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Re: If x and y are integers and xy does not equal 0, is xy < [#permalink]
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
Re: If x and y are integers and xy does not equal 0, is xy < [#permalink]
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.
Re: If x and y are integers and xy does not equal 0, is xy < [#permalink]
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.
Re: If x and y are integers and xy does not equal 0, is xy < [#permalink]
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
Re: If x and y are integers and xy does not equal 0, is xy < [#permalink]
21 Aug 2009, 16:50
1
This post received KUDOS
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.
Re: If x and y are integers and xy does not equal 0, is xy < [#permalink]
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
Re: If x and y are integers and xy does not equal 0, is xy < [#permalink]
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
Re: If x and y are integers and xy does not equal 0, is xy < [#permalink]
30 Nov 2011, 09:35
1
This post received KUDOS
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
Re: If x and y are integers and xy does not equal 0, is xy < [#permalink]
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.
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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