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If xy > 0, which of the following CANNOT be true? A. x > 0 [#permalink]
1
It can be.
If \(y < 0\) & \(x < 0\) then \(xy > 0\)

Armandohosseini wrote:
GreenlightTestPrep wrote:
Carcass wrote:
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


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

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

In other words, x/y cannot be negative

Answer: E



Yes, but given the same logic, B also cannot be true.
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If xy > 0, which of the following CANNOT be true? A. x > 0 [#permalink]
xy > 0
This means that Product of two numbers x and y is > 0

Theory: If Product of two numbers is > 0 then it means that both numbers have the same sign. Either both are positive or both are negative.

=> both x and y have the same sign
=> Either both x and y are positive or both are negative.

Let's take each option choice one by one

A. x > 0 -> This can be true as both x and y can be positive
B. y < 0 -> This can be true as both x and y can be negative
C. x + y > 0 -> This can be true as both x and y can be positive, making x + y > 0
D. x/y > 0 -> This is true as this also means that both x and y have the same sign. xy > 0 and x/y > 0 mean the same thing
E. x/y < 0 -> NOT True, as this will mean that both x and y have different signs

So, answer will be E
Hope it helps!

To learn more about inequality watch the below video

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Re: If xy > 0, which of the following CANNOT be true? A. x > 0 [#permalink]
If xy > 0, which of the following CANNOT be true?
if xy > 0, then x and y must have the same sign

Correct Answer: E
x/y < 0 => Both positive and both negative integers will result in values > 0
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Re: If xy > 0, which of the following CANNOT be true? A. x > 0 [#permalink]
Armandohosseini wrote:
GreenlightTestPrep wrote:
Carcass wrote:
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


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

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

In other words, x/y cannot be negative

Answer: E



Yes, but given the same logic, B also cannot be true.



B can be true when x is less than 0 also. But in whatever scenario that satisfies xy>0, x/y will never be less than 0
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