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Bunuel
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A certain jar contains n amoebas at 8:00. After every hour, each of 09 May 2025, 00:30
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55% (hard)

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66% (02:01) correct 34% (02:25) wrong based on 114 sessions

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A certain jar contains n amoebas at 8:00. After every hour, each of the amoebas in the jar splits into 2 amoebas. At the end of every two hours, after splitting, 3 amoebas die. How many amoebas, in terms of n, will be in the jar at 12:00?

(A) n
(B) 4n - 9
(C) 16n - 15
(D) 16n - 12
(E) 4n + 7

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ManifestDreamMBA
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A certain jar contains n amoebas at 8:00. After every hour, each of 09 May 2025, 04:58
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8:00n
9:002n
10:004n-3
11:008n-6
12:0016n-12-3 = 16n-15


Answer is 16n-15
Bunuel
A certain jar contains n amoebas at 8:00. After every hour, each of the amoebas in the jar splits into 2 amoebas. At the end of every two hours, after splitting, 3 amoebas die. How many amoebas, in terms of n, will be in the jar at 12:00?

(A) n
(B) 4n - 9
(C) 16n - 15
(D) 16n - 12
(E) 4n + 7

­

Gentle note to all experts and tutors: Please refrain from replying to this question until the Official Answer (OA) is revealed. Let students attempt to solve it first. You are all welcome to contribute posts after the OA is posted. Thank you all for your cooperation!
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kingbucky
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A certain jar contains n amoebas at 8:00. After every hour, each of 11 May 2025, 10:15
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At the end of every two hours, after splitting, 3 amoebas die. ( and not "At the end of every two hours, 3 amoebas die"). That is, in my understanding, the death of 3 amoebas happen every hour starting with 10:00.

TimeNumber
8:00nstart
9:002nsplit
10:004n-3split and 2 hours after split at 8, 3 die
11:008n-9split and 2 hours after split at 9, 3 die
12:0016n-21split and 2 hours after split at 11, 3 die

Bunuel Now, this is my line of thinking, can you tell me what I'm missing ? Shouldn't the OA be 16n-21 ?
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ODST117
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A certain jar contains n amoebas at 8:00. After every hour, each of 11 May 2025, 12:58
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I'm not Bunuel but I think I can alleviate your confusion.
The question states "at the end of every two hours, after splitting, 3 amoebas die", which means, after every two hour interval, in addition to the amoebas doubling every hour, three of them also die. The setup starts at 8:00 and after the first two hour interval, we come to 10:00, then after the next two hour interval, we come to 12:00.
So, at 8:00 the population is \(n\).
At 9:00, the population is \(2n\).
At 10:00 (which is the end of the first two hour interval) the population doubles from what it was at 9:00 and 3 amoeba die, i.e, \(2(2n)-3 = 4n-3\).
At 11:00 it's \(2(4n-3) = 8n-6\).
Then, finally, at 12:00 (which is the end of the second two hour interval), the population doubles from what it was at 11:00 and 3 amoeba die, i.e, \(2(8n-6)-3 = 16n-12-3 = 16n-15\).
kingbucky
At the end of every two hours, after splitting, 3 amoebas die. ( and not "At the end of every two hours, 3 amoebas die"). That is, in my understanding, the death of 3 amoebas happen every hour starting with 10:00.

TimeNumber
8:00nstart
9:002nsplit
10:004n-3split and 2 hours after split at 8, 3 die
11:008n-9split and 2 hours after split at 9, 3 die
12:0016n-21split and 2 hours after split at 11, 3 die

Bunuel Now, this is my line of thinking, can you tell me what I'm missing ? Shouldn't the OA be 16n-21 ?
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kingbucky
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A certain jar contains n amoebas at 8:00. After every hour, each of 11 May 2025, 13:12
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"At the end of every two hours, after splitting, 3 amoebas die"....
Why dont we interpret that as, at the end of every two hours after the splitting has occured, 3 amoebas die ?

ODST117
I'm not Bunuel but I think I can alleviate your confusion.
The question states "at the end of every two hours, after splitting, 3 amoebas die", which means, after every two hour interval, in addition to the amoebas doubling every hour, three of them also die. The setup starts at 8:00 and after the first two hour interval, we come to 10:00, then after the next two hour interval, we come to 12:00.
So, at 8:00 the population is \(n\).
At 9:00, the population is \(2n\).
At 10:00 (which is the end of the first two hour interval) the population doubles from what it was at 9:00 and 3 amoeba die, i.e, \(2(2n)-3 = 4n-3\).
At 11:00 it's \(2(4n-3) = 8n-6\).
Then, finally, at 12:00 (which is the end of the second two hour interval), the population doubles from what it was at 11:00 and 3 amoeba die, i.e, \(2(8n-6)-3 = 16n-12-3 = 16n-15\).
kingbucky
At the end of every two hours, after splitting, 3 amoebas die. ( and not "At the end of every two hours, 3 amoebas die"). That is, in my understanding, the death of 3 amoebas happen every hour starting with 10:00.

TimeNumber
8:00nstart
9:002nsplit
10:004n-3split and 2 hours after split at 8, 3 die
11:008n-9split and 2 hours after split at 9, 3 die
12:0016n-21split and 2 hours after split at 11, 3 die

Bunuel Now, this is my line of thinking, can you tell me what I'm missing ? Shouldn't the OA be 16n-21 ?
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