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Question: Answered & Verified by Expert
Number of 4-digit numbers that are less than or equal to 2800 and either divisible by 3 or by 11 , is equal to _____ .
MathematicsSequences and SeriesJEE MainJEE Main 2023 (31 Jan Shift 1)
Solution:
1362 Upvotes Verified Answer
The correct answer is: 710

Four-digit numbers that are less than or equal to 2800 are 1000,1001,1002,....,2800

Numbers divisible by 3 are 1002, 1005, ....,2796,2799

Let total numbers be n, then

1002+n-1 3=2799 

n=600

Numbers divisible by 11 are 1001, 1012, ..., 2794

Let total numbers be m, then

2794=1001+m-111

m=164

Numbers divisible by 33 are

1023,1056,...,2772

Let total numbers be r, then

2772=1023+r-133

r=54

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

=600+164-54=710

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