Quantitative

hi samihamumtahina

Asked: If xy<0 and y>0 which of the following must be positive?
y>0
xy<0
x<0

a)x-y<0
b) 2x-3y<0
c) x+10/y+2: x+10 may be +ve or -ve; y+2>0
d)(-y-2)/x: -y-2<0; x<0; (-y-2)/x >0
e)2y²-x>0

Options D & E are positive

hi samihamumtahina

The question needs correction since:-

"2x = 3y" is incorrect and should be "2x-3y"
"2y^2 = x" is incorrect and should be "2y^2-x"

But Both Options D & E are positive

Please correct the question accordingly

Since xy < 0 and y > 0, it must be true that x < 0.

Answer choice A: Since x < 0 and -y < 0, x - y is always negative.

Answer choice B: Since x < 0 and y > 0, 2x cannot be equal to 3y. If you meant to write 2x - 3y or 2x * 3y or 2x/3y, then all of these expressions are negative. If you meant to write 2x + 3y, then it can be positive or negative. So this answer choice is not correct either.

Answer choice C: Since y > 0, y + 2 is positive; however, x + 10 can be positive, negative, or 0 (depending on whether x is greater than -10, less than -10, or equal to -10). So the expression (x + 10)/(y + 2) can be positive, negative, or 0.

Answer choice D: Since y > 0, -y < 0, which implies -y - 2 < 0. Since both the numerator and the denominator of (-y - 2)/x are negative, this expression must be positive.

Answer choice E: Since 2y² is positive and x is negative, 2y² cannot equal x. If you meant to write 2y² - x, then it is positive. If you meant to write 2y² * x or 2y²/x, then it is negative. If you meant to write 2y² + x, then it can be either positive or negative.

So answer choice D is correct and answer choice E can be correct depending on what is meant by the = sign.