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The total number of four digit numbers such that each of first three digits is divisible by the last digit, is equal to ______.
Option: 1
1086

Option: 2
-

Option: 3
-

Option: 4
-

Answers (1)

best_answer

$\mathrm{abcd}$

1. When $\mathrm{d=1}$ , $\mathrm{a}$ can take any value from $\mathrm{1\: to\: 9}$ and $\mathrm{b\: and \: c}$ can take any value from $\mathrm{0\: to\: 9}$

$\mathrm{\therefore \quad 9 \times 10 \times 10=900}$ such numbers

2. $\mathrm{d=2, a \: can\: be \: 2,4,6,8, b \: and\: c \: can \: be \: 0,2,4,6,8}$

$\mathrm{\therefore 4 \times 5 \times 5=100}$

3. $\mathrm{d=3, a=3 / 6 / 9, \text { b\: and } c=0 / 3 / 6 / 9 }\\$

$\mathrm{\therefore 3 \times 4 \times 4=48 }$

4. $\mathrm{d=4, \quad a=4 / 8, b\: and \: c=0 / 4 / 8}\\$

$\mathrm{\therefore 2\times3\times3=18}\\$

5. $\mathrm{d=5, a=5, b\: and \: c=5/0}\\$

$\mathrm{ \therefore d=1 \times 2 \times 2=4}\\$

6. $\mathrm{d=6, a=6, \quad b\: and \: c=6/0}\\$

$\mathrm{1 \times 2 \times 2=4}$

Similarly for $\mathrm{d=7,8,9 \Rightarrow \text { numbers }=4,4,4}$

$\mathrm{\text{Total}=900+100+48+18+4+4+4+4+4=1086}$

Hence answer is $\mathrm{1086}$

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