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  • Number of 4-digit numbers that are less than or equal to 2800 and either divisible by 3 or by 11 , is equal toOption: 1 710<div

Number of 4-digit numbers that are less than or equal to 2800 and either divisible by 3 or by 11 , is
equal to

Option: 1

710


Option: 2

210


Option: 3

320


Option: 4

415


Answers (1)

best_answer

4 digit number which are less then 2800 are 1000 – 2799
Number which are divisible by 3

            2799 = 1002 + (n – 1) 3

                     n = 600

Number which are divisible by 11 in 1000 – 2799
= (Number which are divisible by 11 in 1 – 2799)
– (Number which are divisible by 11 in 1 – 999)

\begin{aligned} & =\left[\frac{2799}{11}\right]-\left[\frac{999}{11}\right] \\ & =254-90 \\ & =164 \end{aligned}

Number which are divisible by 33 in 1000 – 2799
= (Number which are divisible by 33 in 1 – 2799) – (Number which are divisible by 33 in 1 – 999)

\begin{aligned} & =\left[\frac{2799}{33}\right]-\left[\frac{999}{33}\right] \\ & =84-30 =54 \end{aligned}

total number = n(3) + n(11) – n(33)
= 600 + 164 – 54 = 710

Posted by

HARSH KANKARIA

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