Bunuel wrote:
At the start of an experiment, a certain population consisted of x organisms. At the end of each month after the start of the experiment, the population size increased by twice of its size at the beginning of that month. If the total population at the end of five months is greater than 1000, what is the minimum possible value of x?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
The answer is D.
The devil is in this detail:
"At the end of each month after the start of the experiment, the population size
increased by twice of its size at the beginning of that month."
Say we have a size of 10.
Twice of the size 10 is 10*2 = 20.
That 20 should be added to
original 10 to get 30. So 10 increased by twice its size = 30.
10 + 200% of 10 = (10 + 20) = 30
In other words, at the end of each month, the value is
three times the original, not two times.
Try 4. The second number in the sum is the amount added
to an already existing start number that yields a new total at the end of each month:
Month 1: 4 + 8 = 12
Month 2: 12 + 24 = 36
Month 3: 36 + 72 = 108
Month 4: 108 + 216 = 324
Month 5: 324 + 648 = 972
972 < 1,000. A little too small.
Try 5:
Month 1: 5 + 10 = 15
Month 2: 15 + 30 = 45
Month 3: 45 + 90 = 135
Month 4: 135 + 270 = 405
Month 5: 405 + 810 = 1,215
1,215 > 1,000
The answer is D.
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