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 30Find the least value of * for which 4832*18 is divisible by 11.Options :A. 5B. 3C. 7D. 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.
Similar Questions
Find the least value of * for which 4832*18 is divisible by 11.Options :A. 5B. 3C. 7D. 11
If 9A4156B is divisible by 15, then what is the minimum value of A - B?Options :0125
Find the least number exactly divisible by 12, 15, 20 and 27.
What least number must be added to 2010 to obtain a number which is completely divisible by 19?Options :A.5B.4C.3D.None of these
Write the prime factorization of 30. Use exponents when appropriate and order the factors from least to greatest (for example, 2235).
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.