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The question asks: is \(\frac{x}{100}*y \gt \frac{y}{100}*z\)? Since \(y\) is a positive integer we can safely reduce by \(\frac{y}{100}\) and the question becomes: is \(x \gt z\)? Notice that the answer to the question does not depend on the value of \(y\).

(1) \(x=z\). Answer to the question is NO. Sufficient.

(2) \(z-y=y-x\). Rearrange: \(x+z=2y\). Clearly insufficient to say whether \(x \gt z\).

z - y = y - x is the same as x + z = 2y. How does this imply that z > x?

Thanks for your response!!

I could be missing something fundamental, but when I see "z" as any positive number(e.g.8) and subtract "y" any other positive number (e.g. 6) --> "8-6 = 2"

Now, in order to obtain 2 on the RHS(y-x), I have y, which is "6" (as assumed previously) - (x) some positive number (6-x). Now that number,x, is "4" in this case, and therefore less than 8, which is z.

I know when you simplify the equation to x+z=2y , it doesn't result into anything concrete, but if we keep the equation in as-is form, it implies z>x.

As I mentioned earlier, I could be missing something fundamental, therefore apologies in advance if my question is too pedantic. Thanks a lot! D

z - y = y - x is the same as x + z = 2y. How does this imply that z > x?

Thanks for your response!!

I could be missing something fundamental, but when I see "z" as any positive number(e.g.8) and subtract "y" any other positive number (e.g. 6) --> "8-6 = 2"

Now, in order to obtain 2 on the RHS(y-x), I have y, which is "6" (as assumed previously) - (x) some positive number (6-x). Now that number,x, is "4" in this case, and therefore less than 8, which is z.

I know when you simplify the equation to x+z=2y , it doesn't result into anything concrete, but if we keep the equation in as-is form, it implies z>x.

As I mentioned earlier, I could be missing something fundamental, therefore apologies in advance if my question is too pedantic. Thanks a lot! D

hi, you are wrongly assuming that z>y... what if z = 6 and y=8... z-y=6-8=-2.. therefore y-x==-2.... 8-x=-2.. so x=10.. which is greater than z...
_________________

For this question best is to use some smart numbers i think

for statement 1 let x= 5 y = 100 z= x = 5 --> since given

so lets check : is 5% of 100 > 100% of 5 - - no they are equal. - this will hold true for any positive number for x and y and z

so sufficient

Statement 2: first simplify - the given z-x=y-x becomes x+z =2y Again smart numbers - choose numbers that satisfy the above condition Let y =5. -- so x and z should be 2 numbers that add up to 2y here it is 10

so for example x can be 7 and z can be 3

lets check. is 7% of 5 > 5% of 3? --> yes.. greater percent of a bigger number > smaller percent of a smaller number

So lets see if we can get an opposite ans what if x = 3 and z = 7 ( they still add up to 10 which is 2y) now is 3%of 5 > 5% of 7? ---No it is not...

I can give you a couple of examples. M14-28 and M22-20. They are very almost identical. Also, D01-45 has a twin brother somewhere. I had already solved that earlier, and saw it again yesterday in one of my Quizzes.

I can give you a couple of examples. M14-28 and M22-20. They are very almost identical. Also, D01-45 has a twin brother somewhere. I had already solved that earlier, and saw it again yesterday in one of my Quizzes.