Question
If 1234567y is divisible by 11, then what is the value
of y?Solution
To determine if a number is divisible by 11, we use the divisibility rule for 11, which states that a number is divisible by 11 if the alternating sum and difference of its digits (from left to right) is divisible by 11 (or equals 0). Given the number 1234567y, we can apply the rule as follows: Calculate the alternating sum and difference: S=1-2+3-4+5-6+7-y Simplifying: S=(1+3+5+7)-(2+4+6) - у S=16-12-y S=4-y For the number to be divisible by 11, S must be divisible by 11 or equal to 0. Therefore: 4-y =0(mode 11) y=4 Thus, the value of y that makes the number divisible by 11 is 4.
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