Arithmetic

Attend free workshop on Arithmetic shortcuts Register here… 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   Answer is (A) 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.