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# Recently, scientists were able to sequence an individual's humane geno

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Math Expert
Joined: 02 Sep 2009
Posts: 58443
Recently, scientists were able to sequence an individual's humane geno  [#permalink]

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29 Aug 2019, 00:23
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Difficulty:

65% (hard)

Question Stats:

61% (02:44) correct 39% (02:48) wrong based on 57 sessions

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Recently, scientists were able to sequence an individual's humane genome in just 4 weeks using a super fast modern computer. A computer manufactured just 2 years earlier would have taken 24 weeks to do the same amount of work.

For more targeted treatment of his cancer, Steve needs his human genome to be sequenced as soon as possible and scientists plan to use a combination of the same number of "new" computers as "2 year-old" computers to work together. Assuming the computers can tackle discrete components of the genome sequencing process, how many combined sets of computers should the scientists order if they want to finish the genome project in 6 days?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

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Re: Recently, scientists were able to sequence an individual's humane geno  [#permalink]

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29 Aug 2019, 00:43
3
$$\frac{1}{28}x+\frac{1}{168}x=\frac{1}{6}$$
$$\frac{196}{4704}x=\frac{1}{6}$$
x=4
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Joined: 19 May 2019
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Recently, scientists were able to sequence an individual's humane geno  [#permalink]

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29 Aug 2019, 05:54
2
Computer A works at a rate of 1/4 per weeks = 1/28 per day
Computer B works at a rate of 1/24 per weeks = 1/168 per day

We want to find the number of machine n to finish the work in 6 days. So the machines all combined need to work at a rate of 1/6 per day.

1/6 = (1/28 + 1/168) x n

168 is 28 x 6 so we have:
1/6 = (7 / (28 x 6)) x n

Simplify by 1/6 we have

1 = (7 / 28) x n

Then n = 28 / 7 = 4

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Re: Recently, scientists were able to sequence an individual's humane geno  [#permalink]

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04 Sep 2019, 18:26
1
Bunuel wrote:
Recently, scientists were able to sequence an individual's humane genome in just 4 weeks using a super fast modern computer. A computer manufactured just 2 years earlier would have taken 24 weeks to do the same amount of work.

For more targeted treatment of his cancer, Steve needs his human genome to be sequenced as soon as possible and scientists plan to use a combination of the same number of "new" computers as "2 year-old" computers to work together. Assuming the computers can tackle discrete components of the genome sequencing process, how many combined sets of computers should the scientists order if they want to finish the genome project in 6 days?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Let’s first determine how many days it takes for one new and old computer pair to sequence the genome. In one week, a new computer can sequence 1/4 of the genome and an old computer can sequence 1/24 of the genome. Working together, they can sequence

1/4 + 1/24 = 7/24

of the genome in one week. Thus, it will take one pair 24/7 weeks, or 24 days to sequence the genome.

If it takes one pair 24 days to finish the job, then it will take 4 times as many pairs to finish the job in 1/4 of the time i.e. 4 new & old computer pairs are needed to finish in 24/4 = 6 days.

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Re: Recently, scientists were able to sequence an individual's humane geno   [#permalink] 04 Sep 2019, 18:26
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