## RS Aggarwal Class 8 solutions Chapter 5 Playing with Numbers Ex 5B in pdf free download

Contents

**Question 1.**

**Test the divisibility of each of the following numbers by 2:**

**(i) 94**

**(ii) 570**

**(iii) 285**

**(iv) 2398**

**(v) 79532**

**(vi) 13576**

**(vii) 46821**

**(viii) 84663**

**(ix) 66669**

**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.**

**Test the divisibility of each of the following numbers by 5:**

**(i) 95**

**(ii) 470**

**(iii) 1056**

**(iv) 2735**

**(v) 55053**

**(vi) 35790**

**(vii) 98765**

**(viii) 42658**

**(ix) 77990**

**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.**

**Test the divisibility of each of the following numbers by 10:**

**(i) 205**

**(ii) 90**

**(iii) 1174**

**(iv) 57930**

**(v) 60005**

**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.**

**Test the divisibility of each of the following numbers by 3:**

**(i) 83**

**(ii) 378**

**(iii) 474**

**(iv) 1693**

**(v) 20345**

**(vi) 67035**

**(vii) 591282**

**(viii) 903164**

**(ix) 100002**

**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.**

**Test the divisibility of each of the following numbers by 9:**

**(i) 327**

**(ii) 7524**

**(iii) 32022**

**(iv) 64302**

**(v) 89361**

**(vi) 14799**

**(vii) 66888**

**(viii) 30006**

**(ix) 33333**

**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.**

**Test the divisibility of each of the following numbers by 4:**

**(i) 134**

**(ii) 618**

**(iii) 3928**

**(iv) 50176**

**(v) 39392**

**(vi) 56794**

**(vii) 86102**

**(viii) 66666**

**(ix) 99918**

**(x) 77736**

**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.**

**Test the divisibility of each of the following numbers by 8:**

**(i) 6132**

**(ii) 7304**

**(iii) 59312**

**(iv) 66664**

**(v) 44444**

**(vi) 154360**

**(vii) 998818**

**(viii) 265472**

**(ix) 7350162**

**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.**

**Test the divisibility of each of the following numbers by 11:**

**(i) 22222**

**(ii) 444444**

**(iii) 379654**

**(iv) 1057982**

**(v) 6543207**

**(vi) 818532**

**(vii) 900163**

**(viii) 7531622**

**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.**

**Test the divisibility of each of the following numbers by 7:**

**(i) 693**

**(ii) 7896**

**(iii) 3467**

**(iv) 12873**

**(v) 65436**

**(vi) 54636**

**(vii) 98175**

**(viii) 88777**

**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.**

**Find all possible values of x for which the number 7×3 is divisible by 3. Also, find each such number.**

**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.**

**Find all possible values of y for which the number 53yl is divisible by 3. Also, find each such number.**

**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.**

**Find the value of x for which the number x806 is divisible by 9. Also, find the number.**

**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.**

**Find the value of z for which the number 471z8 is divisible by 9. Also, find the number.**

**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.**

**Give five examples of numbers, each one of which is divisible by 3 but not divisible by 9.**

**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.**

**Give five examples of numbers, each one of which is divisible by 4 but not divisible by 8.**

**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

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