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Inequalities: Is {[(x^m)*z]/y^n} > 1 ?

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by tabsang » Sun Nov 18, 2012 11:43 am
If x,y and z are non-zero integers and m and n are positive even integers, where m > n.

Is ((x^m)*z)/(y^n) > 1 ?

(1) |z| > |x| > |y|
(2) x^m > (y^n)/z

I think the answer is E. Please validate.

Cheers,
Taz
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by jkaustubh » Sun Nov 18, 2012 5:42 pm
I think that the answer should be B

Target Question:((x^m)*z)/(y^n) > 1

Statement 1:

The first statement is clearly insufficient, as we have no idea about the values of m and n

Statement 2:

Statement 2 says that
x^m > (y^n)/z

now if we rearrange the terms of the above expression,
we get

((x^m)*z)/(y^n) > 1.

This is precisely what the target question is.

Hence, statement 2 is sufficient.

Hence the answer should be B


How did you get E as an answer? Expert advice is needed here.

Please help!
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by tabsang » Mon Nov 19, 2012 12:05 am
Yep, I too believe that expert advice is needed here.

See the problem with statement 2 is that you don't really know the nature of 'z'.
Since 'z' is a non-zero integer, you have to consider the possibility that 'z' can be negative.
In that case, ((x^m)*z)/y^n < 1.

Using both together too, you don't get a conclusive result.
You may either get a <1 or a >1 result depending on what positive value of 'z' you take.
(Positive coz from the second statement you get z>(y^n/x^m) and y^n/x^m is a positive fraction, therefore z is positive and the final result may be a proper(<1) or an improper(>1) fraction.

Expert advice please :( :(
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by sid128 » Mon Nov 19, 2012 12:08 am
jkaustubh wrote:I think that the answer should be B

Target Question:((x^m)*z)/(y^n) > 1

Statement 1:

The first statement is clearly insufficient, as we have no idea about the values of m and n

Statement 2:

Statement 2 says that
x^m > (y^n)/z

now if we rearrange the terms of the above expression,
we get

((x^m)*z)/(y^n) > 1.

This is precisely what the target question is.

Hence, statement 2 is sufficient.

Hence the answer should be B


How did you get E as an answer? Expert advice is needed here.

Please help!

We can't rephrase choice B as ((x^m)*z)/(y^n) > 1 as we are not sure about the value/sign of Z.
As a thumb rule, we should not cross multiply variables unless we don't know their sign/range

IMO E
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by jkaustubh » Mon Nov 19, 2012 5:26 am
sid128 wrote:
jkaustubh wrote:I think that the answer should be B

Target Question:((x^m)*z)/(y^n) > 1

Statement 1:

The first statement is clearly insufficient, as we have no idea about the values of m and n

Statement 2:

Statement 2 says that
x^m > (y^n)/z

now if we rearrange the terms of the above expression,
we get

((x^m)*z)/(y^n) > 1.

This is precisely what the target question is.

Hence, statement 2 is sufficient.

Hence the answer should be B


How did you get E as an answer? Expert advice is needed here.

Please help!

We can't rephrase choice B as ((x^m)*z)/(y^n) > 1 as we are not sure about the value/sign of Z.
As a thumb rule, we should not cross multiply variables unless we don't know their sign/range

IMO E



Point noted. Thank you
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by soni_pallavi » Fri Nov 23, 2012 1:23 am
sid128 wrote:
jkaustubh wrote:I think that the answer should be B

Target Question:((x^m)*z)/(y^n) > 1

Statement 1:

The first statement is clearly insufficient, as we have no idea about the values of m and n

Statement 2:

Statement 2 says that
x^m > (y^n)/z

now if we rearrange the terms of the above expression,
we get

((x^m)*z)/(y^n) > 1.

This is precisely what the target question is.

Hence, statement 2 is sufficient.

Hence the answer should be B


How did you get E as an answer? Expert advice is needed here.

Please help!

We can't rephrase choice B as ((x^m)*z)/(y^n) > 1 as we are not sure about the value/sign of Z.
As a thumb rule, we should not cross multiply variables unless we don't know their sign/range

IMO E
My take is that In this caseStatement 2 is telling us indirectly that y and z are positive integers hence by taking them to the other side the sign (>) remains the same.With this hint I think we can sufficiently say that ((x^m)*z)/(y^n) > 1; Hence B

But I agree some expert help is needed.
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by tabsang » Tue Dec 04, 2012 9:36 am
EXPERT help needed. Please help us decide.

Cheers,
Taz
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by The Iceman » Tue Dec 04, 2012 11:05 am
tabsang wrote:If x,y and z are non-zero integers and m and n are positive even integers, where m > n.

Is ((x^m)*z)/(y^n) > 1 ?

(1) |z| > |x| > |y|
(2) x^m > (y^n)/z
If we take statement I, we know that |x| > |y| => (x^m)>(y^n) [since m>n, where m and n are +ve integers of the form 2k]

Also, (x^m)>(y^n)=> (x^m)>(y^n)/ Z [since Z can be either +ve or -ve ]. This in turn is the same as statement II. This means that given statement I, statement II is redundant here.

It also means that if Z is +ve, (x^m)*Z >(y^n) or (x^m)*Z/(y^n)> 1
and if Z is -ve, (x^m)*Z <(y^n) or (x^m)*Z/(y^n)< 1

Clearly the answer option is E.

HTH!
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by GMATGuruNY » Wed Dec 05, 2012 6:48 am
tabsang wrote:If x,y and z are non-zero integers and m and n are positive even integers, where m > n.

Is ((x^m)*z)/(y^n) > 1 ?

(1) |z| > |x| > |y|
(2) x^m > (y^n)/z
Statement 2: x^m > (y^n)/z
Since z is nonzero, z² must be positive.
Thus, we can multiply each side by z² without having to worry about the direction of the inequality:
(x^m)z² > ((y^n)/z) * z²
(x^m)z² > (y^n)z
(x^m)z² - (y^n)z > 0
z * ((x^m)z - y^n) > 0.

The result above implies two cases.

Case 1:
If z>0, then (x^m)z - y^n) > 0, implying that (x^m)z > y^n and that ((x^m)*z)/(y^n) > 1.
The following combination satisfies the conditions in the question stem and those in the two statements:
x=2, m=4, z=10, y=1, and n=2.
When we plug these values into the question stem, we get:
(2�)(10) / 1² > 1.

Case 2:
If z<0, then (x^m)z - y^n < 0, implying that (x^m)z < y^n and that ((x^m)*z)/(y^n) < 1.
The following combination satisfies the conditions in the question stem and those in the two statements:
x=2, m=4, z=-10, y=1, and n=2.
When we plug these values into the question stem, we get:
(2�)(-10) / 1² < 1.

Since in the first case ((x^m)*z)/(y^n) > 1, and in the second case ((x^m)*z)/(y^n) < 1, the two statements combined are INSUFFICIENT.

The correct answer is E.
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