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# Data for a certain biology experiment are given in the table

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Intern
Joined: 04 Aug 2011
Posts: 40
Data for a certain biology experiment are given in the table  [#permalink]

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20 Aug 2011, 04:35
2
00:00

Difficulty:

45% (medium)

Question Stats:

64% (01:39) correct 36% (01:32) wrong based on 96 sessions

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AMOUT OF BACTERIA PRESENT

Time Amount
1:00 pm 10.0 grams
4.00 pm x grams
7.00 pm 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 pm?

a) 12.0
b) 12.1
c) 12.2
d) 12.3
e) 12.4
Manager
Joined: 20 Aug 2011
Posts: 128
Re: a GWD math (7) , which hasn't been discussed  [#permalink]

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20 Aug 2011, 08:05
1
Ratio problem

According to the given conditions

x/10=14.4/x
x^2=144
x=12
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Director
Joined: 01 Feb 2011
Posts: 664
Re: a GWD math (7) , which hasn't been discussed  [#permalink]

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20 Aug 2011, 10:11
let p be the fraction by which it increased

1pm 10 gms

4pm x gms = (1+p)10

7pm 14.4 gms = (1+p)x

=> x/10 = 14.4/x

=> x =12

Manager
Joined: 18 Aug 2011
Posts: 51
Re: a GWD math (7) , which hasn't been discussed  [#permalink]

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21 Aug 2011, 01:30
Should the statement say something like "if the growth (or rate of growth) increases". Because if the amount increases by the same fraction, it would always double for example.
Senior SC Moderator
Joined: 22 May 2016
Posts: 2099
Data for a certain biology experiment are given in the table  [#permalink]

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07 Nov 2017, 12:51
Jasontuyj2012 wrote:
AMOUT OF BACTERIA PRESENT

Time Amount
1:00 pm 10.0 grams
4.00 pm x grams
7.00 pm 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 pm?

a) 12.0
b) 12.1
c) 12.2
d) 12.3
e) 12.4

Method I - Algebra - Multiplier

"The amount of bacteria present increased by the same fraction," $$x$$, twice:
$$(x*x) = x^2$$ = the multiplier, twice

$$10 * x^2 = 14.4$$
$$x^2 = \frac{14.4}{10}$$
$$x = \sqrt{1.44}= 1.2 =$$ the multiplier

Number of bacteria at 4 p.m.?

$$10 * 1.2 = 12$$ bacteria present at 4 p.m.
(And $$12 * 1.2 = 14.4$$ at 7 p.m. Correct.)

Method II - Use answer choices

Find one fractional increase:
$$\frac{12.2}{10} = 1.22$$

Result for the second fractional increase:
$$12 * 1.22 = 14.64$$

C's 4 p.m. value is too great. Eliminate D and E, which will be even greater.

Try A, the round number: 12

Fractional increase: $$\frac{12}{10} = 1.2$$
Multiply 4 p.m. value, 12, by 1.2:
$$12 * 1.2 = 14.4$$. Correct.

Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: Data for a certain biology experiment are given in the table  [#permalink]

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12 Nov 2017, 07:22
Jasontuyj2012 wrote:
AMOUT OF BACTERIA PRESENT

Time Amount
1:00 pm 10.0 grams
4.00 pm x grams
7.00 pm 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 pm?

a) 12.0
b) 12.1
c) 12.2
d) 12.3
e) 12.4

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.

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Re: Data for a certain biology experiment are given in the table &nbs [#permalink] 12 Nov 2017, 07:22
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