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22 Dec 2025, 22:10
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A culture of bacteria had a population of 8,000 at 10 AM. The population grew at a fixed percentage rate per hour and reached 64,000 at 7 PM on the same day. If the population continues to grow at that same rate, at what time will the population reach 256,000?
A. 9 PM of the same day
B. 10 PM of the same day
C. 12 AM of the next day
D. 12:30 AM of the next day
E. 1 AM of the next day
Let's consider that population of bacteria grows by x percentage per hour new population after increment every hour will become (1+x/100) times or y times. (1+x/100=y)
Population at 10 AM = 8000
population at 7 PM (9 hours) = 8000y^9=64000 -----> y^9= 8 ---> y^9= 2^3 ----> y= 2^(1/3) ......................(1)
Population after t hours = 256000 = 8000y^t -----> y^t = 32 =2^5 ----> y =2 ^(5/t) .......................................(2)
On comparing 1st and 2nd equation ---
2^(1/3) = 2^(5/t)
1/3=5/t
t=15 hours
Bacteria population will become 256000 at 15 hours after 10 AM ---- 1 AM of the next day. Answer E.
A. 9 PM of the same day
B. 10 PM of the same day
C. 12 AM of the next day
D. 12:30 AM of the next day
E. 1 AM of the next day
Let's consider that population of bacteria grows by x percentage per hour new population after increment every hour will become (1+x/100) times or y times. (1+x/100=y)
Population at 10 AM = 8000
population at 7 PM (9 hours) = 8000y^9=64000 -----> y^9= 8 ---> y^9= 2^3 ----> y= 2^(1/3) ......................(1)
Population after t hours = 256000 = 8000y^t -----> y^t = 32 =2^5 ----> y =2 ^(5/t) .......................................(2)
On comparing 1st and 2nd equation ---
2^(1/3) = 2^(5/t)
1/3=5/t
t=15 hours
Bacteria population will become 256000 at 15 hours after 10 AM ---- 1 AM of the next day. Answer E.
22 Dec 2025, 22:53
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population of 8000 at 10 am
population grew at fixed percentage rate per hour(most imp statement)=so its compounding=
64000/8000=8 Times in 9 hours=2^3----9 hours
2------3 hours
so population is getting double every 3 hours
to go from 64000 to 256000 = 256000/64000=4 times
so it will need 3 hour s for becoming twice
and 6 hours for getting 4 times=
7 pm + 6 hours = 1 am next day
ans is option E
population grew at fixed percentage rate per hour(most imp statement)=so its compounding=
64000/8000=8 Times in 9 hours=2^3----9 hours
2------3 hours
so population is getting double every 3 hours
to go from 64000 to 256000 = 256000/64000=4 times
so it will need 3 hour s for becoming twice
and 6 hours for getting 4 times=
7 pm + 6 hours = 1 am next day
ans is option E
Bunuel
AditiDeokar
Joined: 12 Jan 2025
Last visit: 12 Apr 2026
Posts: 87
Given Kudos: 298
Location: India
Concentration: Finance
Schools: NUS ESSEC MiM '26 ESSEC MiF '26 INSEAD MiM '26 ESADE Imperial ISB '26 ESADE HEC Sept '26 IE INSEAD Jan '26
GMAT Focus 1: 525 Q77 V77 DI74 
GPA: 3.5
Schools: NUS ESSEC MiM '26 ESSEC MiF '26 INSEAD MiM '26 ESADE Imperial ISB '26 ESADE HEC Sept '26 IE INSEAD Jan '26
GMAT Focus 1: 525 Q77 V77 DI74
Posts: 87
22 Dec 2025, 23:04
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The answer is E. 1AM next day. The population is growing at a fixed percentage, it starts off at 8000, at 10AM. Next given information is 64000 at 7PM. In 9 hours it has doubled thrice, therefore it takes 3hrs to double once. Similarly to reach from 64,000 to 256,000 it will double twice, once from 64,000 to 128,000 and second from 128,000 to 256,000 therefore it took 6 hours. 7PM + 6hrs = 1AM.
