Is xy x^2*y^2? (1) 14*x^2 = 3 (2) y^2 = 1

Question

Is xy > x^2*y^2?

(1) 14*x^2 = 3
(2) y^2 = 1

Bunuel · Accepted Answer

Is xy > x^2*y^2? Is xy>x^2*y^2 ? --> is 0a^2 means 0

sfeiner · Answer

E

both statements dont reference both X and Y

and statement 2 leaves Y with both positive and negative values thus it can be greater or less. (also the square of X is less than X but that doesnt matter if the products can be positive or negative)

shalva · Answer

Let's consider both statements together

xy  could be positive or negative;

if  xy<0 , clearly  xy \leq x^2y^2 , no calculations are needed. Inequality in question stem is false

If  xy>0 , than  y=1; x=sqrt{3/14}  or  y=-1; x=-sqrt{3/14} . once more no need to calculate this, just note that  xy<1 . In this case  (xy)^2<xy<1

So, in both cases  xy<x^2y^2

fall2009 · Answer

I don't get this, in the blue part, you mentioned that (xy)^20, because (xy)^2 =3/14 <1 => xy>(xy)^2. Hence E.

shalva · Answer

You're absolutely right :oops:

In one case xyx^2y^2

MHIKER · Answer

if as follows:
xy - x^2*y^2 > 0
xy(1- xy) > 0
so, xy>0
or, x>0 or, y>0
and 1-xy > 0
 xy<1
Thus no statements are sufficient.
Ans. E

What are wrongs with this approach?

amnesia604 · Answer

Hi Bunuel, Can you explain how you got this step? Thanks! Is xy>x2∗y2? --> is 0a^2 means 0

Bunuel · Answer

xy>x^2*y^2 ; xy>(xy)^2 ; xy(1-xy)>0 ; 0solving-quadratic-inequalities-graphic-approach-170528.html Inequality tips: tips-and-hints-for-specific-quant-topics-with-examples-172096.html#p1379270 inequalities-trick-91482.html data-suff-inequalities-109078.html range-for-variable-x-in-a-given-inequality-109468.html everything-is-less-than-zero-108884.html graphic-approach-to-problems-with-inequalities-68037.html All DS Inequalities Problems to practice: search.php?search_id=tag&tag_id=184 All PS Inequalities Problems to practice: search.php?search_id=tag&tag_id=189 700+ Inequalities problems: inequality-and-absolute-value-questions-from-my-collection-86939.html Hope it helps.

stonecold · Answer

Here nothing is specified about the values of x adn y being >0 or <0
so => not sufficient.
hence E

adiagr · Answer

xy > x^2 * y^2 xy - x^2 * y^2 > 0 xy (1-xy) > 0 0 This is our revised problem Statement 1 --> clearly not sufficient, as no info about y. Statement 2 --> clearly not sufficient, as no info about y. Combining (1) and (2) x^2 * y^2 = 3/14. One of the solution of xy lies between 0 and 1; Other solution does not lie between 0 and 1 . So not sufficient. (E) is the answer.

ydmuley · Answer

This is definitely a trap question in DS.

Given: xy > x^2y^2

(1) 14 * x^2 = 3

x^2 = 3/14 =====> x = +/-\sqrt{3/14} ====  Clearly Not Sufficient as we do not know value of y.

(2) y^2 = 1
 
y = +/- 1 =====>  Clearly Not Sufficient as we do not know value of x.

Combining both (1) & (2)

We are still not sure of the value of x & y will be positive or negative. Hence, for the question Is xy > x^2*y^2, we get both the answers YES & NO.

Hence, Answer is E

KanishkM · Answer

KeyWord x and y can be +ive or -ive

from 1 x^2 = 3/14, y can take any value

from 2 y^2 = 1, x can take any value

Now both x and y can be +ive or -ive

different signs of x and y, can result in different answers for the given inequality

E

mrcentauri · Answer

Hi Bunuel,

call me crazy but how do we get from

xy(1−xy)>0;

to

0<xy<10<xy<1.

this part is really confusing me?

thank you.

Bunuel · Answer

Say xy = a, then xy(1- xy) > 0 becomes a(1- a) > 0, which is true when 0 < a < 1.

Basshead · Answer

Is xy > x^2*y^2 ? xy - x^2y^2 > 0? xy - xy(xy) > 0 ? xy (1-xy) > 0 ? 0 < xy < 1 ? (1) 14*x^2 = 3 No information about y. INSUFFICIENT. (2) y^2 = 1 No information about x. INSUFFICIENT. (1&2) Combining both, we can have a negative or positive answer. INSUFFICIENT. Answer is E.

Kimberly77 · Answer

brunel , could you clarify here what do you mean by If x and y have the same sign then yes but no if not? Do you refer to square root sign here? Thanks

bumpbot · Answer

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Is xy > x^2y^2? (1) 14x^2 = 3 (2) y^2 = 1

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Is xy > x^2*y^2? (1) 14*x^2 = 3 (2) y^2 = 1