x percent of y percent of z is decreased by y percent. What is the res

\(\frac{x}{100}*\frac{y}{100}*z(1-\frac{y}{100})\)

Sorry. I'm stuck because for me the right translation is

x/100 * y/100 * z = (1- y/100) or not ??

I'd resolve this question by math because is pretty straighforward than the strategy of target.

anyone can help me ??

Thanks a lot

It can be done by plug-in method though as you are doing with algebra I'll proceed with it.

x percent of y percent of z is decreased by y percent. What is the result?

Step by step:
1. \(y\) percent of \(z\) is \(\frac{y}{100}*z=\frac{yz}{100}\);
2. \(x\) percent of above value is \(\frac{x}{100}*\frac{yz}{100}=\frac{xyz}{10,000}\);
3. The above value is decreased by \(y\) percent: \(\frac{xyz}{10,000}*(1-\frac{y}{100})=\frac{xyz}{10,000}*(\frac{100-y}{100})=\frac{100xyz-xy^2z}{1,000,000}\) (for example 100 is decreased by 10 percent can be expressed as \(100*(1-\frac{10}{100})=100*(1-0.1)=100*0.9=90\)).

Answer: A.

Hope it's clear.

For the % decrease formula we have: Original (1 - %decrease/100)= new

So: xyz/100 * (1 - y/100)..............I do not know why my head told me equals % decrease.......

generally is pretty simple for me this kind of problem.

Thanks Bunel

I see the process you went through but I'm still not sure I understand it. How do you know to multiply (1-y/100) instead of subtracting it? The word decrease makes me automatically think it has to be subtracted.

In this types of problems, are you only going to add/subtract if it says greater than or less than?

The question does not say "decreased by y", it says "decreased y PERCENT".

x percent of y percent of z is decreased by y percent

Making the statement more mathematical friendly

x% of y% of z is decreased by y%

x% of (y% of z) is decreased by y%

\((x% of \frac{yz}{100})\) is decreased by y%

\(\frac{xyz}{100 * 100}\) is decreased by y%

\(\frac{xyz}{100*100} - \frac{xy^2z}{100*100*100}\)

\(\frac{100xyz - xy^2z}{100*100*100}\)

Answer = A


Small Tip:

Number of times you see the % sign (2 zero's), those number of zero's in the denominator

\(a%b = \frac{ab}{10^2}\)

\(a%b%c = \frac{abc}{10000}\)

\(a%b%c%d = \frac{abcd}{10^6}\)

\(a%b%c%d......... n = \frac{abcd......n}{10^{(n-1)}}\)

The OA of this question is very distinct. All the options are levelled with the denominator, so no further simplification required on the OA.

Once you know the trick as stated in earlier post, its quite obvious that answer = A (it has 10^6 in the denominator)

No calculation required!!

really a tough one. m stuck in it what is the result?? can you show it?

Hi All,

This question can certainly be solved by TESTing VALUES. The 'shortcuts' involve selecting nice 'round' numbers for the 3 variables AND recognizing that the 5 answer choices have 'pieces' in common (so you can avoid redoing some of the calculations).

We're told that X percent of Y percent of Z is DECREASED by Y percent. We're asked for the result of all of this math.

IF....
X = 10
Y = 50
Z = 100

First, 50% of 100 = 50
Next, 10% of 50 = 5
Finally, 5 decreased by 50% of itself is 2.5

So we're looking for an answer that equals 2.5 when X=10, Y=50 and Z=100.

Answer A. (100xyz - xy^2z) / 1,000,000 = (5,000,000 - 2,500,000)/1,000,000 = 2,500,000/1,000,000 = 2.5 This is a MATCH
Answer B. (xz - y) / 100 = (1,000 - 50)/100 = 950/100 = 9.5 NOT a match
Answer C. (xz - y) / 10,000 = 950/10,000 = .095 NOT a match
Answer D. (xyz - 2y) / 100 = (50,000 - 100)/100 = 49,900/100 = 499 NOT a match
Answer E. (xyz - 2y) / 10,000 = 49,900/10,000 = 4.99 NOT a match

Final Answer:

GMAT assassins aren't born, they're made,
Rich

x percent of y = x*y/100

Now, x percent of y percent of z = x*y*z/(100*100)

Since z is decreased by y percent,

The result = (1-y/100)*x*y*z/(100*100) = (100x*y*z - x*y^2*z)/100^3

Thus, the correct option is A.