The number of natural numbers less than 400 that are not divisible by 17 or 23 is

Question

The number of natural numbers less than 400 that are not divisible by 17 or 23 is (A) 382 (B) 359 (C) 360 (D) 376

Tardigrade Admin · Accepted Answer

divisible by 17 and less than 400 17, 34, 51, ........ 391 (23) divisible by 23 but less than 400 23, 46, 69,.........391 (17) divisible by both 391 (1) divisible by 17 or 23 = 23 + 17 - 1 = 39 not divisible by 17 or 23 and < 400 = 399 - 39 = 360

Q. The number of natural numbers less than 400 that are not divisible by 17 or 23 is

382

359

360

376

divisible by 17 and less than $400$
$17, 34, 51, ........391 (23)$
divisible by 23 but less than $400$
$23, 46, 69, .........391 (17)$
divisible by both
$391 (1)$
divisible by 17 or $23 = 23 + 17 - 1 = 39$
not divisible by 17 or 23 and $< 400$
$= 399 - 39 = 360$

Q. The number of natural numbers less than 400 that are not divisible by 17 or 23 is

382

359

360

376

divisible by 17 and less than 400 17,34,51,........391(23) divisible by 23 but less than 400 23,46,69,.........391(17) divisible by both 391(1) divisible by 17 or 23=23+17−1=39 not divisible by 17 or 23 and <400 =399−39=360

divisible by 17 and less than $400$
$17, 34, 51, ........391 (23)$
divisible by 23 but less than $400$
$23, 46, 69, .........391 (17)$
divisible by both
$391 (1)$
divisible by 17 or $23 = 23 + 17 - 1 = 39$
not divisible by 17 or 23 and $< 400$
$= 399 - 39 = 360$