Arithmetic

Arithmetic

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CAT typical question: (CAT 1998)
One bacterium splits into eight bacteria of the next generation. But due to environmental condition only 50% survives and remaining 50% dies after producing next generation. If the seventh generation number is 4,096 million, what is the number in first generation?
A] 1 million
B] 2 million
C] 4 million
D] 8 million

Given that the surviving 50% of every generation neither Counts the 7th generation number, nor does it produce any subsequent bacteria.

Detailed Explanation:
Generation 1 :
Number of Bacteria 1
New Produced : 8 Survive To produce Next 4 + Half of Previous

Generation 2 :
Number of Bacteria 4
New Produced : 32 Survive To produce Next 16 + Half of Previous

Generation 3 :
Number of Bacteria 16
New Produced : 128 Survive To produce Next 64 + Half of Previous

Generation 4 :
Number of Bacteria 64
New Produced : 512 Survive To produce Next 256 + Half of Previous

Generation 5 :
Number of Bacteria 256
New Produced : 2048 Survive To produce Next 1024 + Half of Previous

Generation 6 :
Number of Bacteria 1024
New Produced : 8192 Survive To produce Next 4096 + Half of Previous

Generation 7 :
Number of Bacteria 4096
New Produced : 32768 Survive To produce Next 16384 + Half of Previous

Shortcut:
4^(n-1) = 4096 ie n = 7.