JEE MAIN - Mathematics (2023 - 31st January Morning Shift - No. 19)
Number of 4-digit numbers that are less than or equal to 2800 and either divisible by 3 or by 11 , is equal to ____________.
Answer
710
Explanation
Numbers which are divisible by 3 (4 digit) and less than or equal to 2800
$=\frac{2799-1002}{3}+1=600$
Numbers which are divisible by 11 (4 digit) and less than or equal to 2800
$=\frac{2794-1001}{11}+1=164$
Numbers which are divisible by 33 (4 digit) and less than or equal to 2800
$=\frac{2772-1023}{33}+1=54$
$\therefore$ Total numbers = $600+164-54=710$
$=\frac{2799-1002}{3}+1=600$
Numbers which are divisible by 11 (4 digit) and less than or equal to 2800
$=\frac{2794-1001}{11}+1=164$
Numbers which are divisible by 33 (4 digit) and less than or equal to 2800
$=\frac{2772-1023}{33}+1=54$
$\therefore$ Total numbers = $600+164-54=710$
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