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

by subh2273 » Mon Oct 08, 2018 9:46 pm

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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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by deloitte247 » Thu Oct 25, 2018 2:36 pm
New Rate of work = 1/4
For two years old computer =1/24
Note that same number of new and of two year old computer would be used to sequence 1 genome in 6 days
Work is on one genome
Time = 6 days
days converted to weeks =6/7 week
Total number of new and 2 year old computers= x
$$\left(\frac{1}{4}x+\frac{1}{24}x\right)\cdot\frac{6}{7}=1$$
$$\left(\frac{6+1}{24}x\right)\cdot\frac{6}{7}=1$$
$$\left(\frac{7}{24}x\right)\cdot\frac{6}{7}=1$$
$$\left(\frac{7}{24}\right)\cdot x\cdot\frac{6}{7}=1$$
$$\left(\frac{7}{24}\right)\cdot x\cdot\frac{6}{7}=1$$
$$x\cdot\frac{7}{24}\cdot\frac{6}{7}=1$$
$$x=4$$
4 combined sets of both old and new computers should be ordered if they want to finish the genome project in 6 days.
$$Answer\ =option\ D$$
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by fskilnik@GMATH » Sun Oct 28, 2018 12:09 pm
subh2273 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 use UNITS CONTROL, one of the most powerful tools of our method!
$$\left. \matrix{
{{1\,\,{\rm{job}}} \over {\,4\,{\rm{weeks}}\,}}\,\,{\rm{each}}\,\,{\rm{of}}\,\,x\,\,{\rm{new}}\,\,{\rm{computers}}\,\, \Rightarrow \,\,\,{{1 \cdot 6 \cdot x\,\,{\rm{jobs}}} \over {\,4 \cdot 6\,\,{\rm{weeks}}\,}}\,\, \hfill \cr
{{1\,\,{\rm{job}}} \over {\,24\,{\rm{weeks}}\,}}\,\,{\rm{each}}\,\,{\rm{of}}\,\,x\,\,{\rm{old}}\,\,{\rm{computers}}\,\, \Rightarrow \,\,\,{{1 \cdot x\,\,{\rm{jobs}}} \over {\,24\,\,{\rm{weeks}}\,}}\,\,\, \hfill \cr} \right\}\,\,\,\,2x\,\,{\rm{computers ,}}\,\,{\rm{1}}\,\,{\rm{job}}\,\,{\rm{,}}\,\,{\rm{6}}\,\,{\rm{days}}\,\,\,{\rm{;}}\,\,\,\,\,\,\,\,{\rm{?}}\,\,{\rm{ = }}\,\,x$$
$$6\,\,{\rm{days}}\,\,\,\left( {{{1\,\,{\rm{week}}} \over {7\,\,{\rm{days}}}}} \right)\,\,\,\left( {{{7x\,\,{\rm{jobs}}} \over {24\,\,{\rm{weeks}}}}} \right)\,\,\, = \,\,\,1\,\,\,{\rm{job}}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,{{{\rm{6}} \cdot {\rm{7}} \cdot x} \over {7 \cdot 24}} = 1\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = x = 4$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
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