Is xy > x2y2?

[Sanket05]

Is xy > x2y2?
(1) 14x2 = 3
(2) y2 = 1

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

[NikolayZ]

Hello ! i think it is E.

Simplify the expression first. xy(1-xy)>0.
so , must be that xy>0 and 1-xy>0 (1>xy)
OR xy<0, 1-xy<0 (1>xy)

(1) 14x^2=3, x=+sqrt(3/14) and x=-sqrt(3/14). We have nothing about y. so Insufficient.

(2) y^2=1, y=+1,-1. Again nothing about x.

(1)+(2)
e.g. consider x=sqrt(3/14), y=1.
==> xy>0, and xy<1. so, yes, expression is >0.
and x=-sqrt(3/14), y=1.
==> xy<0, and (1-xy)>0, so the expression is <0.

I think it is E.
Am i right ?

[vaibhav.iit2002]

IMO E

same explanation as above

[sumitha_ambati]

ya its E
bcoz v dont know whether x,y are +ve or -ve
n also x2 n y2 values doest determine tat

[mmslf75]

Hello ! i think it is E.

Simplify the expression first. xy(1-xy)>0.
so , must be that xy>0 and 1-xy>0 (1>xy)
OR xy<0, 1-xy<0 (1>xy)

(1) 14x^2=3, x=+sqrt(3/14) and x=-sqrt(3/14). We have nothing about y. so Insufficient.

(2) y^2=1, y=+1,-1. Again nothing about x.

(1)+(2)
e.g. consider x=sqrt(3/14), y=1.
==> xy>0, and xy<1. so, yes, expression is >0.
and x=-sqrt(3/14), y=1.
==> xy<0, and (1-xy)>0, so the expression is <0.

I think it is E.
Am i right ?

In such a sum, do we take all possibilites
I mean
x=+sqrt(3/14) y = 1
x=+sqrt(3/14) y = -1

x=-sqrt(3/14 y=1
x=-sqrt(3/14 y=-1

????????

[bhumika.k.shah]

But the OA is E

Though i aint sure whether it is correct

[sallespadua]

I found the answer as C

Considering both statements, every combination of values provides the negative afirmation, therefore sufficient to answer whether xy>x^2y^2!

[rohan_vus]

I disagree ..combining 2 stmnts you get x^2*y^2 = 4/13---> xy could be (4/13)^.5 or -(4/13)^.5...

If xy = (4/13)^.5 then xy > x^2*y^2 ...
if xy = -(4/13)^.5... then xy < x^2*y^2...

So combining you get 'yes' and 'no'.. So C cant be the ans

[bedazzled]

I agree with rohan. There will b ambiguity with C therefore its E.

[bhumika.k.shah]

well i guess then the OA is correct!
thanks guys

[shashank.ism]

Is xy > x2y2?
(1) 14x2 = 3
(2) y2 = 1

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

for, xy>x2y2 --> 0<xy<1
st.1: 14x2 =3 x= sqrt (3/14) <1 not sufficient we don't know about y
st.2 : y2=1 --> y=+/- 1 not sufficient we don't know about x
combined we get 2 values of xy =+/-sqrt (3/14) certainly 1 value does not lead to xy > x2y2 ...not sufficient.
Ans E