A certain jar contains n amoebas at 8:00. After every hour, each of

Question

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

This is a  PS Butler Question

Check the links to other Butler Projects:

Data Sufficiency Butler  
  Critical Reasoning Butler  
  Reading Comprehension Butler  
  Data Insights Butler

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!

ManifestDreamMBA · Answer

Time 
 Number 
 
  8:00 
 n 
 
  9:00 
 2n 
 
  10:00 
 4n-3 
 
  11:00 
 8n-6 
 
  12:00 
 16n-12-3 =  16n-15

Answer is  16n-15

kingbucky · Answer

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.

Time 
 Number 
 
  8:00 
 n 
 start 
 
  9:00 
 2n 
 split 
 
  10:00 
 4n-3 
 split and 2 hours after split at 8, 3 die 
 
  11:00 
 8n-9 
 split and 2 hours after split at 9, 3 die 
 
  12:00 
   16n-21   
 split 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 ?

ODST117 · Answer

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 · Answer

"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 ?

A certain jar contains n amoebas at 8:00. After every hour, each of

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

Time	Number
8:00	n
9:00	2n
10:00	4n-3
11:00	8n-6
12:00	16n-12-3 = 16n-15

Time	Number
8:00	n	start
9:00	2n	split
10:00	4n-3	split and 2 hours after split at 8, 3 die
11:00	8n-9	split and 2 hours after split at 9, 3 die
12:00	16n-21	split and 2 hours after split at 11, 3 die

GMAT Problem Solving (PS) Questions

A certain jar contains n amoebas at 8:00. After every hour, each of

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards