The number A39K2 is completely divisible by both 8 and 11.
Here both A and K are single digit natural numbers. Which of the
following is a possible value of A+K?
a) 8 b) 10 c) 1 d) 14
Answers
Answer:
This is my answer
This is divisible by 8. Since both A and K are single digit natural numbers, this is not possible. Thus the only possible values of sum are 5, 10 and 13.
Step-by-step explanation:
The number is divisible by 11, so the difference between the sum of the digits at the odd places and the digits at the even places is either 0 or a multiple of 11.
Let the difference be a 0, so
11 + A = 3 + K
=> K – A = 8, the only possible value is 9,1
Now we have to check if it satisfies the divisibility by 8 test.
K= 9 makes the last 3 digits 992. This is divisible by 8.
Let’s check for other cases when the difference is 11
11 + A – 3 – K = 11 => A – K = 3
The possible values in this case are (9,6), ( 8,5), (7,4), (6,3), (5,2), (4,1)
Among these cases only (8,5) and (4,1) will be divisible by 8. So the possible values of sum are
13, 5 and 10
Now difference between the sum of odd and even places cannot be 22
11 + A – 3 – K = 22 => A – K = 14
Since both A and K are single digit natural numbers, this is not possible.
Thus the only possible values of sum are 5, 10 and 13.
In the given options only 10 is there. So it is the correct choice.
Hope this helps you
Answer:
The number is divisible by 11, so the difference between the sum of the digits at the odd places and the digits at the even places is either 0 or a multiple of 11.
Let the difference be a 0, so
11 + A = 3 + K
=> K – A = 8, the only possible value is 9,1
Now we have to check if it satisfies the divisibility by 8 test.
K= 9 makes the last 3 digits 992. This is divisible by 8.
Let’s check for other cases when the difference is 11
11 + A – 3 – K = 11 => A – K = 3
The possible values in this case are (9,6), ( 8,5), (7,4), (6,3), (5,2), (4,1)
Among these cases only (8,5) and (4,1) will be divisible by 8. So the possible values of sum are
13, 5 and 10
Now difference between the sum of odd and even places cannot be 22
11 + A – 3 – K = 22 => A – K = 14
Since both A and K are single digit natural numbers, this is not possible.
Thus the only possible values of sum are 5, 10 and 13.
In the given options only 10 is there. So it is the correct choice.