JEE Mains · Maths · STD 11 - 6. permutation and combination
The total number of \(4 -\)digit numbers whose greatest common divisor with \(18\) is \(3,\) is .... .
- A \(1000\)
- B \(1500\)
- C \(1200\)
- D \(500\)
Answer & Solution
Correct Answer
(A) \(1000\)
Step-by-step Solution
Detailed explanation
Let \(N\) be the four digit number \(\operatorname{gcd}(N, 18)=3\) Hence \(N\) is an odd integer which is divisible by \(3\) but not by \(9 .\) \(4\) digit odd multiples of \(3\) \(1005,1011, \ldots \ldots, 9999 \rightarrow 1500\) \(4\) digit odd multiples of \(9\)…
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