Students can practice TS 6th Class Maths Solutions Chapter 3 Playing with Numbers Ex 3.7 to get the best methods of solving problems.

## TS 6th Class Maths Solutions Chapter 3 Playing with Numbers Exercise 3.7

Question 1.

Which of the following numbers are divisible by 4 ?

(i) 572

Answer:

The given number is 572.

The number formed by its last two digits is 72.

It is divisible by 4. So, the given number is divisible by 4.

(ii) 21,084

Answer:

The given number is 21,084.

The number formed by its last two digits is 84.

It is divisible by 4. So, the given number is divisible by 4.

(iii) 14,560

Answer:

The given number is 14,560.

The number formed by its last two digits is 60.

It is divisible by 4. So, the given number is divisible by 4.

(iv) 1,700

Answer:

The given number is 1,700.

1700 = 1000 + 600 + 100

1000, 600 and 100 are multiples of 100, they are completely divisible by 4.

So, the given number is divisible by 4.

(v) 2,150

Answer:

The given number is 2,150.

The number formed by its last two digits is 50.

It is not divisible by 4.

So, the given number is not divisible by 4.

Question 2.

Test whether the following numbers are divisible by 8.

(i) 9774

Answer:

The given number is 9774.

The number formed by its last three digits is 774.

It is not divisible by 8.

So, the given number is not divisible by 8.

(ii) 531048

Answer:

The given number is 531048.

The number formed by its last three digits is 048.

It is divisible by 8.

So, the given number is divisible by 8.

(iii) 5500

Answer:

The given number is 5500.

The number formed by its last three digits is 500.

It is not divisible by 8.

So, the given number is not divisible by 8.

(iv) 6136

Answer:

The given number is 6136.

The number formed by its last three digits is 136.

It is divisible by 8.

So, the given number is divisible by 8.

(v) 4152

Answer:

The given number is 4152.

The number formed by its last three digits is 152.

It is divisible by 8.

So, the given number is divisible by 8.

Question 3.

Check whether the following numbers are divisible by 11.

(i) 859484

Answer:

The given number is 859484.

Sum of the digits at odd places = 4 + 4 + 5 = 13

Sum of the digits at even places = 8 + 9 + 8 = 25

Their difference = 25 – 13 = 12

This difference is not either 0 or divisible by 11.

So, the given number is not divisible by 11.

(ii) 10824

Answer:

The given number is 10824.

Sum of the digits at odd places. = 4 + 8 + 1 = 13

Sum of the digits at even places = 2 + 0 = 2

Their difference =13 – 2 = 11

This difference 11 is divisible by 11.

∴ The given number is divisible by 11.

(iii) 20801

Answer:

The given number is 20801.

Sum of the digits at odd places = 1 + 8 + 2 = 11

Sum of the digits at even places = 0 + 0 = 0

Their difference = 11 – 0 = 11

This difference 11 is divisible by 11.

∴ The given number is divisible by 11.

Question 4.

Verify whether the following numbers are divisible by 4 and by 8 ?

(i) 2104

Answer:

The given number is 2104.

The number formed by its last two digits is 04.

It is divisible by 4. So, the given number is divisible by 4,

The number formed by its last three digits is 104. It is divisible by 8.

So, the given number is divisible by 8.

(ii) 726352

Answer:

The given number is 726352.

The number formed by its last two ‘ digits is 52.

It is divisible by 4. So, the given number is divisible by 4.

The number formed by its last three digits is 352. It is divisible by 8.

So, the given number is divisible by 8.

(iii) 1800

Answer:

The given number is 1800.

1800 = 1000 + 800

1000 and 800 are multiples of 100.

We know that 100 is divisible by 4. So, the given number is divisible by 4.

The number formed by its last three digits is 800. It is divisible by 8.

So, the given number is divisible by 8.

Question 5.

Find the smallest number that must be added to 289279, so that it is divisible by 8 ?

Answer:

The given number is 289279.

The number formed by its last three digits is 279.

If 279 is to be exactly divisible by 8, we have to add 1 to it.

(i.e.,) 279 + 1 = 280; it is divisible by 8.

So, 1 must be added to the given number, so that it is divisible by 8.

Question 6.

Find the smallest number that can be subtracted from 1965, so that it becomes divisible by 4 ?

Answer:

The given number is 1965.

The number formed by its last two digits is 65.

The smallest number that can be subtracted from 65 is 1, so that it becomes divisible by 4.

(i.e.) 65 – 1 = 64

We know that 64 is divisible by 4.

Question 7.

Write all the possible numbers between 1000 and 1100, that are divisible by 11 ?

Answer:

We know that 990 is divisible by 11 (∵ 90 × 11 = 990)

990 is a multiple of 11.

The possible numbers divisible by 11 are 1001, 1012, 1023, 1034, 1045, 1056, 1067, 1078, 1089.

Question 8.

Write the nearest number to 1240 which is divisible by 11 ?

Answer:

11 × 112 = 1232

11 × 113 = 1243

∴ The nearest number to 1240 is 1243 but not 1232.

∴ 1243 is the nearest number to 1240 which is divisible by 11.

Question 9.

Write the nearest number to 105 which is divisible by 4?

Answer:

We know that 4 × 25 = 100

4 × 26 = 104

4 × 27 = 108

∴ 104 is the nearest number to 105 which is divisible by 4.