Sol:

Method1:

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We know the bacteria quadruples every hour: i.e. if at x hrs, the count is 100, at time x+1 hrs, the count will be 400, x+2: 1600 and so on;

Reverse is also true; if at x hours the count is 1600, x-1 hrs, it would have been 1600/4=400; x-2:400/4=100 and so on...

Same way:

@ 10:00 am: The count was 1/2(Half)

@ 9:00 am: The count would have been (1/2)/4 = 1/8

Thus the bacteria count was 1/8 @ 9:00 AM.

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Method2:

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A more mathematical and little cumbersome approach would be the Geometric Progression:

To find the nth term in a GP;

A_n=a*r^{(n-1)}We know

a=1/2; This is the first term and represents the count of bacteria at time 10:00AM

r=1/4A_n=1/8; This is the

n^{th} term and represents the count of bacteria (n-1) hours before 10

n=?A_n=a*r^{(n-1)}\frac{1}{8}=\frac{1}{2}*(\frac{1}{4})^{(n-1)}\frac{1}{4}=\frac{1}{4^{(n-1)}}Equating the denominator:

n-1=1

n=2;

So; we know the bacteria reached 1/8 @ n=2; Time = 2-1=1 hour before 10:00AM=9:00AM

The latter method may be little subtle but is a generalized way to deal with such questions. The former should be your first choice to solve such questions and latter may be used only as a fall back method.

Ans: "A"

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~fluke

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