Is x greater than 1? (1) (x^2 + 1)x (x^2 + 1) (2) x^2 x

Question

Is x greater than 1?

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

(2)  x^2 > x

ProKiller · Answer

S1 --> (x^2 + 1)x > (x^2 + 1) 
No matter what x is, x^2 is always positive.
Hence, (x^2 + 1) is always positive. Let (x^2 + 1) = y
---> yx > y
---> x > 1
S1 is sufficient.

S2 --> x^2 > x
Take cases. 
C1 - x > 1 - S2 is satisifed.
C2 - 1 > x > 0 - S2 is not satisfied.
Hence, S2 is not sufficient.

Answer: A.

Nidzo · Answer

Is x>1?

1)  (x^2+1)x > (x^2+1)  divide through by (x^2+1)
 x > 1 
Sufficient

2)  x^2 > x 
If x is negative this holds, and if x is positive it holds. Insufficient.

Answer A

sj296 · Answer

Statement 1

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

=>  (x^2 + 1)(x-1) > 0

=>  (x^2 + 1)  is always positive. For the above expression to hold true, x has to be greater than 1.

Statement 1 is sufficient.

Statement 2

x^2 > x

=>  x^2 - x > 0

=> x (x-1) > 0

x > 1 & x < 0 Two sets of values of x

No definitive answer.

Statement 2 is insufficient

Hence, OA should be A

mendax · Answer

The answer should be A, sufficient to get the answer if x is greater than 1 or not
Option1:  (x^2+1)x>(x^2+1) , cancelling  (x^2+1)  both side, we will get x>1...thus sufficient to prove greater than 1

Option 2:  x^2 > x , which implies x can be a positive number greater than 1 or negative number. Thus not sufficient

Is x greater than 1? (1) (x^2 + 1)x > (x^2 + 1) (2) x^2 > x

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