush Nayak
Class6-B
GradeGrade 6
SchoolYBIS
1.
True / False
(1 pts)
Zero is a whole number but not a natural number.
2.
True / False
(1 pts)
The successor of 9,999 is 10,000.
3.
True / False
(1 pts)
Whole numbers are closed under subtraction.
4.
True / False
(1 pts)
In the Indian system, 1,00,000 is called one lakh.
5.
True / False
(1 pts)
The Roman numeral XL represents 60.
6.
True / False
(1 pts)
Every prime number greater than 2 is odd.
7.
True / False
(1 pts)
If a number is divisible by 9, it is always divisible by 3.
8.
True / False
(1 pts)
The number 1 has exactly two distinct factors.
9.
True / False
(1 pts)
The additive identity for whole numbers is 1.
10.
True / False
(1 pts)
Multiplication of whole numbers is commutative.
11.
Multiple Choice
(2 pts)
Which of the following is the greatest number?
12.
Multiple Choice
(2 pts)
In 403,506, what is the value of the digit 5?
13.
Multiple Choice
(2 pts)
Which number is divisible by 6?
14.
Multiple Choice
(2 pts)
Which Roman numeral equals 94?
15.
Multiple Choice
(2 pts)
The LCM of 12 and 15 is:
16.
Multiple Choice
(2 pts)
Which of the following is a composite number?
17.
Multiple Choice
(2 pts)
Starting at 0 on a number line, you make 4 jumps of size 7 to the right. Where do you land?
18.
Multiple Choice
(2 pts)
Round 8,649 to the nearest thousand.
19.
Multiple Choice
(2 pts)
Evaluate: 5 × (12 − 7) + 3
20.
Multiple Choice
(2 pts)
Which is the correct Indian system grouping of 7,200,300?
21.
Fill in the Blank
(2 pts)
The predecessor of 10,000 is _____
22.
Fill in the Blank
(2 pts)
The smallest whole number is _____
23.
Fill in the Blank
(2 pts)
The Roman numeral for 500 is _____
24.
Fill in the Blank
(2 pts)
A number divisible by 10 must end with _____
25.
Fill in the Blank
(2 pts)
According to the distributive property, a × (b + c) = a×b + a×_____
26.
Fill in the Blank
(2 pts)
The place value of 7 in 7,046 is _____
27.
Fill in the Blank
(2 pts)
The sum of the factors of a perfect number equals _____ times the number.
28.
Fill in the Blank
(2 pts)
Moving left three steps of size 4 on a number line decreases the value by _____
29.
Fill in the Blank
(2 pts)
A prime number has exactly _____ distinct factors.
30.
Fill in the Blank
(2 pts)
In the International system, 1,000,000 is read as _____
31.
Word Problem
(5 pts)
You start at 18 on a number line. Move right 6 steps of 4 units each, then move left 5 steps of 3 units each. Where do you land? Show your working.
✎ Worked Solution
Step 1: Total right movement = 6 × 4 = 24
Step 2: Total left movement = 5 × 3 = 15
Step 3: Final position = 18 + 24 − 15 = 27
Answer: 27
32.
Word Problem
(5 pts)
Estimate the sum of 8,649 and 3,378 by rounding each number to the nearest thousand. What is the estimated total? Show your working.
✎ Worked Solution
Step 1: 8,649 rounds to 9,000 (nearest thousand)
Step 2: 3,378 rounds to 3,000 (nearest thousand)
Step 3: Estimated sum = 9,000 + 3,000 = 12,000
Answer: 12,000
33.
Word Problem
(5 pts)
A school has 48 red chairs and 60 blue chairs. They want to arrange each color in rows with the same number of chairs and no chairs left over. What is the greatest number of chairs in each row? Show your working.
✎ Worked Solution
Step 1: Prime factors: 48 = 2⁴ × 3; 60 = 2² × 3 × 5
Step 2: HCF = 2² × 3 = 12
Step 3: Therefore, maximum chairs per row = 12
Answer: 12
34.
Word Problem
(5 pts)
Three bells ring every 18, 24, and 30 minutes respectively. If they all ring together at 8:00 a.m., when will they ring together next? Show your working.
✎ Worked Solution
Step 1: Prime factors: 18 = 2 × 3²; 24 = 2³ × 3; 30 = 2 × 3 × 5
Step 2: LCM = 2³ × 3² × 5 = 8 × 9 × 5 = 360 minutes
Step 3: 360 minutes = 6 hours; 8:00 a.m. + 6 hours = 2:00 p.m.
Answer: 2:00 p.m.
35.
Word Problem
(5 pts)
A factory can pack items in boxes of 45 or in boxes of 60 with no leftovers in either case. What is the smallest number of items the factory can pack to satisfy both conditions? Show your working.
✎ Worked Solution
Step 1: Prime factors: 45 = 3² × 5; 60 = 2² × 3 × 5
Step 2: LCM = 2² × 3² × 5 = 4 × 9 × 5 = 180
Step 3: The smallest number of items that fits both box sizes exactly is the LCM
Answer: 180
36.
Word Problem
(5 pts)
Without long division, determine whether 8,415 is divisible by 9 and by 11. Show your working.
✎ Worked Solution
Step 1: Test for 9: Sum of digits = 8 + 4 + 1 + 5 = 18 (divisible by 9)
Step 2: Test for 11: (8 + 1) − (4 + 5) = 9 − 9 = 0 (multiple of 11)
Step 3: Therefore, 8,415 is divisible by both 9 and 11
Answer: Divisible by 9: Yes; Divisible by 11: Yes
37.
Word Problem
(5 pts)
Convert 3,06,50,090 (Indian system) to the International system and write it in words (International system). Show your working.
✎ Worked Solution
Step 1: 3,06,50,090 = 3 crore + 6 lakh + 50 thousand + 90
Step 2: 3 crore = 30,000,000; 6 lakh = 600,000; total = 30,600,000 + 50,000 + 90 = 30,650,090
Step 3: In International format: 30,650,090 = thirty million six hundred fifty thousand ninety
Answer: 30,650,090; Thirty million six hundred fifty thousand ninety
38.
Word Problem
(5 pts)
Evaluate the expression using brackets: 7 × (18 − 5) − 4 × (6 + 1). Show your working.
✎ Worked Solution
Step 1: Compute inside brackets: (18 − 5) = 13 and (6 + 1) = 7
Step 2: Multiply: 7 × 13 = 91 and 4 × 7 = 28
Step 3: Subtract: 91 − 28 = 63
Answer: 63
39.
Word Problem
(5 pts)
In a 3×3 grid, the numbers are:
Row 1: 11, 14, 9
Row 2: 8, 20, 13
Row 3: 7, 16, 10
A supercell is larger than its neighbors directly above, below, left, and right. Is 20 a supercell? Show your working.
✎ Worked Solution
Step 1: Identify neighbors of 20: up = 14, down = 16, left = 8, right = 13
Step 2: Compare: 20 > 14, 20 > 16, 20 > 8, 20 > 13
Step 3: Since 20 is greater than all four neighbors, it is a supercell
Answer: Yes, 20 is a supercell
40.
Word Problem
(5 pts)
Find the smallest 5-digit number that is divisible by both 12 and 15. Show your working.
✎ Worked Solution
Step 1: LCM(12, 15) = 60 (since 12 = 2² × 3 and 15 = 3 × 5, LCM = 2² × 3 × 5 = 60)
Step 2: Smallest 5-digit number is 10,000; compute 10,000 ÷ 60 ≈ 166.66, so take next whole number 167
Step 3: 167 × 60 = 10,020
Answer: 10,020