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If x and y are integers and xy does not equal 0, is xy <
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09 Aug 2009, 05:02
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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
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Re: If x and y are integers and xy does not equal 0, is xy <
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09 Aug 2009, 05:12
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(x1), 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 <
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09 Aug 2009, 05:18
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 <
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09 Aug 2009, 06:39
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 <
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Updated on: 09 Aug 2009, 12:53
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(x1), 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.
Originally posted by Economist on 09 Aug 2009, 06:49.
Last edited by Economist on 09 Aug 2009, 12:53, edited 1 time in total.



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Re: If x and y are integers and xy does not equal 0, is xy <
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09 Aug 2009, 07:04
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(x1), 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 <
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10 Aug 2009, 01:32
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 <
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20 Aug 2009, 11:35
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(X1) 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 <
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21 Aug 2009, 17:50
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 <
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24 Aug 2009, 18:37
I got C too..Correct answer? 1.can solve to y = x^4  x^3 = x^3(x1)..so xy = x^4(x1)..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 <
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20 Nov 2011, 15:10
I) x^4x^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 <
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30 Nov 2011, 10:35
1) says y=X^4x^3 or y=x^3(x1) multiply both sides by x xy=x^4(x1) 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(x1) x^4 is def. +ve (x1) >=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 <
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24 Sep 2013, 06:19
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 <
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27 Aug 2014, 07:20
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 \(x^4(x1)<0?\)
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. \(x^4(x1)=0\) gives us x = 0 and x = 1.
Testing on our number line: for x<0 we see that \(xy = x^4(x1)\) 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 <
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08 Sep 2015, 08:52
Question Stem  Does X and Y are opposite signs ?
Statement 1  Y = (X^4  X^3)
X^3(X  1) = X cannot take the value 1 as Y not equal to zero.
Whether X is negative or positive Y will always be positive. X = 2 then Y = 8. If X = 2 then Y = 8. Therefore not suff...
Statement 2 X is positive Nothing on Y therefore Not Suff...
Combined Y is always positive and x is positive , therefore suff...



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Re: If x and y are integers and xy does not equal 0, is xy <
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15 Sep 2015, 03:36
here X and Y are integers. , xy doesn't equal to 0 . It means either of the integers is not 0. It is xy<0.
Two possibilities are there 1: x>0 and Y<0. 2; X<0 and Y>0.
Statement 1 y=X^4X^3. Minimum value of X we can take in positive integers is 2 and in negative integer is 1.
if we take X=1, then Y=0. it is not acceptable.
if X=2,X>0. Y=168=8.
take If X=1 then, Y=1(1)=1+1+2.
In both cases Y>0. we dont know x is +ve or ve.so not sufficient.
Statement 2 X is right to 0 on number line . it means X>0 is +ve . but we dont know value of y.
Both statements combine X>0 and Y>0. so XY>0
So option c is correct.



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Re: If x and y are integers and xy does not equal 0, is xy <
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28 May 2017, 02:44
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 1  y= x^3(x1) since question says x and y are integers and different from 0 you have 2 possible solution if x<0, y>0 so xy<0 if x>0 (or x>=1) , y>0 so xy>0 1 NOT SUFF 2 CLEARLY NOT SUFF 1&2 2 force the solution > x>0, y<0 and so xy < 0



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Re: If x and y are integers and xy does not equal 0, is xy <
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28 May 2017, 19:55
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 The goal is to determine if xy < 0 or if xy => 0. Statement 1) y = x^3(x1) Now test cases for x x = 1, y = 1(2) = 2, xy = 2 x = 2, y = 8(1) = 8, xy = 16. Not sufficient. Statement 2) Rephrased it states that x > 0 or x is positive. However, we do not know the value of y. Insufficient. Statements 1+2) Now we know that the cases in which x < 0 are invalid, so now y = x^3(x1), and x != 1, so this solution is always positive. Sufficient.



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Re: If x and y are integers and xy does not equal 0, is xy <
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27 Jul 2018, 07:29
Can someone help with a clearer solution with explanation?



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Re: If x and y are integers and xy does not equal 0, is xy <
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02 Oct 2018, 02:10
shivangis wrote: Can someone help with a clearer solution with explanation? We have to check xy < 0. Given xy != 0 and Integers. So x!= 0 and y!= 0 Cond1 : y = x^4 x^3One point to note is y != 0 Hence x != 1 As x!= 0 we can safely multiply x on both the sides. xy= x^5  x^3 = x^4( x  1 ) Now as X^4 is always positive we can focus on (x1) Thus sign of xy depends on sign of ( x  1 ) So if x<1 => xy < 1 and if x> 1 => xy > 1 Insufficient Cond2 : x in on the right side of the 0 i.e. x > 0 But nothing is said about y and hence xy can be less than or greater than 0 Insufficient On Mixing both of them: x > 0 ( Given by Cond2 ) and x > 1 ( Deduced by Cond1 ), we can say x > 1 ( always ) Hence xy = x^4 ( x 1 ) shall always be positive. Hence both of the conditions are sufficient to answer the question.




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