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14 Mar 2020, 19:46
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B
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Difficulty:
65%
(hard)
Question Stats:
54% (01:47) correct
46%
(01:32)
wrong
based on 120
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GMATBusters’ Quant Quiz Question -10
If x and y are non-zero integers. Is \(\frac{(x+y)}{(x-y)}\)>0?
1) x > y
2) |x| > |y|
14 Mar 2020, 19:57
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If x and y are non-zero integers. Is (x+y)/(x−y)>0?
The question basically asks are both x+y and x-y positive or negative?
(1) x > y
x-y> 0 => x-y is positive
says nothing about x+y which can either be positive or negative
Insufficient
(2) |x| > |y|
√(x^2 ) > . √(y^2 )
x^2-y^2 > 0
(x+y)(x-y) > 0
so both x+y and x-y can be positive or both x+y and x-y can be negative
This means that x+y /x-y will always be positive and greater than 0
Sufficient
Imo. B
The question basically asks are both x+y and x-y positive or negative?
(1) x > y
x-y> 0 => x-y is positive
says nothing about x+y which can either be positive or negative
Insufficient
(2) |x| > |y|
√(x^2 ) > . √(y^2 )
x^2-y^2 > 0
(x+y)(x-y) > 0
so both x+y and x-y can be positive or both x+y and x-y can be negative
This means that x+y /x-y will always be positive and greater than 0
Sufficient
Imo. B
14 Mar 2020, 21:46
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Given: X and Y are Non-Zero Integers
We know that X and Y are Integers. X and Y is not equal to 0.
We do not know X and Y is either Positive / Negative ir Even / Odd.
1) X > Y
Both x and y positives - Lets consider x=3, y= 2 , (x+y)/(x-y) > 0
Both x and y negatives - lets consider x=-2, y=-3 , (x+y)/(x-y) < 0
We get 2 different answers, so option 1 is not sufficient.
2) |x| > |y|
Both x and y positives , lets consider x=2,y=1 , (x+y)/(x-y) > 0
Both x and y negatives, lets consider x=-3 , y=-2, (x+y)/(x-y) > 0
In both the choices we get (x+y) / (x-y) > 0
Option B alone is sufficient.
Ans: B
We know that X and Y are Integers. X and Y is not equal to 0.
We do not know X and Y is either Positive / Negative ir Even / Odd.
1) X > Y
Both x and y positives - Lets consider x=3, y= 2 , (x+y)/(x-y) > 0
Both x and y negatives - lets consider x=-2, y=-3 , (x+y)/(x-y) < 0
We get 2 different answers, so option 1 is not sufficient.
2) |x| > |y|
Both x and y positives , lets consider x=2,y=1 , (x+y)/(x-y) > 0
Both x and y negatives, lets consider x=-3 , y=-2, (x+y)/(x-y) > 0
In both the choices we get (x+y) / (x-y) > 0
Option B alone is sufficient.
Ans: B
