RBSE Solutions for Class 6 Maths Chapter 3 Playing With Numbers Ex 3.3

Rajasthan Board RBSE Solutions for Class 6 Maths Chapter 3 Playing With Numbers Ex 3.3 Textbook Exercise Questions and Answers.

RBSE Class 6 Maths Solutions Chapter 3 Playing With Numbers Ex 3.3

Question 1.
Using divisibility tests, determine which of the following numbers are divisible by 2; by 3; by 4; by 5; by 6; by 8; by 9; by 10; by 11 (say, yes or no): 
Answer:

 

Question 2.
Using divisibility tests, determine which of the following numbers are divisible by 4; by 8 :
(a) 572 
Answer:

• Number is divisible by 4 as its last two digits are divisible by 4.
• Number is not divisible by 8 as its last three digits are not divisible by 8.

(b) 726352 
Answer:

• The last two digits, i.e. 52 is divisible by 4. So the given number is divisible by 4.
• The last three digits, i.e. 352 is divisible by 8. So the given number is divisible by 4.

(c) 5500
Answer:

• The last two digits are 00. So it is divisible by 4.
• The last three digits are 500. Since 500 is not divisible by 8, the given number is not divisible by 8.

(d) 6000 
Answer:

• Divisible by 4, as its last two digits are 00.
• Divisible by 8, as its last three digits are 000.

(e) 12159 
Answer:
Not divisible by 4 and 8, as it is an odd number.

(f) 14560
Answer:

• Divisible by 4, as its last two digits are divisible by 4.
• Divisible by 8, as its last three digits, i. e. 560 is divisible by 8.

(g) 21084 
Answer:

• Divisible by 4, as its last two digits, i. e. 84 is divisible by 4.
• Not divisible by 8, as its last three digits, i.e. 084 is not divisible by 8.

(h) 31795072 
Answer:

• Divisible by 4, as its last two digits, i. e. 72 is divisible by 4.
• Divisible by 8, as its last three digits, i.e. 072 is divisible by 8.

(i) 1700
Answer:

• Divisible by 4, as its last two digits, i.e. 00 is divisible by 4.
• Not divisible by 8, as its last two digits, i.e. 700 is not divisible by 8.

(j) 2150
Answer:

• Not divisible by 4, as its last two digits, i.e. 50 is not divisible by 4.
• Not divisible by 8, as its last two digits, i.e. 150 is not divisible by 8.

Question 3.
Using divisibility tests, determine which of the following numbers are divisible by 6:
(a) 297144
Answer:

• Divisible by 2, as digit at units place
• Divisible by 3, as sum of its digits, i.e. 27 is divisible by 3.

Since the number is divisible by both 2 and 3, therefore, it is also divisible by 6.

(b) 1258
Answer:

• Divisible by 2, as digit at units place is an even number.
• Not divisible by 3, as sum of its digits, i.e. 16 is not divisible by 3.

Since the number is not divisible by both 2 and 3, therefore, it is not divisible by 6.

(c) 4335
Answer:

• Not divisible by 2, as digit at units place is not an even number.
• Divisible by 3, as sum of its digits, i.e. 15 is divisible by 3.

Since the number is not divisible by both 2 and 3, therefore, it is not divisible by 6.

(d) 61233
Answer:

• Not divisible by 2, as digit at units place is not an even number.
• Divisible by 3, as sum of its digits, i.e. 15 is divisible by 3.

Since the number is not divisible by both 2 and 3, therefore, it is not divisible by 6.

(e) 901352
Answer:

• Divisible by 2, as digit at units place is an even number.
• Not divisible by 3, as sum of its digits, i.e. 20 is not divisible by 3.

Since the number is not divisible by both 2 and 3, therefore, it is not divisible by 6.

(f) 438750
Answer:

• Divisible by 2, as digit at units place is an even number.
• Divisible by 3, as sum of its digits, i.e. 27 is divisible by 3,

Since the number is divisible by both 2 and 3, therefore it is divisible by 6.

(g) 1790184
Answer:

• Divisible by 2, as digit at units place is an even number.
• Divisible by 3, as sum of its digits, i.e. 30 is divisible by 3.

Since the number is divisible by both 2 and 3, therefore it is divisible by 6.

(h) 12583
Answer:

• Not divisible by 2, as digit at units place is not an even number.
• Not divisible by 3, as sum of its digits, i.e. 19 is not divisible by 3.

Since the number is not divisible Ijy both 2 and 3, therefore it is not divisible by 6.

(i) 639210 
Answer:

• Divisible by 2, as digit at units place is an even number.
• Divisible by 3, as sum of its digits, i.e. 21 is divisible by 3.

Since the number is divisible by both 2 and 3, therefore, it is divisible by 6.

(j) 17852
Answer:

• Divisible by 2, as digit at units place is an even number.
• Not divisible by 3, as sum of its digit, i.e. 23 is not divisible by 3.

Since the number is not divisible by both 2 and 3, therefore, it is not divisible by 6.

Question 4.
Using divisibility tests, determine which of the following numbers are divisible by 11:
(a) 5445
Answer:
Sum of the digits at odd places = 4 + 5 = 9
Sum of the digits at even places = 4 + 5 = 9
Difference of both sums = 9 - 9 = 0
Since, the difference is 0, therefore, the number is divisible by 11.

(b) 10824
Answer:
Sum of the digits at odd places = 4 + 8 + 1 = 13
Sum of the digits at even places = 2 + 0 = 2
Difference of both sums = 13 - 2 = 11
Since, the difference is 11, therefore, the number is divisible by 11.

(c) 7138965
Answer:
Sum of the digits at odd places = 5 + 9 + 3 + 7 = 24
Sum of the digits at even places = 6 + 8 + 1 = 15
Difference of both sums = 24 - 15 = 9
Since, the difference is neither 0 nor 11, therefore, the number is not divisible by 11.

(d) 70169308
Answer:
Sum of the digits at odd places = 8 + 3 + 6 + 0 = 17
Sum of the digits at even plaees = 0 + 9 + 1 + 7 = 17
Difference of both sums = 17 - 17 = 0
Since, the difference is 0, .therefore, the number is divisible by 11.

(e) 10000001
Answer:
Sum of the digits at odd places = 1 + 0 + 0 + 0 = 1
Sum of the digits at even places = 0 + 0 + 0 + 1 = 1
Difference of both sums = 1 - 1 = 0
Since, the difference is 0, therefore, the number is divisible by 11.

(f) 901153
Answer:
Sum of the digits at odd places = 3 + 1 + 0 = 4
Sum of the digits at even places = 5 + 1 + 9 = 15
Difference of both sums = 15 - 4 = 11 
Since, the difference is 11, therefore, the number is divisible by 11.

Question 5.
Write the smallest digit and the greatest digit in the blank space of each of the following numbers so that the number formed is divisible by 3 :
(a) ____ 6724
Answer:
We know that a number is divisible by 3 if the sum of all digits is divisible by 3.
Therefore, Smallest digit: 2 → 26724 = 2 + 6 + 7 + 2 + 4 = 21
Greatest digit: 8 → 86724 = 8 + 6 + 7 + 2 + 4 = 27

(b) ____ 4765
Answer:
We know that a number is divisible by 3 if the sum of all digits is divisible by 3.
Therefore, Smallest digit: 0 → 476502 = 4 + 7 + 6 + 5 + 0 + 2 = 24
Greatest digit: 9 → 476592 = 4 + 7 + 6 + 5 + 9 + 2 = 33

Question 6.
Write a digit in the blank space of each of the following numbers so that the number formed is divisible by 11.
(a) 92 __ 389
Answer:
Let the required digit = x
Sum of digits at odd places from the right = 9 + 3 + 2 = 14
Sum of digits at even places from the right = 8 + x + 9 = (17 + x)
Now, Difference of these sums = (17 + x) - 14 = 3 + x
For the above difference to be divisible by 11, required digit is 8. (∵ 3 + x = 11 ⇒ x = 8)
Hence, the required number is 928389.

(b) 8 __ 9484
Answer:
Let the required digit = x
Sum of digits at odd places from the right = 4 + 4 + x = 8 + x
Sum of digits at even places from the right = 8 + 9 + 8 = 25
Now, difference of these sums = 25 - (8 + x) = (17 - x)
For the above difference to be divisible by 11, required digit = 6 (∵ 17 - x = 11 or 17 - 11 = x or x = 6)