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All questions of Number Play for Class 6 Exam

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Which of the following is not a twin prime?
  • a)
    (11, 13)
  • b)
    (17, 19)
  • c)
    (23, 31)
  • d)
    (41, 43) 
Correct answer is option 'C'. Can you explain this answer?

Anita Menon answered
(23, 31) is not a twin prime. 
A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair (17, 19) or (41, 43).

Which greatest number of 4 digits is exactly divisible by 12, 16, 28 & 36?
  • a)
    6072
  • b)
    8072
  • c)
    8972
  • d)
    9072
Correct answer is option 'D'. Can you explain this answer?

Shreya Sarkar answered
Here is the answer.

LCM of 12, 16, 24, 28 and 36

12= 3x2x2
16=2x2x2x2
24=2x2x2x3
28=2x2x7
36=2x2x3x3

so, LCM is 2x2x2x2x3x3x7= 1008

And the greatest 4-digit no. is 9999

so, dividing 9999 by 1008 we get, 9 as quotient and 927 as reminder .

So, the largest 4-digit no. divisible by all these nos. is 9999-927= 9072.

Which of the following number is not divisible by 9?
  • a)
    387459
  • b)
    904806
  • c)
    758934
  • d)
    879134
Correct answer is option 'D'. Can you explain this answer?

Prachi chauhan answered
3 + 8 + 7 + 4 + 5 + 9 = 36
9 + 0 + 4 + 8 + 0 + 6 = 27
7 + 5 + 8 + 9 +3 + 4 = 36
8 + 7 + 9 + 1 + 3 + 4 = 32
∴ 32 is not divisible by 9.
∴ 879134 is not divisible 9.

Four bells ring at intervals of 6, 8, 12 & 20 minutes. They ring simultaneously at 7 a.m. At what time will they ring together?
  • a)
    8 a.m.
  • b)
    9 a.m.
  • c)
    10 a.m.
  • d)
    9:30 a.m. 
Correct answer is option 'B'. Can you explain this answer?

Varun Kapoor answered
Required time = LCM of 6, 8, 12 and 20

∴ Required time = 2 × 2 × 3 × 2 × 5
= 120 minutes = 2 hr.
∴ bell will again ring together at (7 + 2)
= 9 a.m.

The smallest number which when diminished by 3 is divisible by 21, 28, 36 and 45 is
  • a)
    1163
  • b)
    1263
  • c)
    1283
  • d)
    1293
Correct answer is option 'B'. Can you explain this answer?

Rohini khanna answered
LCM of 21, 28, 36 and 45 is

∴ LCM of 21, 28, 36 and 45
= 3 × 2 × 3 × 2 × 7 × 5
= 36 × 35 
= 1260
∴ Required number = 1260 + 3 = 1263

What is sum of first five multiples of 23?
  • a)
    341
  • b)
    342
  • c)
    343
  • d)
    345
Correct answer is option 'D'. Can you explain this answer?

Ishan Choudhury answered
Sum of first five multiples of 23 = 23 + 23 × 2 + 23 × 3 + 23 × 4 + 23 × 5 
= 23 (1 + 2 + 3 + 4 + 5)
= 23 × 15 
= 345 

Which of the following numbers is divisible by 3?
  • a)
    24357806
  • b)
    33336433
  • c)
    35769812
  • d)
    83479560 
Correct answer is option 'D'. Can you explain this answer?

Dhruv Malik answered
2 + 4 + 3 + 5 + 7 + 8 + 0 + 6 = 35
3 + 3 + 3 + 3 + 6  + 4 + 3 + 3 = 28
3 + 5 + 7 + 6 + 9 + 8 + 1 + 2 = 41 
8 + 3 + 4 + 7 + 9 + 5 + 6 + 0 = 42
Since 42 is divisible by 3 then (d) is divisible by 3. 

Four bells toll at intervals 4, 7, 12 & 84 seconds. The bells toll together at 7 o’clock. How many times will they again toll together in 28 minutes?
  • a)
    15
  • b)
    20
  • c)
    25
  • d)
    30
Correct answer is option 'B'. Can you explain this answer?

Siddharth Chavan answered
They will toll together for a 'common multiple' of (4,7,12,84), which is the l.c.m of these numbers.
4= 2^2
7 = 7
12 = 2^2 * 3
84 = 12 * 7 = 2^2 * 3 * 7
l.c.m(4,7,12,84) = 2^2 * 3 * 7 = 84 s
84 s = 1 min 24 sec
Hence they will toll together 84 seconds after 5 o'clock or 5:01:24 hrs ( 1 min 24 sec past 5 o'clock)
28 mins = 28*60 = 1680 sec
84 sec== toll 1 time
1680 sec== X times
X = 20 times
Hence,
They toll together at 5:01:24 hrs
In 28 mins they toll (together) 20 times.

Which of the following is not equal to zero?
  • a)
    (5 - 0) ÷ 5
  • b)
    (10 - 10) ÷ 5
  • c)
    0 ÷ 5
  • d)
    0 × 5
Correct answer is option 'A'. Can you explain this answer?

Charvi Chauhan answered
Understanding the Options
To determine which option is not equal to zero, let's analyze each one step by step.
Option A: (5 - 0) ÷ 5
- Calculation:
- 5 - 0 = 5
- 5 ÷ 5 = 1
- Result: This equals 1, which is not zero.
Option B: (10 - 10) ÷ 5
- Calculation:
- 10 - 10 = 0
- 0 ÷ 5 = 0
- Result: This equals 0.
Option C: 0 ÷ 5
- Calculation:
- 0 ÷ 5 = 0
- Result: This equals 0.
Option D: 0 × 5
- Calculation:
- 0 × 5 = 0
- Result: This equals 0.
Conclusion
- The only option that does not equal zero is Option A: (5 - 0) ÷ 5, which equals 1.
- All other options (B, C, and D) result in zero.
Therefore, the correct answer is indeed Option A. This exercise helps reinforce the understanding of basic arithmetic operations and their outcomes.

The successor of 100199 is
  • a)
    100199
  • b)
    100200
  • c)
    101000
  • d)
    none of these
Correct answer is option 'B'. Can you explain this answer?

Anirban Saini answered
Understanding Successors
The concept of a successor in mathematics refers to the number that comes directly after a given number. In this case, we are looking for the successor of the number 100199.
Finding the Successor
To find the successor:
- Add 1 to the number: The rule for finding a successor is simple. You just need to add 1 to the number in question.
- Calculation:
- 100199 + 1 = 100200
Thus, the successor of 100199 is 100200.
Options Analysis
Let's analyze the provided options to confirm the correct answer:
- Option a: 100199 - This is the original number, not the successor.
- Option b: 100200 - This is the correct answer, as it is the result of adding 1 to 100199.
- Option c: 101000 - This number is significantly larger and not the direct successor.
- Option d: none of these - This is incorrect as we have identified the correct successor.
Conclusion
The correct answer is indeed option 'B', which is 100200. By understanding the concept of successors and applying the simple addition rule, we can easily determine the number that follows any given integer.

The number of whole numbers between 22 and 54 is
  • a)
    31
  • b)
    32
  • c)
    42
  • d)
    30
Correct answer is option 'A'. Can you explain this answer?

Palak Nambiar answered
Understanding the Range
To find the number of whole numbers between 22 and 54, we first need to clarify what "between" means in this context. We are looking for whole numbers that are greater than 22 and less than 54.
Identifying Whole Numbers
The whole numbers between 22 and 54 include:
- 23
- 24
- 25
- ...
- 53
Counting the Whole Numbers
To count these numbers, we can use the formula for counting integers in a range:
1. Identify the starting point and endpoint:
- Starting point: 23 (the first whole number greater than 22)
- Endpoint: 53 (the last whole number less than 54)
2. Count the total numbers:
- The formula for counting whole numbers between two numbers is:
(Endpoint - Starting point) + 1
- Plugging in our numbers:
(53 - 23) + 1 = 30 + 1 = 31
Conclusion
Thus, the total number of whole numbers between 22 and 54 is 31. Therefore, the correct answer is option 'A'.
This approach shows how to systematically find the count of numbers in a given range, ensuring clarity and accuracy in the solution.

Which of the following is the smallest whole number?
  • a)
    0
  • b)
    1
  • c)
    2
  • d)
    none of these
Correct answer is option 'A'. Can you explain this answer?

Get Idea answered
Whole numbers include all non-negative integers starting from 0. They are defined as:
  • 0
  • 1
  • 2
  • 3
  • 4
  • 5
  • and so on.
This makes 0 the smallest whole number.

The product of the predecessor and the successor of the greatest 2-digit number is
  • a)
    9800
  • b)
    9700
  • c)
    none of these
  • d)
    9900
Correct answer is option 'A'. Can you explain this answer?

Sneha Rane answered
Understanding the Problem
To solve the problem, we first need to identify the greatest two-digit number.
Step 1: Identify the Greatest Two-Digit Number
- The greatest two-digit number is 99.
Step 2: Determine the Predecessor and Successor
- The predecessor of 99 is 98 (99 - 1).
- The successor of 99 is 100 (99 + 1).
Step 3: Calculate the Product
Now, we need to find the product of the predecessor and the successor:
- Predecessor (98) × Successor (100)
Step 4: Perform the Multiplication
- 98 × 100 = 9800
Conclusion
The product of the predecessor and the successor of the greatest two-digit number (99) is indeed 9800.
Thus, the correct answer is option 'A'.

Number of whole numbers between 38 and 68 is
  • a)
    28
  • b)
    29
  • c)
    30
  • d)
    31
Correct answer is option 'B'. Can you explain this answer?

Palak Nambiar answered
Understanding the Problem
To find the number of whole numbers between 38 and 68, we need to focus on what "between" means. This implies we should not include the endpoints, 38 and 68, themselves.
Identifying the Range
The whole numbers we are interested in are:
- Start: 39 (the first whole number after 38)
- End: 67 (the last whole number before 68)
Counting the Whole Numbers
Now, we can count the whole numbers from 39 to 67:
- The sequence of numbers is: 39, 40, 41, ..., 67.
Calculating the Count
To find how many numbers are in this range, we can use the formula:
- Count = (Last number - First number) + 1
Plugging in our values:
- Count = (67 - 39) + 1
This simplifies to:
- Count = 28 + 1 = 29
Conclusion
Thus, the total number of whole numbers between 38 and 68 is 29. Therefore, the correct answer is option 'B'.
Summary of Steps
- Identify the starting number (39) and ending number (67)
- Count the numbers in the range
- Use the formula to calculate the total
This method ensures that you accurately find the count of whole numbers in any given range.

What is the least 5-digit number which is exactly divisible by 20, 25, 30?
  • a)
    10200
  • b)
    10300
  • c)
    10400
  • d)
    10100
Correct answer is option 'A'. Can you explain this answer?

Sonakshi dasgupta answered
LCM of 20, 25, 30 is

∴ LCM of 20, 25, 30 = 2 × 5 × 2 × 5 × 3
= 300
∴ Ieast 5-digit number which is exactly divisible by 20, 25, 30 = 10200.

5 added to the smallest 6-digit number gives
  • a)
    1005
  • b)
    10005
  • c)
    1000005
  • d)
    100005
Correct answer is option 'D'. Can you explain this answer?

Get Idea answered
The smallest 6-digit number is 100000. Adding 5 to this number results in:
  • 100000 + 5 = 100005
Therefore, the correct answer is D.

The value of (93 × 63 + 93 × 37) is
  • a)
    9300
  • b)
    93000
  • c)
    none of these
  • d)
    930
Correct answer is option 'A'. Can you explain this answer?

Aniket Mukherjee answered
Understanding the Expression
The expression we need to evaluate is (93 × 63 + 93 × 37). This can be simplified using the distributive property of multiplication.
Applying the Distributive Property
The distributive property states that a(b + c) = ab + ac. We can factor out the common term (93) from both parts of the expression:
- 93 × (63 + 37)
Calculating the Sum Inside the Parentheses
Next, we calculate the sum inside the parentheses:
- 63 + 37 = 100
Substituting Back into the Expression
Now, we substitute this sum back into our expression:
- 93 × (100)
Final Calculation
Finally, we multiply:
- 93 × 100 = 9300
Conclusion
Thus, the value of (93 × 63 + 93 × 37) is 9300. Therefore, the correct answer is option 'A'.

In 467 * 381 replace * by which smallest digit to make it divisible by 3?
  • a)
    1
  • b)
    2
  • c)
    3
  • d)
    4
Correct answer is option 'A'. Can you explain this answer?

Veena Menon answered
467 * 381 
The sum of digits of the above number
= 4 + 6 + 7 + * + 3 + 8 + 1
= 10 + 7 + * + 3 + 8 + 1
= 29 + *
If, ∗  = 1, then, the sum of digits will become 30.
∴ required number = 1

Find the largest number that will divide 76, 113 and 186 leaving remainder 4, 5, 6 respectively.
  • a)
    24
  • b)
    12
  • c)
    36
  • d)
    54
Correct answer is option 'C'. Can you explain this answer?

Debanshi Roy answered
Solution:
The largest number that will divide 76, 113 and 186 leaving remainder 4, 5, 6 respectively is also known as the highest common factor (HCF) of (76-4), (113-5) and (186-6).

Step-by-step solution:
• Subtract the remainder from each number to get the actual number.
• So, the actual numbers are 72, 108, and 180.
• Now, find the common factors of these numbers.
• The common factors of 72, 108, and 180 are 1, 2, 3, 4, 6, 9, 12, 18, 36.
• Out of these common factors, select the highest one which leaves the same remainder when divided by 4, 5, and 6 respectively.
• The highest common factor (HCF) of (76-4), (113-5) and (186-6) is 36.
• Hence, the correct option is (c) 36.

Therefore, the largest number that will divide 76, 113 and 186 leaving remainder 4, 5, 6 respectively is 36.

1870 is divisible by 22. Which two numbers nearest to 1870 are each divisible by 22?
  • a)
    1848, 1892
  • b)
    1893, 1914
  • c)
    1826, 1914
  • d)
    None of these 
Correct answer is option 'A'. Can you explain this answer?

Preethi Dasgupta answered
To determine the two numbers nearest to 1870 that are each divisible by 22, we can use the concept of divisibility and apply it to the given options.

Divisibility Rule of 22: A number is divisible by 22 if it is divisible by both 2 and 11.

Let's analyze the given options one by one to see if they satisfy the divisibility rule of 22.

a) 1848, 1892:
- 1848: This number is divisible by 2 because the last digit is even (8). However, to determine if it is divisible by 11, we can use the divisibility rule of 11, which states that the difference between the sum of the digits in the odd place and the sum of the digits in the even place should be either 0 or a multiple of 11.
- In this case, 1 - 8 + 4 - 8 = -11, which is a multiple of 11. Therefore, 1848 is divisible by 11 and consequently divisible by 22.
- 1892: This number is divisible by 2 because the last digit is even (2). However, to determine if it is divisible by 11, we can use the divisibility rule of 11.
- In this case, 1 - 8 + 9 - 2 = 0, which is a multiple of 11. Therefore, 1892 is divisible by 11 and consequently divisible by 22.

Since both 1848 and 1892 satisfy the divisibility rule of 22, option A is correct.

b) 1893, 1914:
- 1893: This number is not divisible by 2 because the last digit is odd (3). Therefore, it is not divisible by 22.
- 1914: This number is divisible by 2 because the last digit is even (4). However, it is not divisible by 11 since 1 - 9 + 1 - 4 = -11, which is not a multiple of 11. Therefore, it is not divisible by 22.

Option B is incorrect.

c) 1826, 1914:
- 1826: This number is divisible by 2 because the last digit is even (6). However, it is not divisible by 11 since 1 - 8 + 2 - 6 = -11, which is not a multiple of 11. Therefore, it is not divisible by 22.
- 1914: This number is divisible by 2 because the last digit is even (4). However, it is not divisible by 11 since 1 - 9 + 1 - 4 = -11, which is not a multiple of 11. Therefore, it is not divisible by 22.

Option C is incorrect.

d) None of these:
Since we have found that option A is correct, option D is incorrect.

Therefore, the two numbers nearest to 1870 that are each divisible by 22 are 1848 and 1892, as stated in option A.

Find the smallest possible number which on adding 19 becomes exactly divisible by 28, 36 and 45.
  • a)
    1239
  • b)
    1241
  • c)
    1243
  • d)
    1245
Correct answer is option 'B'. Can you explain this answer?

Nishanth Iyer answered
To find the smallest possible number that is divisible by 28, 36, and 45, we need to find the least common multiple (LCM) of these three numbers.

Step 1: Find the prime factors of each number.
- Prime factors of 28: 2, 2, 7 (2 x 2 x 7)
- Prime factors of 36: 2, 2, 3, 3 (2 x 2 x 3 x 3)
- Prime factors of 45: 3, 3, 5 (3 x 3 x 5)

Step 2: Identify the largest exponent for each prime factor.
- Largest exponent of 2: 2 (from 2 x 2)
- Largest exponent of 3: 3 (from 3 x 3)
- Largest exponent of 7: 1 (from 7)
- Largest exponent of 5: 1 (from 5)

Step 3: Multiply the prime factors with their largest exponents.
2^2 x 3^3 x 7^1 x 5^1 = 4 x 27 x 7 x 5 = 3780

Step 4: Add 19 to the result.
3780 + 19 = 3799

Hence, the smallest possible number that on adding 19 becomes exactly divisible by 28, 36, and 45 is 3799.

Therefore, option B (1241) is incorrect.

The predecessor of the smallest 4-digit number is
  • a)
    999
  • b)
    1000
  • c)
    1001
  • d)
    99
Correct answer is option 'A'. Can you explain this answer?

Saranya Chakraborty answered
Understanding the Concept of Predecessor
The predecessor of a number is the number that comes immediately before it. This concept is essential in understanding the sequence of numbers, especially when dealing with whole numbers.
Identifying the Smallest 4-Digit Number
- The smallest 4-digit number is 1000.
- A 4-digit number is defined as any number from 1000 to 9999.
Finding the Predecessor
- To find the predecessor of 1000, we simply subtract 1 from it.
- Therefore, the calculation is: 1000 - 1 = 999.
Understanding the Options
- a) 999
- b) 1000 (This is the number itself, not the predecessor)
- c) 1001 (This is the successor, not the predecessor)
- d) 99 (This is not related to 1000 as it falls outside the 4-digit range)
Conclusion
- The correct answer is indeed option A: 999.
- This is because 999 is the number that comes right before the smallest 4-digit number, 1000.
Understanding these concepts helps in grasping number sequences, which is vital in mathematics.

The number of whole numbers between the smallest whole number and the greatest 2-digit number is
  • a)
    98
  • b)
    88
  • c)
    99
  • d)
    100
Correct answer is option 'A'. Can you explain this answer?

Coders Trust answered
To find the number of whole numbers between the smallest whole number and the greatest 2-digit number, we can follow these steps:
  • The smallest whole number is 0.
  • The greatest 2-digit number is 99.
  • To find the numbers between 0 and 99, we count from 1 to 98.
  • This gives us a total of 98 whole numbers.
Therefore, the number of whole numbers between the smallest whole number and the greatest 2-digit number is 98.
.
 

Which of the following statement is true?
  • a)
    13 - 21 is not a whole number
  • b)
    21 × 1 = 21 × 0
  • c)
    21 - 13 is not a whole number
  • d)
    21 – (13 - 5) = (21 - 13) - 5
Correct answer is option 'A'. Can you explain this answer?

Get Idea answered
Whole numbers are non-negative integers (e.g., 0, 1, 2, ...).
  • For option A: 13 - 21 = -8, which is not a whole number. Therefore, statement A is true.
  • Option B: 21 × 1 = 21 and 21 × 0 = 0. Since 21 ≠ 0, statement B is false.
  • Option C: 21 - 13 = 8, which is a whole number. Therefore, statement C is false.
  • Option D:
    • Left side: 21 - (13 - 5) = 21 - 8 = 13;
    • Right side: (21 - 13) - 5 = 8 - 5 = 3.
    Since 13 ≠ 3, statement D is false.
Thus, the correct answer is A.

The greatest number that will divide 445, 572 & 699 leaving remainder 4, 5, 6 respectively.
  • a)
    84
  • b)
    42
  • c)
    49
  • d)
    63
Correct answer is option 'D'. Can you explain this answer?

Shruti Mishra answered
Solution-> 445 - 4 = 441 
                 572 - 5 = 567 
                 699 - 6 = 693 

Now find the greatest common factor of those 3 numbers: 
441 = 3 x 3 x 7 x 7 
572 = 3 x 3 x 3 x 3 x 7 
693 = 3 x 3 x 7 x 11 

The common factors are 3 x 3 x 7 = 63 
HCF Of (441,567,693) = 63 

445 / 63 = 7 remainder 4 
572 / 63 = 9 remainder 5 
699 / 63 = 11 remainder 6 

63 is the largest divisor that will give the desired remainders.

The HCF of two numbers is 23 and their LCM is 1449. If one of the numbers is 161 what is the other?
  • a)
    107
  • b)
    117
  • c)
    167
  • d)
    207
Correct answer is option 'D'. Can you explain this answer?

Amrita Roy answered
HCF = 23
LCM = 1449

Let the two numbers be a and b. Let a = 161. We have to find b.

We know that

HCF(a,b) * LCM(a,b) = a*b
∴23 * 1449 = 161 * b
∴23*1449/161 = b
∴b = 23*9
∴b = 207

Thus, the other number is 207.

The whole number which does not have a predecessor in the whole number system is
  • a)
    0
  • b)
    1
  • c)
    2
  • d)
    none of these
Correct answer is option 'A'. Can you explain this answer?

Shubham Gupta answered
Understanding Whole Numbers
Whole numbers are the set of numbers that include all the natural numbers along with zero. The set of whole numbers is represented as {0, 1, 2, 3, ...} and so on.
What is a Predecessor?
A predecessor is a number that comes just before another number in a sequence. For instance:
  • The predecessor of 1 is 0.
  • The predecessor of 2 is 1.
  • The predecessor of 3 is 2.

Why 0 is Special?
In the context of whole numbers:
  • 0 is the smallest whole number.
  • There is no whole number that comes before 0.
  • Thus, 0 does not have a predecessor in the whole number system.

Conclusion
Since 0 is the smallest whole number and does not have a predecessor, the correct answer to the question is option 'A'.
  • 0 is unique in the whole number system.
  • It serves as the starting point for counting.

In summary, the whole number that does not have a predecessor in the whole number system is indeed 0.

Find the greatest 3-digit number which is divisible by 8, 10 and 12.
  • a)
    840
  • b)
    480
  • c)
    960
  • d)
    980
Correct answer is option 'C'. Can you explain this answer?

Gayatri Roy answered
L.C.M of 8, 10, 12 = 2 x 2 x 2 x 3 x 5 = 120


We have to find the greatest 3 digit multiple of 120


It can be seen that 120 x 8 =960 and 120 x 9 =1080.


Hence, the greatest 3- digit number exactly divisible by 8 , 10 and 12 is 960

Which of the following statement is true?
  • a)
    1509344 is divisible by 8.
  • b)
    72493 is divisible by 11.
  • c)
    8569 is not divisible by 11.
  • d)
    115 is a multiple of 19.
Correct answer is option 'A'. Can you explain this answer?

Surbhi Patel answered
Explanation:

Divisibility by 8:
- To determine if a number is divisible by 8, we need to check if the last three digits of the number are divisible by 8.
- In the number 1509344, the last three digits are 344, which is divisible by 8 because 344 ÷ 8 = 43.
- Therefore, 1509344 is divisible by 8.

Divisibility by 11:
- To determine if a number is divisible by 11, we can use the rule that states that the difference between the sum of the digits at odd places and the sum of the digits at even places should be a multiple of 11.
- For the number 72493, the sum of the digits at odd places (7 + 4 + 3 = 14) is 14, and the sum of the digits at even places (2 + 9 = 11) is 11.
- The difference between 14 and 11 is 3, which is not a multiple of 11.
- Therefore, 72493 is not divisible by 11.

Conclusion:
- Based on the explanations above, the statement "1509344 is divisible by 8" is true.

The sum of the successor of the greatest 3-digit number and the predecessor of the smallest 3-digit number is
  • a)
    1099
  • b)
    1101
  • c)
    1100
  • d)
    1000
Correct answer is option 'A'. Can you explain this answer?

Coders Trust answered
The greatest 3-digit number is 999; its successor is 999 + 1 = 1000.
The smallest 3-digit number is 100; its predecessor is 100 − 1=99.
The sum is 1000 + 99 = 1099.

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