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

It is currently 03 Sep 2015, 15:57
GMAT Club Tests

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Is (7x)^1/2 an integer?

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
5 KUDOS received
Intern
Intern
avatar
Joined: 18 Mar 2012
Posts: 48
GMAT 1: 690 Q V
GPA: 3.7
Followers: 0

Kudos [?]: 92 [5] , given: 117

Is (7x)^1/2 an integer? [#permalink] New post 13 Jan 2013, 07:22
5
This post received
KUDOS
16
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

30% (02:08) correct 70% (01:09) wrong based on 807 sessions
Is \(\sqrt{7x}\) an integer?

(1) \(\sqrt{\frac{x}{7}}\) is an integer

(2) \(\sqrt{28x}\) is an integer

[Reveal] Spoiler:
Can someone please explain why point 2 is not correct? What I did is that 28 is factored into => 2*2*7 so therefore I concluded x must have at least one 7. so if x has one seven then \sqrt{7x} must be an integer. Am I doing something wrong here?

Thanks!
Alex
[Reveal] Spoiler: OA

Last edited by Bunuel on 05 Jun 2013, 02:49, edited 3 times in total.
Renamed the topic and edited the question.
Expert Post
13 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29205
Followers: 4751

Kudos [?]: 50276 [13] , given: 7540

Re: Is (7x)^1/2 an integer? [#permalink] New post 13 Jan 2013, 07:58
13
This post received
KUDOS
Expert's post
7
This post was
BOOKMARKED
Is \(\sqrt{7x}\) an integer?

Notice that we are not told that x is an integer.

(1) \(\sqrt{\frac{x}{7}}\) is an integer. Given that \(\sqrt{\frac{x}{7}}=integer\) --> square it: \(\frac{x}{7}=integer^2\) --> \(x=7*integer^2\). So, \(\sqrt{7x}=\sqrt{7*(7*integer^2)}=7*integer=integer\). Sufficient.

(2) \(\sqrt{28x}\) is an integer. If \(x=\frac{1}{28}\), then \(\sqrt{7x}=\frac{1}{2}\neq{integer}\) BUT if \(x=0\), then \(\sqrt{7x}=0=integer\). Not sufficient.

Answer: A.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. 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?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

SVP
SVP
User avatar
Joined: 05 Jul 2006
Posts: 1516
Followers: 5

Kudos [?]: 144 [0], given: 39

GMAT ToolKit User
Re: Is (7x)^1/2 an integer? [#permalink] New post 13 Jan 2013, 08:01
[quote="alexpavlos"]Is \(\sqrt{7x}\) an integer?

(1) \(\sqrt{\frac{x}{7}}\) is an integer

(2) \(\sqrt{28x}\) is an integer



for sqt 7x to be an integer , x has to have the form 7^a*z^b, where a is an odd integer and z is an integer and b a an even intiger.

from 1

x is in the form 7^a*z^b

from 2
2sqt 7x is an integer....this means that sqt 7x is in the form k/2 however , it says nothing about the form of x itself... thus insuff

A
Intern
Intern
avatar
Joined: 18 Mar 2012
Posts: 48
GMAT 1: 690 Q V
GPA: 3.7
Followers: 0

Kudos [?]: 92 [0], given: 117

Re: Is (7x)^1/2 an integer? [#permalink] New post 13 Jan 2013, 08:16
Bunuel wrote:
Is \(\sqrt{7x}\) an integer?

Notice that we are not told that x is an integer.

(1) \(\sqrt{\frac{x}{7}}\) is an integer. Given that \(\sqrt{\frac{x}{7}}=integer\) --> square it: \(\frac{x}{7}=integer^2\) --> \(x=7*integer^2\). So, \(\sqrt{7x}=\sqrt{7*(7*integer^2)}=7*integer=integer\). Sufficient.

(2) \(\sqrt{28x}\) is an integer. If \(x=\frac{1}{28}\), then \(\sqrt{7x}=\frac{1}{2}\neq{integer}\) BUT if \(x=0\), then \(\sqrt{7x}=0=integer\). Not sufficient.

Answer: A.



Thanks sorry for asking again... But could you please explain if my method/ logic was completely wrong? ie if we break out 28 int primes we see that it has 2,2,7 so x must have at least one 7? therefore we can assume that \sqrt{7x} should be integer?

Thanks again!
Alex
Expert Post
2 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29205
Followers: 4751

Kudos [?]: 50276 [2] , given: 7540

Re: Is (7x)^1/2 an integer? [#permalink] New post 13 Jan 2013, 08:29
2
This post received
KUDOS
Expert's post
alexpavlos wrote:
Bunuel wrote:
Is \(\sqrt{7x}\) an integer?

Notice that we are not told that x is an integer.

(1) \(\sqrt{\frac{x}{7}}\) is an integer. Given that \(\sqrt{\frac{x}{7}}=integer\) --> square it: \(\frac{x}{7}=integer^2\) --> \(x=7*integer^2\). So, \(\sqrt{7x}=\sqrt{7*(7*integer^2)}=7*integer=integer\). Sufficient.

(2) \(\sqrt{28x}\) is an integer. If \(x=\frac{1}{28}\), then \(\sqrt{7x}=\frac{1}{2}\neq{integer}\) BUT if \(x=0\), then \(\sqrt{7x}=0=integer\). Not sufficient.

Answer: A.



Thanks sorry for asking again... But could you please explain if my method/ logic was completely wrong? ie if we break out 28 int primes we see that it has 2,2,7 so x must have at least one 7? therefore we can assume that \sqrt{7x} should be integer?

Thanks again!
Alex


If x is NOT an integer you cannot make its prime factorization.

If we were told that x IS an integer, then \(\sqrt{28x}=2\sqrt{7x}=integer\). Thus x must be of the form \(7^{odd}*integer^2\), so in this case \(\sqrt{7x}=\sqrt{7*(7^{odd}*integer^2)}=\sqrt{7^{even}*integer^2}=integer\).

Hope it's clear.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. 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?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

Manager
Manager
User avatar
Joined: 07 May 2012
Posts: 76
Location: United States
Followers: 3

Kudos [?]: 78 [0], given: 23

Re: Is (7x)^1/2 an integer? [#permalink] New post 26 May 2013, 20:17
alex1233 wrote:
Is \(\sqrt{7x}\) an integer?

(1) \(\sqrt{\frac{x}{7}}\) is an integer

(2) \(\sqrt{28x}\) is an integer



Can someone please explain why point 2 is not correct? What I did is that 28 is factored into => 2*2*7 so therefore I concluded x must have at least one 7. so if x has one seven then \sqrt{7x} must be an integer. Am I doing something wrong here?

Thanks!
Alex



Quote:
\(\sqrt{7x}\) = integer ? or 7x= int^2 ?



(1) \(\sqrt{\frac{x}{7}}\) is an integer ---- lets say b
x/7 = b^2 --> where b is an integer
x= 7 *b^2
7x = (7*b) ^2
hence 7x=int^2--- sufficient


(2) \(\sqrt{28x}\) is an integer ---- lets say c

28x= c^2
7x=c^2/4 = (c/2)^2
If C is odd , then ans is No and if C is even then yes . ( If you knew that x was an integer , then this would have sufficed)
Insufficient.
_________________

Jyothi hosamani

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29205
Followers: 4751

Kudos [?]: 50276 [0], given: 7540

Re: Is (7x)^1/2 an integer? [#permalink] New post 05 Jun 2013, 02:55
Expert's post
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on roots problems: math-number-theory-88376.html

All DS roots problems to practice: search.php?search_id=tag&tag_id=49
All PS roots problems to practice: search.php?search_id=tag&tag_id=113

Tough and tricky exponents and roots questions (DS): tough-and-tricky-exponents-and-roots-questions-125967.html
Tough and tricky exponents and roots questions (PS): new-tough-and-tricky-exponents-and-roots-questions-125956.html

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. 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?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

Expert Post
4 KUDOS received
Verbal Forum Moderator
Verbal Forum Moderator
User avatar
Joined: 10 Oct 2012
Posts: 629
Followers: 64

Kudos [?]: 775 [4] , given: 135

Premium Member
Re: Is (7x)^1/2 an integer? [#permalink] New post 05 Jun 2013, 22:53
4
This post received
KUDOS
Expert's post
alex1233 wrote:
Is \(\sqrt{7x}\) an integer?

(1) \(\sqrt{\frac{x}{7}}\) is an integer

(2) \(\sqrt{28x}\) is an integer


From F.S 1 , we know that \(\sqrt{\frac{x}{7}}\) = Integer(I)--> \(\sqrt{\frac{x*7}{7*7}}\) = \(\sqrt{7x}*\frac{1}{7}\) = I--> \(\sqrt{7x}\) = 7*I. Thus, an integer. Sufficient.

From F.S 2, we know that \(\sqrt{28x}\) = Integer(I) --> \(\sqrt{7*4x}\) = 2*\(\sqrt{7x}\) = I.
Thus, \(\sqrt{7x}\) =\(\frac{I}{2}\). Depending on I being odd/even, the given expression will be a non-integer/integer. Insufficient.

A.
_________________

All that is equal and not-Deep Dive In-equality

Hit and Trial for Integral Solutions

Intern
Intern
avatar
Joined: 12 Apr 2013
Posts: 3
Location: Viet Nam
GMAT 1: 630 Q49 V27
GPA: 3.3
Followers: 0

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

GMAT ToolKit User
Re: Is (7x)^1/2 an integer? [#permalink] New post 21 Dec 2013, 05:09
(1) \(\sqrt{7x}\) = 7\(\sqrt{\frac{x}{7}}\)

7 and \(\sqrt{\frac{x}{7}}\) are integers so \(\sqrt{7x}\) is an integer---Sufficient

(2) \(\sqrt{7x}\) = \(\sqrt{28x}/2\)

We know that \(\sqrt{28x}\) is an integer but not sure if it is divisible by 2 or not---Insufficient

Hence the answer is A
1 KUDOS received
Manager
Manager
avatar
Joined: 25 Oct 2013
Posts: 173
Followers: 0

Kudos [?]: 33 [1] , given: 56

Re: Is (7x)^1/2 an integer? [#permalink] New post 03 Feb 2014, 05:29
1
This post received
KUDOS
(1) \(\sqrt{\frac{x}{7}}\) is integer.

Let this integer be p. then

\(\sqrt{\frac{x}{7}} = p\)

\(\frac{x}{7} = p^2\)

\(x=7*p^2\)

\(7x=7^2*p^2\)

\(\sqrt{7x}=7*p\) an integer. (1) is sufficient

(2) \(\sqrt{28x}\) is integer.

Let this integer be q.

\(\sqrt{28x} = q\)

\(\sqrt{4*7x} = q\)

\(2*\sqrt{7x} = q\)

\(\sqrt{7x} = \frac{q}{2}\)

It is given that q is integer, but \(\frac{q}{2}\) may or may not be an integer. not sufficient.

A is the soln.
_________________

Click on Kudos if you liked the post!

Practice makes Perfect.

Intern
Intern
User avatar
Joined: 13 Apr 2014
Posts: 14
Followers: 1

Kudos [?]: 0 [0], given: 1

Re: Is (7x)^1/2 an integer? [#permalink] New post 15 Apr 2014, 07:04
(1) \sqrt{\frac{x}{7}} is integer.

Let this integer be p. then

\sqrt{\frac{x}{7}} = p

\frac{x}{7} = p^2

x=7*p^2

7x=7^2*p^2

\sqrt{7x}=7*p an integer. (1) is sufficient

(2) \sqrt{28x} is integer.

Let this integer be q.

\sqrt{28x} = q

\sqrt{4*7x} = q

2*\sqrt{7x} = q

\sqrt{7x} = \frac{q}{2}

It is given that q is integer, but \frac{q}{2} may or may not be an integer. not sufficient.

A is the soln.

tnx for this
_________________

www.gmatacademy.ir
best for iranian

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29205
Followers: 4751

Kudos [?]: 50276 [0], given: 7540

Re: Is (7x)^1/2 an integer? [#permalink] New post 15 Apr 2014, 07:09
Expert's post
gmatonline wrote:
(1) \sqrt{\frac{x}{7}} is integer.

Let this integer be p. then

\sqrt{\frac{x}{7}} = p

\frac{x}{7} = p^2

x=7*p^2

7x=7^2*p^2

\sqrt{7x}=7*p an integer. (1) is sufficient

(2) \sqrt{28x} is integer.

Let this integer be q.

\sqrt{28x} = q

\sqrt{4*7x} = q

2*\sqrt{7x} = q

\sqrt{7x} = \frac{q}{2}

It is given that q is integer, but \frac{q}{2} may or may not be an integer. not sufficient.

A is the soln.

tnx for this


I think this is the post you are looking for: rules-for-posting-please-read-this-before-posting-133935.html#p1096628

Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. 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?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 6203
Followers: 346

Kudos [?]: 71 [0], given: 0

Premium Member
Re: Is (7x)^1/2 an integer? [#permalink] New post 16 Apr 2015, 09:54
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Expert Post
EMPOWERgmat Instructor
User avatar
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 3509
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Followers: 149

Kudos [?]: 943 [0], given: 57

Re: Is (7x)^1/2 an integer? [#permalink] New post 16 Apr 2015, 10:54
Expert's post
Hi All,

This question can be solved by TESTing VALUES, but you have to really be thorough with your TESTs (and think about what X COULD be given the information in the Facts).

We're asked if Root(7X) is an integer. This is a YES/NO question.

Fact 1: Root(X/7) is an integer.

This Fact tells us that X has to be a specific type of multiple of 7....

IF....
X = 7
the Root(7/7) = 1 and is an integer
Root(49) = 7 and the answer to the question is YES

IF....
X = 28
the Root(28/7) = 2 and is an integer
Root(196) = 14 and the answer to the question is YES

This hints at the pattern that X will be a "perfect square times a multiple of 7', which means that the answer to the question is ALWAYS YES. You can also use prime-factorization to prove that this is the case.
Fact 1 is SUFFICIENT

Fact 2: Root(28X) is an integer.

This Fact tells us that X has to be a specific type of multiple of 7....

IF....
X = 7
the Root(196) = 14 and is an integer
Root(49) = 7 and the answer to the question is YES

IF....
X = 1/28
the Root(1) = 1 and is an integer
Root(7/28) = 1/2 and the answer to the question is NO
Fact 2 is INSUFFICIENT

Final Answer:
[Reveal] Spoiler:
A


GMAT assassins aren't born, they're made,
Rich
_________________

Official Guide 2016 Question Breakdown:
http://gmatclub.com/forum/empowergmat-blog-198415.html#p1527977

Rich Cohen
Rich.C@empowergmat.com
http://www.empowergmat.com

GMAT Club Verified Reviews for EMPOWERgmat & Special Discount

EMPOWERgmat Podcast - A Wild Secret About The GMAT Algorithm


Re: Is (7x)^1/2 an integer?   [#permalink] 16 Apr 2015, 10:54
    Similar topics Author Replies Last post
Similar
Topics:
Experts publish their posts in the topic If a is an integer, is b an integer? Bunuel 8 03 Apr 2015, 03:47
4 Is a an integer? JusTLucK04 1 31 Oct 2014, 12:35
4 Experts publish their posts in the topic If x is an integer, is y an integer? Bunuel 7 28 Feb 2014, 03:01
1 Experts publish their posts in the topic If x is an integer, is y an integer? boomtangboy 14 28 Apr 2012, 20:25
1 Experts publish their posts in the topic If p is an integer, is q an integer? enigma123 2 11 Feb 2012, 17:41
Display posts from previous: Sort by

Is (7x)^1/2 an integer?

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.