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![If z > 0, is [m][fraction](x+z)/(y+z)[/fraction] > [fraction]x/y[/frac](/forum/styles/gmatclub_light/imageset/icon_post_target_unread.svg "If z > 0, is [m][fraction](x+z)/(y+z)[/fraction] > [fraction]x/y[/frac"){kind=icon}
20 Oct 2018, 10:40
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A
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Difficulty:
45%
(medium)
Question Stats:
69% (01:59) correct
31%
(01:23)
wrong
based on 58
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If z > 0, is \(\frac{(x+z)}{(y+z)} > \frac{x}{y}\)?
1) 0< x< y
2) x< y
1) 0< x< y
2) x< y
GMATbuster's Weekly GMAT Quant Quiz #5 Ques No 9
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
20 Oct 2018, 10:49
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Answer is d:
we do not need to know that x and y are positive you can plug in negative values to test this
let x = -3 and y = -2 and z = 1
therefore
LHS: (-3 + 1) / (-2+1)
=2
RHS: -3/-2
=3/2
Therefore LHS > RHS
we do not need to know that x and y are positive you can plug in negative values to test this
let x = -3 and y = -2 and z = 1
therefore
LHS: (-3 + 1) / (-2+1)
=2
RHS: -3/-2
=3/2
Therefore LHS > RHS
20 Oct 2018, 10:54
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1) 0< x< y
2) x< y
Option A: 0<x<y
which says 0<x/y<1
hence lets take x/y=1/2....if you add any value of Z as positive to the positive number , it will always be greater than original
that is (x+z)/(y+z) will always be greater than x/y if z>0,
to illustrate x= 1, y= 2 and z= 0.1 which gives x/y= 1/2= 0.5
but (x+z)/(y+z)= 1.1/2.1> 0.5 as it is euual to 0.55
hence sufficient
Option B
x<y
which means x and y can be negative as well
if x= -2 and y = -1
x/y= 2
if we take z= 0.5, it becomes (x+z)/(y+z)=-1.5/-0.5= 3, which is more than original x/y= 2
but if we take z= 2, it becomes 0/1= 0 which is less
hence not sufficient
A is the answer
2) x< y
Option A: 0<x<y
which says 0<x/y<1
hence lets take x/y=1/2....if you add any value of Z as positive to the positive number , it will always be greater than original
that is (x+z)/(y+z) will always be greater than x/y if z>0,
to illustrate x= 1, y= 2 and z= 0.1 which gives x/y= 1/2= 0.5
but (x+z)/(y+z)= 1.1/2.1> 0.5 as it is euual to 0.55
hence sufficient
Option B
x<y
which means x and y can be negative as well
if x= -2 and y = -1
x/y= 2
if we take z= 0.5, it becomes (x+z)/(y+z)=-1.5/-0.5= 3, which is more than original x/y= 2
but if we take z= 2, it becomes 0/1= 0 which is less
hence not sufficient
A is the answer
