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Math Expert V
Joined: 02 Sep 2009
Posts: 57191
M11-33  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 64% (01:26) correct 36% (01:54) wrong based on 105 sessions

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If $$x$$, $$y$$, and $$z$$ are positive integers, is $$x\%$$ of $$y$$ greater than $$y\%$$ of $$z$$?

(1) $$x = z$$

(2) $$z - y = y - x$$

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Math Expert V
Joined: 02 Sep 2009
Posts: 57191
Re M11-33  [#permalink]

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2
Official Solution:

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 $$x \gt z$$.

Answer: A
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Re: M11-33  [#permalink]

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Hi Bunel,

I might have gone bonkers over here. Can you explain why B is not correct? As all the numbers are positive, z-y = y -x will certainly give z>x.

Thanks
D
Math Expert V
Joined: 02 Sep 2009
Posts: 57191
Re: M11-33  [#permalink]

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Ronin30 wrote:
Hi Bunel,

I might have gone bonkers over here. Can you explain why B is not correct? As all the numbers are positive, z-y = y -x will certainly give z>x.

Thanks
D

z - y = y - x is the same as x + z = 2y. How does this imply that z > x?
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Re: M11-33  [#permalink]

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Quote:
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
Math Expert V
Joined: 02 Aug 2009
Posts: 7755
Re: M11-33  [#permalink]

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Ronin30 wrote:
Quote:
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...
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Re: M11-33  [#permalink]

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Makes complete sense.. As i thought, fundamental is amiss... Thanks a lot!!
D
Intern  Joined: 24 Jun 2012
Posts: 10
Re: M11-33  [#permalink]

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1
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...

So this statement is not suff

So
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Re: M11-33  [#permalink]

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1
How is this question any different from M24-21 ? I had noticed this earlier as well - a lot of questions are just simple repeats.
Math Expert V
Joined: 02 Sep 2009
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Re: M11-33  [#permalink]

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FacelessMan wrote:
How is this question any different from M24-21 ? I had noticed this earlier as well - a lot of questions are just simple repeats.

Thank you for the feedback. We removed M24-21 from the tests. Can you please tell me which other questions are also duplicates?
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Re: M11-33  [#permalink]

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1
Bunuel,

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.
Math Expert V
Joined: 02 Sep 2009
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Re: M11-33  [#permalink]

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FacelessMan wrote:
Bunuel,

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.

Thank you.
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Re: M11-33  [#permalink]

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Bunuel, Please help.

second statemnt y-x=z-y

From this doesnt it form that no.s x, y and z are in Aritmetic progression.
Thus, x%of y is always coming less from y%of x.

I am unable to think of any combination where it is going to fail.
Intern  B
Joined: 04 Jun 2017
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GMAT 1: 700 Q47 V39 GPA: 4
Re: M11-33  [#permalink]

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S1 - Given x = z. Lets assume x=10 y =100 and z =10
this will given me x% of y = y% of z.
Can you please explain where i am going wrong here?
Manager  S
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Re: M11-33  [#permalink]

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gbshrey wrote:
S1 - Given x = z. Lets assume x=10 y =100 and z =10
this will given me x% of y = y% of z.
Can you please explain where i am going wrong here?

Your question doesn't make sense. What you wrote is exactly what the question is asking so where is the confusion?
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Re: M11-33  [#permalink]

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Hi chetan2u
Facing problem with B
Stem Is y(x-z)>0

From B 2y=x+z. Substituting in stem---> (x+z)(x-z)>0 x+z is positive... x-z must be positive :O
Not able to figure out my mistake
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Intern  B
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M11-33  [#permalink]

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Bunuel
The second option boils down to x+z = 2y
We know that both x and z are positive integers.
So we can assume the only values x and z can take is y?
y+y =2y
Math Expert V
Joined: 02 Sep 2009
Posts: 57191
Re: M11-33  [#permalink]

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poojap wrote:
Bunuel
The second option boils down to x+z = 2y
We know that both x and z are positive integers.
So we can assume the only values x and z can take is y?
y+y =2y

Why? 1 + 3 = 2*2, 5 + 1 = 2*3...
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Re: M11-33  [#permalink]

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ShankSouljaBoi wrote:
Hi chetan2u
Facing problem with B
Stem Is y(x-z)>0

From B 2y=x+z. Substituting in stem---> (x+z)(x-z)>0 x+z is positive... x-z must be positive :O
Not able to figure out my mistake

Bunuel

same concern here. What's wrong with this ? Re: M11-33   [#permalink] 02 Aug 2019, 10:20
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