Here are two problems I can't figure out.

[Mclaughlin]

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.

Also I'd love to know how to solve this and what "type" of questions this is so I can look for and practice others like this one.

[bnkothari]

The answer will be choice A.

It says the culture quadraples every hour.
Meaning every hour, it increases 4x.

At 10.00 AM, the container is half (1/2) full.

At 9.00 AM, it will be 1/4th of what it is at 10.00 AM
meaning (1/4)*(1/2) = 1/8.

Hence, the answer is (A).

This falls in the fractions category.

Hope this helps.

[tmmyc]

You can also pick some numbers to make this easier.

Assume container capacity is 8.

We need to find the time for when it is 1/8 full.
(1/8) * 8 = 1
So we need to find what time the container was at 1.


We are given that the container is half full at 10AM
10AM -> (1/2) * 8 = 4

We are also given that the bacteria quadruples ever hour.

9AM -> 1
10AM -> 4
11AM -> 16

Therefore, the answer is A, since the container was at 1 at 9AM. Hope that helps.

[Scott@TargetTestPrep]

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.

This problem is easily solved if you work it forwards, starting from the time the container was â…› full. Let's start there:

1/8 x 4 = 1/2

So we see it took 1 hour to go from 1/8 full to 1/2 full. So at 9 am it was 1/8 full.

Alternate Solution:

Since the number of bacteria quadruple every hour, let's go backwards in time from the point where the container was ½ full:

(½)/4 = (½)/(4/1) = (½) x (¼) = ⅛.

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

Answer: A