Data Sufficiency

Methods or strategies.

Thanks.

x^n = x^(n+2)
x^n = x^n * x^2
x^2 = 1
x= -1 or +1

Statement (1)
if x=-1
x = x^2-2
x= 1-2 = -1.
x=1
x = 1-2 = -1
Sufficient.

Statement (2)
2x < x^5
x=-1
-2 < -1, x negative.

x=1
2 < 1, this case cannot exist. Sufficient.

Thus, D.

OA?

Correct... The OA is D..

Thanks...

Morgoth wrote:x^n = x^(n+2)
x^n = x^n * x^2------ THis is wrong
x^n =0 or x^2 = 1
x= -1 or +1

Statement (1)
if x=-1
x = x^2-2
x= 1-2 = -1.
x=1
x = 1-2 = -1
Sufficient.

Statement (2)
2x < x^5
x=-1
-2 < -1, x negative.

x=1
2 < 1, this case cannot exist. Sufficient.

Thus, D.

OA?

x^n = x^n * x^2
x^n =0 or x^2 = 1

Morgoth..I still have a doubt in your explanation

x^n=x^n*x^2
x^n(1-x^2)=0
x=0,1,-1

Question: Is x positive?

statement 1:
x=x^2-2
x^2-x-2=0
(x-2)(x+1)=0
x=2,-1
Still we cant infer whether is positive or not

Statement 2:
2x<x^5

x^5-2x>0
x(x^4-2)>0
x>0 or x^4>2
even if x=-3 condition x^4>2 is satisfied....

Still we cant infer whether is positive or not

pls let know whats wrong in my explanation....

I guess you guys are misinterpreting the statement.

statement (1)

x = x^2 - 2

x cannot be 0 here because if x=0
0 = 0-2
0 = -2
LHS is not equal to RHS,

You dont have to prove the above statement, the above statement is a given fact.

if x^2=1, we only get one answer i.e. x= -1

Thus, Sufficient.

Hope this helps.