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

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1
5 00:00

Difficulty:   65% (hard)

Question Stats: 46% (01:33) correct 54% (01:26) wrong based on 115 sessions

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How many integer values of n satisfy the inequality $$3√n >√n^3$$?

A. 0

B. 1

C. 2

D. 4

E. Infinitely many

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

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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.

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e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3158
Re: How many integer values of n satisfy the inequality  [#permalink]

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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.

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

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

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Why can the values be negative, i don't understand,

9n>n^3

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

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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.
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Intern  B
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]

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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
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