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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]

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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
[Reveal] Spoiler: OA
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Re: If x and y are integers and xy does not equal 0, is xy < [#permalink]

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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(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]

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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.

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

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]

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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 < [#permalink]

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09 Aug 2009, 06:49
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, 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 < [#permalink]

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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(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]

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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 < [#permalink]

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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(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

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Re: If x and y are integers and xy does not equal 0, is xy < [#permalink]

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21 Aug 2009, 17:50
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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]

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24 Aug 2009, 18:37
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]

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19 Nov 2011, 12:21
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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, 06:30, 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]

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20 Nov 2011, 15:10
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]

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30 Nov 2011, 10:35
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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]

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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 < [#permalink]

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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 $$x^4(x-1)<0?$$

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.

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]

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18 Sep 2014, 10:09
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Re: If x and y are integers and xy does not equal 0, is xy < [#permalink]

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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 < [#permalink]

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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^4-X^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=16-8=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 < [#permalink]

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25 Apr 2017, 06:00
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If x and y are integers and xy does not equal 0, is xy <   [#permalink] 25 Apr 2017, 06:00
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