Which of the following decribes all values of n for which

Hi All,

We're asked which of the following describes all values of N for which (N^2 - 1) is greater than or equal to 0. This question can be solved in a couple of different ways, but you might find it easiest to TEST VALUES.

Since we're SQUARING the value of N, we know that there will be positive values AND negative values of N that will 'fit' the given information. For example, N could be +2 or -2, so we need an answer that accounts for BOTH of those options. There's only one answer that does that....

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

BTGmoderatorLU wrote:Source: Veritas Prep

$$\text{ Which of the following describes all values of n for which }n^2-1\ \ge0.$$
$$A.\ n\ge1$$
$$B.\ n\le1$$
$$C.\ 0\le n\le1$$
$$D.\ n\le-1\ \text{or}\ n\ge1$$
$$E.\ -1\le n\le1$$
The OA is D.

Another approach is to test values and eliminate answer choices

For example, one value of n that satisfies the equation n² - 1 ≥ 0 is n = 2
Notice that 2² - 1 = 4 - 1 = 3 and 3 ≥ 0
Now check the answer choices. . .
Answer choice B says that n CANNOT equal 2 (since it says n ≤ 1)
As such, we can ELIMINATE B
Likewise, C and E also say that n CANNOT equal 2
So, ELIMINATE C and E

We're left with A and D

Let's find another value of n that satisfies the equation n² - 1 ≥ 0
How about n = -2
Notice that (-2)² - 1 = 4 - 1 = 3 and 3 ≥ 0
Now check the remaining answer choices. . .
Answer choice A says that n CANNOT equal -2 (since it says n ≥ 1)
As such, we can ELIMINATE B

By the process of elimination, the correct answer is D

Cheers,
Brent

BTGmoderatorLU wrote:Source: Veritas Prep

$$\text{ Which of the following describes all values of n for which }n^2-1\ \ge0.$$
$$A.\ n\ge1$$
$$B.\ n\le1$$
$$C.\ 0\le n\le1$$
$$D.\ n\le-1\ \text{or}\ n\ge1$$
$$E.\ -1\le n\le1$$
The OA is D.

Simplifying, we have:

n^2 ≥ 1

|n| ≥ 1

Because this is an absolute value equation, we have two possibilities:

n ≥ 1

or

-n ≥ 1

n ≤ -1

So we have:

n ≤ -1 or n ≥ 1

Answer: D