Which of the following describes all values of $n$ for which $n^2-1\ge 0.$

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by M7MBA » Wed Oct 07, 2020 10:19 am

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Which of the following describes all values of $n$ for which $n^2-1\ge 0.$

(A) $n\ge 1$
(B) $n\le1$
(C) $0\le n \le 1$
(D) $n\le -1$ or $n \ge 1$
(E) $-1\le n\le 1$

Answer: D

Source: Veritas Prep

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Source: Beat The GMAT — Problem Solving | Wed Oct 07, 2020 10:19 am

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8155; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: Which of the following describes all values of $n$ for which $n^2-1\ge 0.$

by Scott@TargetTestPrep » Fri Oct 16, 2020 5:57 am

M7MBA wrote: ↑
Wed Oct 07, 2020 10:19 am
Which of the following describes all values of $n$ for which $n^2-1\ge 0.$

(A) $n\ge 1$
(B) $n\le1$
(C) $0\le n \le 1$
(D) $n\le -1$ or $n \ge 1$
(E) $-1\le n\le 1$

Answer: D

Solution:

Simplifying, we have:

n^2 ≥ 1

√(n^2) ≥ √1

|n| ≥ 1

n ≥ 1 or -n ≥ 1 → n ≤ -1

Answer: D

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