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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.

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]

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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.

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.

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

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.

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

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]

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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

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

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.

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]

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18 Sep 2014, 10:09

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