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

 It is currently 05 Dec 2019, 10:59

### 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

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

# How many integer values of n satisfy the inequality

Author Message
TAGS:

### Hide Tags

BSchool Forum Moderator
Status: Valar Dohaeris
Joined: 31 Aug 2016
Posts: 302
GMAT 1: 700 Q49 V37
How many integer values of n satisfy the inequality  [#permalink]

### Show Tags

18 Feb 2019, 08:34
1
5
00:00

Difficulty:

65% (hard)

Question Stats:

46% (01:33) correct 54% (01:26) wrong based on 115 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
Joined: 17 May 2018
Posts: 48
How many integer values of n satisfy the inequality  [#permalink]

### Show Tags

18 Feb 2019, 10:45
1
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.

_________________
¿Tienes que presentar el GMAT y no sabes por dónde empezar?
¡Visita GMAT para Principiantes y recibe el curso completo gratis!
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3158
Re: How many integer values of n satisfy the inequality  [#permalink]

### Show Tags

18 Feb 2019, 19:10
2

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.

_________________
Intern
Joined: 11 Jul 2016
Posts: 2
How many integer values of n satisfy the inequality  [#permalink]

### Show Tags

15 May 2019, 09:03
EgmatQuantExpert n<-3 would also satisfy the equation. Don't you think it should be E. I used the the wavy line method
Manager
Joined: 11 Jun 2018
Posts: 110
GMAT 1: 500 Q39 V21
Re: How many integer values of n satisfy the inequality  [#permalink]

### Show Tags

16 May 2019, 10:12
Why can the values be negative, i don't understand,

9n>n^3

try -8 & -4
they satisfy the equation.
Intern
Joined: 17 May 2018
Posts: 48
Re: How many integer values of n satisfy the inequality  [#permalink]

### Show Tags

17 May 2019, 02:59
We can't consider negative numbers because in GMAT we don't work with square roots of negative numbers. It seems you're missing the square roots in the stem.
_________________
¿Tienes que presentar el GMAT y no sabes por dónde empezar?
¡Visita GMAT para Principiantes y recibe el curso completo gratis!
Intern
Joined: 09 Feb 2019
Posts: 9
Location: India
Concentration: Statistics, Economics
Schools: Rotman '22
Re: How many integer values of n satisfy the inequality  [#permalink]

### Show Tags

21 May 2019, 13:37
Can this be done as?

Posted from my mobile device
Re: How many integer values of n satisfy the inequality   [#permalink] 21 May 2019, 13:37
Display posts from previous: Sort by