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

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Math Expert
Joined: 02 Sep 2009
Posts: 59724
At the start of an experiment, a certain population consisted of x org  [#permalink]

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02 Jul 2017, 02:37
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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

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Re: At the start of an experiment, a certain population consisted of x org  [#permalink]

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02 Jul 2017, 02:39
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

This is a modified question of the the following OG question: https://gmatclub.com/forum/at-the-start ... 07202.html
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Re: At the start of an experiment, a certain population consisted of x org  [#permalink]

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02 Jul 2017, 05:36
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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

At the end of each month, the population is 3 times than that of the beginning, since it is said that the population size increases by twice the initial amount.

At end of 5th month, population is 3^5 times the original, say x.

Thus, 243x > 1000

=> x = 5

Option D
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Re: At the start of an experiment, a certain population consisted of x org  [#permalink]

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02 Jul 2017, 06:10
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
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Re: At the start of an experiment, a certain population consisted of x org  [#permalink]

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02 Jul 2017, 06:47
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

$$x ====> 2x$$

$$2x ===> 4x$$

$$4x ===> 8x$$

$$8x ===> 16x$$

$$16x ===> 32x$$

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 $$4$$

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At the start of an experiment, a certain population consisted of x org  [#permalink]

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03 Jul 2017, 09:08
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1
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 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

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Re: At the start of an experiment, a certain population consisted of x org  [#permalink]

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05 Jul 2017, 00:17
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

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
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Re: At the start of an experiment, a certain population consisted of x org  [#permalink]

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04 Aug 2019, 11:33
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

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.

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Re: At the start of an experiment, a certain population consisted of x org   [#permalink] 04 Aug 2019, 11:33
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