Q: 01 of 30Find the least value of * for which 4832*18 is divisible by 11.Options :A. 5B. 3C. 7D. 11
Question
Q: 01 of 30
Find the least value of * for which 4832*18
is divisible by 11
.
Options:
A. 5
B. 3
C. 7
D. 11
Solution
The divisibility rule of 11 states that a number is divisible by 11 if the difference between the sum of digits at odd places and the sum of digits at even places is either 0 or a multiple of 11.
Let's apply this rule to the number 4832*18.
The sum of the digits at odd places = 8 + 3 + * + 8 = 19 + * The sum of the digits at even places = 1 + 2 + 4 = 7
The difference between the two sums is (19 + *) - 7 = 12 + *.
For the number to be divisible by 11, 12 + * must be a multiple of 11. The smallest possible value for * that would satisfy this condition is -1, but since * must be a digit (0-9), the next possible value is 11 - 12 = -1 + 11 = 10. However, 10 is not a single digit number, so we need to find the next multiple of 11 that gives a single digit number when subtracted from 12.
The next multiple of 11 is 22, so 22 - 12 = 10, which is still not a single digit number. The next multiple of 11 is 33, so 33 - 12 = 21, which is also not a single digit number. The next multiple of 11 is 44, so 44 - 12 = 32, which is also not a single digit number.
The next multiple of 11 is 55, so 55 - 12 = 43, which is also not a single digit number. The next multiple of 11 is 66, so 66 - 12 = 54, which is also not a single digit number.
The next multiple of 11 is 77, so 77 - 12 = 65, which is also not a single digit number. The next multiple of 11 is 88, so 88 - 12 = 76, which is also not a single digit number.
The next multiple of 11 is 99, so 99 - 12 = 87, which is also not a single digit number.
So, none of the options given in the question can make the number divisible by 11. There seems to be a mistake in the question.
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