The number of positive integers from 1 to 1000, which are not divisible by 2, 3 or 5 are

Question

The number of positive integers from 1 to 1000, which are not divisible by 2, 3 or 5 are (A) 266 (B) 265 (C) 267 (D) 734

Tardigrade Admin · Accepted Answer

n (2)=[(1000/2)]=500 n (3)=[(1000/3)]=333 n (5)=[(1000/5)]=200 n (2 ∩ 3)=166, n (3 ∩ 5)=66 n (5 ∩ 2)=100 n (2 ∩ 3 ∩ 5)=33, n (2 ∪ 3 ∪ 5)=734 n (2 prime ∩ 3 prime ∩ 5 prime)=1000-734=266

Q. The number of positive integers from 1 to 1000, which are not divisible by 2, 3 or 5 are

266

265

267

734

$n (2) = [\frac{1000}{2}] = 500$
$n (3) = [\frac{1000}{3}] = 333$
$n (5) = [\frac{1000}{5}] = 200$
$n (2 \cap 3) = 166, n (3 \cap 5) = 66$
$n (5 \cap 2) = 100 n (2 \cap 3 \cap 5) = 33, n (2 \cup 3 \cup 5) = 734$
$n (2^{'} \cap 3^{'} \cap 5^{'}) = 1000 - 734 = 266$

Q. The number of positive integers from 1 to 1000, which are not divisible by 2, 3 or 5 are

266

265

267

734

n(2)=[21000​]=500 n(3)=[31000​]=333 n(5)=[51000​]=200 n(2∩3)=166,n(3∩5)=66 n(5∩2)=100n(2∩3∩5)=33,n(2∪3∪5)=734 n(2′∩3′∩5′)=1000−734=266

$n (2) = [\frac{1000}{2}] = 500$
$n (3) = [\frac{1000}{3}] = 333$
$n (5) = [\frac{1000}{5}] = 200$
$n (2 \cap 3) = 166, n (3 \cap 5) = 66$
$n (5 \cap 2) = 100 n (2 \cap 3 \cap 5) = 33, n (2 \cup 3 \cup 5) = 734$
$n (2^{'} \cap 3^{'} \cap 5^{'}) = 1000 - 734 = 266$