It is currently 17 Oct 2017, 01:10

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If x is a positive integer, is x^1/2 an integer ?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41872

Kudos [?]: 128493 [0], given: 12179

If x is a positive integer, is x^1/2 an integer ? [#permalink]

Show Tags

New post 15 Jan 2015, 07:09
Expert's post
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

68% (00:58) correct 32% (01:50) wrong based on 101 sessions

HideShow timer Statistics

If x is a positive integer, is \(\sqrt{x}\) an integer?

(1) \(\sqrt{36x}\) is an integer

(2) \(\sqrt{3x + 4}\) is an integer

Kudos for a correct solution.
[Reveal] Spoiler: OA

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 128493 [0], given: 12179

3 KUDOS received
Manager
Manager
User avatar
Joined: 27 Jun 2014
Posts: 75

Kudos [?]: 50 [3], given: 125

Location: New Zealand
Concentration: Strategy, General Management
GMAT 1: 710 Q43 V45
GRE 1: 324 Q161 V163
GRE 2: 325 Q159 V166
GPA: 3.6
WE: Editorial and Writing (Computer Software)
Premium Member
Re: If x is a positive integer, is x^1/2 an integer ? [#permalink]

Show Tags

New post 15 Jan 2015, 18:09
3
This post received
KUDOS
Bunuel wrote:
If x is a positive integer, is \(\sqrt{x}\) an integer?

(1) \(\sqrt{36x}\) is an integer

(2) \(\sqrt{3x + 4}\) is an integer

Kudos for a correct solution.


Have started following you Bunuel and this is my first crack at any of your questions.

1. Sufficient: Can be written as \(\sqrt{36}\) * \(\sqrt{x}\). \(\sqrt{36}\) is an integer and therefore \(\sqrt{x}\) must be an integer given that x is a positive integer.
2. Insufficient: Let's take x to be 7 in which case \(\sqrt{3x + 4}\) = \(\sqrt{25}\), which is an integer, but root of 7 is not an integer. On the other hand, if you take x=4, then the statement holds true and root of x is also an integer.

Answer is A. Will I get my first Kudo from you? :D If the solution is incorrect, your feedback will be more valuable than a Kudo :)
_________________

"Hardwork is the easiest way to success." - Aviram

One more shot at the GMAT...aiming for a more balanced score.

Kudos [?]: 50 [3], given: 125

1 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 02 Dec 2014
Posts: 374

Kudos [?]: 90 [1], given: 349

Location: Russian Federation
Concentration: General Management, Economics
GMAT 1: 640 Q44 V33
WE: Sales (Telecommunications)
Re: If x is a positive integer, is x^1/2 an integer ? [#permalink]

Show Tags

New post 17 Jan 2015, 09:43
1
This post received
KUDOS
If x is a positive integer, is \sqrt{x} an integer?

(1) \sqrt{36x} is an integer

(2) \sqrt{3x + 4} is an integer
Statement 1. \sqrt{36x}=6(x^(1/2)). Hence 6 is an integer then (x^1/2) should be integer too. Sufficient
Statement 2. X can be 4 and then (x^1/2) is an integer. Or x=7 then (x^1/2) is not an integer. Insufficient.
Answer A
_________________

"Are you gangsters?" - "No we are Russians!"

Kudos [?]: 90 [1], given: 349

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41872

Kudos [?]: 128493 [0], given: 12179

Re: If x is a positive integer, is x^1/2 an integer ? [#permalink]

Show Tags

New post 19 Jan 2015, 04:39

Kudos [?]: 128493 [0], given: 12179

Senior Manager
Senior Manager
User avatar
Status: Math is psycho-logical
Joined: 07 Apr 2014
Posts: 437

Kudos [?]: 139 [0], given: 169

Location: Netherlands
GMAT Date: 02-11-2015
WE: Psychology and Counseling (Other)
Re: If x is a positive integer, is x^1/2 an integer ? [#permalink]

Show Tags

New post 07 Feb 2015, 10:36
Well, I am not sure if I am off here, but this is what I though:

x>0, is \sqrt{x} an integer?

For SQRT of x to be an integer, then x=1, or x>=4 and a perfect square (otherwise the SQRT would not be an integer). Just some initial thoughts.

[1] says that SQRT of 36x is an integer.
Based on my thinking above, 36x must be a perfect square, apparently greater than 36. For this to be true, x must be a perfect square. Any perfect square multiplied by 36 would have a SQRT that is an integer. So, if x is a perfect sqaure its SQRT will be an integer. So, [1] is sufficient.

[2] says that SQRT of 3x+4 is an integer.
For x=4, we have 3*4+4=16, and SQRT 16 is 4, which is an integer.
For x=5, we have 3*5+4=19, and SQRT 19 is not a integer. So, [2] is not sufficient. ANS A.

Am I right...?

Kudos [?]: 139 [0], given: 169

Intern
Intern
avatar
Joined: 03 Aug 2014
Posts: 19

Kudos [?]: [0], given: 18

Re: If x is a positive integer, is x^1/2 an integer ? [#permalink]

Show Tags

New post 10 Feb 2015, 18:14
Hi Bunuel - I'm a little confused about the OA. If X = 1, then (1)^(1/2) is an integer but if X = 2, then 2^(1/2) is not an integer. Why is A correct?

Kudos [?]: [0], given: 18

Senior Manager
Senior Manager
avatar
Joined: 02 Dec 2014
Posts: 374

Kudos [?]: 90 [0], given: 349

Location: Russian Federation
Concentration: General Management, Economics
GMAT 1: 640 Q44 V33
WE: Sales (Telecommunications)
If x is a positive integer, is x^1/2 an integer ? [#permalink]

Show Tags

New post 11 Feb 2015, 02:29
Hi cg0588!
We are told that \(\sqrt{36x}\) is an integer. Hence if you square out 6 then root of x should be integer (in order to \sqrt{36x} to be integer). Hence you can't say that x=2 since square root of 2 is not an integer. Hope it is clear
_________________

"Are you gangsters?" - "No we are Russians!"

Kudos [?]: 90 [0], given: 349

CEO
CEO
User avatar
G
Joined: 17 Jul 2014
Posts: 2604

Kudos [?]: 392 [0], given: 182

Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
GMAT ToolKit User Premium Member Reviews Badge CAT Tests
Re: If x is a positive integer, is x^1/2 an integer ? [#permalink]

Show Tags

New post 03 May 2016, 19:45
Bunuel wrote:
If x is a positive integer, is \(\sqrt{x}\) an integer?

(1) \(\sqrt{36x}\) is an integer

(2) \(\sqrt{3x + 4}\) is an integer

Kudos for a correct solution.


1. sqrt(36x) = 6*sqrt(x) if this is an integer, then sqrt(x) is an integer. sufficient

2. if x=4, then yes. if x=7 then no. 2 alone not sufficient.

answer A.

Kudos [?]: 392 [0], given: 182

Manager
Manager
avatar
B
Status: To infinity and beyond
Joined: 26 Sep 2017
Posts: 55

Kudos [?]: 12 [0], given: 5

Location: India
Concentration: Finance, Technology
GMAT 1: 660 Q50 V30
GPA: 3.31
WE: Engineering (Computer Software)
Reviews Badge
Re: If x is a positive integer, is x^1/2 an integer ? [#permalink]

Show Tags

New post 05 Oct 2017, 20:21
(1) 36x−−−√36x is an integer since x is a positive integer root[x] needs to be an integer

(2) 3x+4−−−−−√3x+4 is an integer : if x is 7 then answer will be 5 hence not sufficient

A it is

Kudos [?]: 12 [0], given: 5

Re: If x is a positive integer, is x^1/2 an integer ?   [#permalink] 05 Oct 2017, 20:21
Display posts from previous: Sort by

If x is a positive integer, is x^1/2 an integer ?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


cron

GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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®.