JEE MAIN - Mathematics (2022 - 29th June Evening Shift - No. 18)
The total number of four digit numbers such that each of first three digits is divisible by the last digit, is equal to ____________.
Answer
1086
Explanation
If unit digit is 1 then $\rightarrow 9 \times$ s $10 \times 10=900$ numbers
If unit digit is 2 then $\rightarrow 4 \times 5 \times 5=100$ numbers
If unit digit is 3 then $\rightarrow 3 \times 4 \times 4=48$ numbers
If unit digit is 4 then $\rightarrow 2 \times 3 \times 3=18$ numbers
If unit digit is 5 then $\rightarrow 1 \times 2 \times 2=4$ numbers
If unit digit is 6 then $\rightarrow 1 \times 2 \times 2=4$ numbers
For $7,8,9 \rightarrow 4+4+4=12$ Numbers
Total $=1086$ Numbers
If unit digit is 2 then $\rightarrow 4 \times 5 \times 5=100$ numbers
If unit digit is 3 then $\rightarrow 3 \times 4 \times 4=48$ numbers
If unit digit is 4 then $\rightarrow 2 \times 3 \times 3=18$ numbers
If unit digit is 5 then $\rightarrow 1 \times 2 \times 2=4$ numbers
If unit digit is 6 then $\rightarrow 1 \times 2 \times 2=4$ numbers
For $7,8,9 \rightarrow 4+4+4=12$ Numbers
Total $=1086$ Numbers
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