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03 Oct 2016, 00:51
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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
A. 20pages B. 24pages C. 26pages D. 30pages E. 32pages
03 Oct 2016, 01:47
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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
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.
06 Oct 2016, 05:44
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==> n(3)=the number of pages with white sticks and n(4)=the number of pages with black sticks. If so, n(3U4)=n(3)+n(4)-n(3∩4)=16+12-4=24. However, the question is about the number of pages without white sticks and black sticks, so 50-24=26. C is the answer
Answer: C
Answer: C
