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

It is currently 25 Mar 2019, 23:32

Close

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.

Close

Request Expert Reply

Confirm Cancel

How many integer values of n satisfy the inequality

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

Hide Tags

 
Senior Manager
Senior Manager
User avatar
P
Joined: 31 Aug 2016
Posts: 265
Location: India
Concentration: Operations, Finance
GMAT 1: 680 Q49 V33
GMAT 2: 700 Q49 V37
GPA: 2.81
Premium Member Reviews Badge CAT Tests
How many integer values of n satisfy the inequality  [#permalink]

Show Tags

New post 18 Feb 2019, 08:34
2
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

51% (01:18) correct 49% (01:06) wrong based on 44 sessions

HideShow timer Statistics

How many integer values of n satisfy the inequality \(3√n >√n^3\)?

A. 0

B. 1

C. 2

D. 4

E. Infinitely many

_________________
Intern
Intern
User avatar
B
Joined: 17 May 2018
Posts: 48
How many integer values of n satisfy the inequality  [#permalink]

Show Tags

New post 18 Feb 2019, 10:45
1
Let's pick some numbers.
If n = 1, we have 3>1. Correct.
If n = 2, we have \(3\sqrt{2}>2\sqrt{2}\). Correct.
If n = 3, we have \(3\sqrt{3}=3\sqrt{3}\). Doesn't work.

We have understood that on the left side of the inequality we'll have \(3\sqrt{n}\) and on the right side \(n\sqrt{n}\). The inequality will only work for 1 and 2. We can't plug negative numbers because of the square root, so the answer is 2.

Answer C.
_________________
¿Tienes que presentar el GMAT y no sabes por dónde empezar?
¡Visita GMAT para Principiantes y recibe el curso completo gratis!
e-GMAT Representative
User avatar
D
Joined: 04 Jan 2015
Posts: 2722
Re: How many integer values of n satisfy the inequality  [#permalink]

Show Tags

New post 18 Feb 2019, 19:10

Solution



Given:
    • The number n is an integer

To find:
    • The number of values possible for n such that 3√n > √n3

Approach and Working:
Squaring both sides of the given inequality, we get
    • \(3√n > √n^3\)
    Or, \(9n > n^3\)
    Or, \(n^3 – 9n < 0\)
    Or, \(n (n^2 – 9) < 0\)

As n > 0, we can say \(n^2 – 9 < 0\), which implies
    • \(n^2 < 9\)
    Or, -3 < n < 3

But n cannot be negative.
Hence, range of possible values of n: 0 < n < 3
    • As n is integer, possible values of n = 1, 2

Hence, the correct answer is option C.

Answer: C

Image

_________________







Register for free sessions
Number Properties:- Get 5 free video lessons, 50 practice questions | Algebra:-Get 4 free video lessons, 40 practice questions
Quant Workshop:- Get 100 practice questions | Free Strategy Session:- Key strategy to score 760

Success Stories
Q38 to Q50- Interview call form Wharton | Q35 to Q50 | More Success Stories

Ace GMAT
Articles and Questions to reach Q51 | Question of the week | Tips From V40+ Scorers | V27 to V42:- GMAT 770 | Guide to Get into ISB-MBA

Must Read Articles
Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets



| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

GMAT Club Bot
Re: How many integer values of n satisfy the inequality   [#permalink] 18 Feb 2019, 19:10
Display posts from previous: Sort by

How many integer values of n satisfy the inequality

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.