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If x and y are integers and xy does not equal 0, is xy <

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If x and y are integers and xy does not equal 0, is xy < [#permalink] New post 09 Aug 2009, 04:02
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If x and y are integers and xy does not equal 0, is xy < 0?

(1) y = x^4 – x^3

(2) x is to the right of 0 on the number line
[Reveal] Spoiler: OA
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Re: If x and y are integers and xy does not equal 0, is xy < [#permalink] New post 09 Aug 2009, 04:12
lbsgmat wrote:
If x and y are integers and xy does not equal 0, is xy < 0?

(1) y = x^4 – x^3
(2) x is to the right of 0 on the number line.


does xy have different signs

y = x^3(x-1), if x -ve then y is +ve , and if x is +ve we have 2 cases y can be either -ve or +ve (-ve if /x/<1)

from 2

x is +ve....insuff

both together

still insuff... E
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Re: If x and y are integers and xy does not equal 0, is xy < [#permalink] New post 09 Aug 2009, 04:18
lbsgmat wrote:
If x and y are integers and xy does not equal 0, is xy < 0?

(1) y = x^4 – x^3
(2) x is to the right of 0 on the number line.


my answer is C

St 1. x can be any number but -1 or 0 (according to the question stem). Any other interger +ve or -ve will produce a +ve y
however it is not sufficient since if x is +ve then xy>0, if x is -ve then xy<0 INSF

St. 2 tell us only about x sign, nothing about y

Statements combined yield only one answer: XY>0
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Re: If x and y are integers and xy does not equal 0, is xy < [#permalink] New post 09 Aug 2009, 05:39
my ans would be c too, pls post the ans
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Re: If x and y are integers and xy does not equal 0, is xy < [#permalink] New post 09 Aug 2009, 05:49
yezz wrote:
lbsgmat wrote:
If x and y are integers and xy does not equal 0, is xy < 0?

(1) y = x^4 – x^3
(2) x is to the right of 0 on the number line.


does xy have different signs

y = x^3(x-1), if x -ve then y is +ve , and if x is +ve we have 2 cases y can be either -ve or +ve (-ve if /x/<1)

from 2

x is +ve....insuff

both together

still insuff... E

Marked in Red, since x and y are integers we have to ignore the condition |x|<1. So C(edited) should be the answer as y will always be +ve for any integer x other than 0.

Last edited by Economist on 09 Aug 2009, 11:53, edited 1 time in total.
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Re: If x and y are integers and xy does not equal 0, is xy < [#permalink] New post 09 Aug 2009, 06:04
Economist wrote:
yezz wrote:
lbsgmat wrote:
If x and y are integers and xy does not equal 0, is xy < 0?

(1) y = x^4 – x^3
(2) x is to the right of 0 on the number line.


does xy have different signs

y = x^3(x-1), if x -ve then y is +ve , and if x is +ve we have 2 cases y can be either -ve or +ve (-ve if /x/<1)

from 2

x is +ve....insuff

both together

still insuff... E

Marked in Red, since x and y are integers we have to ignore the condition |x|<1. So A should be the answer as y will always be +ve for any integer x other than 0.


another silly mistake , thanks Econ....C it is
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Re: If x and y are integers and xy does not equal 0, is xy < [#permalink] New post 10 Aug 2009, 00:32
C it is...

On combining both the stmts you get an answer to the question asked i.e. xy>0....
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Re: If x and y are integers and xy does not equal 0, is xy < [#permalink] New post 20 Aug 2009, 10:35
If x and y are integers and xy does not equal 0, is xy < 0?

(1) y = x^4 – x^3
(2) x is to the right of 0 on the number line.


We know xy not equals 0 , it can be +ve or -ve. Possible scenarios are X(+,+,-,-) , Y (+,-,-,+)

Now from Stmt 1 y = X^3(X-1) if X is +ve, then the question is X>1. If yes then Y will be +ve , if not then 0<x<1 then Y will be - ve . No information regarding value of x is given .

If X is -ve, then Y will be + ve irrespective of value of X . So there are two cases with this statement so statement is no sufficient.


From statement X is to right of 0 , and from question statement xy not equals 0 that means neither x nor y is zero.

Combining these two statement means X is positive and is greater than 1 , so xy will be positive

Answer should be C
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Re: If x and y are integers and xy does not equal 0, is xy < [#permalink] New post 21 Aug 2009, 16:50
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C fo shiz.

I almost got tripped up in my own trickyness here - need to note that X and Y are integers, therefore 0 < x <1 is not possible. Once you have eliminated this condition, the two statements are sufficient.

These are key things to look out for:

If X and Y are integers
If X and Y are positive integers
If X and Y and different integers

My big tip here is to pay attention to the question and go back and double check the parameters for X and Y.
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Re: If x and y are integers and xy does not equal 0, is xy < [#permalink] New post 24 Aug 2009, 17:37
I got C too..Correct answer?
1.can solve to y = x^4 - x^3 = x^3(x-1)..so xy = x^4(x-1)..whether xy is +ve or -ve depends on value of x,as x^ 4 will always be +ve
2.x is +ve,dont know anything about y

combining xy is > 0
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Re: If x and y are integers and xy does not equal 0, is xy < [#permalink] New post 19 Nov 2011, 11:21
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If x and y are integers and xy does not equal 0, is xy < 0?

(1) y = x^4 – x^3

(2) x is to the right of 0 on the number line
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Last edited by Bunuel on 24 Sep 2013, 05:30, edited 1 time in total.
Renamed the topic and edited the question.
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Re: If x and y are integers and xy does not equal 0, is xy < [#permalink] New post 20 Nov 2011, 14:10
I) x^4-x^3 is always greater than or equal to 0. But in both cases xy must be equal to 0. So this case is impossible. That means y is always greater than 0. INSUFF.
2) if x is at right of 0 that means x is greater than 0.INSUFF.
Both together, x>0 and y>0 xy>0. C
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Re: If x and y are integers and xy does not equal 0, is xy < [#permalink] New post 30 Nov 2011, 09:35
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1) says y=X^4-x^3
or
y=x^3(x-1)
multiply both sides by x
xy=x^4(x-1)
since we do not know anything about x it can be positive or negative. x^4 is always +ve. hence insufficient
2) Says X is >=1 does not say anything about y. Hence insufficient

Both together,
xy=x^4(x-1)
x^4 is def. +ve
(x-1) >=0 if x>=1

hence xy>=0 hence it CANNOT be < 0

Hence C.
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Re: If x and y are integers and xy does not equal 0, is xy < [#permalink] New post 24 Sep 2013, 05:19
In statement one you forgot to put the "^" sign!!!
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Re: If x and y are integers and xy does not equal 0, is xy < [#permalink] New post 27 Aug 2014, 06:20
Quote:
I think the OA is incorrect here.

1) y = x^4 - x^3. Thus, we know that xy = x(x^4 - x^3) = x^5 - x^4 = x^4(x - 1). Our question is then, is x^4(x-1)<0?

Since we have no idea about x this is clearly insufficient.

2) If y is positive, then NO, but if y is negative then YES. Insufficient.

Taking the two statements together. We need to find out if x^4(x - 1)<0.

To find where this function changes signs, we set it equal to zero and then test values between our critical points. x^4(x-1)=0 gives us x = 0 and x = 1.

Testing on our number line: for x<0 we see that xy = x^4(x-1) is negative; for 0<x<1, we see that xy is STILL negative; for x>1 we see that xy IS POSITIVE.

Therefore, simply knowing that x is positive does not provide us with enough information. We still need to know whether x>1 or x<1.

Answer: E


Edit: Just saw that x and y are integers! Very sneaky! I'm leaving this post because I think it's valuable to see this thought process anyway.
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Re: If x and y are integers and xy does not equal 0, is xy < [#permalink] New post 18 Sep 2014, 09:09
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Re: If x and y are integers and xy does not equal 0, is xy <   [#permalink] 18 Sep 2014, 09:09
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