RS Aggarwal Solutions: Exercise 5D - Playing With Numbers | Mathematics (Maths) Class 8 PDF Download

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Solution:
a
0
If a number is divisible by 3, then the sum of the digits is also divisible by 3.
6 +4 +y +8 = 18 +y
This is divisible by 3 as y is equal to 0.
Question:38
Tick
? the correct answer
If 7x8 is exactly divisible by 9, then the least value of x is
a
0
b
2
c
3
d
5
Solution:
c
3
If a number is exactly divisible by 9, the sum of the digits must also be divisible by 9.
7 +x +8 = 15 +x
18 is divisible by 9.
? 15 +x = 18 ? x = 3
Question:39
Tick
? the correct answer
If 37y4 is exactly divisible by 9, then the least value of y is
a
2
b
3
c
1
d
4
Solution:
d
4
A number is divisible by 9 if the sum of the digits is divisible by 9.
3 +7 +y +4 = 14 +y
For this sum to be divisible by 9:
14 +y = 18 ? y = 4
Question:40
Tick
? the correct answer
If 4xy7 is exactly divisible by 3, then the least value of (x + y) is
a
1
b
4
c
5
d
7
Solution:
a
1
If a number is divisible by 3, the sum of the digits is also divisible by 3.
4 +x +y +7 = 11 +(x +y)
For the sum to be divisible by 3:
11 +(x +y) = 12 ? (x +y) = 1
Question:41
Tick
? the correct answer
If x7y5 is exactly divisible by 3, then the least value of (x + y) is
a
6
b
0
c
4
d
3
Solution:
d
3
Page 3


  
  
  
       
                                        
                       
   
           
          
             
     ?                               
   
   
  
 
 
 
                               
 
 
   
             
                  
    
    
  
 
   
   
   
             
Solution:
a
0
If a number is divisible by 3, then the sum of the digits is also divisible by 3.
6 +4 +y +8 = 18 +y
This is divisible by 3 as y is equal to 0.
Question:38
Tick
? the correct answer
If 7x8 is exactly divisible by 9, then the least value of x is
a
0
b
2
c
3
d
5
Solution:
c
3
If a number is exactly divisible by 9, the sum of the digits must also be divisible by 9.
7 +x +8 = 15 +x
18 is divisible by 9.
? 15 +x = 18 ? x = 3
Question:39
Tick
? the correct answer
If 37y4 is exactly divisible by 9, then the least value of y is
a
2
b
3
c
1
d
4
Solution:
d
4
A number is divisible by 9 if the sum of the digits is divisible by 9.
3 +7 +y +4 = 14 +y
For this sum to be divisible by 9:
14 +y = 18 ? y = 4
Question:40
Tick
? the correct answer
If 4xy7 is exactly divisible by 3, then the least value of (x + y) is
a
1
b
4
c
5
d
7
Solution:
a
1
If a number is divisible by 3, the sum of the digits is also divisible by 3.
4 +x +y +7 = 11 +(x +y)
For the sum to be divisible by 3:
11 +(x +y) = 12 ? (x +y) = 1
Question:41
Tick
? the correct answer
If x7y5 is exactly divisible by 3, then the least value of (x + y) is
a
6
b
0
c
4
d
3
Solution:
d
3
When a number is divisible by 3, the sum of the digits must also be divisible by 3.
x +7 +y +5 = (x +y)+12
This sum is divisible by 3 if  x+y+12 is 12 or 15.
For x+y+12 = 12:
x+y=0
But x+y cannot be 0 because then x and y both will have to be 0.
Since x is the first digit, it cannot be 0.
? x+y+12 = 15
or x+y = 15-12=3
Question:42
Tick
? the correct answer
If x4y5z is exactly divisible by 9, then the least value of (x + y + z) is
a
3
b
6
c
9
d
0
Solution:
c
9
A number is divisible by 9 if the sum of the digits is divisible by 9.
x +4 +y +5 +z = 9 +(x +y +z)
The lowest value of (x +y +z) is equal to 0
 for the number x4y5z to be divisible by 9.
In this case, all x, y and z will be 0.
But x is the first digit, so it cannot be 0.
? x+4+y+5+z = 18
or x+y+z+9 = 18
or x+y+z = 9
Question:43
Tick
? the correct answer
If 1A2B5 is exactly divisible by 9, then the least value of (A + B) is
a
0
b
1
c
2
d
10
Solution:
b
1
For a number to be divisible by 9, the sum of the digits must also be divisible by 9.
1 +A +2 +B +5 = (A +B)+8
The number will be divisible by 9 if (A +B) = 1
.
Question:44
Tick
? the correct answer
If the 4-digit number x27y is exactly divisible by 9, then the least value of (x + y) is
a
0
b
3
c
6
d
9
Solution:
d
9
If a number is divisible by 9, then the sum of the digits is divisible by 9.
x +2 +7 +y = (x +y)+9
For this to be divisible by 9, the least value of (x +y) is 0
.
But for x+y = 0, x and y both will be zero.
Since x is the first digit, it can never be 0.
? x + y + 9 = 18
or  x + y = 9