JEE Main 2022 · 29 Jun · Shift 2 · Mathematics Q28

← JEE Main 2022 · 29 Jun · Shift 2

MathematicsInteger+4 / -1Question 28 of 90

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

Your answer

Answer and worked solution

Official answer: 1086

Fix the last digit $d$ (1 to 9). The first digit is a non-zero multiple of $d$ ; the second and third are multiples of $d$ from 0 to 9.

Counts. $d=1$ : $9\cdot10^2=900$ ; $d=2$ : $4\cdot5^2=100$ ; $d=3$ : $3\cdot4^2=48$ ; $d=4$ : $2\cdot3^2=18$ ; $d=5$ to $9$ : $1\cdot2^2=4$ each, 20.

Total 1086.

Answer: 1086

Topics:Fundamental principle of counting

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JEE Main 2022 · 29 Jun · Shift 2, Mathematics question 28