A certain research group plans to create computer models of

Question

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

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

Bunuel · Accepted Answer

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.

dngboy89nh · Answer

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"   and "reduce by"  
So, the number of bacterial species after reducing: 100x*(105 - x)/100 = (x)*(105 - x)
Ans is B.

DelSingh · Answer

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

ROFLZZZ · Answer

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 =/

tchang · Answer

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 B

t1000

ashish8 · Answer

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  B  yields 2750.

jlgdr · Answer

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 Cheers J

GGMAT760 · Answer

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

Thanks in advance

PareshGmat · Answer

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)

TooLong150 · Answer

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.

sunaimshadmani · Answer

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

Bunuel · Answer

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

buddyisraelgmat · Answer

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

Bunuel · Answer

Yes, that's correct.

Lucky2783 · Answer

10000 X% (100 - (X-5) )% 
 X(105 - X )

mvictor · Answer

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

B is the answer.

targetbusiness · Answer

Does (B) not comes to 50*55 if X=50?

exc4libur · Answer

before: x%10000
after: reduce the original by (x-5)% or multiply original by (1-(x-5)%)

(x/100)(10000)•(1-(x-5)/100)=(x)(100-x+5)=x(105-x)

Ans (B)

Kinshook · Answer

x% of 10,000 = 100x

Balance selection = 100 - (x-5) = (105-x)%

Species of bacteria to model = 100x * (105-x)/100 = x (105-x)

IMO B

A certain research group plans to create computer models of

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A certain research group plans to create computer models of

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