If n is positive, is root(n) > 100 ? : GMAT Data Sufficiency (DS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 18 Jan 2017, 17:11

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:

Hide Tags

Manager
Status: Current MBA Student
Joined: 19 Nov 2009
Posts: 127
Concentration: Finance, General Management
GMAT 1: 720 Q49 V40
Followers: 13

Kudos [?]: 350 [3] , given: 210

If n is positive, is root(n) > 100 ? [#permalink]

Show Tags

11 Jan 2011, 16:57
3
KUDOS
6
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

67% (02:10) correct 33% (01:07) wrong based on 360 sessions

HideShow timer Statistics

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: 36548
Followers: 7077

Kudos [?]: 93113 [4] , given: 10552

Re: Quant Rev DS #51 [#permalink]

Show Tags

11 Jan 2011, 17:08
4
KUDOS
Expert's post
5
This post was
BOOKMARKED
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: 7121
Location: Pune, India
Followers: 2133

Kudos [?]: 13640 [5] , given: 222

Re: Quant Rev DS #51 [#permalink]

Show Tags

11 Jan 2011, 18:30
5
KUDOS
Expert's post
1
This post was
BOOKMARKED
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

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Manager Joined: 15 Apr 2011 Posts: 70 Followers: 0 Kudos [?]: 17 [0], given: 45 Re: If n is positive, is \sqrt {n} > 100 ? 1. \sqrt {n-1} [#permalink] Show Tags 09 Apr 2012, 11:07 I didn't understand why statement 1 is not sufficient. Can someone please explain? thanks. _________________ http://mymbadreamz.blogspot.com Math Expert Joined: 02 Sep 2009 Posts: 36548 Followers: 7077 Kudos [?]: 93113 [1] , given: 10552 Re: If n is positive, is \sqrt {n} > 100 ? 1. \sqrt {n-1} [#permalink] Show Tags 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: 7121 Location: Pune, India Followers: 2133 Kudos [?]: 13640 [2] , given: 222 Re: If n is positive, is \sqrt {n} > 100 ? 1. \sqrt {n-1} [#permalink] Show Tags 09 Apr 2012, 21:05 2 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 Get started with Veritas Prep GMAT On Demand for$199

Veritas Prep Reviews

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13439
Followers: 575

Kudos [?]: 163 [0], given: 0

Re: If n is positive, is root(n) > 100 ? [#permalink]

Show Tags

27 Oct 2015, 00:42
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Senior Manager
Joined: 17 Jun 2015
Posts: 270
GMAT 1: 540 Q39 V26
GMAT 2: 680 Q46 V37
GMAT 3: Q V
Followers: 3

Kudos [?]: 20 [0], given: 165

Re: If n is positive, is root(n) > 100 ? [#permalink]

Show Tags

24 Dec 2015, 03:34
Important consideration: n is not an integer, not stated explicitly; assuming the same would given an incorrect conclusions

Statement 1 gives many values which could be greater than 99 but not greater than 100, or greater than 100. Insufficient

Statement 2 gives a sure conclusion that it is greater. Hence, sufficient
_________________

Fais de ta vie un rêve et d'un rêve une réalité

Director
Joined: 11 Sep 2015
Posts: 903
Followers: 106

Kudos [?]: 859 [1] , given: 108

Re: If n is positive, is root(n) > 100 ? [#permalink]

Show Tags

22 Aug 2016, 14:00
1
KUDOS
Top Contributor
1
This post was
BOOKMARKED
tonebeeze wrote:
If n is positive, is $$\sqrt {n} > 100$$?

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

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

Target question: Is √n > 100?

This is a good candidate for REPHRASING the target question.
Take √n > 100 and square both sides to get n > 10,000
So, we get: REPHRASED target question: Is n > 10,000?

Statement 1: √(n - 1) > 99
Square both sides to get n - 1 > 99²
Evaluate: n - 1 > 9801
Add 1 to both sides to get: n > 9802
So, x COULD equal 9803, in which case n < 10,000
Conversely, x COULD equal 10,001, in which case n > 10,000
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: √(n + 1) > 101
Square both sides to get n + 1 > 101²
Evaluate: n + 1 > 10,201
Subtract 1 from both sides to get: n > 10,200
If x is greater than 10,200, then we can be certain that x > 10,000
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

[Reveal] Spoiler:
B

RELATED VIDEO

_________________

Brent Hanneson – Founder of gmatprepnow.com

Brent also tutors students for the GMAT

Re: If n is positive, is root(n) > 100 ?   [#permalink] 22 Aug 2016, 14:00
Similar topics Replies Last post
Similar
Topics:
1 Let m and n be positive integers. Is mn > 100? 4 08 Dec 2016, 12:06
1 If n is an integer, and n ≠ 0, is (100 + n^2)/n a positive integer? 2 01 Sep 2016, 02:53
2 If n is a positive integer, is n + 2 > z? 3 17 Mar 2016, 02:59
25 If n is positive, is root(n) > 100 ? 11 23 Jan 2014, 02:23
2 If n is a positive integer is n equal to 100? 6 10 May 2009, 18:26
Display posts from previous: Sort by