R.S Aggarwal Class 8 Chapter 5 Playing with Numbers Test Paper Solution
The 5th Chapter of RS Aggarwal book of Class 8 is called Playing with numbers and in this post we have provided complete written solution for the test paper 5 . The solutions are prepared by our team of expert teachers.
Complete RS Aggarwal solution for class 8 is also available in our website.
Test Paper 5
A)
1) Find all possible values of x for which the 4-digit number 320x is divisible by 3. Also, find the numbers.
Ans: According to the problem the number 320x must be divisible by 3.
∴ The sum of the digits of the number = 3+2+0+x = 5+x
5+x must be divisible by 3
For 5+x to be divisible by 3 the possible values of x are 1, 4 and 7.
The Possible numbers are 3201, 3204 and 3207.
2) Find all possible values of y for which the 4-digit number 64y3 is divisible by 9. Also, find the numbers.
Ans: According to the problem the number 64y3 must be divisible by 9.
∴ The sum of the digits of the number = 6+4+y+3 = 13+y
13+y must be divisible by 9
For 13+y to be divisible by 9 the possible value of y is 5.
The Possible number is 6453.
3) The sum of the digits of a 2-digit number is 6. The number obtained by interchanging its digits is 18 more than the original number. Find the original number.
Ans: Let the tens digit be a and the unit digit be b.
∴ a + b = 6 ——— (i)
The original number is 10a+b
And the number obtained by interchanging the digits is 10b+a
According to the question the difference between two numbers is 18
10b+a – 10a – b = 18
Or, 9b – 9a = 18
Or, (b – a) = 2 ———- (ii)
By adding equation (i) and (ii) we get
2b = 8
Or, b = 4
By putting b = 4 in equation 1 we get
a + 4 = 6
∴ a = 2
The original number is 10×2+4 = 24
4) Which of the following numbers are divisible by 9?
(i) 524618
(ii) 7345845
(iii) 8987148
Ans:
A number is divisible by 9 when the sum of the digits of the number is also divisible by 9.
i) The sum of the digits of 524618 is 5+2+4+6+1+8 = 26, which is not divisible by 9. So the number 524618 is not divisible by 9.
ii) The sum of the digits of 7345845 is 7+3+4+5+8+4+5= 36, which is divisible by 9. So the number 7345845 is divisible by 9.
iii) The sum of the digits of 8987148 is 8+9+8+7+1+4+8 = 45, which is divisible by 9. So the number 8987148 is divisible by 9.
5) Replace A, B, C by suitable numerals:
Ans:
Since (11 – 8) = 3, so A = 3 and 1 is taken away from 7.
Since (16 – 7) = 9, so B = 7 and 1 is taken from 5
Now, 4 – 2 = 2, so C = 2
∴ A = 3, B = 7 and C = 2
6) Replace A, B, C by suitable numerals:
Ans: It is clear that B = 3 and C = 9
Now, 56 + 6 = 62
∴ A = 2
So, A = 2, B = 3, C = 9
7) Find the values of A, B C when
Ans: B × A = B
∴ A = 1
Now, we have
(1+B2) is single digit and A≠B
So B must be equal to 2
So C = 1+22= 5
∴ A = 1, B = 2, C = 5
B) Mark (✓) against the correct answer in each of the following:
8) If 7*8 is exactly divisible by 3, then the least value of * is
a) 3 (✓)
b) 0
c) 6
d) 9
Ans: For a number to divisible by 3 the sum of the digits of that number must be divisible by 3.
The sum of the digits of the number 7+*+8 = 15+*
For 15+* to be divisible by 3 the least value of * from the options is 3.
∴ The least value of * is 3.
9) If 6×5 is exactly divisible by 9, then the least value of x is
a) 1
b) 4
c) 7 (✓)
d) 0
Ans: According to the problem the number 6×5 must be divisible by 9.
∴ The sum of the digits of the number = 6+x+5 = 11+ x must be divisible by 9
For 11+ x to be divisible by 9 the least possible value of x from the given options is 7.
The number is 675.
10) If x48y is exactly divisible by 9, then the least value of (x + y) is
a) 4
b) 0
c) 6 (✓)
d) 7
Ans: According to the problem the number x48y must be divisible by 9.
∴ The sum of the digits of the number = x+4+8+y = 12+x+y
12+x+y must be divisible by 9
For 12+x+y to be divisible by 9 the least possible value of (x+y) is 6.
11) If 486*7 is divisible by 9, then the least value of * is
a) 0
b) 1
c) 3 (✓)
d) 2
Ans: According to the problem the number 486*6 must be divisible by 9.
∴ The sum of the digits of the number = 4+8+6+*+6 = 24+*.
24+* must be divisible by 9.
For 24+* to be divisible by 9 the least possible value of * from the given options is 3.