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

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

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New post 26 Jul 2013, 15:58
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A
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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

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 ?

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

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New post 26 Jul 2013, 16:09
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) \(-1\leq{n}\leq{1}\)]


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 ?


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

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New post 29 Oct 2015, 02:40
Which of the following describes all values of n for which n^2– 1 ≥ 0?

(A) n ≥ 1
(B) n ≤ –1
(C) 0 ≤ n ≤ 1
(D) n ≤ –1 or n ≥ 1
(E) –1 ≤ n ≤ 1
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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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New post 29 Oct 2015, 02:55
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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New post 29 Oct 2015, 04:43
iikarthik wrote:
Which of the following describes all values of n for which n^2– 1 ≥ 0?

(A) n ≥ 1
(B) n ≤ –1
(C) 0 ≤ n ≤ 1
(D) n ≤ –1 or n ≥ 1
(E) –1 ≤ n ≤ 1


Merging topics. Please refer to the solution above.

Similar questions to practice:
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Other Resources on Inequalities


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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

Hope it helps.
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Collection of Questions:
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DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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

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New post 29 Oct 2015, 18:53
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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New post 31 May 2018, 16:16
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

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

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New post 31 May 2018, 19:47
(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
1.png [ 6.05 KiB | Viewed 237 times ]


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