Chapter 13: Playing with Numbers

Solution: The correct answer is option (b) 3

Explanation:

Option (b) – 3 is the correct answer because the divisibility test of 3 says that if the sum of the digits of a number is divisible by 3, then the number is always divisible by 3.

Solution: The correct answer is option (a) an odd multiple of 3

Explanation:

Given that, the sum of the digits xyz is given as x+y+z is 6, where z is an odd integer.

The divisibility test of 3, the number xyz is divisible by z. Since the last digit is an odd digit, then xyz is an odd multiple of 3.

Solution: The correct answer is option (c) A = 2, B = 1

Explanation:

In the 1’s column A +3 = 5

When A is added with 3, it gives 5

Since A is a digit, it should be between 0 and 9

When you substitute A = 2, you will get 2+3 = 5

Similarly, repeat the process for 10’s column

Then we will get B= 1

Therefore A= 2, and B = 1

Solution: The correct answer is option (a) 13

Explanation:

From the question,

In 1’s place, we have to add 3+B = 0

Since B is a digit, the value of B should be between 0 and 9

When you substitute the value of B = 7, then you will get

3+7 = 10

So here, the unit digit is 0.

Now carry 1 to the 10’ s place,

Repeat the same process for 10’s place, you will get the value of A

So, A = 6

Therefore, A+B = 6+7 = 13

Solution: The correct answer is option (c) 7

Explanation:

In the 1’s place, the product of A and A gives 9

Here, A is a number whose multiplication gives the two digit number having 9 in its 1’s place.

So, the product of 7 and 7 gives 49, where 1’s place is 9.

Solution: The correct answer is option (a) -2

Explanation:

Given that, 6 A × B = A 8 B

So, AB = B

Therefore A = 1

Now substitute A = 1 in the given equation

6B = A8

6B = 18

B = 18/6 = 3

Now, A – B = 1 -3 = -2

Solution: The correct answer is option (b) 114345

Explanation:

If a number is divisible is 99, it should be divisible by both 9 and 11.

From the given option, option (b) 114345 is divisible by both 9 and 11.

All other numbers are either divisible by 9 or 11, but not both 9 and 11.

In questions 18 to 33, fill in the blanks to make the statements true.

Solution: 9

Explanation:

Adding all the digits in the given number, we get 27, which is divisible by 3 and 9.

Solution: 1 or 4 or 7

Explanation:

It is known that, when a number is a multiple of 3, if the sum of digits in the number is a multiple of 3

By equating the closet multiple of 3, such as 6, 9, and 12, we get the digit

Either the digit x should be 1 or 4 or 7.

Solution: 1

Explanation:

It is known that, if a number is a multiple of 9, then the sum of the digits of a number is divisible by 9.

From, the given equation, we can write it as:

3+x+5 = x + 8

It means that x+8 is divisible by 8, if x+8 is equal to 9,

Then the value of x is 1.