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Does the population of rats in a zoo double every day?

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AweSome777
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Does the population of rats in a zoo double every day? [#permalink] New post   10 Jul 2019, 04:59
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Does the population of rats in a zoo double every day?

(1) The population increased by 12 on a particular day.
(2) The population increased by 18 on a particular day.

Source: Nova's
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C
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Re: Does the population of rats in a zoo double every day? [#permalink] New post   10 Jul 2019, 06:57
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I don't think this question makes much sense. If the population increased by 12 one day, then if it were true that the population were doubling each day, the population would need to be increasing from 12 to 24 that day. But then what happened three days ago? The population cannot have increased from 1.5 rats to 3 rats. Since the question doesn't specify a time period or starting point for the doubling, the answer to the question is "no" regardless of what the statements say. That said, it's certainly impossible that the population was doubling each day if it increased by 12 one day and 18 another, because that would mean one day the population was exactly 12, and another day it was exactly 18, and you can't get from 12 to 18 by doubling.
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Re: Does the population of rats in a zoo double every day? [#permalink] New post   10 Jul 2019, 13:57
I translated it this way:
we have a geometric sequence \((a , ar , ar^2 , ... , ar^x, ... , ar^y , ... )\) and we are asked whether \(r = 2\)?

statement (1) says that \(ar^x = 12\) --> clearly insufficient
statement (2) says that \(ar^y = 18\) --> clearly insufficient

combining (1) and (2),
if \(r = 2\), then dividing any value in the sequence by any lower value in the sequence will give a power of 2 (\(2^n\) where n is an integer) (such as 2,4,8,16,.....),
but dividing \(\frac{ar^y}{ar^x} = r^{y-x} = \frac{3}{2} = 1.5\), which can't be rewritten into the \(2^n\) formula. Thus the population can't be doubling every day --> sufficient
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Re: Does the population of rats in a zoo double every day? [#permalink] New post   11 Jul 2019, 00:41
"Increased by 12" does not mean that on a particular date the number of rat was 12. So how did you write ar^x = 12?

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Does the population of rats in a zoo double every day? [#permalink] New post   11 Jul 2019, 04:10
nazmul2016 wrote:
"Increased by 12" does not mean that on a particular date the number of rat was 12. So how did you write ar^x = 12?

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you are correct, it does't mean so. I am just testing the possibility that r of the sequence equals 2.

statement 1 said that the numbers increased by 12.
If we merged this info with our tested assumption that the number is doubled, this means that the population was 12 before doubling.
so we can conclude from statement (1) as well as statement (2) that 12 and 18 are two elements in the sequence.
but upon assuming that 12 and 18 are in the same sequence whose r = 2, we realize that this assumption is impossible.

I want also to note that if the answer was yes (valid), we will not be able to choose C because if r = 2 is valid, r = 4 is also valid, so we will not be sure whether it is doubled or quadrupled or something else.
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Re: Does the population of rats in a zoo double every day? [#permalink] New post   02 Aug 2021, 00:50
AweSome777 wrote:
Does the population of rats in a zoo double every day?

(1) The population increased by 12 on a particular day.
(2) The population increased by 18 on a particular day.

Source: Nova's


Statement 1 : Insufficient
We do not know anything about the rats on previous or after day.

Statement 2 : Insufficient
Same reason as in (1)

Combining both, we get
Rate can be = 18/12 = 1.5 not equal to 2
The population of rats do not double.

Hence, OA is (C).
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Re: Does the population of rats in a zoo double every day? [#permalink]
02 Aug 2021, 00:50
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