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A certain research group plans to create computer models of

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

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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
[Reveal] Spoiler: OA

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Last edited by suyash23n on 09 Sep 2013, 22:34, edited 3 times in total.

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

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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.

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

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New post 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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New post 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.

Plug in 50% for all the answers, and D=4,500.

I may be reading the questions wrong, though =/

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

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New post 09 Sep 2013, 20:35
Let's say that x = 10

So 10% of 10,000 = 1,000 types of bacteria

After the budget cuts, this 1,000 is reduced by (10-5)% = 5%

5% of 1,000 = 50

1,000 - 50 = 950

Plug x=10 into the answers and find 950.

Answer
[Reveal] Spoiler:
B


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

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New post 09 Sep 2013, 21:33
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[Reveal] Spoiler:
B


Non algebra approach:

X = 50

Before budget cost the sample contains \(10000 * .50 = 5000\) bacteria

Budget cut will reduce sample by \((50-5)% = 45%\)

\(45% of 5000 = 2250\)

\(5000-2250 = 2750\)

-----------------------------------
After plugging in 50 into the answer choices only
[Reveal] Spoiler:
B
yields 2750.

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

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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


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

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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)

Let's see answer choices, x = 50, target (50)(45)

B does it

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

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


Merging topics.

Please refer to the discussion above.
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Re: A certain research group plans to create computer models of [#permalink]

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New post 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.

Thanks in advance

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

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New post 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

x% = 100x

\((x-5)% of 100x = 100x * \frac{(x-5)}{100}\)

\(Reduction = 100x - 100x * \frac{(x-5)}{100}\)

\(= 100x * (1 - \frac{x-5}{100})\)

= x (105-x)
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A certain research group plans to create computer models of [#permalink]

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New post 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.

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

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New post 28 Sep 2014, 06:53
Bunuel can you plz explain why is it 1-(x-5)/100 and not simply just x-5/100. Thanks

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

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New post 28 Sep 2014, 23:54
Thanks, got your point :)

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sunaimshadmani wrote:
Bunuel can you plz explain why is it 1-(x-5)/100 and not simply just x-5/100. Thanks


Let me ask you: if x reduced by 10%, what we get 0.1x or x - 0.1x = 0.9x ?



Just to get some TRICKY basics clear

1) If 500 is reduced TO 10% ; we get 50
2) If 500 is reduced BY 10% ; we get 500 - 10% of 500 = 450

3) Similarly, x% less / more than y = y - / + x% of y


Correct?

Thanks

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buddyisraelgmat wrote:
Bunuel wrote:
sunaimshadmani wrote:
Bunuel can you plz explain why is it 1-(x-5)/100 and not simply just x-5/100. Thanks


Let me ask you: if x reduced by 10%, what we get 0.1x or x - 0.1x = 0.9x ?



Just to get some TRICKY basics clear

1) If 500 is reduced TO 10% ; we get 50
2) If 500 is reduced BY 10% ; we get 500 - 10% of 500 = 450

3) Similarly, x% less / more than y = y - / + x% of y


Correct?

Thanks


Yes, that's correct.
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Re: A certain research group plans to create computer models of [#permalink]

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New post 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



\(10000 X% (100 - (X-5) )%\)
\(X(105 - X )\)
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Re: A certain research group plans to create computer models of [#permalink]

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New post 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)

B is the answer.

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Re: A certain research group plans to create computer models of   [#permalink] 21 Nov 2016, 09:33

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