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

Show Answer

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 $=450+300-150-64-43+21=514$