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A population of a colony of bacteria increases by 20

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A population of a colony of bacteria increases by 20 [#permalink] New post 02 Jun 2018, 03:50
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Question Stats:

62% (01:40) correct 37% (02:38) wrong based on 8 sessions
A population of a colony of bacteria increases by 20 percent every 3 minutes. If at 9:00am the colony had a population of 144,000, what was the population of the colony at 8:54am?

(A) 100,000
(B) 112,000
(C) 120,000
(D) 121,000
(E) 136,000
[Reveal] Spoiler: OA

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Re: A population of a colony of bacteria increases by 20 [#permalink] New post 07 Jun 2018, 23:57
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sandy wrote:
A population of a colony of bacteria increases by 20 percent every 3 minutes. If at 9:00am the colony had a population of 144,000, what was the population of the colony at 8:54am?

(A) 100,000
(B) 112,000
(C) 120,000
(D) 121,000
(E) 136,000


Let the value at 8:45 be x

now for every 3 minutes the values increases by 20% and we have total six minutes.

For first 3 minutes -> x + x(20%) = 1.2x

Now next 3 minutes = 1.2x + 20%(1.2x)

Now this values 1.2x + 20%(1.2x) = 144000

=> 12/10(x) + 24/100 (x) = 144000
=> 120x + 24x / 100 = 144000
=> 144x / 100 = 144000
=> x = 100000

Option A.
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Re: A population of a colony of bacteria increases by 20 [#permalink] New post 05 Jul 2018, 19:16
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sandy wrote:
A population of a colony of bacteria increases by 20 percent every 3 minutes. If at 9:00am the colony had a population of 144,000, what was the population of the colony at 8:54am?

(A) 100,000
(B) 112,000
(C) 120,000
(D) 121,000
(E) 136,000

To get this answer, what I did was multiply the increment of 20% twice (1.2 x 1.2) to get 1.44 and the divided 144,000 by 1.44 since we were going back in time by 6 mins. If they asked for the time 6 mins into the future, I would have multiplied 144,000 by 1.44.

Hope this helps somebody
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Re: A population of a colony of bacteria increases by 20 [#permalink] New post 14 Jul 2018, 04:43
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Explanation

Every 3 minutes, the population increases by 20% (which is the same as multiplying by 1.2).

Beginning at 8:54am, this change would occur at 8:57am and again at 9:00am. Use the variable x to represent the original quantity. Note that the 20% increase occurs twice:

x(1.2)(1.2) = 144,000
x = 100,000

Note that you cannot just reduce 144,000 by 20% twice, because 20% is not a percent of 144,000—it is a percent of the unknown, original number.

Alternatively, begin from 144,000 and calculate “backwards”:

From 8:57am to 9:00am: y(1.2) = 144,000, so y =\(\frac{144,000}{1.2}\) = 120,000.

From 8:54am to 8:57am: z(1.2) = 120,000, so z = \(\frac{120,000}{1.2}\)= 100,000.
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Re: A population of a colony of bacteria increases by 20 [#permalink] New post 17 Jul 2018, 10:51
sandy wrote:
A population of a colony of bacteria increases by 20 percent every 3 minutes. If at 9:00am the colony had a population of 144,000, what was the population of the colony at 8:54am?

(A) 100,000
(B) 112,000
(C) 120,000
(D) 121,000
(E) 136,000



Total time span : 6 mins. So there will be 2 phases.

Increase rate : 20% in every 3 minutes. That can be expressed as follows :

\((1.2)^2\).

let assume the number of bacteria at the very beginning was x.

x*(1.2)^2= 144000

x = 144000 / 1.44

x = 14400000 / 144

x = 100000.

The best answer is A.
Re: A population of a colony of bacteria increases by 20   [#permalink] 17 Jul 2018, 10:51
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