Sequences And Series Question 20
Question 20 - 01 February - Shift 1
The number of 3-digit numbers, that are divisible by either 2 or 3 but not divisible by 7 is
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Answer: 514
Solution:
Formula: Some important results on number of elements in sets
Divisible by $2 \to 450$
Divisible by $3 \to 300$
Divisible by $7 \to 128$
Divisible by $2 ; ; \text{and} ; ; 7 \to 64$
Divisible by $3 ; ; \text{and} ; ; 7 \to 43$
Divisible by $2 ; ; \text{and}; ; 3 \to 150$
Divisible by $2,3 ; ; \text{and} ; ; 7 \to 21$
$\therefore$ Total numbers $=450+300-150-64-43+21=514$
