Is y^4 < x^2y^2 ? (1) x < y (2) y < 0

Re-arranging:

Is \(y^4 -x^2y^2 < 0 \)

Is \(y^2 (y^2 - x^2 ) <0 \)

Expression will be \(<\) zero when \(|x|> |y|\)

(1) x < y

\(x=1\) and \(y=2\) ... NO to the stem

\(x=-4\) and \(y=2\) .. Yes to the stem

INSUFF.

(2) y < 0

\(x=1\) and \(y=-2\) ... No to the stem

\(x=-4\) and \(y=-2\) ...Yes to the stem.

INSUFF.

1+2

Since \(y < 0 \) and \(x < y\), then \(|x| > |y|\) e.g. \(x=-3\) and \(y =-1\), and we can answer a definite YES to the stem.

SUFF.

Ans C

Hope it helps.

My approach, please anybody correct me if i'm wrong:

1) x < y -> let's test a couple of cases here, if we get a NO and YES answer to the prompt this statement will be insufficient:
case 1 (both positive): let x = 2 and y = 3, \((2^2)(3^2) = 36\) -> 3^4 < 36 (NO)
case 2 (both negative): \((-3^2)(-2^2) = 36\) -> 2^4 < 36 (YES)
no need to do any other cases, we already got a YES and NO answer from this statement

2) y < 0 -> this statement says that y = negative, again let's use 2 cases where x is positive and negative:
case 1 ( x > 0): \((3^2)(-2^2) = 36\) -> 2^4 < 36 (YES)
case 2 (x < 0): \((-2^2)(-5^2) = 100\) -> 5^4 < 100 (NO)
no need for other cases, got a NO and YES again

1/2) x < y and y < 0 (so both numbers are negative)
case 1: \((-3^2)(-2^2) = 36\) -> 2^4 < 36 (YES)
case 2: \((-5^2)(-3^2) = 175\) -> 3^4 < 175 (YES)
as you can see no matter what the values are, as long as x < y \(y^4\) will always be smaller than x^2y^2

Answer: C