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John is reading a 50-page book, starting from 1 page. He pla

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John is reading a 50-page book, starting from 1 page. He pla

by Max@Math Revolution » Sun Oct 02, 2016 11:52 pm
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
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by MBA Challengers » Wed Oct 05, 2016 1:31 am
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.
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