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4 Inequality DS Questions

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by knight247 » Tue Aug 23, 2011 4:36 am
1. If x,y,m and n are positive integers, where m>n, is x^m/y^n>1?
(1)x>y
(2)x^m>y^m

2.If x and y are positive integers, m and n are integers, where m>n, is x^m/y^n>1
(1)x>y
(2)x^m>y^m

3.If x and y are non zero integers and m and n are positive integers, where m>n is x^m/y^n>1?
(1)x>y
(2)x^m>y^m

4.If x,y and z are non zero integers, 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

Sorry but I don't have the OAs for any of them. Detailed explanations would be appreciated. Many Thanks.
Last edited by knight247 on Wed Aug 24, 2011 2:03 am, edited 3 times in total.
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Source: — Data Sufficiency |
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by GmatKiss » Tue Aug 23, 2011 5:10 am
1. If x,y,m and n are positive integers, where m>n, is x^m/y^n>1?
(1)x>y
(2)x^m>y^n

IMO:D
Last edited by GmatKiss on Tue Aug 23, 2011 5:41 am, edited 2 times in total.
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by GmatKiss » Tue Aug 23, 2011 5:13 am
2.If x and y are positive integers, m and n are integers, where m>n, is x^m/y^n>1
(1)x>y
(2)x^m>y^n

IMO:B
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by GmatKiss » Tue Aug 23, 2011 5:15 am
3.If x and y are non zero integers and m and n are positive integers, where m>n is x^m/y^n>1?
(1)x>y
(2)x^m>y^n

IMO:B
Last edited by GmatKiss on Tue Aug 23, 2011 5:41 am, edited 1 time in total.
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by GmatKiss » Tue Aug 23, 2011 5:17 am
4.If x,y and z are non zero integers, 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

IMO:D
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by HeintzC2 » Tue Aug 23, 2011 6:30 am
I disagree with GmatKiss on #3. IMO E

x & y are non zero integers, m & n are positive integers m>n

1.)x>y;
-choose x = -2, y = -3, also choose m = 2, n = 1. x^m/y^n = 4/-3, x^m/y^n < 1
-choose x = -2, y = -3, also choose m = 4, n = 2. x^m/y^n = 16/9, x^m/y^n > 1
insufficient.

2.)x^m>y^n
-choose x = -2, y = -3, also choose m = 2, n = 1. x^m = 4, y^n = -3, x^m/y^n < 1
-choose x = -2, y = -3, also choose m = 4, n = 2. x^m = 16, y^n = 9, x^m/y^n > 1
insufficient.

Combining these 2 statements yields no useful information (noted as we used the exact same data sets to show both statements are insufficient.)

Therefore, IMO E
GmatKiss wrote:3.If x and y are non zero integers and m and n are positive integers, where m>n is x^m/y^n>1?
(1)x>y
(2)x^m>y^n

IMO:B
[/quote]
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by AbhiJ » Wed Aug 24, 2011 1:18 am
Dude, whats the source looks like good questions.
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by n@resh » Thu Aug 25, 2011 7:32 pm
HeintzC2 wrote:I disagree with GmatKiss on #3. IMO E

x & y are non zero integers, m & n are positive integers m>n

1.)x>y;
-choose x = -2, y = -3, also choose m = 2, n = 1. x^m/y^n = 4/-3, x^m/y^n < 1
-choose x = -2, y = -3, also choose m = 4, n = 2. x^m/y^n = 16/9, x^m/y^n > 1
insufficient.

2.)x^m>y^n
-choose x = -2, y = -3, also choose m = 2, n = 1. x^m = 4, y^n = -3, x^m/y^n < 1
-choose x = -2, y = -3, also choose m = 4, n = 2. x^m = 16, y^n = 9, x^m/y^n > 1
insufficient.

Combining these 2 statements yields no useful information (noted as we used the exact same data sets to show both statements are insufficient.)

Therefore, IMO E
GmatKiss wrote:3.If x and y are non zero integers and m and n are positive integers, where m>n is x^m/y^n>1?
(1)x>y
(2)x^m>y^n

IMO:B
[/quote]
Actual Question is : 3.If x and y are non zero integers and m and n are positive integers, where m>n is x^m/y^n>1?
(1)x>y
(2)x^m>y^m

Ans is C!

By using the statement 1, we can conclude statement 2, X^m > y^m ...that's sufficient to ans.
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by Frankenstein » Thu Aug 25, 2011 7:56 pm
n@resh wrote: Actual Question is : 3.If x and y are non zero integers and m and n are positive integers, where m>n is x^m/y^n>1?
(1)x>y
(2)x^m>y^m

Ans is C!

By using the statement 1, we can conclude statement 2, X^m > y^m ...that's sufficient to ans.
Hi,
The question has been changed one day after HeintzC2 posted. Earlier, statement(2) was x^m>y^n.
Anyway, coming to the modified version of Q3, I don't think it is C.
From(1):
if x=2, y=1, m=2,n=1, x^m/y^n = 4>1
if x=2, y=-1, m=2,n=1, x^m/y^n = -4<1
Not sufficient

From(2):
Use the same set
Not sufficient

Both(1) and (2):
Same set
Not sufficient

Hence, E
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by Frankenstein » Thu Aug 25, 2011 8:01 pm
1. If x,y,m and n are positive integers, where m>n, is x^m/y^n>1?
(1)x>y
(2)x^m>y^m
From(1):
x>y
So, x^m > y^m
m>n. So, y^m >= y^n
So, x^m > y^n
Sufficient

From(2):
x^m > y^m
As m>n, y^m >= y^n.
So, x^m > y^n
Sufficient

Hence, D
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by Frankenstein » Thu Aug 25, 2011 8:14 pm
2.If x and y are positive integers, m and n are integers, where m>n, is x^m/y^n>1
(1)x>y
(2)x^m>y^m
From(1):
if x=2, y=1, m=2, n=1, x^m/y^n = 4>1
if x=2, y=1, m=-1 n=-2, x^m/y^n = 1/2<1
Not Sufficient

From(2):
x^m>y^m
As y>0, and m>n
y^m >= y^n
So, x^m > y^n
As y is positive, y^n is always positive.
So, multiplying by 1/y^n will not change sign.
So, x^m/y^n > 1
Sufficient

Hence, B
Last edited by Frankenstein on Thu Aug 25, 2011 8:29 pm, edited 1 time in total.
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by Frankenstein » Thu Aug 25, 2011 8:25 pm
4.If x,y and z are non zero integers, 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
From(1):
if x=2,y=1,z=4, m=4,n=2, x^m*z/y^n = 2^16>1
if x=2,y=1,z=-4, m=4,n=2, x^m*z/y^n = 2^-16<1
Not sufficient

From(2):
Same set
Not sufficient

Both (1)and (2):
Not sufficient

Hence, E

I hope I haven't made any silly mistakes in my posts. If I have made any, please let me know.
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