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605-655 (Medium)|   Inequalities|            
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valeriacastro11
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What values of x have a corresponding value of y that satisfies both x 15 Aug 2022, 18:11
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Thank you! this is explanation is great and much easy

TusharViv
What values of x have a corresponding value of y that satisfies both xy > 0 and xy = x + y ?


A. x≤1

B. −1<x≤0

C. 0<x≤1

D. x>1

E. All real numbers

xy > 0 this means either:

1. x>0 AND y>0
2. x<0 AND y<0

xy = x + y

Now the other part of the question. Therefore x+ y > 0 since xy > 0

x + y > 0 can only be true if x or y are positive or both. And since we have the 2 statements above. x<0 AND y<0 can be eliminated.

Therefore eliminate A, B, E

Now between C and D. Get y on one side

xy = x + y

xy - y = x

y(x-1) = x

y = x / (x-1)

x cannot be 1. Eliminate C Hence answer is D
Also if x=1 was not part of C. The denominator would be negative if x was a fraction between 0 and 1, hence giving a negative y value but we know this cannot be true since BOTH x AND y must be positive
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What values of x have a corresponding value of y that satisfies both x 29 Nov 2024, 10:07
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We know that xy>0 so we also know that x/y>0. Keep also in mind that x and y cannot be 0.
Now just rewrite the second equation as x-(x/y)=1 and it becomes clear that x must be >1

parkhydel
What values of x have a corresponding value of y that satisfies both xy > 0 and xy = x + y ?


A. \(x \leq 1\)

B. \(-1 < x \leq 0\)

C. \(0 < x \leq 1\)

D. \(x > 1\)

E. All real numbers


PS22680.02
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What values of x have a corresponding value of y that satisfies both x 30 Dec 2024, 02:23
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XY>0
Both have same signs - Either both positive or both negative. None 0

XY=X+Y
Both cant be -ve as RHS will be -ve but LHS will be +ve

X,Y must be>0
Eliminates A,B,E
Now between C and E
Lets take a value greater than 1
If both x and y are 2 each the equation is held. So D

parkhydel
What values of x have a corresponding value of y that satisfies both xy > 0 and xy = x + y ?


A. \(x \leq 1\)

B. \(-1 < x \leq 0\)

C. \(0 < x \leq 1\)

D. \(x > 1\)

E. All real numbers


PS22680.02
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What values of x have a corresponding value of y that satisfies both x 02 Jun 2025, 22:35
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Bunuel
Could you change the option (A) to reflect exactly what Quant Review text has ?
The above screenshot taken from Quant Review 2025-26.
parkhydel
What values of x have a corresponding value of y that satisfies both xy > 0 and xy = x + y ?


A. \(x \leq 1\)

B. \(-1 < x \leq 0\)

C. \(0 < x \leq 1\)

D. \(x > 1\)

E. All real numbers


PS22680.02
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GMAT-Club-Forum-qgminx21.png [ 17.33 KiB | Viewed 520 times ]
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Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
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What values of x have a corresponding value of y that satisfies both x 02 Jun 2025, 23:51
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kingbucky

Bunuel
Could you change the option (A) to reflect exactly what Quant Review text has ?
The above screenshot taken from Quant Review 2025-26.
parkhydel
What values of x have a corresponding value of y that satisfies both xy > 0 and xy = x + y ?


A. \(x \leq 1\)

B. \(-1 < x \leq 0\)

C. \(0 < x \leq 1\)

D. \(x > 1\)

E. All real numbers


PS22680.02
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Edited the option. Thank you! +1
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What values of x have a corresponding value of y that satisfies both x 14 Mar 2026, 03:28
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I didn't do much calculation in this, considering i went through with logic here, if xy is greater than 0, both can be -ve or +ve and not one can be 0, both can't be negative because xy=x+y will give us a negative value if both are negative, so in order to satisfy both, both have to be positive. now if we consider 0.2 and 0.3, the point moves 2 places when we multiply, whereas one if we add, so x has to be greater than 1?
parkhydel
What values of x have a corresponding value of y that satisfies both xy > 0 and xy = x + y ?

A. \(x \leq -1\)

B. \(-1 < x \leq 0\)

C. \(0 < x \leq 1\)

D. \(x > 1\)

E. All real numbers


PS22680.02
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What values of x have a corresponding value of y that satisfies both x 23 May 2026, 10:13
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Here is a more simpler way to do it.
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What values of x have a corresponding value of y that satisfies both x 04 Aug 2026, 09:50
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Strange, this is classified as easy...
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What values of x have a corresponding value of y that satisfies both x 04 Aug 2026, 10:28
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Essentially, there is no special formula/concept.
It is mainly an algebra + sign reasoning question:
xy > 0
=> x, y have the same sign
Also:
xy = x + y > 0
If x and y were both negative:
x + y < 0
But xy = x + y > 0
Contradiction.
Therefore:
x > 0 and y > 0
Now manipulate:


xy = x + y

Divide by y:

x = x/y + 1

Since:

x > 0 and y > 0

=> x/y > 0

Therefore:

x = 1 + positive number

=> x > 1

-----

Way 2: Division Method
xy = x + y
Divide by y:
x = x/y + 1
Since x > 0 and y > 0:
x/y > 0
Therefore:
x > 1
-----

Way 3: Plug Values
Try x = 1/2:
(1/2)y = 1/2 + y
y = 1 + 2y
y = -1
xy < 0
Does not work.
Try x = 2:
2y = 2 + y
y = 2
xy = 4 > 0
Works.
Therefore:
x > 1
-----

Best method:
xy = x + y
x = x/y + 1
x/y > 0
Therefore x > 1.
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