N is the largest two-digit number which,when | vedclass

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Question

(A) Let the number be $N$. The divisors are $3, 4, 6$ and the respective remainders are $1, 2, 4$.Observe the difference between the divisor and the r

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(A) Let the number be $N$. The divisors are $3, 4, 6$ and the respective remainders are $1, 2, 4$.Observe the difference between the divisor and the remainder:$3 - 1 = 2$$4 - 2 = 2$$6 - 4 = 2$The constant difference is $2$.To find $N$,we first find the $LCM$ of $(3, 4, 6)$,which is $12$.The general form of the number is $N = 12k - 2$,where $k$ is an integer.For the largest two-digit number,we set $12k - 2 Taking $k = 8$,we get $N = 12(8) - 2 = 96 - 2 = 94$.Now,we find the remainder when $N = 94$ is divided by $5$.$94 = 5 	imes 18 + 4$.Therefore,the remainder is $4$.

$N$ is the largest two-digit number which,when divided by $3, 4,$ and $6,$ leaves the remainders $1, 2,$ and $4$ respectively. What is the remainder when $N$ is divided by $5$?

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