JEE Main 2021 — Sequences And Series Question with Solution
From: JEE Main 2021 (Online) 26th February Evening Shift
Question
The total number of 4-digit numbers whose greatest common divisor with 18 is 3, is _________.
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Show full solutionCorrect answer: 1000
Correct answer
1000
Step-by-step explanation
Let N be the four digit number
gcd(N, 18) = 3
Hence N is an odd integer which is divisible by 3 but not by 9.
4 digit odd multiples of 3
1005, 1011, ..........., 9999 1500
4 digit odd multiples of 9
1017, 1035, ..........., 9999 500
Hence number of such N = 1000
gcd(N, 18) = 3
Hence N is an odd integer which is divisible by 3 but not by 9.
4 digit odd multiples of 3
1005, 1011, ..........., 9999 1500
4 digit odd multiples of 9
1017, 1035, ..........., 9999 500
Hence number of such N = 1000
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