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

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Intern
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Joined: 03 Dec 2012
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GMAT Date: 08-31-2013
Which of the following describes all values of n for which n  [#permalink]

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26 Jul 2013, 14:58
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15% (low)

Question Stats:

74% (01:04) correct 26% (00:56) wrong based on 207 sessions

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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

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 ?

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Posts: 51072
Re: Which of the following describes all values of n for which n  [#permalink]

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26 Jul 2013, 15:09
1
hb wrote:
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) $$-1\leq{n}\leq{1}$$]

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 ?

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 $$n\geq{1}$$.

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.
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Re: Which of the following describes all values of n for which n^2– 1 ≥ 0?  [#permalink]

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29 Oct 2015, 01:55
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.
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Re: Which of the following describes all values of n for which n  [#permalink]

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29 Oct 2015, 17:53
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...

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Re: Which of the following describes all values of n for which n  [#permalink]

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31 May 2018, 15:16
hb wrote:
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) $$-1\leq{n}\leq{1}$$]

Simplifying, we have:

n^2 ≥ 1

|n| ≥ 1

n ≥ 1

Or

-n ≥ 1

n ≤ -1

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Which of the following describes all values of n for which n  [#permalink]

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31 May 2018, 18:47
(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:
Attachments

1.png [ 6.05 KiB | Viewed 610 times ]

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Re: Which of the following describes all values of n for which n  [#permalink]

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19 Sep 2018, 06:38
Top Contributor
hb wrote:
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) $$-1\leq{n}\leq{1}$$]

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 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
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
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Re: Which of the following describes all values of n for which n &nbs [#permalink] 19 Sep 2018, 06:38
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