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Alex notices that a certain bacterium splits into 2 separate bacteria

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Alex notices that a certain bacterium splits into 2 separate bacteria  [#permalink]

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New post 09 Jan 2018, 07:47
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

79% (01:46) correct 21% (01:22) wrong based on 42 sessions

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Alex notices that a certain bacterium splits into 2 separate bacteria once every 15 minutes. If there was one bacterium on a slide 3 hours ago, how many bacteria are there on the slide now?

(A) 8192
(B) 2048
(C) 4096
(D) 256
(E) 1180

source: aristotle
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Re: Alex notices that a certain bacterium splits into 2 separate bacteria  [#permalink]

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New post 09 Jan 2018, 07:57
chesstitans wrote:
Alex notices that a certain bacterium splits into 2 separate bacteria once every 15
minutes. If there was one bacterium on a slide 3 hours ago, how many bacteria are
there on the slide now?

(A) 8192
(B) 2048
(C) 4096
(D) 256
(E) 1180

source: aristotle


There are 12 15 minute splits in 3 hours. Since there was 1 bacterium 3 hours ago, it will split into 2 in the first 15 minute split.

Thereafter, in the next 11 15 minute split it will go from being 2 to \(2^{12}\) which is 4096(Option C)
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Alex notices that a certain bacterium splits into 2 separate bacteria  [#permalink]

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New post 10 Jan 2018, 08:20
chesstitans wrote:
Alex notices that a certain bacterium splits into 2 separate bacteria once every 15 minutes. If there was one bacterium on a slide 3 hours ago, how many bacteria are there on the slide now?

(A) 8192
(B) 2048
(C) 4096
(D) 256
(E) 1180

source: aristotle


There will be 12 ( 15 minutes interval in 3 hours )

Thus, After 3 hours the total number of bacteria will be \(2^{12} = 4096\)

Hence, answer will be (C) 4096
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Re: Alex notices that a certain bacterium splits into 2 separate bacteria  [#permalink]

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New post 10 Jan 2018, 09:18
one split every 15 minutes.
4x15 = one hour

3*4 = 12 splits total

2^12 = 2^8 * 2^8 = 256 * 256

Since the units digits must = 6 we can eliminate A, B and E. And as the result will be 256 x 256 we can eliminate D either.

Correct answer = C
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Re: Alex notices that a certain bacterium splits into 2 separate bacteria &nbs [#permalink] 10 Jan 2018, 09:18
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Alex notices that a certain bacterium splits into 2 separate bacteria

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