Is ∣x∣<1 ?

[M7MBA]

Is ∣x∣<1?

1) x = 1/(3+y^2)
2) y =-2

The OA is the option A.

Why is sufficient the first statement? We don't know the value of y. <i class="em em-neutral_face"></i>

[GMATGuruNY]

Is ∣x∣<1?

1) x = 1/(3+y^2)
2) y =-2

Statement 1:
Since the square of a value must be NONNEGATIVE, y² ≥ 0.
If y²=0, then x = 1/3.
If y²>0, then x = 1/(more than 3), implying that x < 1/3.
Since x≤1/3, the answer to the question stem is YES.
SUFFICIENT.

Statement 2:
No information about x.
INSUFFICIENT.

The correct answer is A.

[Vincen]

Hello M7MBA.

I will solve it as follows:

1) x = 1/(3+y^2)

We have the following equations: $$y^2\ge0\ \ and\ \ \ \ 0<1<3\ \ \Rightarrow\ \ \ 0<\ 1<3+y^2\ \ \ \Rightarrow\ \ 0<\frac{1}{3+y^2}<1$$ $$Since\ x=\frac{1}{3+y^2}\ \ \ \Rightarrow\ \ \ \ 0 < x < 1\ \ \ \Leftrightarrow\ \ \ \left|x\right| < 1.$$ Therefore, this statement is SUFFICIENT.

2) y =-2

This statement doesn't tell us anything about x. Therefore, is NOT SUFFICIENT.

The correct answer is the option A. <i class="em em---1"></i><i class="em em-sunglasses"></i>