DS - 1 problem

[cardoc]

Is x^2 + y^2 > 6?
(1) (x + y)^2 > 6
(2) xy = 2

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.

[neelgandham]

Is x^2 + y^2 > 6?
(1) (x + y)^2 > 6
x^2 + y^2 + 2*x*y > 6
x^2 + y^2 > 6 -2*x*y,
This condition is insufficient, as the values or signs of x,y are unknown.

(2) xy = 2

xy = 2, if x = 2 then y = 1 and x^2 + y^2 <6
xy = 2, if x = 8 then y = 1/4 and x^2 + y^2 >6
This condition is insufficient too

Joining 1 and 2

x^2 + y^2 > 6 -2*x*y
x^2 + y^2 > 6 -2*2
x^2 + y^2 > 2
so x^2 + y^2 can be 3 or 8
=> x^2 + y^2 can be >6 or < 6,
Insufficient

IMO E

[tpr-becky]

When you are dealing with squares and square roots, especially with inequalities you have to consider fractions and decimals. if you square an integer the answer is larger than the original, when you square a fraction the answer is smaller than the original.

Thus if (x + y)^2 > 6 you have to consider what would happen with fractions. For instance (.75 + 2.3)^2 is greater than 6 BUT if you separate them the fraction will get smaller and thus x^2 + y^2 will not be greater than 6. With an integer the two will always be greater than 6 because integers increase when squared. Thus, you can eliminate AD.

the second statement is insufficient becuase of introduction of fractions in another way - as mentioned above if x= 2 and y = 1 then you won't get a square greater than 6 but if you add in fractions then you can. Thus B is eliminated.

If you put them together then you know that (x + 2x)^2 >6 or that (2y + y)^2> 6 - you will still have an issue with fractions vs. integers so this will nto be sufficient. And the anwer is E.

[vaibhavgupta]

Is x^2 + y^2 > 6?
(1) (x + y)^2 > 6
(2) xy = 2

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.

+1 for E