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A certain research group plans to create computer models of [#permalink]

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09 Sep 2013, 10:59

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A certain research group plans to create computer models of x% of a list of 10,000 bacterial species known to inhabit the human body. After a budget cut, the group finds it must reduce this selection by (x − 5)%. In terms of x, how many species of bacteria will the group be able to model?

A. x*x – 5x B. (x)(105 – x) C. (100)(105 – x) D. (100)(95 – x) E. (x-5)/100

Re: A certain research group plans to create computer models of [#permalink]

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09 Sep 2013, 13:35

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suyash23n wrote:

A certain research group plans to create computer models of x% of a list of 10,000 bacterial species known to inhabit the human body. After a budget cut, the group finds it must reduce this selection by (x − 5)%. In terms of x, how many species of bacteria will the group be able to model?

a) x*x – 5x b) (x)(105 – x) c) (100)(105 – x) d) (100)(95 – x) e) (x-5)/100

Initial: (x/100)*10000 = 100x (bacterial species) After reduce BY (x - 5)%, the percentage of bacterial species = 1 - (x - 5)% = 1 - (x - 5)/100 = (105 - x)/100 Note: Difference between "reduce to" [means: the remain] and "reduce by" [means: the remain = 1 - "reduce by"] So, the number of bacterial species after reducing: 100x*(105 - x)/100 = (x)*(105 - x) Ans is B.

Re: A certain research group plans to create computer models of [#permalink]

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09 Sep 2013, 17:20

suyash23n wrote:

A certain research group plans to create computer models of x% of a list of 10,000 bacterial species known to inhabit the human body. After a budget cut, the group finds it must reduce this selection by (x − 5)%. In terms of x, how many species of bacteria will the group be able to model?

a) x*x – 5x b) (x)(105 – x) c) (100)(105 – x) d) (100)(95 – x) e) (x-5)/100

I believe the OA may be wrong. I got:

x% of 10000 is: \(\frac{x}{100}(10,000) = 100x\)

The reduced percentage can be stated as follows: \((1 - \frac{x-5}{100})\) \(=\) \((\frac{105-x}{100})\)

Multiplying the selection by the reduced percentage: \(100x\) \((\frac{105-x}{100})\) \(=\) \(x(105-x)\)

B
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Re: A certain research group plans to create computer models of [#permalink]

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09 Sep 2013, 18:38

I think OA is wrong too, but i got D.

out of 10,000 samples, 10,000(x-5)% will be studied. If x was originally 50%, that means 5,000 would have been studied. now at 50%-5%, 4,500 will be studied.

A certain research group plans to create computer models of x% of a list of 10,000 bacterial species known to inhabit the human body. After a budget cut, the group finds it must reduce this selection by (x − 5)%. In terms of x, how many species of bacteria will the group be able to model?

a) x*x – 5x b) (x)(105 – x) c) (100)(105 – x) d) (100)(95 – x) e) (x-5)/100

The number of species that the group plans to model = \(10,000*\frac{x}{100} = 100x\).

After a budget cut, the group finds it must reduce this selection by (x − 5)%, thus the group will be able to model \(100x*(1-\frac{x-5}{100})=x(105-x)\).

Re: A certain research group plans to create computer models of [#permalink]

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10 Jan 2014, 07:14

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suyash23n wrote:

A certain research group plans to create computer models of x% of a list of 10,000 bacterial species known to inhabit the human body. After a budget cut, the group finds it must reduce this selection by (x − 5)%. In terms of x, how many species of bacteria will the group be able to model?

a) x*x – 5x b) (x)(105 – x) c) (100)(105 – x) d) (100)(95 – x) e) (x-5)/100

Use smart numbers.

OK lets say x = 50

So then 50% of 10,000 = 5000 Now after budget cut = 5000*45/100 = (50)(45)

A certain research group plans to create computer models of x% of a list of 10,000 bacterial species known to inhabit the human body. After a budget cut, the group finds it must reduce this selection by (x − 5)%. In terms of x, how many species of bacteria will the group be able to model?

A. \(\frac{x-5}{100}\) B. x^2 – 5x C. (x)(105 – x) D. (100)(105 – x) E. (100)(95 – x)

Merging topics.

Please refer to the discussion above.
_________________

Re: A certain research group plans to create computer models of [#permalink]

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22 Jul 2014, 13:13

Bunuel wrote:

suyash23n wrote:

A certain research group plans to create computer models of x% of a list of 10,000 bacterial species known to inhabit the human body. After a budget cut, the group finds it must reduce this selection by (x − 5)%. In terms of x, how many species of bacteria will the group be able to model?

a) x*x – 5x b) (x)(105 – x) c) (100)(105 – x) d) (100)(95 – x) e) (x-5)/100

The number of species that the group plans to model = \(10,000*\frac{x}{100} = 100x\).

After a budget cut, the group finds it must reduce this selection by (x − 5)%, thus the group will be able to model \(100x*(1-\frac{x-5}{100})=x(105-x)\).

Answer: B.

Hope it's clear.

Hi why you wrote 1- (x-5)% in the last step? could not understand the step.

Re: A certain research group plans to create computer models of [#permalink]

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22 Jul 2014, 23:57

GGMAT760 wrote:

Bunuel wrote:

suyash23n wrote:

A certain research group plans to create computer models of x% of a list of 10,000 bacterial species known to inhabit the human body. After a budget cut, the group finds it must reduce this selection by (x − 5)%. In terms of x, how many species of bacteria will the group be able to model?

a) x*x – 5x b) (x)(105 – x) c) (100)(105 – x) d) (100)(95 – x) e) (x-5)/100

The number of species that the group plans to model = \(10,000*\frac{x}{100} = 100x\).

After a budget cut, the group finds it must reduce this selection by (x − 5)%, thus the group will be able to model \(100x*(1-\frac{x-5}{100})=x(105-x)\).

Answer: B.

Hope it's clear.

Hi why you wrote 1- (x-5)% in the last step? could not understand the step.

Thanks in advance

Actually its a reduction of (x-5)%; so written in that way

A certain research group plans to create computer models of [#permalink]

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10 Aug 2014, 19:22

Based on the answer choices and the question, this question begs the use of x=5 as a sample number. Initial = 5%*10000 = 500 Reduction = 5-5=0%, so no math required here to calculate the reduction; just make sure that you can calculate 500 in your answer.

A. x*x – 5x = 0; No B. (x)(105 – x) = 500; Winner! C. (100)(105 – x) > 500; No D. (100)(95 – x) > 500; No E. (x-5)/100 = 0; No

B

I was a strong believer in using algebra for percent problems, but after missing 95% of them because of some careless error, I was converted to the sample number method. Generally speaking, picking smart numbers for percent problems will get you the correct answer more quickly and with the least errors.

Re: A certain research group plans to create computer models of [#permalink]

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20 Mar 2015, 23:19

suyash23n wrote:

A certain research group plans to create computer models of x% of a list of 10,000 bacterial species known to inhabit the human body. After a budget cut, the group finds it must reduce this selection by (x − 5)%. In terms of x, how many species of bacteria will the group be able to model?

A. x*x – 5x B. (x)(105 – x) C. (100)(105 – x) D. (100)(95 – x) E. (x-5)/100

Re: A certain research group plans to create computer models of [#permalink]

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26 Apr 2016, 04:23

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Re: A certain research group plans to create computer models of [#permalink]

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21 Nov 2016, 09:33

suyash23n wrote:

A certain research group plans to create computer models of x% of a list of 10,000 bacterial species known to inhabit the human body. After a budget cut, the group finds it must reduce this selection by (x − 5)%. In terms of x, how many species of bacteria will the group be able to model?

A. x*x – 5x B. (x)(105 – x) C. (100)(105 – x) D. (100)(95 – x) E. (x-5)/100

oh...I see where I made the mistake... i chose A...what a trap...

first chose: x/100 * 10,000 = 100x out of these, they need to reduce by (x-5)%

100x * [(1 - (x-5/100)] = 100x - x^2 +5x = 105x - x^2 -> factor out an x -> x(105-x)