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

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Manager
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If xy > 0, which of the following CANNOT be true?  [#permalink]

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15 Jun 2011, 07:46
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If xy > 0, which of the following CANNOT be true?

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

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Re: If xy > 0, which of the following CANNOT be true?  [#permalink]

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15 Jun 2011, 08:52
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

xy>0 means x and y have same signs;
if x=+ve, then y=+ve
if x=-ve, then y=-ve

A: x>0 possible; x=1, y=1
B.y<0 possible; x=-1, y=-1
C.x+y>0 possible; x=1, y=1
D.x/y>0; possible; x=1, y=1
E.x/y<0; NOT POSSIBLE; since both x and y have same sign; x/y will always be more than 0.

Ans: "E"
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Re: If xy > 0, which of the following CANNOT be true?  [#permalink]

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19 Jun 2017, 14:05
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]

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19 Jun 2017, 15:13
Top Contributor
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

When it comes to positive and negative numbers, the rules for multiplication are THE SAME as the rules for division.
So....
(POSITIVE)(POSITIVE) = POSITIVE and POSITIVE/POSITIVE = POSITIVE
(POSITIVE)(NEGATIVE) = NEGATIVE and POSITIVE/NEGATIVE = NEGATIVE
(NEGATIVE)(NEGATIVE) = POSITIVE and NEGATIVE/NEGATIVE = POSITIVE

Given: xy is POSITIVE
So, it must also be true that x/y is POSITIVE

In other words, x/y cannot be negative

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Re: If xy > 0, which of the following CANNOT be true?  [#permalink]

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20 Jun 2017, 01:42
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]

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20 Jun 2017, 02:13
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]

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20 Jun 2017, 18:10
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]

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20 Jun 2017, 22:26
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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29 Jan 2019, 14:34
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Re: If xy > 0, which of the following CANNOT be true?   [#permalink] 29 Jan 2019, 14:34
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