Is y^4

Question

Is  y^4<x^2y^2 ?

(1) x < y
(2) y < 0

chaitanyapatil · Answer

The stem asks us the question of whether y^2<x^2.
If the variables are positive Y<X may suffice and if the variables are negative Y>X would do.

St.1
X<Y 
Not sufficient since we do not know the signs of the variables

St.2
Y<0
As Y is negative but there is no information on X.

Combining both we can definitely state that y^2<x^2.

Rishikesh113 · Answer

statement 1 : X<Y .....here it is not said if x and y are positive or negative , so no conclusion can be made.

statement 2 : y<0 .. we know Y is less than 0, but we don't know any relation of y with x.

Combining 1 and 2 :
 
 x<y and y<0...

we can surely conclude that Is y^4 < x^2y^2

stne · Answer

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.

nasgmatbag · Answer

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

werty_123 · Answer

Can I do like below:
Taking square root on both the sides, I got:
y^2<xy
y^2-xy<0
y(y-x)<0

Bunuel · Answer

No, becasue  \sqrt{x^2}=|x| , not simply |x|. Thus, if we tke the square root from y^4 < x^2y^2 we get:

|y^2| < |xy|

Since |y^2| = y^2, this gives:

y^2 < |xy|

werty_123 · Answer

If it was mentioned that both are positive numbers, then we could have taken square root? 
Or is it square root for inequalities cannot be taken for any numbers, whether positive or negative?

Posted from my mobile device

Bunuel · Answer

If both x and y were positive or negative, then y^2 < |xy| would give y^2 < xy. Becasue in this case xy would be positive and thus |xy| would equal to xy.

unraveled · Answer

Is  y^4<x^2y^2 ?

In these type of questions where sign of the variable/s is not known, we need to check what we have on the table.

(1) x < y
Sign is not sure from this. 
A) x = 1, y = 2, NO
B) x = -2, y = -1, YES

INSUFFICIENT.

(2) y < 0
B case of St. 1) above with more possiblities can be applied.
A) x = 1, y = -1, NO
B) x = -2, y = -1, YES

INSUFFICIENT.

Together 1 & 2
only St. 1 B) case remains

SUFFICIENT.

Answer C.

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

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