GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 26 Aug 2019, 02:19 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. ### Request Expert Reply # Is |n| < 1 ?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Intern  Joined: 26 Feb 2014
Posts: 2
Is |n| < 1 ?  [#permalink]

### Show Tags

8 00:00

Difficulty:   55% (hard)

Question Stats: 63% (02:15) correct 38% (02:15) wrong based on 176 sessions

### HideShow timer Statistics

Is |n| < 1 ?

(1) n^x - n < 0
(2) x^(-1) = -2

My sol:
1. n (n^(x-1) - 1) < 0
so either n is less than zero OR n^(x-1) - 1 < 0

2. x = -1/2

Clueless on how to analyze above and conclude some answer.

Originally posted by faceharshit on 26 Feb 2014, 09:52.
Last edited by Bunuel on 27 Feb 2014, 05:45, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
##### Most Helpful Expert Reply
Math Expert V
Joined: 02 Sep 2009
Posts: 57297
Re: Is |n| < 1 ?  [#permalink]

### Show Tags

2
4
faceharshit wrote:
Is |n| < 1 ?

(1) n^x - n < 0
(2) x^(-1) = -2

My sol:
1. n (n^(x-1) - 1) < 0
so either n is less than zero OR n^(x-1) - 1 < 0

2. x = -1/2

Clueless on how to analyze above and conclude some answer.

Is |n| < 1 ?

Notice that the question basically asks whether $$-1<n<1$$.

(1) n^x - n < 0. Well, this one is clearly insufficient: if $$n=2$$ and $$x=0$$, the answer is NO but if $$n=\frac{1}{2}$$ and $$x=2$$, the answer is YES. Not sufficient.

(2) x^(-1) = -2 --> $$\frac{1}{x}=-2$$ --> $$x=-\frac{1}{2}$$. Not sufficient.

(1)+(2) When we combine we have: $$n^{-\frac{1}{2}} - n < 0$$ --> $$\frac{1}{\sqrt{n}}-n<0$$.

From $$\frac{1}{\sqrt{n}}$$, we can get that n must be a positive number: $$n>0$$ (the expression under the square root must be non-negative, also since it's in the denominator it must be greater than 0).

$$\frac{1}{\sqrt{n}}-n<0$$ --> $$1<\sqrt{n}n$$. If $$0<n\leq{1}$$, then obviously $$1\geq{\sqrt{n}n}$$, thus $$n>1$$. We have a NO answer to the question. Sufficient.

Answer: C.

Hope it's clear.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to rules 3 and 7. Thank you.
_________________
##### General Discussion
Magoosh GMAT Instructor G
Joined: 28 Dec 2011
Posts: 4483
Re: Inequality - Data Sufficiency Problem  [#permalink]

### Show Tags

1
1
faceharshit wrote:
Hi friends,
Need your help to approach below Inequality problem :-

Is |n| < 1 ?

1) n^x - n < 0 2) x^-1 = -2

My sol:

1. n (n^(x-1) - 1) < 0
so either n is less than zero OR n^(x-1) - 1 < 0

2. x = -1/2

Clueless on how to analyze above and conclude some answer.

Dear faceharshit,
I'm happy to respond. In writing these questions, I would urge you to pay more attention to mathematical grouping symbols. You can read more about this concept here:
http://magoosh.com/gmat/2013/gmat-quant ... g-symbols/

In this question, clearly statement #1 is insufficient by itself, because we know nothing about x. Clearly, statement #2 is insufficient by itself because we know nothing about n. Clearly, we have to combine them to figure anything out.

From #2, you are correct, we get x = -1/2. Plug this into #1

[n^(-1/2)] - n < 0

Notice, first of all, that we could not make any sensible statement if n were negative, because the square root of a negative is outside the real number system. The fact that this is an ordinary sensible statement automatically precludes negatives. It also precludes n - 0, because 0^(-1/2) is undefined. Add n to both sides.

n^(-1/2) < n

Since we know that n^(-1/2) is positive, divide both sides by that.

1 < n * n^(+1/2) = n^(3/2)

If the 3/2 power of a number is greater than one, then that number must be greater than one. We can answer an affirmative and definitive "no" to the prompt question. Because we can arrive at an answer, that means the combined statements must be sufficient.

Answer = (C)

Does all this make sense?

Mike _________________
Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
Intern  B
Joined: 22 Dec 2018
Posts: 4
Concentration: Healthcare, International Business
WE: Medicine and Health (Health Care)
Re: Is |n| < 1 ?  [#permalink]

### Show Tags

Bunuel wrote:
faceharshit wrote:
Is |n| < 1 ?

(1) n^x - n < 0
(2) x^(-1) = -2

My sol:
1. n (n^(x-1) - 1) < 0
so either n is less than zero OR n^(x-1) - 1 < 0

2. x = -1/2

Clueless on how to analyze above and conclude some answer.

Is |n| < 1 ?

Notice that the question basically asks whether $$-1<n<1$$.

(1) n^x - n < 0. Well, this one is clearly insufficient: if $$n=2$$ and $$x=0$$, the answer is NO but if $$n=\frac{1}{2}$$ and $$x=2$$, the answer is YES. Not sufficient.

(2) x^(-1) = -2 --> $$\frac{1}{x}=-2$$ --> $$x=-\frac{1}{2}$$. Not sufficient.

(1)+(2) When we combine we have: $$n^{-\frac{1}{2}} - n < 0$$ --> $$\frac{1}{\sqrt{n}}-n<0$$.

From $$\frac{1}{\sqrt{n}}$$, we can get that n must be a positive number: $$n>0$$ (the expression under the square root must be non-negative, also since it's in the denominator it must be greater than 0).

$$\frac{1}{\sqrt{n}}-n<0$$ --> $$1<\sqrt{n}n$$. If $$0<n\leq{1}$$, then obviously $$1\geq{\sqrt{n}n}$$, thus $$n>1$$. We have a NO answer to the question. Sufficient.

I am unable to understand the highlighted part. Could you please explain how did we arrive at n>1?
Apologies but i do find inequality a little difficult.

Thanks so much Re: Is |n| < 1 ?   [#permalink] 02 Aug 2019, 10:38
Display posts from previous: Sort by

# Is |n| < 1 ?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

#### MBA Resources  