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

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

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:

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

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"