A scientist is studying bacteria whose cell population

[star.estella.li]

This question is from CAT #1. I understand what the question is asking but didn't understand the answer explanation.

QUESTION:

A scientist is studying bacteria whose cell population doubles at constant intervals, at which times each cell in the population divides simultaneously. Four hours from now, immediately after the population doubles, the scientist will destroy the entire sample. How many cells will the population contain when the bacteria is destroyed?

(1) The population just divided and, since the population divided two hours ago, the population has quadrupled, increasing by 3,750 cells.

(2) The population will double to 40,000 cells with one hour remaining until the scientist destroys the sample.

ANSWER: Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

We need two additional pieces of information to solve this problem, which can be rephrased as "How frequently does the population double, and what is the population size at any given time immediately after it has doubled?"

(1) SUFFICIENT: If the population quadrupled during the last two hours, it doubled twice during that interval, meaning that the population doubled at 60 minute intervals. Since it has increased by 3,750 bacteria, we have:

Population (Now) - Population (2 hours ago) = 3750
Population (Now) = 4·Population (2 hours ago)

Substituting, we get 4·Population (2 hours ago) - Population (2 hours ago) = 3750
Population (2 hours ago) = 1250.
The population will double 6 times from that point to 4 hours from now

Population (4 hours from now) = 26·1,250=80,000.

(2) INSUFFICIENT: This statement does not give any information about how frequently the population is doubling.

[blink005]

Could you be more specific?

[jnelson0612]

Please see this thread about the problem: a-scientist-is-studying-bacteria-t11381.html

[limchudick]

We need two additional pieces of information to solve this problem, which can be rephrased as "How frequently does the population double, and what is the population size at any given time immediately after it has doubled?"

(1) SUFFICIENT: If the population quadrupled during the last two hours, it doubled twice during that interval, meaning that the population doubled at 60 minute intervals. Since it has increased by 3,750 bacteria, we have:

Population (Now) - Population (2 hours ago) = 3750
Population (Now) = 4·Population (2 hours ago)

Substituting, we get 4·Population (2 hours ago) - Population (2 hours ago) = 3750
Population (2 hours ago) = 1250.
The population will double 6 times from that point to 4 hours from now
[color=#BF4040][b](may I ask why does it double 6 times instead of 4 times)

Population (4 hours from now) = 26·1,250=80,000.

[tim]

not sure where the 26 comes from in your last line, but it looks like you're asking why the population doubles six times. well, we are measuring it from two hours ago, and we need to go to four hours from now. this is a total of six hours, and once we have determined that the population doubles every hour, this gives six doublings..

[pranabiitkgp]

I am claryfing my understading .

If 2 hours ago it was X , Now it is 4X
1 hr from now - 8X
2 ,, ,, ,, - 16X
3 ,, ,, ,, - 32X
4 ,, ,, ,, - 64X .

So I think when you are talking about the multiplier 6 , it is in the form of "2 to the power 6" which is 64.

Anyway the main point is that one you can solve with the statement 1 .

Thanks,
PM.

[limchudick]

Hey Tim
Thanks, I got it...
2 hours ago plus 4 hours from now making it all together 6 hours.

[jnelson0612]

Great, thanks for letting us know that you got it!