8. If 148101a 095 is a multiple of 11, where a is a
digit, the value of a is
(a)0
(b) 4
(c) 1
(d) 2
Answers
Given : Number 148101a095 is divisible by 11, where a is a digit.
To find : What are the possible value of a ?
Solution :
According to the divisibility rule of 11,
We must subtract and then add the digits in an alternating pattern from left to right. If the answer is O or 11, then the result is divisible by 4
Taking first alternative terms,
Si=1+8+0+ a +9
S1 = 18 + a
Taking second alternative terms,
S2 = 4+1+1+0+5
S2 = 11 =
Now subtract,
S1 – S2 = 18 + a – 11 = 7+a
So, 7+a is divisible by 11 we check on different values of a
If a=1, 7+1=8 not divisible by 11
If a=2, 7+2=9 not divisible by 11
If a=3, 7+3=10 not divisible by 11
If a=4, 7+4=11 is divisible by 11
hence the possible value is 4.
Answer:
Value of a = 4
Step-by-step explanation:
Divisibility rule -:
The sum of all number of even places subtracted from the sum of all number at the odd places . In the number will divided by 11 or the answer will come zero then the number is divisible by 11 .
Solution :
Odd places -:
1,8,0,a,9
Sum:
= 1+8+a+9
=9+a+9
=18+a
Even places -:
4,1,1,0,5
Sum:
=4+1+1+5
=6+5
=11
Now , subtract -:
So , in odd is 18+a . And at even is 11 .
After subtracting then subtract the value of a with the 11 .
=> 18+a-11
=> 18-11=a
=> 7=a
Now ,
=> 11-7=a
=> 4=a
So , the value of a will be 4 .
Verification :
Sum of odd places -:
= 1+8+4+9
= 22
Sum of even places -:
= 4+1+1+5
= 11
Subtraction -:
= 22-11
= 11
So , the 11 is divisible by 11 .
Hence , proved .