Which of the following describes all values of n for which n

Question

Which of the following describes all values of n for which  n^2-1\geq{0}

(A)  n\geq{1} 
(B)  n\leq{1} 
(C)  0\leq{n}\leq{1} 
(D)  n\leq{-1}  or  n\geq{1} 
(E)  -1\leq{n}\leq{1} ]

Disclaimer: I have used the Search Box Before Posting. I used the first sentence of the question or a string of words exactly as they show up in the question below for my search. I did not receive an exact match for my question.

Source: Veritas Prep; Book 04
Chapter: Homework
Topic: Algebra
Question: 77
Question: Page 210
Edition: Third

Answer:
Equation:  n^2-1\geq{0}

(n+1).(n-1)\geq{0}

The above inequality can be broken down into the following two inequalities. 
 (n+1) \geq{0}  and  (n-1)\geq{0}

(n+1) \geq{0} 
 n\geq{-1}

(n-1) \geq{0} 
 n\geq{1}

The Official Answer is D. Why am i not getting the  n\leq{-1}  ? What am i doing wrong above in my calculation ?

Bunuel · Accepted Answer

You are missing the case when both multiples are negative: (n+1) \leq{0} --> n\leq{-1} ; (n-1) \leq{0} --> n\leq{1} . Common range n\leq{-1} . This can be solved in another way: n^2-1\geq{0} --> n^2\geq{1} --> n\leq{-1} or n\geq{1} . Or: n^2-1\geq{0} --> n^2\geq{1} --> |n|\geq{1} --> n\leq{-1} or n\geq{1} . Answer: D. Solving inequalities: x2-4x-94661.html#p731476 inequalities-trick-91482.html data-suff-inequalities-109078.html range-for-variable-x-in-a-given-inequality-109468.html everything-is-less-than-zero-108884.html graphic-approach-to-problems-with-inequalities-68037.html inequations-inequalities-part-154664.html inequations-inequalities-part-154738.html Hope it helps.

iikarthik · Answer

I tried to solve it using this method.But not able to figure out where i went wrong.any help would be much appreciated.

n^2– 1 ≥ 0

(n+1)(n-1)≥0

n+1≥0 therefore n≥-1 -->1

n-1≥0 therefore n≥1 -->2

Combining 1 & 2, n≥1 is my solution but its wrong as per the official answer.

EMPOWERgmatRichC · Answer

Hi iikarthik,

From a logic-standpoint, since we're dealing with a squared-term, there MUST be some values of N that 'fit' this inequality and are NEGATIVE. Your solution doesn't account for any negative answers, so something must be 'off' about it.

You would probably find it easiest to avoid a 'math' approach altogether and TEST VALUES.

Since  n^{2}  − 1 ≥ 0

IF....
N = 2
4 - 1 = 3 which IS ≥ 0
So N COULD be 2

IF....
N = -2
4 - 1 = 3 which IS ≥ 0
So N COULD also be -2

There's only one answer that accounts for BOTH of those possibilities...

Final Answer:  D

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

JeffTargetTestPrep · Answer

Simplifying, we have:

n^2 ≥ 1

|n| ≥ 1

n ≥ 1

Or

-n ≥ 1

n ≤ -1

Answer: D

Hero8888 · Answer

(D)  n\leq{-1}  or  n\geq{1}

The fastest way for quadratic equations.

First of all find points in which the function = 0. Point them on the line (for parabola going up + - + /for parabola going down - + - ): see attachment below:

BrentGMATPrepNow · Answer

One 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  2 ² - 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

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Which of the following describes all values of n for which n

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

GMAT Problem Solving (PS) Questions

Which of the following describes all values of n for which n

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia