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

Question

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

PareshGmat · Accepted Answer

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

manpreetsingh86 · Answer

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

mcelroytutoring · Answer

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

generis · Answer

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 whether the answer matches 2,000.

1.  I started with (C) 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 A, 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 A

rever08 · Answer

Ouch this hurts... Read the question twice..thrice and every time saw 1000 instead of 2000

sahilsnpt · Answer

Bunuel Why can't we use the ARITHMETIC PROGRESSION FORMULA as the bacteria is multiplying at a constant rate?
I tried it but I got 86666 as the answer. Any help would be appreciated.

Thanks in advance.

Bunuel · Answer

Because here we have a geometric progression, not arithmetic.

conniezh · Answer

simple approach this problem:

First, we take out the last 3 zeros for simplicity's sake.

hr 1 = 2
hr 2 = unknown
hr 3 = unknown
hr 4 = 250

Since we know that it is growing at a constant rate, we could assume that there is a patter between the four numbers. Next we look at 250 and see its factors.
250 = 2 x 5 x 5 x 5 <-- notice that there is a 2 here and 3 five's. If the number is growing at a constant rate, then we could plug in the only difference here - the five's

hr 1 = 2
hr 2 = 2 x 5
hr 3 = 2 x 5 x 5 = 50,000 (don't forget the zeros we took out in the beginning)
hr 4 = 2 x 5 x 5 x 5

Answer is A

abhishekdadarwal2009 · Answer

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

Let the rate of growth = x

2 AM ....................... 2000x^1

3 AM ......................... 2000x^2

4 AM ......................... 2000x^3

Given that 2000x^3=250000

at 3 AM =50000

NishantR · Answer

For this question I just did trial and error and got the answer and here are my quick observations. I deleted D & E quickly because they were obviously incorrect. I started my working with C & realised quickly that it was wrong. Hence I was left with B&A. I worked on B and come to the conclusion that it was wrong & hence was left with A.

A. 50,000 
250,000/5 = 50,000/5 = 10,000/5= 2000

Correct answer

B. 62,500
Goes into 62,500 x 4 = 250,000 hence 62,500/4 = 15625/4 is greater than 3000 hence wrong
 
C. 65,000
Start here. 250,000 not divisible by 65,000 hence wrong

D. 86,666 
Delete option since it wont divide 250,000 completely

E. 125,000
250,000/2 = 125,000/2 = 62,500/2 = 31,250 hence wrong.

Archit3110 · Answer

given rate of growth is constant so 
1Pm = 2000
2pm = 2000*x
3PM = 2000*x^2
4pm = 2000*x^3
2000*x^3 = 250000
solve for x = 5
so at 3PM = 2000*25 ; 50,000
option A

martinfzb · Answer

multiplies at a constant rate can be expressed as (1+m)^n
so the equation for this question is 
2000 * (1+m)^3 = 250000
(1+m)^3=125
1+m=5
m=4
the population at 3pm multiplies two times after 1pm,
2000*(1+4)^2 = 2000*25=50000
choose A

bumpbot · Answer

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

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