Data for a certain biology experiment are given in the table

Question

AMOUNT OF BACTERIA PRESENT 
Time Amount 
1:00 P.M. 10.0 grams 
4:00 P.M. x grams 
7:00 P.M. 14.4 grams

Data for a certain biology experiment are given in the table above. If the amount of bacteria present increased by the same fraction during each of the two 3-hour periods shown, how many grams of bacteria were present at 4:00 P.M.?

A. 12.0 
B. 12.1 
C. 12.2 
D. 12.3 
E. 12.4

Please point out my flaw:
We know,
in 6 hrs. bacteria increased 14.4-10=4.4
So,since it is increasing by a constant,
in 3 hrs>> 4.4 x 3/6 = 2.2

Therefore,
1:00 P.M. 10.0 grams 
4:00 P.M.  12.2  grams
7:00 P.M. 14.4 grams IMO:C

AKProdigy87 · Accepted Answer

Let X represent the amount of bacteria present at 4:00 PM. Since the fractional increase must remain constant from 1 to 4pm as it is from 4pm to 7pm:

Fractional increase from 1 PM to 4 PM = X / 10.0
Fractional increase from 4 PM to 7 PM = 14.4 / X

\frac{X}{10.0} = \frac{14.4}{X}

X^2 = (14.4)(10.0)

X^2 = 144

X = 12

Therefore, the correct answer is  A: 12.0 .

JeffTargetTestPrep · Answer

We can let n = the multiplier for each 3-hour period. So, we have:

1 p.m. = 10 grams

4 p.m. = 10n

7 p.m. = 10n^2

We can create the following equation:

10n^2 = 14.4

n^2 = 1.44

n = 1.2

Thus, we have 10n = 10(1.2) = 12 grams of bacteria at 4 p.m.

Alternate Solution:

Since the fractional increase is the same for both 3-hour periods, we must have:

x/10 = 14.4/x

x^2 = 144

x = 12 or x = -12

Since the number of bacteria cannot be negative, the answer is 12.

Answer: A

hgp2k · Answer

IMO A. Note that the bacteria did not increase by same amount, but by same FRACTION. So the answer has to be less than 12.2, i.e. either A or B. Assuming A is correct: 10+10*F = 12 F = 1/5 12+12*F = 14.4 So answer is A. Please let me know if you want me to explain further. ___________________________ Consider KUDOS for good posts :beer

tejal777 · Answer

I am sorry its not clear..could you please give a detailed expalnation? got my mistake though..its says same fraction .. :oops:

hgp2k · Answer

Sure. As we know that the bacterias are increasing at a constant Fraction, we can write the following equation: 10 + 10*F = X , where F = Fraction by which bacterias increases, and X = amount of bacterias after 3 hrs. After 6 hrs, number of bacterias will be: X+X*F = 14.4 Substituting value of X from above equation, X+X*(X-10)/10 = 14.4 X^2=144 X=12 I hope it is clear now

_________________________ Consider KUDOS for good posts :beer

Maxswe · Answer

Change/Initial value...

Let's call X the value we want to find

(X-10)/10=(14,4-X)/X
X^2-10x=144-10X
X^2=144
X=12

Mimster · Answer

The way I solved the question:

Goal: amount of bacteria @ 4.00 PM which means 10 multiplied by something equals answer.
  
The difference between 7.00 PM and 1.00 PM is

14.4 - 10 = 4.4

We know that the original amount 10 is increased (or in this case - multiplied) by a fraction EACH 3 hours and there are 2 periods.

10 * x * x = 14.4

x^2 = \frac{14.4}{10} = x^2 =1.44

\sqrt{x^2} = \sqrt{1.44}

x = 1.2

From this we solve for X which equals to 1.2.

x * 10 = 1.2 * 10 = 12.0

I then multiplied 10 by 1.2 thereby arriving at the answer choice (A)

JeffTargetTestPrep · Answer

We can let n = the multiplier for each 3-hour period. So, we have:

1 p.m. = 10 grams

4 p.m. = 10n

7 p.m. = 10n^2

We can create the following equation:

10n^2 = 14.4

n^2 = 1.44

n = 1.2

Thus, we have 10n = 10(1.2) = 12 grams of bacteria at 4 p.m.

Alternate Solution:

Since the fractional increase is the same for both 3-hour periods, we must have:

x/10 = 14.4/x

x^2 = 144

x = 12 or x = -12

Since the number of bacteria cannot be negative, the answer is 12.

Answer: A

sadikabid27 · Answer

Bunuel ,  VeritasKarishma ,  chetan2u  your take on this question please? Thanks.

KarishmaB · Answer

The question says ""If the amount of bacteria present increased by the same fraction during each of the two 3-hour periods shown"

10, x, 14.4 
This means that x increases by a fraction and 14.4 increases by the same fraction (it means they are multiplied by the same number to get the next term)
So they form a Geometric Progression.

x = Geometric mean of (10, 14.4)  = \sqrt{10*14.4} = 12

Answer (A)

PriyamRathor · Answer

Hi ,
 avigutman

Why the below method is wrong ?

It is given that   the amount of bacteria present increased by the same fraction during each of the two 3-hour periods shown  
Hence,

14.4-x = x-10
So ,
24.4 = 2x 
x = 12.2 
Hence choice C

Thanks.

avigutman · Answer

When we say "increase by a fraction" or "increase by a factor" or "increase by a percent", we are talking multiplicatively. When we say "increase by a certain quantity or amount", we are talking additively. Here are some examples, all using 50 as a starting point:
Increase by 5 = 55
Increase by a factor of 5 = 250
Increase by 10% = 55
Increase by 10 = 60
Increase by a fraction of 1/5 = 50*(6/5) = 60
I hope this helps,  PriyamRathor !

nishantswaft · Answer

Bunuel

can you please explain how fractional increase is represented in this form? 
 I think I'm missing a basic concept here
 
 here x is numerator   Fractional increase from 1 PM to 4 PM = X / 10.0   ?

and here x is in denominator   Fractional increase from 4 PM to 7 PM = 14.4 / X   ?

Nsp10 · Answer

we can also assume it as increase by a %
hence,
10(1+a/100)=x.............Equation 1
and
x(1+a/100)=14.4............Equation 2
divide equation 1 and 2
we get
10/x=x/14.4
thus 144=x raised to the power 2
x=12

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Data for a certain biology experiment are given in the table

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