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The algae on the surface of a pond increases in size by 10% each day.
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13 Mar 2024, 23:08
13 Mar 2024, 23:08
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62% (03:03) correct
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The algae on the surface of a pond increases in size by 10% each day. At night the algae on the surface of the same pond is reduced by 5%.
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
The number of days it takes for the algae to go from 15% of the pond's surface to 50% |
The number of days it takes for the algae to go from 50% of the pond's surface to 100% |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
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The algae on the surface of a pond increases in size by 10% each day.
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11 Jun 2024, 14:07
11 Jun 2024, 14:07
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OE
You are given that each day the algae on the surface of a pond grows by 10% but then retracts 5% each night.
You are asked to compare the number of days it takes the algae to grow from 15% to 50% to the time it takes to grow from 50% to 100% of the pond surface.
Begin by calculating the growth each day:
(1 + .10)(1 - .05) = (1.10)(.95) = 1.045
Now set up the formula for geometric growth: start amount * growth rate^{time} = end amount
\(growth rate^{time}=\frac{end amount}{start amount }\) (it is essentially the percentage change formula)
At this point you can see that you don't actually need to calculate the number of days. Because the growth rate is the same for both Quantities you can see that whichever quantity is greater will result in a greater value for end amount
Therefore you only need to compare the ratios of the starting and ending amounts. start amount
\(\frac{50}{15}\) % \(\therefore \) \(\frac{100}{50}\) %
\(3.35>2\)
A is the answer
You are given that each day the algae on the surface of a pond grows by 10% but then retracts 5% each night.
You are asked to compare the number of days it takes the algae to grow from 15% to 50% to the time it takes to grow from 50% to 100% of the pond surface.
Begin by calculating the growth each day:
(1 + .10)(1 - .05) = (1.10)(.95) = 1.045
Now set up the formula for geometric growth: start amount * growth rate^{time} = end amount
\(growth rate^{time}=\frac{end amount}{start amount }\) (it is essentially the percentage change formula)
At this point you can see that you don't actually need to calculate the number of days. Because the growth rate is the same for both Quantities you can see that whichever quantity is greater will result in a greater value for end amount
Therefore you only need to compare the ratios of the starting and ending amounts. start amount
\(\frac{50}{15}\) % \(\therefore \) \(\frac{100}{50}\) %
\(3.35>2\)
A is the answer
gmatclubot
The algae on the surface of a pond increases in size by 10% each day. [#permalink]
11 Jun 2024, 14:07
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