Does x + y = xy?

Statement One Alone:

x is neither a positive integer nor a negative integer.

This means x is either 0 or a non-integer decimal. If x = 0, then we have:

0 + y = 0 * y ?

y = 0 ?

Since we don’t know anything about y, we can’t answer the question.

If x is a decimal, say x = 0.5, then we have:

0.5 + y = 0.5y ?

0.5 = -0.5y ?

-1 = y ?

Since we don’t know anything about y, we can’t answer the question.

Statement one alone is not sufficient.

Statement Two Alone:

y is neither a positive integer nor a negative integer.

We can use the exact argument in statement one (by interchanging x and y) to show that statement two alone is not sufficient also.

Statements One and Two Together:

From both statements, we could have the following cases

If both x and y are 0, then we have:

0 + 0 = 0 * 0 ?

0 = 0 ? ---> Yes!

We see that x + y = xy would be true if both x and y are 0.

If both x and y are decimals, say both are 0.5, then we have:

0.5 + 0.5 = 0.5 * 0.5 ?

1 = 0.25 ? ---> No!

We see that x + y = xy would be false if both x and y are decimals.

Thus, the two statements together are still not sufficient to answer the question.

Answer: E

When trying to solve for x or y
x + y = xy
x + y - x = xy - x
y = xy - x
y = x(y - 1)
x = y/(y - 1) or y = x/(x - 1)

as long as x or y is not 1, since dividing by 0 is undefined

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Now back to the question
Since x and y are not negative integer or positive integer, then whole numbers are out of the question, but it can still be a real number therefore either both x and y are zeros, x and y are different fractional numbers. The only exception is if one of x or y is a fractional number that forces the other variable x and y to be a whole number.

For example.
since we know that:
x = y/(y - 1)
and we use:
y = 0.5
x = 0.5/(0.5 - 1)
x = 1
~~~~~~~~
if y = 1.5
x = 3
so following the problem above than x and y cannot equal to a number that is 0.5 or 1.5, but it can be many other fractional numbers.
For example.
y = 105.7
when plug into the equation x = y/(y - 1)
x = 1.0095510983763132760267430754537
and double checking x + y = xy with the above two numbers should still be correct

Im pretty sure that 0.5, 1.5 and 1 are not the numbers for x and y.