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# If x is a positive integer, is \sqrt{x} \lt 2.5x - 5? 1. x

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If x is a positive integer, is \sqrt{x} \lt 2.5x - 5? 1. x [#permalink]

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05 Mar 2008, 17:31
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

If x is a positive integer, is $$\sqrt{x} \lt 2.5x - 5?$$

1. $$x \lt 3$$
2. $$x$$ is a prime number

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Director
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05 Mar 2008, 17:45
Statement 1:
X < 3, Take 2 cases, 1 x=2, and one x=2.99, x=2 => Sqrt(x) = 1.414 is greater that 2.5*2 - 5, however x=2.99 => Sqrt(x) = 1.731 is less than 2.5*2.99 - 5
So this option is insufficient

Statement 2:
X can be any prime number. Take 2 cases x=2, and x=3. Again it is insufficient.

Combining both statements:
we get x<3 and is also a prime number, so only value x can have is 2.

for x = 2, Sqrt(x) = 1.414 is greater that 2.5*2 - 5

So question can be answered using both the statement together, Answer C.

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Director
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05 Mar 2008, 17:51
It should be 'B'

Stmt1: x =1,2
For x=1, No
For x=2, Yes
So Insuff

Stmt2: x=2,3,5,7....
For all of them it's Yes
So Suff

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06 Mar 2008, 16:33
i get A

from stat 1 , x can only be 1 or 2. with both values, we see that LS is not less than RS (Ls=left side, RS=right side)

from stat 2, x=2,3,5,7,11.... for some values, inequality is true, i.e.x=3, and for some, its false, i.e. x=2.

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VP
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06 Mar 2008, 21:00
pmenon wrote:
i get A

from stat 1 , x can only be 1 or 2. with both values, we see that LS is not less than RS (Ls=left side, RS=right side)

from stat 2, x=2,3,5,7,11.... for some values, inequality is true, i.e.x=3, and for some, its false, i.e. x=2.

Got A with the same logic

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Manager
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18 May 2008, 16:38

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Director
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18 May 2008, 16:48
suntaurian wrote:
If x is a positive integer, is $$\sqrt{x} \lt 2.5x - 5?$$

1. $$x \lt 3$$
2. $$x$$ is a prime number

A

statement 1: if x is a positive integer less than 3, then x = 1 or 2
sqrt(x) is either 1 or ~1.4
if x = 1, then sqrt(x) > 2.5x - 5 , and if x = 2, then sqrt(x) > 2.5x - 5

statement 2: if x is a prime number, x could be 1 or 83
if x = 1, then sqrt(x) > 2.5x - 5 , BUT if x = 83, then sqrt(x) < 2.5x - 5

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18 May 2008, 18:29
i get a as well

from stem, x is a postive integer, and so x=1 or 2. plug in x=1 you get 1<-2.5 ... plug in x=2 you get 1.4<0. in either case, the answer is 'no', so we can definitively answer the question

from stat 2, x=1 or x=3. for x=3 you have 1.7<2.5, which is true, but for x=1, the inequality isnt true. so insuff.

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Director
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18 May 2008, 20:36
E for me

rewriting the equation to 2.5(x-2)>sqrt(x)

using 1

x could be 1 or 2 then
plugging in 1 for we get -2.5 >+- 1
plugging in 2 we get 0> +- sqrt (2)

thus 1 is insufficient

using stmt -2
x could be 2,3,5,7.. for all the primes but for 2 the equation holds good but for 2 we run into the same problem as we did in plugging in 2 for x above thus insufficient

now combining both 1& 2 we still have the uncertainty about 0>+- sqrt(2) thus E for me
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Re: Maths: X ?   [#permalink] 18 May 2008, 20:36
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# If x is a positive integer, is \sqrt{x} \lt 2.5x - 5? 1. x

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