Dear Reader,
Below are three problems dealing with some divisibility rules.
Question 1
If 628X435 is exactly divisible by 3 then the minimum value which fits in the place of X is:
a) 5 b) 4 c) 3 d) 2
Answer : d) 2.
Solution :
Note that, "if a number is divisible by 3 then sum of its digits must be divisible by 3".
Given number is 628X435.
Sum of its digits = 6 + 2 + 8 + X + 4 + 3 + 5 = 28 + X which must be divided by 3.
Therefore, X will be 2 or 5 or 8.
We have to find the minimum value, hence the answer is 2.
Question 2
If the number 12987X6 is completely divisible by 8 then the value of X is equal to:
a) 5 b) 3 c) 1 d) none of these
Answer : b) 3.
Solution :
Note that, "if the last 3 digits of a number is divisible by 8 then the number also divisible by 8".
Here, given number is 12987X6, then the number formed by last 3 digits is 7X6.
Therefore, 7X6 must be divisible by 8.
Now, try with 0, 1, 2, 3, and so on.
Then, 706, 716, 726 are not divisible by 8.
and, 736 and 776 are the possible numbers for divisible by 8.
Therefore, the answer is either 3 or 7.
From the given option, answer is 3.
Question 3
Which of the following is exactly divisible by 33?
a) 8129 b) 9228 c) 4161 d) 7953
Answer : d) 7953
Solution :
Since, 33 = 11 x 3 and 11, 3 are co-primes.
Therefore, if a number is divisible by 33 then it will be divisible by both 3 and 11.
Note the rule to check the number is divisible by 11:
If you add every second digit and then subtract all other digits and the answer is either 0 or divisible by 11
Check with given options:
a) 8129 -> sum of the digits = 8+1+2+9 = 17 which is not a multiple of 3.
Hence 8129 is not divisible by 33.
b) 9228 -> sum of the digits = 9+2+2+8 = 21 which is a multiple of 3.
Now, check for 11:
(8+2) - (9+2) = 10-11 = -1 which not divisible by 11.
Hence 9228 is not the answer.
c) 4161 -> sum of the digits = 4+1+6+1 = 12 which is a multiple of 3.
Now, check for 11:
(1+1) - (4+6) = 2-10 = -8 which not a multiple of 11.
Hence 4161 is not the answer.
Therefore,option d 7953 is the answer.
Now, check for d,
Sum of its digits = 7+9+5+3 = 24 which is a multiple of 3.
And, (9+3) - (7+5) = 12 - 12 = 0.
Therefore, 7953 is divisible by 3 and 11.
And, 7953 is divisible by 33.
Below are three problems dealing with some divisibility rules.
Question 1
If 628X435 is exactly divisible by 3 then the minimum value which fits in the place of X is:
a) 5 b) 4 c) 3 d) 2
Answer : d) 2.
Solution :
Note that, "if a number is divisible by 3 then sum of its digits must be divisible by 3".
Given number is 628X435.
Sum of its digits = 6 + 2 + 8 + X + 4 + 3 + 5 = 28 + X which must be divided by 3.
Therefore, X will be 2 or 5 or 8.
We have to find the minimum value, hence the answer is 2.
Question 2
If the number 12987X6 is completely divisible by 8 then the value of X is equal to:
a) 5 b) 3 c) 1 d) none of these
Answer : b) 3.
Solution :
Note that, "if the last 3 digits of a number is divisible by 8 then the number also divisible by 8".
Here, given number is 12987X6, then the number formed by last 3 digits is 7X6.
Therefore, 7X6 must be divisible by 8.
Now, try with 0, 1, 2, 3, and so on.
Then, 706, 716, 726 are not divisible by 8.
and, 736 and 776 are the possible numbers for divisible by 8.
Therefore, the answer is either 3 or 7.
From the given option, answer is 3.
Question 3
Which of the following is exactly divisible by 33?
a) 8129 b) 9228 c) 4161 d) 7953
Answer : d) 7953
Solution :
Since, 33 = 11 x 3 and 11, 3 are co-primes.
Therefore, if a number is divisible by 33 then it will be divisible by both 3 and 11.
Note the rule to check the number is divisible by 11:
If you add every second digit and then subtract all other digits and the answer is either 0 or divisible by 11
Check with given options:
a) 8129 -> sum of the digits = 8+1+2+9 = 17 which is not a multiple of 3.
Hence 8129 is not divisible by 33.
b) 9228 -> sum of the digits = 9+2+2+8 = 21 which is a multiple of 3.
Now, check for 11:
(8+2) - (9+2) = 10-11 = -1 which not divisible by 11.
Hence 9228 is not the answer.
c) 4161 -> sum of the digits = 4+1+6+1 = 12 which is a multiple of 3.
Now, check for 11:
(1+1) - (4+6) = 2-10 = -8 which not a multiple of 11.
Hence 4161 is not the answer.
Therefore,option d 7953 is the answer.
Now, check for d,
Sum of its digits = 7+9+5+3 = 24 which is a multiple of 3.
And, (9+3) - (7+5) = 12 - 12 = 0.
Therefore, 7953 is divisible by 3 and 11.
And, 7953 is divisible by 33.
