A certain research group plans to create computer models of

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

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 =/

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

t1000

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 yields 2750.

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

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)

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.

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.

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

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.

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

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)

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