## ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 5 Playing with Numbers Objective Type Questions

Mental Maths
Question 1.
Fill in the blanks:
(i) The sum of a 2-digit number and number obtained by reversing the digits is always divisible by 11 and ……….
(ii) The difference of a 2-digit number and number obtained by reversing the digits is always divisible by ………. and ……….
(iii) The difference of a 3=digit number a b c (a > c) and the number obtained by reversing the digits is always divisible by ………. and ……….
(iv) The next number of the series 0, 1, 1, 2, 3, 5, 8, 13, ………. is ……….
(v) The general form of a 2 digit number 57 is ……….
(vi) Usual form of number 100 × 7 + 10 × 4 + 1 is ……….
(vii) If the division N ÷ 5 leaves remainder 4 and the division N ÷ 2 leaves remainder 1, then unit’s digit of N must be ……….
(viii)If 213×52 is divisible by 9, then digit x is ……….
Solution:
(i) The sum of a 2-digit number and number obtained by
reversing the digits is always divisible by 11 and sum of digits.
(ii) The difference of a 2-digit number and number obtained by
reversing the digits is always divisible by 9 and difference of the digits.
(iii) The difference of a 3=digit number a b c (a > c)
and number obtained by reversing the digits is always divisible by 99 and (a – c).
(iv) The next number of the series 0, 1, 1, 2, 3, 5, 8, 13, is 21 and 34.
{∵ 8 + 13 = 21
21 + 13 = 34}
(v) General form of a 2 digit number 57 is 10 × 5 + 7 × 1.
(vi) Usual form of number 100 × 7 + 10 × 4 + 1 is 100 × 7 + 10 × 4 + 1 is 741.
(vii) If the division N ÷ 5 leaves remainder 4 and the division
N ÷ 2 leaves remainder 1, then unit’s digit of N must be 9.
(viii) If 213×52 is divisible by 9, then digit x is 5.
Sum of digits = 2 + 1 + 3 + 5 + 2 + x is divisibility 9
= 13 + x is divisible by 9
∴ x = 5 or 13 + 5 = 18 – 9 = 2

Question 2.
State whether the following statements are true (T) or false (F):
(i) If the division N ÷ 5 leaves a remainder 4, then unit’s digit of N maybe 1 or 6.
(ii) If the division N ÷ 2 leaves a remainder 1, then unit’s digit of N maybe 1, 3, 5, 7 or 9.
(iii) If a number is divisible by any number m, then it will also be divisible by each of the factors of m.
(iv) If a number is divisible by sum of two numbers then it will also be divisible by each of the two numbers separately.
(v) If 3651x is divisble by 9, then value of digit x is 3.
(vi) If 42×7 is divisible by 3, then value of digit x is 4.
(vii) The number 152875 is divisible by 9.
(viii)The number 389072 is divisible by 8.
(ix) The number 27402 is divisible by 6.
(x) The number 359249 is not divisible by 11.
Solution:
(i) If the division N = 5 leaves a remainder 4,
then unit’s digit of N may be 1 or 6. False
Correct:
The unit digit will be 4 or 9.
(ii) If the division N ÷ 2 leaves a remainder 1,
then unit’s digit of N may be 1, 3, 5, 7 or 9. True
(iii) If a number is divisible by any number m,
then it will also be divisible by each of the factors of m. True
(iv) If a number is divisible by sum of two numbers then
it will also be divisible by each of the two numbers separately. False
Correct:
As if 33 is divisible by 7 + 4 = 11, then it will not divisibly by 7 or 4 seperately.
(v) If 3651x is divisble by 9, then value of digit x is 3. True
(vi) If 42×7 is divisible by 3, then value of digit x is 4. False
Correct:
As in 4247, sum of digits 4 + 2 + 4 + 7 = 17 is not divisible by 3.
(vii) The number 152875 is divisible by 9. False
Correct:
As digits of 152875 = 1 + 5 + 2 + 8 + 7 + 5 = 28
which is not divisible by 9.
(viii)The number 389072 is divisible by 8. True
(ix) The number 27402 is divisible by 6. True
(x) The number 359249 is not divisible by 11.
False
Correct:
As it is divisible by 11

Multiple Choice Questions
Choose the correct answer from the given four options (3 to 13):
Question 3.
When the sum of a 2-digit number ab and number obtained by reversing the digits is divided by (a + b), then quotient is
(a) a – b
(b) 9
(c) 11
(d) None of these
Solution:
A 2-digit number ab and number obtained by
reversing the digit is divided by (a + b), then the quotient is 11. (c)

Question 4.
When the sum of a 3-digit number abc and numbers obtained by changing the order of the digits cyclically is divided by 111, then quotient is
(a) 37
(b) a – b + c
(c) a + b + c
(d) 3
Solution:
Sum of 3-digit number abc and number obtained by
changing the order of the digits cyclically is divided by 111,
then quotient is a + b + c. (c)

Question 5.
If A + A + A = BI, where A and B are different digits, then
(a) A = 1, B = 5
(b) A = 5, B = 2
(c) A = 5, B = 1
(d) A = 7, B = 2
Solution:
A + A + A = BI, where A and B are different digits then A = 7, B = 2.
As unit digit of sum = 1
∴ A will be $$\frac{21}{3}$$ = 7
{∵ $$\frac{11}{3}, \frac{31}{3}$$ are not naturals}
∴ A = 7, B = 2 (c)

Question 6.
Which of the following numbers is not divisible by 2?
(a) 437218
(b) 437821
(c) 437812
(d) 437182
Solution:
Which of the following is not divisible by 2
437821 as it’s unit digit is 1. (b)

Question 7.
Which of the following numbers is not divisible by 10?
(a) 32570
(b) 32750
(c) 32500
(d) 32075
Solution:
Which of the given number is not divisible by 10
32075, (as it’s unit digit is not zero) (d)

Question 8.
Which of the following numbers is divisible by 4?
(a) 98764
(b) 98746
(c) 98674
(d) 98647
Solution:
Which of given number is divisible by 4.
98764 as number forming last two digits is 64
which is divisible by 4. (a)

Question 9.
Which of the following numbers is divisible by 8?
(a) 32466
(b) 32476
(c) 32486
(d) 32456
Solution:
Which of the following is divisible by 8.
32456 as number formed by last three digits 456 is divisible by 8. (d)

Question 10.
Which of the following numbers is divisible by 11?
(a) 725824
(b) 752824
(c) 725842
(d) 725482
Solution:
Which of the following is divisible by 11.
725824 as the difference of the sum of digits at odd places
and sum of digit an even place is divisible by 11. (a)

Question 11.
Which of the following numbers is not divisible by 9?
(a) 24354
(b) 24453
(c) 24534
(d) 24564
Solution:
Which of the following is not divisible by 9.
24564 as the sum of its digits is not divisible by 9. (d)

Question 12.
If 467×8 is divisible by 3, then value of x
(a) 1
(b) 2
(c) 3
(d) 4
Solution:
∵ 467×8 is divisible by 3
∴ 4 + 6 + 7 + 8 + x = 25 + x is divisible by 3
∴ 25 + x = 27, 30, 33
∴ x = 2, 5, 8
x = 2 (b)

Question 13.
If 36x52y8 is divisible by 9, then x + y is
(a) 2
(b) 3
(c) 4
(d) 5
Solution:
∵ 36x52y8 is divisible by 9
∴ 3 + 6 + 5 + 2 + 8 + x + y
⇒ 24 + x + y is divisible by 9
24 + (x + y) = 27
x + y = 27 – 24 = 3 (b)

Value Based Question
Question 1.
Rishabh plays a game with two dice in a fete. He draw three columns on a chart paper.In the left most column he write the digits less than 7 and in the right most column he write the numbers greater than 7. In the middle column he write digit 7 only. He offter people to keep money on any one of the column. He throws two dice together, if the sum of the digits on the two dice is less than 7, he doubles the money kept on the left most column and collect the money kept on remaining two columns. Similarly, he doubles the money on right most column if the sum of digits is greater than 7 and triples on the middle column if sum of the digits is 7. What digits should he write on left most and right most columns?
Is this game a sort of gambling? Is gambling a good way of earning money?
Solution:
Two dice are thrown:

 Less than 7 More than 7 1 7 2 8 3 9 4 10 5 11 6 12

It is a sort of gambling which is against
the law of government as well as society.
It should be stopped.

Higher Order Thinking Skills (Hots)
Question 1.
If the difference of two digit number and number obtained by reversing the digits is 45, then write all possible 2-digit numbers.
Solution:
The difference of 2-digit number and
the number obtained by reversing the digits is 45,
then the two numbers will be
16, 61 (∵ 61 – 16 = 45)
27, 72 (∵ 72 – 27 = 45)
38, 83 (∵ 83 – 38 = 45)
49, 94 (∵ 94 – 49 = 45)