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

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Director
Joined: 18 Feb 2008
Posts: 786

Kudos [?]: 130 [0], given: 25

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

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14 Jun 2008, 13:11
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If x is a positive integer, is $$\sqrt{x} \lt 2.5x - 5?$$

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

Kudos [?]: 130 [0], given: 25

Intern
Joined: 08 Jun 2008
Posts: 47

Kudos [?]: 9 [0], given: 0

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14 Jun 2008, 13:24
IMO , ans is A

if X < 3 then x can be 2 u can take it as 1 too if u consider 1 as prime .. i dont

use both values in the stem equation .. u get same ans - No hence sufficient

statement 2 says x is prime

if u take x as 2 u get sqrt (2) < o which is false
if u take x as 3 u get sqrt (3) < 2.5 which is true .. hence statement is insufficient

Kudos [?]: 9 [0], given: 0

Director
Joined: 14 Oct 2007
Posts: 751

Kudos [?]: 232 [0], given: 8

Location: Oxford
Schools: Oxford'10

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14 Jun 2008, 13:27
billyjeans wrote:
If x is a positive integer, is $$\sqrt{x} \lt 2.5x - 5?$$

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

1) x can be either 1 or 2
trying these we get either 1 > -2.5 or sqrt(2) > 0
as seen both of these yield a NO to the question
sufficient

2) x is prime
we already know from 1) that for 2 we get a NO

lets try other values
3: sqrt(3) < 2.5
5: sqrt(5) < 7.5

so definitely insufficient

Kudos [?]: 232 [0], given: 8

Re: DS is x   [#permalink] 14 Jun 2008, 13:27
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