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CAT 1998 — QA Question 5

PercentageEasy

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?

Answer & solution

Correct answer: 1 million

  • 1 million

  • B

    2 million

  • C

    4 million

  • D

    8 million

Solution

Let there be x bacteria in the first generation i.e. n1 = x

∴ n₂ = 8x, but only 50% survives

⇒ n2, survived =  8x2=4x

n3 = 8(4x), but only 50% survives

n3, survived = 42 x

n3, survived = 47-1 x = 4096 million

∴ x = 1 million

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CAT 1998 QA Q5: One bacterium splits into eight bacteria of the next generation. But due to environmental condition only 50% s — Solution | TheCATExam