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# Is 3^x < x^3? (1) 3^x > 1 (2) 0 < x < 1

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Math Expert
Joined: 02 Sep 2009
Posts: 52108
Is 3^x < x^3? (1) 3^x > 1 (2) 0 < x < 1  [#permalink]

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10 Sep 2017, 20:46
00:00

Difficulty:

75% (hard)

Question Stats:

53% (02:00) correct 47% (01:46) wrong based on 109 sessions

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Is $$3^x < x^3$$?

(1) $$3^x > 1$$

(2) $$0 < x < 1$$

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Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3334
Location: India
GPA: 3.12
Re: Is 3^x < x^3? (1) 3^x > 1 (2) 0 < x < 1  [#permalink]

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10 Sep 2017, 21:30
1
(1) $$3^x > 1$$
If x=1 or 3, the equation $$3^x < x^3$$ is not true
But, if x = $$\frac{5}{2}$$, the equation $$3^x < x^3$$ is true.(Insufficient)

(2) $$0 < x < 1$$
If value of x is between 0 and 1,
x could be $$\frac{1}{4}$$ or $$\frac{1}{2}$$
When we plug x=$$\frac{1}{2}$$, $$3^x < x^3$$ is false
Similarly when we plug x=$$\frac{1}{4}$$ also, $$3^x < x^3$$ is false.
Whatever the value of x in this range, the equation is always false(Sufficient) (Option B)

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Retired Moderator
Joined: 25 Feb 2013
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Is 3^x < x^3? (1) 3^x > 1 (2) 0 < x < 1  [#permalink]

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01 Dec 2017, 19:58
Bunuel wrote:
Is $$3^x < x^3$$?

(1) $$3^x > 1$$

(2) $$0 < x < 1$$

Statement 1: implies that $$x>0$$ but at $$x=3$$; $$3^x=x^3$$ so the relation does not always hold true. Insufficient

Statement 2: this implies $$x$$ is positive.

Any number which is greater than 1 raised to any positive power will yield a number greater than 1. this can be derived as -

$$3>1$$ now raise both sides of the inequality to power $$x$$

so $$3^x>1^x =>3^x>1$$

again as $$x<1$$, raise both sides of the inequality to power $$3$$

so $$x^3<1^3 => x^3<1$$

So we have $$3^x>x^3$$. Hence a NO for our question stem. Sufficient

Option B

You can also use the plug-in method to arrive at Option B but I guess it will involve multiple testing and calculations.
Intern
Joined: 11 Dec 2013
Posts: 14
Location: India
Concentration: Operations, Strategy
Schools: Marshall '21 (D)
GMAT 1: 710 Q49 V38
GPA: 3.7
Re: Is 3^x < x^3? (1) 3^x > 1 (2) 0 < x < 1  [#permalink]

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03 Dec 2017, 07:15
Bunuel wrote:
Is $$3^x < x^3$$?

(1) $$3^x > 1$$

(2) $$0 < x < 1$$

what should be ideal approach for this question plugin or concept??
Retired Moderator
Joined: 25 Feb 2013
Posts: 1220
Location: India
GPA: 3.82
Re: Is 3^x < x^3? (1) 3^x > 1 (2) 0 < x < 1  [#permalink]

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03 Dec 2017, 07:33
dhruv solanki wrote:
Bunuel wrote:
Is $$3^x < x^3$$?

(1) $$3^x > 1$$

(2) $$0 < x < 1$$

what should be ideal approach for this question plugin or concept??

Hi dhruv solanki

Any approach that helps you solve the question within 2 minutes and strike you first should be the ideal approach.
The so called short-cut methods you might have come across will rarely give you confidence under GMAT exam pressure and chances are you might miss a hidden concept required to solve the question.

Anyways so far I have not come across a real GMAT question that cannot be solved within 2 minutes using proper mathematical concept
Math Expert
Joined: 02 Aug 2009
Posts: 7199
Re: Is 3^x < x^3? (1) 3^x > 1 (2) 0 < x < 1  [#permalink]

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03 Dec 2017, 07:51
dhruv solanki wrote:
Bunuel wrote:
Is $$3^x < x^3$$?

(1) $$3^x > 1$$

(2) $$0 < x < 1$$

what should be ideal approach for this question plugin or concept??

Hi..

you will agree any question done on concept is surely correct and increases your confidence level..
as here if you know -
x is negative :- 3^x will be <1... it in all probability will be a positive fraction AND x^3 will be negative
x is 0 :- 3^x will be 1 AND x^3 will be 0
and so x>0 will give you a value more than 3^0 or 1 AND x^3 is less than 1 if 0<x <1

so when you know these, you will be sure of answer..

OR you will have to plug three values - highest possible, lowest possible and something in middle and still can be in some doubt.
ofcourse if you do not know concept, go for substitution

substitution on the other hand is very effective in few cases
when you are asked for value of x in some equation and choices are given
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Intern
Joined: 11 Dec 2013
Posts: 14
Location: India
Concentration: Operations, Strategy
Schools: Marshall '21 (D)
GMAT 1: 710 Q49 V38
GPA: 3.7
Re: Is 3^x < x^3? (1) 3^x > 1 (2) 0 < x < 1  [#permalink]

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03 Dec 2017, 08:33
chetan2u wrote:
dhruv solanki wrote:
Bunuel wrote:
Is $$3^x < x^3$$?

(1) $$3^x > 1$$

(2) $$0 < x < 1$$

what should be ideal approach for this question plugin or concept??

Hi..

you will agree any question done on concept is surely correct and increases your confidence level..
as here if you know -
x is negative :- 3^x will be <1... it in all probability will be a positive fraction AND x^3 will be negative
x is 0 :- 3^x will be 1 AND x^3 will be 0
and so x>0 will give you a value more than 3^0 or 1 AND x^3 is less than 1 if 0<x <1

so when you know these, you will be sure of answer..

OR you will have to plug three values - highest possible, lowest possible and something in middle and still can be in some doubt.
ofcourse if you do not know concept, go for substitution

substitution on the other hand is very effective in few cases
when you are asked for value of x in some equation and choices are given

in this question, suppose x=3 then it will be equal so is the information insufficient?
Math Expert
Joined: 02 Aug 2009
Posts: 7199
Re: Is 3^x < x^3? (1) 3^x > 1 (2) 0 < x < 1  [#permalink]

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04 Dec 2017, 06:13
dhruv solanki wrote:
Bunuel wrote:
Is $$3^x < x^3$$?

(1) $$3^x > 1$$

(2) $$0 < x < 1$$

in this question, suppose x=3 then it will be equal so is the information insufficient?

Hi..

If one of the statement said that x=3..
so our answer for "Is $$3^x<x^3$$ ?" will be NO and the statement will be sufficient as it is giving us a clear NO
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Re: Is 3^x < x^3? (1) 3^x > 1 (2) 0 < x < 1 &nbs [#permalink] 04 Dec 2017, 06:13
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# Is 3^x < x^3? (1) 3^x > 1 (2) 0 < x < 1

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