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# What is the value of positive integer x ?

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Manager
Joined: 17 Apr 2013
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Location: United States
Concentration: Other, Finance
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What is the value of positive integer x ?  [#permalink]

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15 Sep 2014, 00:20
2
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Difficulty:

55% (hard)

Question Stats:

66% (02:02) correct 34% (01:47) wrong based on 178 sessions

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What is the value of positive integer x ?

(1) $$x^4 < 1000$$

(2) $$2^x < x^2$$

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Joined: 02 Sep 2009
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Re: What is the value of positive integer x ?  [#permalink]

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15 Sep 2014, 00:36
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What is the value of positive integer x ?

Notice that we are told that x is a positive integer.

(1) $$x^4 < 1000$$. x could be 1, 2, 3, 4, or 5. Not sufficient.

(2) $$2^x < x^2$$. Test values:
If x = 1, then (2^x = 2) > (x^2 = 1);
If x = 2, then 2^x = 4 = x^2;
If x = 3, then (2^x = 8) < (x^2 = 9);
If x = 4, then 2^x = 16 = x^2;
If x > 4, then 2^x > x^2.

So, x can only be 3. Sufficient.

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##### General Discussion
Manager
Joined: 17 Apr 2013
Posts: 56
Location: United States
Concentration: Other, Finance
Schools: SDSU '16
GMAT 1: 660 Q47 V34
GPA: 2.76
WE: Analyst (Real Estate)
Re: What is the value of positive integer x ?  [#permalink]

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15 Sep 2014, 00:45
even with testing values i got tricked and mistakenly chose C !
is there another way to solve it or at least understand that 3 is a good fit ?
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Re: What is the value of positive integer x ?  [#permalink]

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15 Sep 2014, 00:49
clipea12 wrote:
even with testing values i got tricked and mistakenly chose C !
is there another way to solve it or at least understand that 3 is a good fit ?

I think it's the easiest way to solve. The key here is to see that when x is 4 or more, 2^x will be more than or equal to x^2. So, you have to test only 3 values: 1, 2, and 3.
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Manager
Joined: 17 Apr 2013
Posts: 56
Location: United States
Concentration: Other, Finance
Schools: SDSU '16
GMAT 1: 660 Q47 V34
GPA: 2.76
WE: Analyst (Real Estate)
Re: What is the value of positive integer x ?  [#permalink]

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15 Sep 2014, 01:00
Yea I got it thank you bunuel
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Re: What is the value of positive integer x ?  [#permalink]

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16 Mar 2018, 19:02
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: What is the value of positive integer x ?   [#permalink] 16 Mar 2018, 19:02
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