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  • The number of 3 digit numbers, that are divisible by either 3 or 4 but not divisible by 48, isOption: 1 507<str

The number of 3 digit numbers, that are divisible by either 3 or 4 but not divisible by 48, is

Option: 1

507


Option: 2

432


Option: 3

472


Option: 4

400


Answers (1)

best_answer

Nos div. by 3

\begin{aligned} & 102,105,108 \quad \ldots \ldots \ldots 999 \\ & \text { A.P. } \mathrm{a}=102 \quad \mathrm{~d}=3 \quad \ell=999 \\ & \mathrm{n}=\frac{\ell-\mathrm{a}}{\mathrm{d}}+1=\frac{999-102}{3}+1=300 \end{aligned}

Numbers div. by 4

\begin{aligned} & 100,104,108 \ldots \ldots \ldots 996 \\ & \text { A.P. } \mathrm{a}=100 \quad \mathrm{~d}=4 \quad \ell=996 \\ & \mathrm{n}=\frac{996-100}{4}+1=\frac{896}{4}+1=224+1=225 \end{aligned}

Numbers div. by 12

\begin{aligned} & 108,120, \ldots \ldots \ldots .996 \\ & \text { A.P. } \mathrm{a}=108 \quad \mathrm{~d}=12 \quad \ell=996 \\ & \mathrm{n}=\frac{996-108}{12}+1=\frac{888}{12}+1=74+1=75 \end{aligned}

Numbers div. by 48

\begin{aligned} & \text { 144, } 192, \ldots \ldots \ldots .960 \\ & \text { A.P. } \mathrm{a}=144 \quad \mathrm{~d}=48 \quad \ell=960 \\ & \mathrm{n}=\frac{996-144}{12}+1=\frac{816}{48}+1=17+1=18 \end{aligned}

\therefore \, \, No. \, \, Div. \, \, by \, \, 354 \, \, but \, \, not\, \, by \, \, 48

$$ \begin{aligned} & 300+225-75-18 \\ & =450-18=432 \end{aligned}

Posted by

manish painkra

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