It is currently 10 Dec 2017, 22:57

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

Author Message
Senior Manager
Joined: 06 Jul 2006
Posts: 291

Kudos [?]: 76 [0], given: 0

Location: SFO Bay Area
Schools: Berkeley Haas
If x is a positive integer, is \sqrt{x} \lt 2.5x - 5? 1. x [#permalink]

Show Tags

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

Kudos [?]: 76 [0], given: 0

Director
Joined: 10 Sep 2007
Posts: 933

Kudos [?]: 361 [0], given: 0

Show Tags

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.

Kudos [?]: 361 [0], given: 0

Director
Joined: 14 Jan 2007
Posts: 775

Kudos [?]: 183 [0], given: 0

Show Tags

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

Kudos [?]: 183 [0], given: 0

SVP
Joined: 28 Dec 2005
Posts: 1543

Kudos [?]: 188 [0], given: 2

Show Tags

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.

Kudos [?]: 188 [0], given: 2

VP
Joined: 03 Apr 2007
Posts: 1339

Kudos [?]: 875 [0], given: 10

Show Tags

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

Kudos [?]: 875 [0], given: 10

Manager
Joined: 11 May 2007
Posts: 105

Kudos [?]: 43 [0], given: 0

Show Tags

18 May 2008, 16:38

Kudos [?]: 43 [0], given: 0

Director
Joined: 23 Sep 2007
Posts: 782

Kudos [?]: 254 [0], given: 0

Show Tags

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

Kudos [?]: 254 [0], given: 0

SVP
Joined: 28 Dec 2005
Posts: 1543

Kudos [?]: 188 [0], given: 2

Show Tags

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.

Kudos [?]: 188 [0], given: 2

Director
Joined: 05 Jan 2008
Posts: 684

Kudos [?]: 627 [0], given: 0

Show Tags

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
_________________

Persistence+Patience+Persistence+Patience=G...O...A...L

Kudos [?]: 627 [0], given: 0

Re: Maths: X ?   [#permalink] 18 May 2008, 20:36
Display posts from previous: Sort by

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

Moderator: chetan2u

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.