Playing With Numbers - MCQ - Class 8 MCQ

To find the one's digit of the number M, we need to find a number that satisfies the condition M ÷ 5 gives a remainder of 1.
Step 1:
Let's start by listing out the multiples of 5 and their remainders when divided by 5:
- 5 ÷ 5 = 1, remainder 0
- 10 ÷ 5 = 2, remainder 0
- 15 ÷ 5 = 3, remainder 0
- 20 ÷ 5 = 4, remainder 0
- 25 ÷ 5 = 5, remainder 0
- 30 ÷ 5 = 6, remainder 0
- 35 ÷ 5 = 7, remainder 0
Step 2:
We can see that all the multiples of 5 have a remainder of 0 when divided by 5. To find a number with a remainder of 1, we can add 1 to any multiple of 5. Let's try it:
- 6 ÷ 5 = 1, remainder 1
- 11 ÷ 5 = 2, remainder 1
- 16 ÷ 5 = 3, remainder 1
- 21 ÷ 5 = 4, remainder 1
- 26 ÷ 5 = 5, remainder 1
- 31 ÷ 5 = 6, remainder 1
- 36 ÷ 5 = 7, remainder 1
Step 3:
From the above calculations, we can see that any number that is 1 greater than a multiple of 5 will have a remainder of 1 when divided by 5.
Therefore, the one's digit of M can be either 1 or 6.
Conclusion:
The correct answer is option C: 1 or 6.

To determine which numbers are divisible by 9, we need to understand the divisibility rule for 9. According to the rule, a number is divisible by 9 if the sum of its digits is divisible by 9.
Let's consider an example: 135. The sum of the digits is 1 + 3 + 5 = 9, which is divisible by 9. Therefore, 135 is divisible by 9.
Now, let's analyze the given options:
A: 3
- 9 is divisible by 3, so any number divisible by 9 is also divisible by 3. Therefore, option A is correct.
B: 6
- 6 is not a factor of 9, so it cannot be concluded that a number divisible by 9 is also divisible by 6. Therefore, option B is incorrect.
C: 11
- 11 is not a factor of 9, so it cannot be concluded that a number divisible by 9 is also divisible by 11. Therefore, option C is incorrect.
D: none of these
- As discussed above, option A (3) is correct, so option D is incorrect.
Therefore, the correct answer is option A, which states that a number divisible by 9 is also divisible by 3.

To determine the least value of X, we need to find the smallest digit that makes the number [3X 74] divisible by 9.
To check if a number is divisible by 9, we can use the divisibility rule for 9, which states that a number is divisible by 9 if the sum of its digits is divisible by 9.
In the given number [3X 74], the sum of the digits is 3 + X + 7 + 4 = 14 + X.
To make the number divisible by 9, the sum of the digits must be divisible by 9.
We need to find the smallest value of X that makes 14 + X divisible by 9.
By trying different values of X, we find that X = 4 is the smallest value that satisfies this condition.
When X = 4, the sum of the digits is 14 + 4 = 18, which is divisible by 9.
Therefore, the least value of X is 4.
Answer: D. 4

To find the least value of X, Y, and Z, we need to consider the divisibility rule of 9.
The divisibility rule of 9 states that a number is divisible by 9 if the sum of its digits is divisible by 9.
Let's find the sum of the digits in [1X 2Y 6Z]:
Sum of digits = 1 + X + 2 + Y + 6 + Z = 9 + X + Y + Z
Since [1X 2Y 6Z] is divisible by 9, the sum of its digits must also be divisible by 9.
To find the least value of X, Y, and Z, let's consider the smallest possible values for X, Y, and Z:
- If X = 0, Y = 0, and Z = 0, the sum of digits = 9 + 0 + 0 + 0 = 9, which is divisible by 9.
Therefore, the least value of X, Y, and Z is 0.
Hence, the answer is option A: 0.

To determine whether the number 28221 is divisible by a certain number, we need to check if the sum of its digits is divisible by that number.
1. Divisible by 2:
The number 28221 is divisible by 2 if its last digit is divisible by 2. Since the last digit is 1, it is not divisible by 2.
2. Divisible by 3:
To check if the number is divisible by 3, we need to find the sum of its digits.
2 + 8 + 2 + 2 + 1 = 15
Since 15 is divisible by 3, the number 28221 is divisible by 3.
3. Divisible by 6:
A number is divisible by 6 if it is divisible by both 2 and 3. Since the number is not divisible by 2, it is not divisible by 6.
4. Divisible by 9:
To check if the number is divisible by 9, we need to find the sum of its digits.
2 + 8 + 2 + 2 + 1 = 15
Since 15 is not divisible by 9, the number 28221 is not divisible by 9.
Therefore, the number 28221 is only divisible by 3, which is option B.

Yes,c is correct answer...because when 8÷5=1 and remember is 3.so c is correct answer....

To find the least value of (X Y), we need to find the smallest possible values for X and Y that make the 4-digit number 2X Y7 divisible by 3.
For a number to be divisible by 3, the sum of its digits must be divisible by 3. Therefore, we need to find the values of X and Y that make the sum of the digits 2, X, Y, and 7 divisible by 3.
The sum of the digits 2, X, Y, and 7 is 9 + X + Y. For this sum to be divisible by 3, 9 + X + Y must be a multiple of 3.
The smallest possible value for X is 0, since it is a 4-digit number. In this case, the sum of the digits is 9 + 0 + Y + 7 = 16 + Y. For the sum to be divisible by 3, Y must be 2 or 5.
If Y is 2, the sum is 16 + 2 = 18, which is divisible by 3. Therefore, the least value of (X Y) is 02, which is equivalent to 2.
Therefore, the correct answer is A: 3.

To determine which one's digit cannot be in a number divisible by 2, we need to consider the divisibility rule for 2. A number is divisible by 2 if its one's digit is even, i.e., it can be 0, 2, 4, 6, or 8.
We can eliminate the options one by one:
A: 0 can be the one's digit in a number divisible by 2. For example, 10, 20, 30, etc.
B: 1 cannot be the one's digit in a number divisible by 2 because it is an odd number. If the one's digit is 1, the number is not divisible by 2.
C: 2 can be the one's digit in a number divisible by 2. For example, 12, 22, 32, etc.
D: 4 can be the one's digit in a number divisible by 2. For example, 14, 24, 34, etc.
Therefore, the one's digit that cannot be in a number divisible by 2 is 1. Hence, the answer is B: 1.

To determine the possible ones digit of a number divisible by 5, we need to understand the divisibility rule for 5. A number is divisible by 5 if and only if its ones digit is either 0 or 5.
Let's analyze each option:
A: 2
- The number 2 is not divisible by 5, so this cannot be the ones digit of a number divisible by 5.
B: 3
- The number 3 is not divisible by 5, so this cannot be the ones digit of a number divisible by 5.
C: 4
- The number 4 is not divisible by 5, so this cannot be the ones digit of a number divisible by 5.
D: 5
- The number 5 is divisible by 5, so this can be the ones digit of a number divisible by 5.
Therefore, the only possible ones digit for a number divisible by 5 is 5. Thus, the correct answer is option D.

To determine the possible one's digit of a number divisible by 10, we need to consider the divisibility rule of 10. A number is divisible by 10 if and only if its one's digit is 0.
Let's examine the options given:
A: 0
- The number 10 is divisible by 10, and its one's digit is 0, so this option is valid.
B: 1
- The number 11 is not divisible by 10, so this option is not valid.
C: 3
- The number 13 is not divisible by 10, so this option is not valid.
D: 5
- The number 15 is not divisible by 10, so this option is not valid.
Therefore, the only possible one's digit for a number divisible by 10 is 0. Hence, option A is correct.