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# If xy > 0, which of the following CANNOT be true?

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Re: If xy > 0, which of the following CANNOT be true? [#permalink]
Easy question to solve, should not take more than 1 min of your time.

xy>0

Which means either:

x & y are +ve
x & y are -ve

Let check the options now.

A. x>0 - Possible (as x and y can have +ve values)
B. y<0 - Possible (as x and y can have -ve values)
C. x+y>0 - possible (as x and y can have +values and hence addition will give as a +ve number)
D. x/y>0 - possible (as x and y can have +values and hence division will give as a +ve number)
E. x/y<0 - NOT POSSIBLE (as x & y can both be +ve - which gives us +ve number post division and x & y can be -ve which again gives us positive number post division)

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Re: If xy > 0, which of the following CANNOT be true? [#permalink]
Since xy>0, it means either both x and y are positive or both are negative.
However, according to E, only one term is positive, so E is not possible and hence the answer
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Re: If xy > 0, which of the following CANNOT be true? [#permalink]
xy>0
This implies the product is positive
X and Y can have only same signs

X,Y will be either (-ve,-ve) or (+ve,+ve)

Hence, $$\frac{x}{y}$$= cannot be negative

Alternatively, One can assume a value for the product and check for the possible conditions
For example

xv=6 (which is >0)
Possible values of x,y are (-3,-2), (3,2), (-1/6,-36), (1/6,36)
Substitute any values in the options, Option E alone will not be possible
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Re: If xy > 0, which of the following CANNOT be true? [#permalink]
AnkitK wrote:
If xy>0, which of the foll cannot be true?

A. x>0
B. y<0
C. x+y>0
D. x/y>0
E. x/y<0

Since xy > 0, x and y have the same sign. We see that x and y are either both positive or both negative. Thus, x/y could never be negative.

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Re: If xy > 0, which of the following CANNOT be true? [#permalink]
imo e
x and y will have same sign hence e is not possible .
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Re: If xy > 0, which of the following CANNOT be true? [#permalink]
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Re: If xy > 0, which of the following CANNOT be true? [#permalink]
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