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![[Post New]](/templates/default/images/icon_minipost_new.gif) 5 Dec 2007 16:49:38 IST
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How many integers between 100 and 150, inclusive, cannot be evenly divided by 3 nor 5?
regards
rachu
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8 Dec 2007 20:30:46 IST
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The numbers are 105, 120 and 135. Rate me if i'm right.
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11 Dec 2007 08:26:08 IST
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The number is integers between 100 and 150, which are evenly divisible by 3 is 17 (102,105,108,.....150)
The number is integers between 100 and 150, which are evenly divisible by 5 is 11 (100,105,110,....150)
The number is integers between 100 and 150, which are evenly divisible by both 3 and 5 is 4 (105,120,135,150)
Let A be the set of integers between 100 and 150, which not evenly divisible by 3.
Let A be the set of integers between 100 and 150, which not evenly divisible by 5.
So, we have, n(A)=17, n(B)=11, n(AnB)=4.
Therefore, n(AuB)=17+11-4=24.
Here we are asked to find the no of integers which are neither divisible by 3 nor 5.
ie, we need to find n(A'nB'), where A' represents complimentary set of A.
By De'Morgans law, n(A'nB') = n((AuB)')=51-n(AuB)=51-24 = 27.
So, the answer is 27.
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Satyaram B V,
General Secretary, Mandakini Hostel,
IIT Madras |
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11 Dec 2007 08:27:36 IST
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Visit
http://en.wikipedia.org/wiki/De_Morgan's_laws
for details on Demorgans laws
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Satyaram B V,
General Secretary, Mandakini Hostel,
IIT Madras |
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