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Math Expert V
Joined: 02 Sep 2009
Posts: 64234
If xy + x = z, is |x + y| > z?  [#permalink]

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17 00:00

Difficulty:   55% (hard)

Question Stats: 64% (02:11) correct 36% (02:02) wrong based on 280 sessions

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If xy + x = z, is |x + y| > z?

(1) x < 0
(2) y > 0

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Intern  Joined: 11 Aug 2013
Posts: 24
Location: India
Concentration: Finance, General Management
GMAT 1: 620 Q47 V28
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Re: If xy + x = z, is |x + y| > z?  [#permalink]

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1
1
Re-writing xy+x=z as x(y+1)=z --(a)
Now looking at the question we can definitely say
|x+y|>z if a) z is -ve as mod of any number is always +ve
OR b) it can be proved that z is positive and > x+y
Taking i) x< 0 our modified equation (a) suggests that sign of z depends on sign of (y+1) so it can be both +ve or -ve. There is no data on the actual numeric value of x ,y or z. so. Not sufficient
Taking ii) y>0 our modified equation (a) suggests that sign of z depends on sign of x so it can be both +ve or -ve. There is no data on the actual numeric value of x ,y or z. so. Not sufficient

Combining i and ii and looking at eq -(a)
x< 0 and y>0 => (y+1)>0. Hence x(y+1) <0 => z <0. From our earlier inference if z<0 then |x+y|>z. Sufficient.
Intern  Joined: 18 Sep 2016
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Re: If xy + x = z, is |x + y| > z?  [#permalink]

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neither statement can give us much
but if we combine both here is the interesting thing we can find: whether |x+y|> xy+x

if x is negative and y is positive, then xy will be negative and plus negative will always be negative, and if we sum negative and negative the result will be negative so, xy+x is negative if we combine statements 1) and 2)

|x+y| though will be positive no matter what, so the answer will be a definite yes, so, the answer is C (both 1 &2 are sufficient together)
Intern  B
Joined: 10 May 2017
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Re: If xy + x = z, is |x + y| > z?  [#permalink]

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1
By manipulating the condition we get x+y>z? or x+y<-z
Therefore x+y>xy+x => is y(x-1)<0?
x+y<-(xy+x)=> is y(x+1)+2x<0?
We clearly need the signs of x and y
1) No sign of y.Insufficient
2)No sign of X. Insufficient

1)+2)=>Sufficient to prove above statements
Retired Moderator D
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Re: If xy + x = z, is |x + y| > z?  [#permalink]

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2
Bunuel wrote:
If xy + x = z, is |x+y|>z?

(1) x < 0
(2) y > 0

Given $$x(y+1)=z$$, we need the values of $$x$$, $$y$$ & $$z$$ to determine whether $$|x+y|>z$$, where LHS is always positive

Statement 1: implies $$x$$ is negative so $$x(y+1)$$ i.e. $$z$$ can be negative or it can be positive depending upon the value of $$(y+1)$$. But nothing is mentioned about $$y$$. So insufficient

Statement 2: implies $$y$$ is positive so $$x(y+1)$$ i.e. $$z$$ can be negative or it can be positive depending upon the value of $$x$$. But nothing is mentioned about $$x$$. So insufficient

Combining 1 & 2 we get $$x<0$$ & $$(y+1)>0$$ so $$x(y+1)<0$$ i.e. $$z<0$$

but $$|x+y|$$ is always positive hence we get a Yes for our question stem. Sufficient

Option C
Intern  B
Joined: 09 Mar 2018
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If xy + x = z, is |x + y| > z?  [#permalink]

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According me E is correct since y is less than zero so y=-1 x= 1 therefore z can be neget ive or +'ve while combining plz correct me if I am wrong
Retired Moderator D
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Re: If xy + x = z, is |x + y| > z?  [#permalink]

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Krishaa12 wrote:
According me E is correct since y is less than zero so y=-1 x= 1 therefore z can be neget ive or +'ve while combining plz correct me if I am wrong

Hi Krishaa12

y>0, hence it is positive, rather x<0 i.e negative

Posted from my mobile device
Intern  B
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Re: If xy + x = z, is |x + y| > z?  [#permalink]

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Bunuel wrote:
If xy + x = z, is |x + y| > z?

(1) x < 0
(2) y > 0

An alternate explanation

x(y+1) - z = 0
First take 1 and 2 both, if x is negative and y is positive, then term x(y+1) is negative, so for x(y+1) - z =0 to be true, z has to be negative so that -z is positive and x(y+1) - z =0. So from this we can deduce that z is also negative--So question stem---> |x+y| is always positive and if z is negative, so |x+y| >z is true.
Now C is correct unless we can make one out of 1 and 2 individually correct or both individually correct. Let's analyze

Take 1) x < 0, if x is negative (and y is positive or negative), nothing can be said about sign of z so we can never know |x+y| >z.
Take 2) y > 0, if y is positive (x can be positive or negative), nothing can be said about sign of z so we can never know |x+y| >z. Re: If xy + x = z, is |x + y| > z?   [#permalink] 08 Aug 2019, 10:06

# If xy + x = z, is |x + y| > z?  