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# If only one of the three integers x, y and z is negative, is x

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Math Expert
Joined: 02 Aug 2009
Posts: 7102
If only one of the three integers x, y and z is negative, is x  [#permalink]

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06 Jul 2018, 08:07
00:00

Difficulty:

55% (hard)

Question Stats:

65% (00:49) correct 35% (01:24) wrong based on 26 sessions

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If only one of the three integers x, y and z is negative, is x>yz?
(1) $$\frac{x}{y}>z$$
(2) $$xy>0$$

New question

_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: If only one of the three integers x, y and z is negative, is x  [#permalink]

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06 Jul 2018, 09:19
chetan2u wrote:
If only one of the three integers x, y and z is negative, is x>yz?
(1) $$\frac{x}{y}>z$$
(2) $$xy>0$$

New question

St1:-
$$x/y>z$$
This holds true when x and y are non-negative & z is negative.(y can't be zero).
Since magnitude of x,y and z are not known,We have to consider z as negative in order to validate the inequality.
So yz is negative.
Hence x>yz is true.
Sufficient.

St2:-
xy > 0
So both x and y are positive.
Question tells us that only one of x,y, and z is a negative integer.since st2 is not dependent on polarity and magnitude of z,hence,we can consider z as an integer(+/-/0).
So x>yz may or mayn't be true.
So insufficient.

And. A

P.S.- chetan2u Sir, Request your kind perusal.

Posted from my mobile device
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Regards,

PKN

Rise above the storm, you will find the sunshine

Math Expert
Joined: 02 Aug 2009
Posts: 7102
If only one of the three integers x, y and z is negative, is x  [#permalink]

### Show Tags

06 Jul 2018, 09:33
chetan2u wrote:
If only one of the three integers x, y and z is negative, is x>yz?
(1) $$\frac{x}{y}>z$$
(2) $$xy>0$$

New question

PKN, you have correctly found the info but went wrong while solving..

Only one of x, y and z is negative

1) $$\frac{x}{y}>z$$
If any of x or y is negative, then z is positive.
In that case x/y will be negative and z will be positive, so x/y>z will not hold true
So z is negative and x and y are positive so x>yz as yz <0 and x>0
Suff

(2) $$xy>0$$
This says either both x and y are positive or both are negative..
But there is only one negative so both x and y are positive and z is negative.
And so x>yz
Sufficient

D
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 931
WE: Supply Chain Management (Energy and Utilities)
Re: If only one of the three integers x, y and z is negative, is x  [#permalink]

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06 Jul 2018, 09:53
New question[/quote]

PKN, you have correctly found the info but went wrong while solving..

Only one of x, y and z is negative

1) $$\frac{x}{y}>z$$
If any of x or y is negative, then z is positive.
In that case x/y will be negative and z will be positive, so x/y>z will not hold true
So z is negative and x and y are positive so x>yz as yz <0 and x>0
Suff

(2) $$xy>0$$
This says either both x and y are positive or both are negative..
But there is only one negative so both x and y are positive and z is negative.
And so x>yz
Sufficient

D[/quote]

Thank you Sir. I would've considered "if clause" info as a mandatory one since question stem is asked in that condition only.
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

Re: If only one of the three integers x, y and z is negative, is x &nbs [#permalink] 06 Jul 2018, 09:53
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