It is currently 17 Jan 2018, 06:53

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, x^(1/2) an integer?

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

Hide Tags

Study Buddy Forum Moderator
avatar
P
Joined: 04 Sep 2016
Posts: 574

Kudos [?]: 139 [0], given: 313

Location: India
WE: Engineering (Other)
Premium Member CAT Tests
If x is a positive integer, x^(1/2) an integer? [#permalink]

Show Tags

New post 24 Nov 2017, 15:40
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

72% (00:53) correct 28% (01:12) wrong based on 54 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
[Reveal] Spoiler: OA

_________________

Press kudos if you liked this post


Last edited by Bunuel on 24 Nov 2017, 23:13, edited 2 times in total.
Renamed the topic, edited the question and edited the tags.

Kudos [?]: 139 [0], given: 313

Expert Post
Math Expert
User avatar
D
Joined: 02 Aug 2009
Posts: 5518

Kudos [?]: 6410 [0], given: 122

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

Show Tags

New post 24 Nov 2017, 18:42
Expert's post
1
This post was
BOOKMARKED
adkikani 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


is \(\sqrt{x}\) an integer?

1. \(\sqrt{36x}\) is an integer.
\(\sqrt{36x}=\sqrt{6^2x}=6\sqrt{x}\)
Now if \(6\sqrt{x}\) is a n integer and x is a positive integer, \(\sqrt{x}\) has to be an integer
sufficient

2. \(\sqrt{3x+4}\) is an integer
there can be various possiblities....
x = 4, \(\sqrt{3x+4} = \sqrt{3*4+4}\sqrt{16}=4\)
here \(\sqrt{x} =2\) is an integer ...yes
x = 7, \(\sqrt{3x+4} = \sqrt{3*7+4}\sqrt{25}=5\)
here \(\sqrt{5} =2\) is not an integer ...
insuff

A
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html


BANGALORE/-

Kudos [?]: 6410 [0], given: 122

Study Buddy Forum Moderator
avatar
P
Joined: 04 Sep 2016
Posts: 574

Kudos [?]: 139 [0], given: 313

Location: India
WE: Engineering (Other)
Premium Member CAT Tests
Re: If x is a positive integer, x^(1/2) an integer? [#permalink]

Show Tags

New post 24 Nov 2017, 22:20
chetan2u niks18 Bunuel

Can any of rules be applied universally?

(1) \(\sqrt{ab}\) = \(\sqrt{a}\) * \(\sqrt{b}\)

is it necessary for a and b to be distinct?


(2) \(\sqrt{a+b}\) = \(\sqrt{a}\) + \(\sqrt{b}\)
_________________

Press kudos if you liked this post

Kudos [?]: 139 [0], given: 313

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43307

Kudos [?]: 139278 [1], given: 12782

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

Show Tags

New post 24 Nov 2017, 23:44
1
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
If x is a positive integer, is \(\sqrt{x}\) an integer?

The square root of any positive integer is either an integer or an irrational number. So, \(\sqrt{integer}\) cannot be a fraction, for example it cannot equal to 1/2, 3/7, 19/2, ... It MUST be an integer (0, 1, 2, 3, ...) or irrational number (for example \(\sqrt{2}\), \(\sqrt{3}\), \(\sqrt{17}\), ...). So, as given that \(x\) is a positive integer then \(\sqrt{x}\) is either an integer itself or an irrational number.

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

\(\sqrt{36x} = 6\sqrt{x}\). As discussed above, \(\sqrt{x}\) cannot be a fraction, say 1/6 and integer*irrational cannot be an integer. Therefore, for this statement to be true, \(\sqrt{x}\) must be an integer. Sufficient.

(2) \(\sqrt{3x+4}\) is an integer. If x = 4, then the answer is YES but if x = 7, then the answer is NO. Not sufficient.

Answer: A.

Similar questions:
https://gmatclub.com/forum/if-n-p-q-p-a ... 01475.html
https://gmatclub.com/forum/if-d-is-a-po ... 09384.html
https://gmatclub.com/forum/if-x-is-a-po ... 65976.html
https://gmatclub.com/forum/if-d-is-a-po ... 67950.html
https://gmatclub.com/forum/if-z-is-a-po ... 01464.html
https://gmatclub.com/forum/if-y-is-a-po ... 08287.html
https://gmatclub.com/forum/if-sqrt-4a-i ... 06886.html
https://gmatclub.com/forum/what-is-the- ... 07195.html
https://gmatclub.com/forum/is-s-an-odd- ... 06562.html

Hope it helps.
_________________

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 [?]: 139278 [1], given: 12782

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43307

Kudos [?]: 139278 [1], given: 12782

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

Show Tags

New post 24 Nov 2017, 23:47
1
This post received
KUDOS
Expert's post
adkikani wrote:
chetan2u niks18 Bunuel

Can any of rules be applied universally?

(1) \(\sqrt{ab}\) = \(\sqrt{a}\) * \(\sqrt{b}\)

is it necessary for a and b to be distinct?


(2) \(\sqrt{a+b}\) = \(\sqrt{a}\) + \(\sqrt{b}\)


(1) Always true: \(\sqrt{ab}\) = \(\sqrt{a}\) * \(\sqrt{b}\)

(2) Generally, \(\sqrt{a+b}\) \neq \(\sqrt{a}\) + \(\sqrt{b}\). Does \(\sqrt{1+1}\)=\(\sqrt{1}\) + \(\sqrt{1}\)?

8. Exponents and Roots of Numbers



Check below for more:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread

Hope it helps.
_________________

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 [?]: 139278 [1], given: 12782

Expert Post
Math Expert
User avatar
D
Joined: 02 Aug 2009
Posts: 5518

Kudos [?]: 6410 [0], given: 122

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

Show Tags

New post 25 Nov 2017, 01:38
adkikani wrote:
chetan2u niks18 Bunuel

Can any of rules be applied universally?

(1) \(\sqrt{ab}\) = \(\sqrt{a}\) * \(\sqrt{b}\)

is it necessary for a and b to be distinct?


(2) \(\sqrt{a+b}\) = \(\sqrt{a}\) + \(\sqrt{b}\)



Hi...
Ofcourse Bunuel has already answered that √a*√b=√(ab)..

Just add on to the second point..
√a+√b will generally be NOT equal to √(a+b)..
Only exception is when either or both of them are 0..
An algebraic way to look at it...

\(√a+√b=√(a+b)\)
Square both sides..
a+b+2√(ab)=a+b........
2√(ab)=0
Only possible When either of a or b or BOTH of a and b are 0..
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html


BANGALORE/-

Kudos [?]: 6410 [0], given: 122

Re: If x is a positive integer, x^(1/2) an integer?   [#permalink] 25 Nov 2017, 01:38
Display posts from previous: Sort by

If x is a positive integer, 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®.