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# m0515

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Joined: 17 Jan 2009
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m0515 [#permalink]  30 Jan 2009, 06:11
If x is a positive integer, is sqrt{x} < 2.5x - 5?

1. x < 3
2. x is a prime number

The answer I chose was E but the correct answer is A -

My rationale -

From Statement 1, we know x can only be 1 or 2, since x is a positive integer. We need to test if the answer is the same for both x . If x=1 , the answer to the question is CANNOT DETERMINE sqrt{1} = +/- 1: sqrt{1} < 2.5*1 - 5 .
For x = 2 : sqrt{2} < 0. The answer is CANNOT DETERMINE. Thus, Statement 1 is insufficient.

Statement 2 does not help much as x can be 2 or 11. The inequality does not hold consistent for both of these values. Insufficient.

Statement 1 and 2 together x = 2

Thanks
CEO
Joined: 17 Nov 2007
Posts: 3578
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
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Re: m0515 [#permalink]  30 Jan 2009, 07:57
Expert's post
abdemt wrote:
...the answer to the question is CANNOT DETERMINE sqrt{1} = +/- 1: sqrt{1} < 2.5*1 - 5 ....

$$\sqrt{1}=1$$ not $$\pm1$$

This was discussed in some threads that $$\sqrt{n}$$ represents a positive root and solution of equitation $$x^2=n$$ is $$\pm\sqrt{n}$$, where $$\sqrt{n}$$ is a positive number
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Intern
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Re: m0515 [#permalink]  30 Jan 2009, 08:09
Thank you - that clears my doubt

Regards
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Joined: 29 Aug 2007
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Re: m0515 [#permalink]  30 Jan 2009, 13:27
abdemt wrote:
If x is a positive integer, is $$sqrt{x}$$ < (2.5x - 5)?

1. x < 3
2. x is a prime number

The answer I chose was E but the correct answer is A - Thanks

59-p564448?t=75172#p564448
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Re: m0515   [#permalink] 30 Jan 2009, 13:27
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