Problem Solving

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

Hi,

In this question the idea is to count the multiples of 3 and multiples of 4 and subtracting common multiples (Multiples of 12), as those would be the pages which will hold the stickers put in by John, with 2 stickers on pages with common multiples.

Thus, the pages where John will put a sticker are:
White sticker = multiples of 3 between 1 and 50 = 16 (3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48)
Black sticker = multiples of 4 between 1 and 50 = 12 (4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48)
Both stickers = multiples of 12 between 1 and 50 = 4 (12, 24, 36, 48)

The pages which will not have any stickers = Total pages - (White sticker pages + Black sticker pages - Both sticker pages) = 50 - (16 + 12 - 4) = 50 - 24 = 26

Thus, the answer is 26 pages, which is option C.