RS Aggarwal Class 8 Math Fifth Chapter Playing with Numbers Exercise 5B Solution

RS Aggarwal Class 8 Math Fifth Chapter Playing with Numbers Exercise 5B Solution

EXERCISE 5B

(1) Test the divisibility of each of the following numbers by 2.

Rule: A given number is divisible by 2 only when its unit digit is 0, 2, 4, 6 or 8.

(i) 94 = Divisible

(ii) 570 = Divisible

(iii) 285 = Not Divisible

(iv) 2398 = Divisible

(v) 79532 = Divisible

(vi) 13576 = Divisible

(vii) 46821= Not Divisible

(viii) 84663 = Not Divisible

(ix) 66669 = Not Divisible

(2) Test the divisibility of each of the following numbers by 5:

Rule: A given number is divisible by 5 only when its unit digit is 0 or 5.

(i) 95 = Divisible by 5.

(ii) 470 = Divisible by 5.

(iii) 1056 = Not divisible by 5.

(iv) 2735 = Divisible by 5.

(v) 55053 = Not divisible by 5.

(vi) 35790 = Divisible by 5.

(vii) 98765 = Divisible by 5.

(viii) 42658 = Not divisible by 5.

(ix) 77990 = Divisible by 5.

(3) Test the divisibility of each of the following numbers by 10:

Rule: A given number is divisible by 10 only when its units digit 10.

(i) 205 = Not divisible by 10.

(ii) 90 = Divisible by 10.

(iii) 1174 = Not divisible by 10.

(iv) 57930 = Divisible by 10.

(v) 60005 = Not divisible by 10.

(4) Test the divisibility of each of the following numbers by 3:

Rule: A given number is divisible by 3 only when the sum of its digits is divisible by 3.

(i) 83 = (8 + 3) = 11 is not divisible by 3.

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

(iii) 474 = (4 + 7 + 40) = 15 is divisible by 3.

(iv) 1693 = (1 + 6 + 9 + 3) = 19 is not 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 + 2) = 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.

(5) Test the divisibility of each of the following numbers by 9:

Rule: A given number is divisible by 9 only when the sum of its digit divisible by 9.

(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.

(6) Test the divisibility of each of the following numbers by 4:

Rule: A given number is divisible by 4 only when the number formed by its last two digit is divisible by 4.

(i) 134 = Number formed by its last two digits is 34, which is clearly not divisible by 4.

(ii) 618 = Number formed by its last two digits is 18, which is clearly not divisible by 4.

(iii) 3928 = Number formed by its last two digits is 28, which is clearly divisible by 4.

(iv) 50176 = Number formed by its last two digits is 76, which is clearly divisible by 4.

(v) 39392 = Number formed by its last two digits is 92, which is clearly divisible by 4.

(vi) 56794 = Number formed by its last two digits is 94, which is clearly not divisible by 4.

(vii) 86102 = Number formed by its last two digits is 02, which is clearly not divisible by 4.

(viii) 66666 = Number formed by its last two digits is 66, which is clearly not divisible by 4.

(ix) 99918 = Number formed by its last two digits is 18, which is clearly not divisible by 4.

(x) 77736 = Number formed by its last two digits is 36, which is clearly divisible by 4.

(7) Test the divisibility of each of the following numbers by 8:

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

(i) 6132 = Number formed by its last three digits is 132, which is clearly not divisible by 8.

(ii) 7304 = Number formed by its last three digits is 304, which is clearly divisible by 8.

(iii) 59312 = Number formed by its last three digits is 312, which is clearly divisible by 8.

(iv) 66664 = Number formed by its last three digits is 664, which is clearly divisible by 8.

(v) 44444 = Number formed by its last three digits is 444, which is clearly not divisible by 8.

(vi) 154360 = Number formed by its last three digits is 360, which is clearly divisible by 8.

(vii) 998818 = Number formed by its last three digits is 818, which is clearly not divisible by 8.

(viii) 265472 = Number formed by its last three digits is 472, which is clearly divisible by 8.

(ix) 7350162 = Number formed by its last three digits is 162, which is clearly not divisible by 8.

(8) Test the divisibility of each of the following numbers by 11:

Rule: 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 0 or a number divisible by 11.

(i) 22222

Solution: Sum of its digits at odd places (2 + 2 + 2) = 6.

Sum of its digits at even places = (2 + 2) = 4.

Difference of the above sums = (6 – 4) = 2.

∴ 22222 is not divisible by 11.

(ii) 444444

Solution: Sum of its digits at odd places = (4 + 4 + 4) = 12

Sum of its digits at even places = (4 + 4 + 4) = 12

Difference of the above sums = (12 – 12) = 0

∴ 444444 is divisible by 11.

(iii) 379654

Solution: Sum of its digits at odd places = (3 + 9 + 5) = 17

Sum of its digits at even places = (7 + 6 + 4) = 17

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

∴ 379654 is divisible by 11.

(iv) 1057982

Solution: Sum of its digits at odd places = (1 + 5 + 9 + 2) = 17

Sum of its digits at even places = (0 + 7 + 8) = 15

Difference of the above sums = (17 – 15) = 2

∴ 1057982 is not divisible by 11.

(v) 6543207

Solution: Sum of its digits at odd places = (6 + 4 + 2 + 7) = 19

Sum of its digits at even places = (5 + 3 + 0) = 8

Difference of the above sums = (19 – 8) = 11

∴ 6543207 is divisible by 11.

(vi) 818532

Solution: Sum of its digits at odd places = (8 + 8 + 3) = 19

Sum of its digits at even places = (1 + 5 + 2) = 8

Difference of the above sums = (19 – 8) = 11

∴ 818532 is divisible by 11.

(vii) 900163

Solution: Sum of its digits at odd places = (9 + 0 + 6) = 15

Sum of its digits at even places = (0 + 1 + 3) = 4

Difference of the above sums = (15 – 4) = 11

∴ 90013 is divisible by 11.

(viii) 7531622

Solution: Sum of its digits at odd places = (7 + 3 + 6 + 2) = 18

Sum of its digits at even places = (5 + 1 + 2) = 8

Difference of the above sums = (18 – 8) = 10

∴ 7531622 is not divisible by 11.

(9) Test the divisibility of each of the following numbers by 7:

(i) 693 = 69 – (3 × 2) = 63 is divisible by 7.

(ii) 7896 = 789 – (6 × 2) = 777 is divisible by 7.

(iii) 3467 = 346 – (7 × 2) = 332 is not divisible by 7.

(iv) 12873 = 1287 – (3 × 2) = 1281 is divisible by 7.

(v) 65436 = 6543 – (6 × 2) = 6531 is divisible by 7.

(vi) 54636 = 5463 – (6 × 2) = 5451 is not divisible by 7.

(vii) 98175 = 9817 – (5 × 2) = 9807 is divisible by 7.

(viii) 88777 = 8877 – (7 × 2) = 8863 is not divisible by 7.

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

Solution: 7 + x + 3 = 10 + x

We know x can only be a single digit number.

And multiples of 3 between 10 to 20 is 12, 15 and 18.

We know that 12 = 10 + 2

15 = 10 + 5

18 = 10 + 8

Therefore the possible number are 2, 5, 8 and the numbers are 723, 753 and 783.

(11) Find all possible values of y for which the number 53y1 is divisible by 3. Also, find each such number.

Solution: 5 + 3 + y + 1 = 9 + y

We know y can only be a single digit number.

And multiples of 3 between 9 to 20 is 12, 15 and 18.

We know that 3 = 9 + 3

15 = 9 + 6

18 = 9 + 9

Therefore the possible number are 3, 6, 9 and the numbers are 5331, 5361 and 5391.

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

Solution: x + 8 + 0 + 6 = 14 + x

The closest multiple of 9 to 14 is 18.

Therefore, 18 = x + 14

⇒ 18 – 14 = x

⇒ x = 4

Therefore the number is 4806.

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

Solution: 4 + 7 + 1 + z + 8 = 20 + z

The closest multiple of 9 to 20 is 27.

Therefore, 27 = 20 + z

⇒ z = 27 – 20

⇒ z = 7

Therefore, the number is 47178.

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

Ans: 21, 24, 30, 33, 39.

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

Ans: 28, 36, 44, 52, 60.