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What values of x have a corresponding value of y that satisfies both x

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valeriacastro11

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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

tombox

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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

Kavicogsci

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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

kingbucky

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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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Bunuel

Math Expert

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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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Attachment:

GMAT-Club-Forum-qgminx21.png

Edited the option. Thank you! +1

Gaurav07

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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