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# A computer can perform 30 identical tasks in six hours. At that rate,

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Math Expert
Joined: 02 Sep 2009
Posts: 55276
A computer can perform 30 identical tasks in six hours. At that rate,  [#permalink]

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06 Dec 2018, 04:44
1
4
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Difficulty:

15% (low)

Question Stats:

78% (01:30) correct 22% (02:14) wrong based on 56 sessions

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A computer can perform 30 identical tasks in six hours. At that rate, what is the minimum number of computers that should be assigned to complete 80 tasks within three hours?

A. 4
B. 5
C. 6
D. 7
E. 8

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A computer can perform 30 identical tasks in six hours. At that rate,  [#permalink]

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Updated on: 06 Dec 2018, 20:36
Bunuel wrote:
A computer can perform 30 identical tasks in six hours. At that rate, what is the minimum number of computers that should be assigned to complete 80 tasks within three hours?

A. 4
B. 5
C. 6
D. 7
E. 8

a computer can do per hour 5 tasks and in 3 hours 15 tasks
so 80 tasks ; 80tasks can be done by 80/15: ~6 comptuers IMO C
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Originally posted by Archit3110 on 06 Dec 2018, 05:41.
Last edited by Archit3110 on 06 Dec 2018, 20:36, edited 1 time in total.
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Joined: 05 Oct 2018
Posts: 11
Re: A computer can perform 30 identical tasks in six hours. At that rate,  [#permalink]

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06 Dec 2018, 12:04
So 5*3=15 tasks in 3 hours.

5*15=75 which isn't enough to complete 80 tasks
6*15=90 so you'll need 6 computers to complete the tasks in at least 3 hours.

C
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Re: A computer can perform 30 identical tasks in six hours. At that rate,  [#permalink]

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06 Dec 2018, 13:10
a computer can do per hour 5 tasks and in 3 hours 15 tasks

anything mire than 5, so 6 is the least

option C
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Posts: 935
Re: A computer can perform 30 identical tasks in six hours. At that rate,  [#permalink]

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06 Dec 2018, 18:59
Bunuel wrote:
A computer can perform 30 identical tasks in six hours. At that rate, what is the minimum number of computers that should be assigned to complete 80 tasks within three hours?

A. 4
B. 5
C. 6
D. 7
E. 8

Let´s use UNITS CONTROL, one of the most powerful tools of our method!

$$? = {\left( {N\,\,{\mathop{\rm int}} } \right)_{\min }}\,\,\,{\rm{for}}\,\,\,\,\,{{80\,\,{\rm{tasks}}} \over {3\,\,{\rm{hours}}}}$$

$$1\,\,{\rm{comp}}\,{\rm{,}}\,\,{\rm{3h}}\,\,\, \to \,\,\,15\,\,{\rm{tasks}}\,\,\,\,\,\left( {{{30\,\,{\rm{tasks}}} \over {6\,\,{\rm{hours}}}} = {{15\,\,{\rm{tasks}}} \over {3\,\,{\rm{hours}}}}} \right)$$

$$N\,\,{\rm{comp}}\,{\rm{,}}\,\,{\rm{3h}}\,\,\, \to \,\,\,N \cdot 15\,\,{\rm{tasks}}\,\,\, \ge \,\,\,80\,\,{\rm{tasks}}$$

$${\rm{N}}\,\, \ge \,\,{{80} \over {15}} = {{16} \over 3} = 5{1 \over 3}\,\,\,\,\, \Rightarrow \,\,\,\,? = 6$$

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

Regards,
Fabio.
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Re: A computer can perform 30 identical tasks in six hours. At that rate,  [#permalink]

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06 Dec 2018, 20:35
Archit3110 wrote:
Bunuel wrote:
A computer can perform 30 identical tasks in six hours. At that rate, what is the minimum number of computers that should be assigned to complete 80 tasks within three hours?

A. 4
B. 5
C. 6
D. 7
E. 8

a computer can do per hour 5 tasks and in 3 hours 15 tasks
so 80 tasks ; 80tasks can be done by 80/15: ~6comptuers required IMO C

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Re: A computer can perform 30 identical tasks in six hours. At that rate,  [#permalink]

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07 Dec 2018, 10:04
Hi there!

There are always many similar ideas/solutions to any given problem.

If a different wording or a more structured presentation helps other members get a better comprehension, I guess the contribution is valid.

Regards,
Fabio.
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Our high-level "quant" preparation starts here: https://gmath.net
Re: A computer can perform 30 identical tasks in six hours. At that rate,   [#permalink] 07 Dec 2018, 10:04
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