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Wes works at a science lab that conducts experiments on bacteria. The

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Wes works at a science lab that conducts experiments on bacteria. The [#permalink]

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Tough and Tricky questions: Word Problems.



Wes works at a science lab that conducts experiments on bacteria. The population of the bacteria multiplies at a constant rate, and his job is to notate the population of a certain group of bacteria each hour. At 1 p.m. on a certain day, he noted that the population was 2,000 and then he left the lab. He returned in time to take a reading at 4 p.m., by which point the population had grown to 250,000. Now he has to fill in the missing data for 2 p.m. and 3 p.m. What was the population at 3 p.m.?

A. 50,000
B. 62,500
C. 65,000
D. 86,666
E. 125,000
[Reveal] Spoiler: OA

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Re: Wes works at a science lab that conducts experiments on bacteria. The [#permalink]

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Bunuel wrote:

Tough and Tricky questions: Word Problems.



Wes works at a science lab that conducts experiments on bacteria. The population of the bacteria multiplies at a constant rate, and his job is to notate the population of a certain group of bacteria each hour. At 1 p.m. on a certain day, he noted that the population was 2,000 and then he left the lab. He returned in time to take a reading at 4 p.m., by which point the population had grown to 250,000. Now he has to fill in the missing data for 2 p.m. and 3 p.m. What was the population at 3 p.m.?

A. 50,000
B. 62,500
C. 65,000
D. 86,666
E. 125,000


let the rate be x, then population of the bacteria after each hour can be given as 2000, 2000x, 2000(x^2), 2000(x^3)

now population at 4pm =250,000
thus we have 2000(x^3) = 250,000
thus x=5

therefore population at 3pm = 2000(25) = 50,000
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Re: Wes works at a science lab that conducts experiments on bacteria. The [#permalink]

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1 AM ................. 2000

Let the rate of growth = x

2 AM ....................... 2000x

3 AM ......................... \(2000 x^2\)

4 AM ......................... \(2000 x^3\)

Given that \(2000 x^3 = 250000\)

x = 5

at 3 AM \(= 2000 * 5^2 = 50000\)

Answer = A
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Re: Wes works at a science lab that conducts experiments on bacteria. The [#permalink]

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Here is a handwritten solution to the question. You could either use the algebraic equation, or try the answers to see which one works.
Attachments

Screen Shot 2016-03-17 at 4.03.05 PM.png
Screen Shot 2016-03-17 at 4.03.05 PM.png [ 185.19 KiB | Viewed 2525 times ]


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Wes works at a science lab that conducts experiments on bacteria. The [#permalink]

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New post 20 Jul 2017, 12:35
Bunuel wrote:

Tough and Tricky questions: Word Problems.



Wes works at a science lab that conducts experiments on bacteria. The population of the bacteria multiplies at a constant rate, and his job is to notate the population of a certain group of bacteria each hour. At 1 p.m. on a certain day, he noted that the population was 2,000 and then he left the lab. He returned in time to take a reading at 4 p.m., by which point the population had grown to 250,000. Now he has to fill in the missing data for 2 p.m. and 3 p.m. What was the population at 3 p.m.?

A. 50,000
B. 62,500
C. 65,000
D. 86,666
E. 125,000

I worked from the answer choices because finding the constant rate looked quick for four of the answers. It was quick.

If we have
1 p.m. -- 2,000
2 p.m. -- ???
3 p.m. -- ???
4 p.m. -- 250,000

Then because the answer choices are for 3 p.m., divide 4 p.m. amount by an answer choice to get the multiplication factor.

Use that factor: divide the 3 p.m. amount by the factor to get the 2 p.m. amount, then once more (2 p.m. amt / factor = 1 p.m. amt) to see if the answer matches 2,000.

1. I started with (E) where 3 p.m. amount is 125,000

\(\frac{250,000}{125,000}\) to get multiplication factor = 2

3:00 --> 2:00 is \(\frac{125,000}{2}\) = 62,500 at 2:00.

Stop. Much too big. The next step, \(\frac{65,000}{2}\) is not going to equal 2,000 at 1 p.m.

2. Try C, where 3 p.m. amount = 50,000

\(\frac{250,000}{50,000}\) = multiplication factor 5

Hour between 2:00 and 3:00 is then \(\frac{50,000}{5}\) = 10,000 at 2:00

2:00 -> 1:00 is \(\frac{10,000}{5}\) = 2,000 at 1 p.m. Correct

Answer C
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Re: Wes works at a science lab that conducts experiments on bacteria. The [#permalink]

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New post 11 Apr 2018, 11:22
Ouch this hurts...

Read the question twice..thrice and every time saw 1000 instead of 2000 :sad:
Re: Wes works at a science lab that conducts experiments on bacteria. The   [#permalink] 11 Apr 2018, 11:22
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