## RS Aggarwal Class 8 Solutions Chapter 5 Playing with Numbers Ex 5B

These Solutions are part of RS Aggarwal Solutions Class 8. Here we have given RS Aggarwal Solutions Class 8 Chapter 5 Playing with Numbers Ex 5B.

**Other Exercises**

- RS Aggarwal Solutions Class 8 Chapter 5 Playing with Numbers Ex 5A
- RS Aggarwal Solutions Class 8 Chapter 5 Playing with Numbers Ex 5B
- RS Aggarwal Solutions Class 8 Chapter 5 Playing with Numbers Ex 5C
- RS Aggarwal Solutions Class 8 Chapter 5 Playing with Numbers Ex 5D

**Question 1.**

**Solution:**

We know that a number is divisible by 2 if its unit digit is 0, 2, 4, 6 or 8

Therefore, (i) 94, (ii) 570, (iv) 2398,(v) 79532 and (vi) 13576 are divisible by 2.

**Question 2.**

**Solution:**

We know that a number is divisible by 5 if its unit digit is 0 or 5.

Therefore, (i) 95, (ii) 470, (iv) 2735, (vi) 35790, (vii) 98765 and (ix) 77990 are divisible by 5.

**Question 3.**

**Solution:**

We know that a number is divisible by 10 if its unit digit is zero.

Therefore, (ii) 90 and (iv) 57930 are divisible by 10.

**Question 4.**

**Solution:**

We know that a number is divisible by 3 if the sum of its digits is divisible by 3. Therefore

(i) 83 – 8 + 3 = 11,not divisible by 3

(ii) 378 – 3 + 7 + 8 = 18, is divisible by 3

(iii) 474 – 4 + 7 + 4 = 15, is divisible by 3

(iv) 1693 – 1 + 6 + 9 + 3 = 19, is divisible by 3

(v) 20345 – 2 + 0 + 3 + 4 + 5 = 14 is not divisible by 3

(vi) 67035 – 6 + 7 + 0 + 3 + 5 = 21 is divisible by 3

(vii)591282 – 5 + 9 + 1 + 2 + 8 = 27 is divisible by 3

(viii)903164 – 9 + 0 + 3 + 1 + 6 + 4 = 23,is not divisible by 3

(ix) 100002 – 1 + 0 + 0 + 0 + 0 + 2 = 3,is divisible by 3

**Question 5.**

**Solution:**

We know that a number is divisible by 9, if the sum of its digits is divisible by 9. Therefore,

(i) 327 = 3 + 2 + 7 = 12,is not divisible by 9

(ii) 7524 = 7 + 5 + 2 + 4 = 18, is divisible by 9

(iii) 32022 = 3 + 2 + 0 + 2 + 2 = 9,is divisible by 9

(iv) 64302 = 6 + 4 + 3 + 0 + 2 = 15, is not divisible by 9

(v) 89361= 8 + 9 + 3 + 6 + 1 = 27 is divisible by 9

(vi)14799 = 1 + 4 + 7 + 9 + 9 = 30,is not divisible by 9

(vii) 66888 = 6 + 6 + 8 + 8 + 8 = 36, is divisible by 9

(viii) 30006 = 3 + 0 + 0 + 0 + 6 = 9, is divisible by 9

(ix) 33333 = 3 + 3 + 3 + 3 + 3 = 15 is not divisible by 9

**Question 6.**

**Solution:**

We know that a number is divisible by 4, only when the number formed by its last two digits is divisible by 4.

Therefore,

(i) 134, is not divisible by 4 as last two digits 34 is not divisible by 4.

(ii) 618, is not divisible by 4 as last two digits 18 is not divisible by 4.

(iii) 3928, is divisible by 4 as last two digits 28 is divisible by 4.

(iv) 50176, is not divisible by 4 as last two digits 76 is not divisible by 4.

(y) 39392, is not divisible by 4 as last two digits 92 is not divisible by 4.

(vi) 56794, is not divisible by 4 as last two digits 94 is not divisible by 4.

(vii) 86102, is not divisible by 4 as last two digits 02 is not divisible by 4.

(viii) 66666, is not divisible by 4 as last two digits 66 is not divisible by 4.

(ix) 99918, is not divisible by 4 as last two digits 18 is not divisible by 4.

(x) 77736, is divisible by 4 as last two digits 36 is divisible by 4.

**Question 7.**

**Solution:**

A given number is divisible by 8 only when the number formed by its last three digits is divisible by 8.

(i) 6132, is not divisible by 8 as last three digits 132 is not divisible by 8.

(ii) 7304, is divisible by 8 as last three digits 304 is not divisible by 8.

(iii) 59312, is divisible by 8 as last three digits 312 is divisible by 8.

(iv) 66664, is divisible by 8 as last three digits 664 is divisible by 8.

(v) 44444, is not divisible by 8 as last three digits 444 is not divisible by 8.

(vi) 154360, is divisible by 8 as last three digits 360 is not divisible by 8.

(vii) 998818, is not divisible by 8 as last three digits 818 is not divisible by 8.

(viii) 265472, is divisible by 8 as last three digits 472 is divisible by 8.

(ix) 7350162, is not divisible by 8 as last three digits 162 is not divisible by 8.

**Question 8.**

**Solution:**

A given number is divisible by 11, if the difference between the sum of its digits at odd places and the sum of its digits at even places, is either O or a number divisible by 11.

(i) 22222

Sum of digit at odd places = 2 + 2 + 2 = 6

Sum of digit at even places = 2 + 2 = 4

Difference of the above sum = 6 – 4 =2,

which is not divisible by 11

22222 is not divisible by 11

(ii) 444444

Sum of digit at odd places = 4 + 4 + 4 = 12

Sum of digit at even places = 4 + 4 + 4 = 12

Difference of the above sum =(12 – 12) = O

444444 is divisible by 11

(iii) 379654

Sum of digit at odd places = 7 + 6 + 4 = 17

Sum of digit at even places = 3 + 9 + 5 = 17

Difference of the above sum = (17 – 17) = 0

379654 is divisible by 11

(iv) 1057982

Sum of digit at odd places = 1 + 5 + 9 + 2 = 17

Sum of digit at even places = 0 + 7 + 8 = 15

Difference of the above sum = (17 – 15) = 2, which is not divisible by 11

1057982 is not divisible by 11

(v) 6543207

Sum of digit at odd places = 6 + 4 + 2 + 7 = 19

Sum of digit at even places = 5 + 3 + 0 = 8

Difference of the above sum = (19 – 8) = 11, Which is divisible by 11

6543207 is divisible by 11

(vi) 818532

Sum of digital to odd places = 1 + 5 + 2 = 8

Sum of digit at even places = 8 + 8 + 3 = 19

Difference of the above sum = 19 – 8 = 11, which is divisible by 11

818532 is divisible by 11

(vii) 900163

Sum of digit at odd places = 0 + 1 + 3 = 4

Sum of digit at even places = 9 + 0 + 6 = 15

Difference of the above sum = (15 – 4) = 11, which is divisible by 11

900163 is divisible by 11

(viii) 7531622

Sum of digit at odd places = 7 + 3 + 6 + 2 = 18

Sum of digit at even places = 5 + 1 + 2 = 8

Difference of the above sum = (18 – 8) = 10, which is not divisible by 11

7531622 is not divisible by 11

**Question 9.**

**Solution:**

For testing the divisibility of a number by 7, we proceed according to the

following steps:

Step 1: Double the unit digit of the given number.

Step 2 : Subtract the above number from the number formed by excluding the unit digit of the given number.

Step 3 : 1f the number so obtained is divisible by 7 then the given number is divisible by 7.

(i) 693

Now, 69 – (2 x 3) = 63, which is divisible by 7

693 is divisible by 7

(ii) 7896

Now 789 – (6 x 2) = 777, which is divisible by 7

7896 is divisible by 7

(iii) 3467

Now, 346 – (7 x 2) = 332, which is not divisible by 7

3467 is not divisible by 7

(iv) 12873

Now,1287 – (3 x 2) = 1281, which is divisible by 7

12873 is divisible by 7

(v) 65436

Now, 6543 – (6 x 2) = 6531, which is divisible by 7

65436 is divisible by 7

(vi) 54636

Now, 5463 – (6 x 2) 5451, which is not divisible by 7

54636 is not divisible by 7

(vii) 98175

Now, 9817 – (5 x 2) 9807, which is divisible by 7

98175 is divisible by7

(viii) 88777

Now, 8877 – (7 x 2) = 8863, which is not divisible by 7

88777 is not divisible by 7

**Question 10.**

**Solution:**

The given number 7×3 is divisible by 3

The sum of its digits is divisible by 3

7 + x + 3 =>10 + x is divisible by 3

Value of x can be 2, 5, 8

The numbers can be 723, 753, 783

**Question 11.**

**Solution:**

The given number 53yl is divisible by 3

Sum of its digits is divisible by 3

i.e., 5 + 3 + y + 1 or 9 + y is divisible by 3

Values of y can be 0, 3, 6, 9

Then the numbers can be 5301, 5331, 5361, 5391

**Question 12.**

**Solution:**

Number x806 is divisible by 9

The sum of its digits is also divisible by 9

or x + 8 + 0 + 6 or 14 + x is divisible by 9

x can be 4

Number will be 4806

**Question 13.**

**Solution:**

The number 471z8 is divisible by 9

The sum of its digits is also divisible by 9

471z8 = 4 + 7 + 1 + z + 8

=> 20 + z is divisible by 9

Value of z can be 7

Number will be 47178

**Question 14.**

**Solution:**

Let the number 21, sum of digits 2 + 1 = 3

which is divisible by 3 not by 9

Let the number 24, sum of digits 2 + 4 = 6

which is divisible by 3 not by 9

Let the number 30, sum of digits 3+0 = 3

which is divisible by 3 not by 9

Let the number 33, sum of digits 3 + 3 = 6

which is divisible by 3 not by 9

Let the number by 39 sum of digits 3 + 9 = 12

which is divisible by 3 not by 9

**Question 15.**

**Solution:**

Consider numbers as 28, 36,44, 52,60 as these numbers are divisible by 4 not by 8.

Let the number 39, sum of digits 3 + 9 = 12

which is divisible by 3 not by 9

Hope given RS Aggarwal Solutions Class 8 Chapter 5 Playing with Numbers Ex 5B are helpful to complete your math homework.

If you have any doubts, please comment below. Learn Insta try to provide online math tutoring for you.

Janak Awasthi says

Good questions but their are some mistakes