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

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Bunuel
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If x and y are integers and xy does not equal 0, is xy < 0? [#permalink] New post   19 Dec 2019, 04:07
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E

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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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C
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chetan2u
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If x and y are integers and xy does not equal 0, is xy < 0? [#permalink] New post   19 Dec 2019, 04:40
Expert Reply
Bunuel 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


Are You Up For the Challenge: 700 Level Questions


xy<0 means do x and y have opposite sign.

(1) \(y = x^4 – x^3=x^3(x-1)\)
OR \(xy = x^5 – x^4=x^4(x-1)\)
If x<1, then x-1<0 and so \(xy<0\).
Otherwise say x=2, xy>0
Insuff

(2) x is to the right of 0 on the number line
This means x is positive, but nothing about y
Insuff


Combined
x>0 and x is also not 1 as turn y will be 0 and xy=0.
So minimum value of x=2 and xy>0
Suff

c
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Re: If x and y are integers and xy does not equal 0, is xy < 0? [#permalink] New post   19 Dec 2019, 04:52
chetan2u wrote:
Bunuel 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


Are You Up For the Challenge: 700 Level Questions


xy<0 means do x and y have opposite sign.

(1) \(y = x^4 – x^3=x^3(x-1)\)
OR \(xy = x^5 – x^4=x^4(x-1)\)
If x<1, then x-1<0 and so \(xy<0\).
Otherwise say x=2, xy>0
Insuff

(2) x is to the right of 0 on the number line
This means x is positive, but nothing about y
Insuff


Combined
x>0
If 0<x<1, then x-1<0 and so \(xy = x^5 – x^4=x^4(x-1)........xy<0\).
Otherwise say x=2, xy>0
Insuff

E
Insuff


chetan2u

I guess we shouldn't consider the highlighted region since we are given that x and y are integers.
IMO, the answer should be C then
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chetan2u
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Re: If x and y are integers and xy does not equal 0, is xy < 0? [#permalink] New post   19 Dec 2019, 05:15
Expert Reply
gmat1393 wrote:
chetan2u wrote:
Bunuel 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


Are You Up For the Challenge: 700 Level Questions


xy<0 means do x and y have opposite sign.

(1) \(y = x^4 – x^3=x^3(x-1)\)
OR \(xy = x^5 – x^4=x^4(x-1)\)
If x<1, then x-1<0 and so \(xy<0\).
Otherwise say x=2, xy>0
Insuff

(2) x is to the right of 0 on the number line
This means x is positive, but nothing about y
Insuff


Combined
x>0
If 0<x<1, then x-1<0 and so \(xy = x^5 – x^4=x^4(x-1)........xy<0\).
Otherwise say x=2, xy>0
Insuff

E
Insuff


chetan2u

I guess we shouldn't consider the highlighted region since we are given that x and y are integers.
IMO, the answer should be C then


Yes, you are correct. Missed out reading the question clearly
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Re: If x and y are integers and xy does not equal 0, is xy < 0? [#permalink] New post   24 Dec 2019, 21:58
Bunuel 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


Are You Up For the Challenge: 700 Level Questions

From 1
Y=X^3(X-1)
XY NOT equal to 0 and both are integers
moreover X can't be equal to 1
when X is positive, X^3 is positive, X-1 is positive so Y is positive
XY>0
when X is negative, X^3 is negative, X-1 is negative so Y is positive
XY<0
not sufficient
From 2
No information about Y
Not sufficient
From 1 and 2
X is positive so XY>0
sufficient
C:)
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Re: If x and y are integers and xy does not equal 0, is xy < 0? [#permalink] New post   31 Mar 2024, 10:50
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Re: If x and y are integers and xy does not equal 0, is xy < 0? [#permalink]
31 Mar 2024, 10:50
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