The number of 3-digit numbers that are divisi | vedclass

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Question

(C) The total number of $3$-digit numbers is $999 - 99 = 900$. $A$ number is divisible by both $2$ and $3$ if it is divisible by $	ext{lcm}(2, 3) = 6

Vedclass · Accepted Answer

$125$

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(C) The total number of $3$-digit numbers is $999 - 99 = 900$. $A$ number is divisible by both $2$ and $3$ if it is divisible by $	ext{lcm}(2, 3) = 6$. The number of $3$-digit numbers divisible by $6$ is $\frac{900}{6} = 150$. $A$ number is divisible by both $4$ and $9$ if it is divisible by $	ext{lcm}(4, 9) = 36$. The number of $3$-digit numbers divisible by $36$ is $\frac{900}{36} = 25$. Since any number divisible by $36$ is also divisible by $6$,the number of $3$-digit numbers divisible by $2$ and $3$ but not by $4$ and $9$ is $150 - 25 = 125$.

The number of $3$-digit numbers that are divisible by $2$ and $3$,but not divisible by $4$ and $9$,is

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