MathRevolution wrote:

John is reading a 50-page book, starting from 1 page. He places a white stick per 3 pages and a black stick per 4 pages. How many pages have neither white sticks nor black sticks?

A. 20pages B. 24pages C. 26pages D. 30pages E. 32pages

Condition 1 : John is placing a white stick per 3 pages...i.e. he'll put at all 3 multiples...i.e. at 3,6,12,.......48 and he can't put the white stick at 51...because the limit is 50 pages...

In total how many multiples of 3 till 50 => 50/3 = max we get 16 .... (count 3,6,12,15,18,21,24,27,30,33,36,39,42,45 and 48 ) => we'll get 16.

Condition 2 : Now John is placing a black stick per 4 pages...i.e..he'll put at 4,8,12,16,20.....48 and he can't put the white stick at 51...because the limit is 50 pages..

In total how many multiples of 4 till 50 => 50/4 = max we get 12 .... (count 4,8,12,16,20,24,28,32,36,40,44 and 48 ) => we'll get 12.

Now if you observe that we have common multiples or numbers for 3 and 4 ( take LCM of 3 and 4..we get 12...if we check multiples of 12 till 50..we get 12,24,36 and 48)...

=> 50/12 - max we get 4 i.e. 12,24,36 and 48 are common in 3 and 4.

we have total 4 numbers common.

Now use formula..

n(WUB) = N(W) + N(B) - N(W∩B) + Neither = > Total pages = only white + only black - both white and black + Neither...

50 = 16+12-4 +Neither.

Neither = 26.