Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 20 Oct 2014, 10:12

### 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 n is positive, is root(n) > 100 ?

Author Message
TAGS:
Current Student
Status: Current MBA Student
Joined: 19 Nov 2009
Posts: 129
Concentration: Finance, General Management
GMAT 1: 720 Q49 V40
Followers: 8

Kudos [?]: 68 [2] , given: 210

If n is positive, is root(n) > 100 ? [#permalink]  11 Jan 2011, 16:57
2
KUDOS
00:00

Difficulty:

35% (medium)

Question Stats:

67% (01:00) correct 33% (01:00) wrong based on 76 sessions
If n is positive, is \sqrt {n} > 100?

(1) \sqrt {n-1} > 99

(2) \sqrt {n+1} > 101

Can someone write out the algebra on this one, I just want to double check work. Thanks.
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 23344
Followers: 3601

Kudos [?]: 28630 [2] , given: 2806

Re: Quant Rev DS #51 [#permalink]  11 Jan 2011, 17:08
2
KUDOS
Expert's post
If n is positive, is \sqrt {n} > 100?

Is \sqrt {n} > 100? --> is n>100^2?

(1) \sqrt {n-1} > 99 --> n-1>99^2 --> n>99^2+1: 99^2+1 is less than 100^2 (as 100^2=(99+1)^2=99^2+2*99+1), so n may or may not be more than this value. Not sufficient.

(2) \sqrt {n+1} > 101 --> n+1>101^2 --> n>101^2-1=(101-1)(101+1)=100*102, so n>100*102>100^2. Sufficient.

 ! Please post PS questions in the PS subforum: gmat-problem-solving-ps-140/Please post DS questions in the DS subforum: gmat-data-sufficiency-ds-141/No posting of PS/DS questions is allowed in the main Math forum.

_________________
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 4870
Location: Pune, India
Followers: 1148

Kudos [?]: 5337 [3] , given: 165

Re: Quant Rev DS #51 [#permalink]  11 Jan 2011, 18:30
3
KUDOS
Expert's post
tonebeeze wrote:
If n is positive, is \sqrt {n} > 100?

1. \sqrt {n-1} > 99

2. \sqrt {n+1} > 101

Can someone write out the algebra on this one, I just want to double check work. Thanks.

Even though you asked for algebra, let me point out that you don't really need algebra to solve this.

When you are considering big numbers, square roots of consecutive numbers differ by very little. e.g. \sqrt {10000} = 100 and \sqrt {9999} = 99.995... Square roots of even small positive numbers differ by less than 1 e.g. \sqrt {1} = 1 and \sqrt {2} = 1.414 - Difference of just 0.414 \sqrt {3} = 1.732 - Difference of just 0.318. The difference just keeps getting smaller and smaller.

So if \sqrt {n-1} > 99, \sqrt {n} will be very close to \sqrt {n-1} and will also be greater than 99. But will it be greater than 100, we cannot say. So not sufficient.

If \sqrt {n+1} > 101, then \sqrt {n} may not be greater than 101, but it will definitely be greater than 100 since between two consecutive integers, the square root difference will not reach 1 (as shown above).
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options. Veritas Prep Reviews Manager Joined: 15 Apr 2011 Posts: 71 Followers: 0 Kudos [?]: 13 [0], given: 45 Re: If n is positive, is \sqrt {n} > 100 ? 1. \sqrt {n-1} [#permalink] 09 Apr 2012, 11:07 I didn't understand why statement 1 is not sufficient. Can someone please explain? thanks. _________________ Math Expert Joined: 02 Sep 2009 Posts: 23344 Followers: 3601 Kudos [?]: 28630 [1] , given: 2806 Re: If n is positive, is \sqrt {n} > 100 ? 1. \sqrt {n-1} [#permalink] 09 Apr 2012, 11:19 1 This post received KUDOS Expert's post mymbadreamz wrote: I didn't understand why statement 1 is not sufficient. Can someone please explain? thanks. Question asks whether n>100^2. From (1) we have that n>99^2+1. Now, since 100^2>99^2+1, then it's possible that n>100^2>99^2+1, which would mean that the answer is YES, as well as that 100^2>n>99^2+1, which would mean that the answer is NO. Two different answers, hence not sufficient. Hope it's clear. _________________ Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 4870 Location: Pune, India Followers: 1148 Kudos [?]: 5337 [1] , given: 165 Re: If n is positive, is \sqrt {n} > 100 ? 1. \sqrt {n-1} [#permalink] 09 Apr 2012, 21:05 1 This post received KUDOS Expert's post mymbadreamz wrote: I didn't understand why statement 1 is not sufficient. Can someone please explain? thanks. Stmnt 1 just tells you that \sqrt{n-1} > 99 Think of 2 diff cases: \sqrt{n-1} = 99.2 \sqrt{n} = 99.205 or \sqrt{n-1} = 112 \sqrt{n} = 112.015 Can you say whether \sqrt{n} is greater than 100? _________________ Karishma Veritas Prep | GMAT Instructor My Blog Save$100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Re: If n is positive, is \sqrt {n} > 100 ? 1. \sqrt {n-1}   [#permalink] 09 Apr 2012, 21:05
Similar topics Replies Last post
Similar
Topics:
8 If n is positive, is root(n) > 100 ? 6 23 Jan 2014, 02:23
If n is a positive integer is n equal to 100? (1) \sqrt{n} 4 10 May 2009, 18:26
Is n an integer? 1) n^2 is an integer 2) square root(n) is 2 04 Mar 2008, 00:47
if n is a positive integer, is n equal to 100? 1) sqrt n 8 28 Dec 2005, 07:07
If n is a positive integer, is n equal to 100? (1) SQRT(n) 3 11 Dec 2005, 10:36
Display posts from previous: Sort by