At the start of an experiment, a certain population consisted of x org

Imo C
Let population be x then
At the end of 1st month population will be =2x
At the end of 2st month population will be=4x
At the end of 3st month population will be=8x
At the end of 4st month population will be=16x
At the end of 5st month population will be=32x

32X>1000 we have x>3
So Minimum value of x is 4

\(x ====> 2x\)

\(2x ===> 4x\)

\(4x ===> 8x\)

\(8x ===> 16x\)

\(16x ===> 32x\)

Which means we are looking for \(x^5\)

\(x^5 > 3,000\)

So we are looking for a smaller number

\(x^4 = 1024\) which is slightly greater than 1000

Hence, the number should be \(4\)

Answer is C

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.

D) FOR SURE

We dont need 4*4*4*4*4
We need 4*2*2*2*2


so 5*2*2*2*2 > 1000
and 4*2*2*2*2 <1000

Hence D

Initial size = x
Increase = 2x
Final size after first increase = \(3x\)

After 5 months Population = \(3^5*x\)

Now, \(3^5*x > 1000\)

i.e. 243x > 1000
i.e. x > 4.1

i.e. \(x_{min} = 5\)

Answer: Option D

At the time of Start is x
Size after 1st Month is 3x (ie x + 2x)
Size after 2nd Month is 9x (ie 3x + 2*3x)
Size after 3rd Month is 27x (ie 9x + 2*9x)
Size after 4th Month is 81x (ie 27x + 2*27x)
Size after 5th Month is 243x (ie 81x + 2*81x)



Or, \(243x > 1000\)

So, \(x > 4.11\), Thus among the given optionthe s, answer must be (D) 5

When the population size increased by twice its size every month, it was tripling every month, as shown here:

End of Month 1: x * 3

End of Month 2: x * 3 * 3 = x * 3^2

End of Month 3: x * 3 * 3 * 3 = x * 3^3

End of Month 4: x * 3 * 3 * 3 * 3 = x * 3^4

End of Month 5: x * 3 * 3 * 3 * 3 * 3 = x * 3^5

Therefore, we can create the inequality

x * 3^5 > 1000

x > 1000/3^5
x > 4.11

Since x is an integer, x is at least 5.

Answer: D

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