IMO : A

A. Since x is NOT = 0, for all values of x, x^2 / |x| < 1

B . If we check with values x = 2 , we get , x^2 / |x| > 1
for x = 1/2 , we get , x^2 / |x| < 1

If x ≠ 0, is (x^2) / |x| < 1?

(1) x < 1
(2) x > -1

Evaluate Statement 1 (x < 1)

To solve Yes or No question plug in some values for x:

x = -1; ((-1)^2) / |-1| = 1 / 1 = 1, Answer: No
x = 1/2; ((1/2)^2) / |1/2| = (1/4) / (1/2) = 1/2, Answer: Yes

Statement 1 is insufficient, so eliminate choices A and D

Evaluate Statement 2 (x > -1)

Again, plug in some values for x and answer Yes or No

x = 1; ((1)^2) / |1| = 1 / 1 = 1, Answer: No
x = 1/2; ((1/2)^2) / |1/2| = (1/4) / (1/2) = 1/2, Answer: Yes

Statement 2 is insufficient, so eliminate choice B

Evaluate Statements 1 & 2 Together (x < 1) and (x > -1)

Combine statements: -1 < x < 1, but x ≠ 0

To solve Yes or No question plug in some values for x:

x = 1/2; ((1/2)^2) / |1/2| = (1/4) / (1/2) = 1/2, Answer: Yes
x = -1/2; ((-1/2)^2) / |-1/2| = (1/4) / (1/2) = 1/2, Answer: Yes
x = 1/4; ((1/4)^2) / |1/4| = (1/16) / (1/4) = 1/4, Answer: Yes
x = -1/4; ((-1/4)^2) / |-1/4| = (1/16) / (1/4) = 1/4, Answer: Yes
etc.

Answer C

mitzwillrockgmat wrote:If x ≠ 0, is x^2 / |x| < 1?

(1) x < 1
(2) x > −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.

Please explain!! thanks

also got C, my thinking
as x^2 and |x| are both +ve
we can square them to get rid off module
and left with
x^4/x^2=x^2
so the prolem asks is x^2<1
the given will be true for
(x-1)(x+1)<0
x<1 and x>-1
so to our statements
(1)x<1 not sufficient
(2) x>-1 alone not sufficient
together
-1<x<1 sifficient
so C