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Recently, scientists were able to sequence an individual's h

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Recently, scientists were able to sequence an individual's h  [#permalink]

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New post 06 Dec 2013, 07:37
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Difficulty:

  45% (medium)

Question Stats:

68% (02:39) correct 32% (02:33) wrong based on 158 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..  [#permalink]

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New post 06 Dec 2013, 09:31
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?

New rate: 1/4
2 year-old rate: 1/24

Now we are told same number of new and 2 year old computers will be used to sequence 1 genome in 6 days

Work: 1 genome
Time: 6 days or 6/7 weeks
Number of new and 2 year-old computers: Both x

(1/4(x)+1/24(x))*6/7=1
7/24(x)*6/7=1
1/4(x)=1
x=4

We are asked for the combination. Both old and new computers = 4, So 4 combos
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Re: Recently, scientists were able to sequence an individual's h  [#permalink]

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New post 26 Dec 2013, 05:44
tusharGupta1 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


x/4 + x/24 = 6/7

x = 144/49

We need four computers

Answer is D

Hope it helps
Cheers!
J :)
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Re: Recently, scientists were able to sequence an individual's h  [#permalink]

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New post 26 Dec 2013, 21:02
1
Convert weeks to days on rates:

New computer: \(\frac{1}{4}\) -> \(\frac{1}{28}\)
Old computer: \(\frac{1}{24}\) -> \(\frac{1}{168}\)

Combine Rates:

\(\frac{1}{28}\)+ \(\frac{1}{168}\)
= \(\frac{1}{24}\)

We need the set of computers to do the job in 6 days, so: if one set takes \(\frac{1}{24}\), we need to add this rate to itself enough times to get \(\frac{1}{6}\)

4 x \(\frac{1}{24}\) gives us \(\frac{1}{6}\)

Therefore answer is 4 (D)
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Re: Recently, scientists were able to sequence an individual's h  [#permalink]

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New post 25 Aug 2018, 01:34
tusharGupta1 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

Here is my approach.

______________\(Work=Rate*Time (weeks)\)
1 new computer:___ \(1 = \frac{1}{4} * 4\)

1 old computer: ___ \(1 = \frac{1}{24} * 24\)

(1 set) Total:______ \(1 = (\frac{1}{4} + \frac{1}{24}) * time\)

(x sets) Total: _____ \(1 = x*(\frac{1}{4} + \frac{1}{24})* \frac{6}{7}\)

-> \(1 = x*(\frac{6}{4*7} + \frac{6}{24*7})\) --> \(x=4\)
Answer D.
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Recently, scientists were able to sequence an individual's h  [#permalink]

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New post 25 Aug 2018, 17:21
afactor4 wrote:
Convert weeks to days on rates:

New computer: \(\frac{1}{4}\) -> \(\frac{1}{28}\)
Old computer: \(\frac{1}{24}\) -> \(\frac{1}{168}\)

Combine Rates:

\(\frac{1}{28}\)+ \(\frac{1}{168}\)
= \(\frac{1}{24}\)

We need the set of computers to do the job in 6 days, so: if one set takes \(\frac{1}{24}\), we need to add this rate to itself enough times to get \(\frac{1}{6}\)

4 x \(\frac{1}{24}\) gives us \(\frac{1}{6}\)

Therefore answer is 4 (D)


Hi,

I have a doubt. Total days taken to complete the job by the two computers is 24. When I solve it as
1set of computers = 24 days
x=6 days
I get x=1/4. Where am I wrong????

When I solve using per day work I get 4 sets.
1 set = 1/24 days
x = 1/6
x= 4 sets
Can you please clarify???
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Re: Recently, scientists were able to sequence an individual's h  [#permalink]

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New post 25 Aug 2018, 19:46
Kezia9 wrote:
afactor4 wrote:
Convert weeks to days on rates:

New computer: \(\frac{1}{4}\) -> \(\frac{1}{28}\)
Old computer: \(\frac{1}{24}\) -> \(\frac{1}{168}\)

Combine Rates:

\(\frac{1}{28}\)+ \(\frac{1}{168}\)
= \(\frac{1}{24}\)

We need the set of computers to do the job in 6 days, so: if one set takes \(\frac{1}{24}\), we need to add this rate to itself enough times to get \(\frac{1}{6}\)

4 x \(\frac{1}{24}\) gives us \(\frac{1}{6}\)

Therefore answer is 4 (D)


Hi,

I have a doubt. Total days taken to complete the job by the two computers is 24. When I solve it as
1set of computers = 24 days
x=6 days
I get x=1/4.
Where am I wrong????

When I solve using per day work I get 4 sets.
1 set = 1/24 days
x = 1/6
x= 4 sets
Can you please clarify???

The more working sets of computers, the shorter the time to complete the job.
1 set of computers = 24 days
x sets of computers = 6 days
--> the time to complete the job decreases 4 times, so the number of sets of computers need to increases 4 times. In other words, x = 4.

Hope it's clear.
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Re: Recently, scientists were able to sequence an individual's h &nbs [#permalink] 25 Aug 2018, 19:46
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