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During an experiment, the population of a bacterium increased ...
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08 Oct 2019, 05:37
08 Oct 2019, 05:37
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During an experiment, the population of a bacterium increased by a factor of ‘k’ every minute. What was the population of the bacterium at the beginning of the experiment?
(1) The population of the bacterium two minutes after the beginning of the experiment was 20,000.
(2) The population of the bacterium four minutes after the beginning of the experiment was 2,000,000.
A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D) Each alone is sufficient
E) Both together are not sufficient
(1) The population of the bacterium two minutes after the beginning of the experiment was 20,000.
(2) The population of the bacterium four minutes after the beginning of the experiment was 2,000,000.
A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D) Each alone is sufficient
E) Both together are not sufficient
During an experiment, the population of a bacterium increased ...
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08 Oct 2019, 05:46
08 Oct 2019, 05:46
1
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Expert Reply
During an experiment, the population of a bacterium increased by a factor of ‘k’ every minute. What was the population of the bacterium at the beginning of the experiment?
Let the population be a, then after n minutes, it will be \(a*k^n\). we are looking for the value of a
(1) The population of the bacterium two minutes after the beginning of the experiment was 20,000.
So, \(a*k^2=20000\).. we require to know k...
(2) The population of the bacterium four minutes after the beginning of the experiment was 2,000,000.
So, \(a*k^4=2000000\).. we require to know k...
Combined..
\(\frac{a*k^4}{a*k^2}=\frac{2000000}{20000}=100........k^2=100....k=10\)
so So, \(a*k^2=20000.....a*10^2=20000.....a=200\)..
C
Let the population be a, then after n minutes, it will be \(a*k^n\). we are looking for the value of a
(1) The population of the bacterium two minutes after the beginning of the experiment was 20,000.
So, \(a*k^2=20000\).. we require to know k...
(2) The population of the bacterium four minutes after the beginning of the experiment was 2,000,000.
So, \(a*k^4=2000000\).. we require to know k...
Combined..
\(\frac{a*k^4}{a*k^2}=\frac{2000000}{20000}=100........k^2=100....k=10\)
so So, \(a*k^2=20000.....a*10^2=20000.....a=200\)..
C
Re: During an experiment, the population of a bacterium increased ...
[#permalink]
08 Oct 2019, 05:50
08 Oct 2019, 05:50
1
Kudos
chetan2u
During an experiment, the population of a bacterium increased by a factor of ‘k’ every minute. What was the population of the bacterium at the beginning of the experiment?
Let the population be a, then after n minutes, it will be \(a*k^n\). we are looking for the value of a
(1) The population of the bacterium two minutes after the beginning of the experiment was 20,000.
So, a*k^2=20000.. we require to know k...
(2) The population of the bacterium four minutes after the beginning of the experiment was 2,000,000.
So, a*k^4=2000000.. we require to know k...
Combined..
\(\frac{a*k^4}{a*k^2}=\frac{2000000}{20000}=100........k^2=100....k=10\)
so So, a*k^2=20000.....a^10^2=20000.....a=200..
C
Let the population be a, then after n minutes, it will be \(a*k^n\). we are looking for the value of a
(1) The population of the bacterium two minutes after the beginning of the experiment was 20,000.
So, a*k^2=20000.. we require to know k...
(2) The population of the bacterium four minutes after the beginning of the experiment was 2,000,000.
So, a*k^4=2000000.. we require to know k...
Combined..
\(\frac{a*k^4}{a*k^2}=\frac{2000000}{20000}=100........k^2=100....k=10\)
so So, a*k^2=20000.....a^10^2=20000.....a=200..
C
here is my hiccup, I know that the answer is C, but How can we say ak^2 = 20000 ? It says that the population of the bacteria two minutes after the beginning is 20000 and not that the population of the 2nd minute is 20k. The way I see it, we have been given the sum of the bacteria i.e. a+ ak +ak^2 = 20000. Similarly for statement 2. This does not change the answer however, if we have both 1 and 2, we have the rate and hence everything thereafter. I am just not convinced either with the language of this question or the explanations I have found which are similar to yours
