The number of bacteria in a petri dish increased by 50 percent every 2

Question

The number of bacteria in a petri dish increased by 50 percent every 2 hours. If there were 108 million bacteria in the dish at 2: 00 p.m., at what time were there 32 million bacteria in the dish?

A. 6: 00 p.m.
B. 8: 00 p.m.
C. 6: 00 a.m.
D. 8: 00 a.m.
E. 10: 00 a.m.

Temurkhon · Answer

32*(1.5)^x=108

(3/2)^x=108/32

(3/2)^x=27/8, so x=3. Meaning that such number was 2*3=6 hours ago.

D

TeamGMATIFY · Answer

Given  : 
he number of bacteria in a petri dish increased by 50 percent every 2 hours
There were 108 million bacteria in the dish at 2: 00 p.m
Since the bacteria is increasing by 50% every 2 hours, this means that the number is multiplied by 1.5 every 2 hours.

Required  : At what time were there 32 million bacteria in the dish?
Assume that there were n intervals of 2 hours between 32 million and 108 million.

32 * (1.5)^n = 108
(3/2)^n = 108/32 = 27/8 = (3/2)^3

Hence n = 3 intervals.
Each interval was of 2 hours. Therefore, the number of hours = 6
Subtracting 6 hours from 2 PM, we get 8 AM as the answer.

Option D

EMPOWERgmatRichC · Answer

Hi All,

This question can be solved by TESTing THE ANSWERS and doing a bit of multiplication.

We're told that the number of bacteria in a petri dish increased by 50 PERCENT every 2 HOURS and that there were 108 million bacteria in the dish at 2:00 pm. We're asked at what time were there 32 million bacteria.

Since a 50% increase every 2 hours is HUGE, chances are that we're looking for a time sometime that 'morning'; answers A and B would be during the prior day's evening, which is so much further in the past that those answers are not logical.

Let's TEST Answer D: 8:00am

IF... there were 32 million bacteria at 8:00am....
there were 32 + (.5)(32) = 48 million bacteria at 10:00am...
there were 48 + (.5)(48) = 72 million bacteria at 12:00pm...
there were 72 + (.5)(72) = 108 million bacteria at 2:00pm...

This is an exact MATCH for what we were told, so this MUST be the answer.

Final Answer:  D

GMAT assassins aren't born, they're made,
Rich

Nunuboy1994 · Answer

We can think of this problem like finance problem

32(1 (1/2))^x= 108
 3/2^x =108/32- simplify
 3/2^x = 27/8

x= 3 -how many times increased- so if its done every 2 hours hours then it was done 6 hours ago which is 8:00 a.m

Thus
 "D"

MHIKER · Answer

32(1.5)^x=108

(1.5)^x=\frac{108}{32}=\frac{27}{8}

(\frac{15}{10})^x=\frac{27}{8}

(\frac{3}{2})^x=\frac{27}{8}

x=3

\frac{27}{8}=\frac{27}{8}

50 percent increases in every 2 hours, So total hours  = 3*2=6

The time when the bacteria were 32 million 2 pm-6 hours = 8 am

Kinshook · Answer

Given: ]The number of bacteria in a petri dish increased by 50 percent every 2 hours. 
Asked: If there were 108 million bacteria in the dish at 2: 00 p.m., at what time were there 32 million bacteria in the dish?

32*1.5ˆ(n/2) = 108
1.5ˆ(n/2) = 108/32 = 1.5ˆ3 
n = 6

After n=6 hours, there were 108 million bacteria in the dish at 2: 00 p.m
At 8:00 am, there were 32 million bacteria in the dish.

IMO D

lucky21 · Answer

A 50% increase means: Add half of the current amount

Start from 32 million and just keep adding half:

Let x (am/pm) : 32
(x+2) : 32+16=48 (Half of 32 is 16)
(x+4) : 48+24=72 (Half of 48 is 24)
(x+6) : 72+36=108 (Half of 72 is 36)

As x+6 = 2pm, x+4=12 am, x+2=10am, x= 8am
D

The number of bacteria in a petri dish increased by 50 percent every 2

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The number of bacteria in a petri dish increased by 50 percent every 2

Prep Toolkit

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

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745 with Only Self-Prep and GMAT Club

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My Rewards