if 756 x is divisible by 11 . what is x and find the value
Answers
The value of x is 8, and the value of 7568 divided by 11 is 688.
• A number is divisible by 11 if the difference between the sum of digits in the odd places and the sum of digits in the even places is either equal to 0 or 11.
• Given number is 756x.
Here, the digits in the odd places (Ist and 3rd positions) are 7 and 6 respectively.
Sum of 7 and 6 = 7 + 6 = 13
• The digits in the even places ( 2nd and 4th positions) are 5 and x respectively.
Sum of 5 and x = 5 + x
• According to the first condition for divisibility by 11,
13 - (5 + x) = 0
=> 13 - 5 - x = 0
=> 8 = x
=> x = 8
• According to the second condition for divisibility by 11,
13 - (5 + x) = 11
=> 13 - 5 - x = 11
=> 8 - x = 11
=> 8 - 11 = x
=> x = - 3
• Since a digit in a number cannot be negative, x = - 3 is discarded.
Therefore, the value of x is 8, and the number is 7568.
• Now, 7568 / 11 = 688