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x,y,z are positive

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x,y,z are positive

by uptowngirl92 » Sat Jul 18, 2009 2:51 am
If x,y,z are positive and y%of x is greater than 100,is x%of z less than 10?
1. z% of y is 10
2. z is less than 10% of y

[spoiler=]Ans:C[/spoiler]
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by tohellandback » Sat Jul 18, 2009 6:20 am
IMO C

uestion stem: y%of x is greater than 100
xy/100 > 100
xy>10000

1) z% of y is 10
yz=1000------> z=1000/y
we are asked "x%of z less than 10"
i.e is xz/100<10 or is xz<1000 or is x<1000/z or is x<y

we know xy>10000, but we can't find x>y or not

INSUFF

2)z<y/10
and we know
xy>10000 INSUFF to find relation between x and y

combining, our equations are
xy>10000
z<y/10 or y>10z
yz=1000 use this to find min value of y
put y=10z
10z*z=1000 or z=10, so min y>100
now in xy>10000 y>100 so x<100

Both sufficient together
uptowngirl, can you tell us where do you find these questions. These are really good
The powers of two are bloody impolite!!
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Re: x,y,z are positive

by gmat740 » Sat Jul 18, 2009 7:24 am
Talking in very Basic Terms

Given, xy>10,000

to find : xz<1000
1. z% of y is 10
yz =1000
thus, y =1000/z

from given eqn : x*(1000/z) > 10,000
x/z>10...........(1')

cant go anywhere with this
2. z is less than 10% of y
z<y/10
so, y>10z
Insuff.

Combine
From (2)
y>10z
multiply both sides by z
yz> 10* z^2

and from (1) yz = 1000

so, 1000> 10*z^2
z^2<100..........(2')

Now From (1'), we had simplified a ratio : x/z > 10
so multiply this inequation with Max of (2')
xz<1000

So C

This is a good Question.
since x,y,z are positive the signs of the inequation will not change. However, if nothing was given about x,y,z, this question would have been way too tough to crack.:D
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