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If a 3-digit number 2y5 is divisible by 11, then the value of digit 'y' is:
7
2
9
3
7
For a 3-digit number abc, the divisibility rule for 11 is (a+c)тИТb=0 or 11. Here, (2+5)тИТy=7тИТy. For divisibility by 11, 7тИТy=0, so y=7.
A 3-digit number 2y5 is divisible by 11.
(Sumof┬аodd┬аplace┬аdigits)тИТ(Sumof┬аeven┬аplace┬аdigits)=0or11k
For a 3-digit number abc, the divisibility rule for 11 is (a+c)тИТb=0 or 11. Here, (2+5)тИТy=7тИТy. For divisibility by 11, 7тИТy=0, so y=7.
Many students mistake the rule for 3 or 9 and add all digits together instead of taking the alternating sum.
State the divisibility rule for 11
A number is divisible by 11 if the difference between the sum of the digits at odd places and the sum of the digits at even places is either 0 or a multiple of 11.
(a+c)тИТb=0┬аor┬а11n
Identify the digits of the number 2y5
The digits are 2 (hundreds place), y (tens place), and 5 (units place).
a=2,b=y,c=5
Apply the rule
Sum of odd positions (first and third digits) = 2+5=7. Sum of even position (second digit) = y. The difference is 7тИТy.
7тИТy=0тЯ╣y=7
A is correct because the difference 7тИТy must equal 0 to satisfy the divisibility rule for 11, which gives y=7.
This concept is a subset of 'Number Systems'. Practice similar problems for divisibility rules of 7, 9, and 13 as they frequently appear in competitive exams.
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