number property, interesting

duongthang wrote:Is square of X + Square of Y is bigger than 6

1, square of (x+y) is bigger than 6

2, xy =2

I do not know how to write "square" inhere. pls, help

If I interpret your question correctly, it should read:

Is x^2 + y^2 > 6 ?

(1) (x+y)^2 > 6

(2) xy =2


Statement 1:
(x + y)^2 > 6
x^2 + 2xy + y^2 > 6

We don't know anything about 2xy. Hence insufficient.

Statement 2:
xy = 2
if x = 4, y = 0.5, then x^2 + y^2 > 6. YES
if x=2, y=1, then x^2 + y^2 <6. NO

Insuffcient.

Both statements together:

x^2 + 2xy + y^2 > 6
x^2 + 2(2) + y^2 > 6
x^2 + y^2 > 2

we can only guarantee that x^2 + y^2 is greater than 2. But we cannot conclude anything about it being greater than 6. Insufficient.

Choose E.

-BM-

Nice explanation BM.
E for me as well.

What is the OA?

Lets pick some numbers to choose between C and E

X=-2 Y=-1 NO

x=12 y=1/6 YES

E

I go with E too..
This problem becomes very simple if we use the Kaplan Method, i.e. Pick Numbers :twisted: