Question: A certain culture of bacteria quadruples every hour. If a container with these bacteria was half full at 10:00 a.m., at what time was it one-eighth full?

(A) 9:00 a.m.
(B) 7:00 a.m.
(C) 6:00 a.m.
(D) 4:00 a.m.
(E) 2:00 a.m.

“A certain culture of bacteria quadruples every hour.”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “The Official Guide for Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation:
Approach Solution 1

Bacteria are known to quadruple every hour. If the number at x hrs is 100, the number at x+1 is 400, x+2: 1600, and so on.
The reverse is also true. If the count of x hours is 1600, then x-1 hours is 1600/4=400. x-2:400/4=100 etc…
Same way:
@ 10:00 AM: count was 1/2 (half)
@ 9:00 AM: The count will be (1/2)/4 = 1/8.
So the bacteria count was 1/8th of what it was at 9am.

Correct Answer: A

Approach Solution 2

Number of bacteria when full tank = 80
At 10:00 when the container is half full = 40
Full ⅛ = ⅛ * 60 * 80 = 10

Bacteria quadruple every hour, so
10*4n=40
4n=4
=> n=1 (hours)
So it took an hour to fill half of 10 (40). So 10am minus 1 hour = 9am

Correct Answer: A

Approach Solution 3

The bacteria count quadruples every hour, so let's go back in time from when the container is half full.

(½)/4 = (½)/(4/1) = (½) x (¼) = ⅛.

We see that one hour earlier, the container was ⅛ full of bacteria. This was at 9 am.

Correct Answer: A

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