GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 22 Apr 2019, 05:17

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

If (4a)^(1/2) integer, is (a)^(1/2) integer?

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

Hide Tags

 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 54434
If (4a)^(1/2) integer, is (a)^(1/2) integer?  [#permalink]

Show Tags

New post 24 Jun 2017, 07:24
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

67% (01:28) correct 33% (01:12) wrong based on 98 sessions

HideShow timer Statistics

Current Student
User avatar
P
Joined: 18 Aug 2016
Posts: 619
Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38
GMAT ToolKit User Reviews Badge
Re: If (4a)^(1/2) integer, is (a)^(1/2) integer?  [#permalink]

Show Tags

New post 24 Jun 2017, 07:43
Bunuel wrote:
If is \(\sqrt{4a}\) integer, is \(\sqrt{a}\) integer?

(1) \(a\) is a positive integer

(2) \(a = n^6\), where n is an integer


\sqrt{4a} is an integer means either a = a perfect square or 1 or 4^3 or perfect square*4. If a is either then \sqrt{a} will be an integer

(1) no new information....but since stem was sufficient ..Sufficient

(2) ok...Sufficient (if n^6 is a then \sqrt{a} is n^3 which will be an integer)

I would say D

Please correct me if i am wrong
_________________
We must try to achieve the best within us


Thanks
Luckisnoexcuse
Retired Moderator
User avatar
P
Joined: 19 Mar 2014
Posts: 931
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5
GMAT ToolKit User
Re: If (4a)^(1/2) integer, is (a)^(1/2) integer?  [#permalink]

Show Tags

New post 01 Jul 2017, 03:33
If is \(\sqrt{4a}\) integer, is \(\sqrt{a}\) integer?

\(\sqrt{4a}\) = Integer

This is only possible when \(\sqrt{a} = Integer\)

(1) \(a\) is a positive integer

This is sufficient as per the given information - \(\sqrt{4a}\) = Integer

Hence, (1) =====> is SUFFICIENT

(2) \(a = n^6\), where n is an integer

As n is an integer and \(a = n^6\)

\(\sqrt{a} = \sqrt{n^6} = n^3\)

As n is integer, \(n^3\) will also be an integer.

Hence, (2) =====> is SUFFICIENT

Hence, Answer is D
_________________
"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."

Best AWA Template: https://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html#p470475
Manager
Manager
avatar
S
Joined: 27 Aug 2016
Posts: 89
Location: India
Schools: HEC Montreal '21
GMAT 1: 670 Q47 V37
GPA: 3
WE: Engineering (Energy and Utilities)
GMAT ToolKit User
Re: If (4a)^(1/2) integer, is (a)^(1/2) integer?  [#permalink]

Show Tags

New post 25 Jul 2017, 03:56
ydmuley wrote:
If is \(\sqrt{4a}\) integer, is \(\sqrt{a}\) integer?

\(\sqrt{4a}\) = Integer

This is only possible when \(\sqrt{a} = Integer\)

(1) \(a\) is a positive integer

This is sufficient as per the given information - \(\sqrt{4a}\) = Integer

Hence, (1) =====> is SUFFICIENT

(2) \(a = n^6\), where n is an integer

As n is an integer and \(a = n^6\)

\(\sqrt{a} = \sqrt{n^6} = n^3\)

As n is integer, \(n^3\) will also be an integer.

Hence, (2) =====> is SUFFICIENT

Hence, Answer is D


Hi,
Nice explanation, just one question though-are we trying to say that number 2 multiplied by a sq. root can shall give an integer only when the sq root itself is an integer or to generalize, a sq root can when doubled always gives an integer? If Yes, can u please provide few examples for the same, If No, please explain why statement 1 is suff?

Thanx
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 54434
Re: If (4a)^(1/2) integer, is (a)^(1/2) integer?  [#permalink]

Show Tags

New post 25 Jul 2017, 04:41
saurabhsavant wrote:
ydmuley wrote:
If is \(\sqrt{4a}\) integer, is \(\sqrt{a}\) integer?

\(\sqrt{4a}\) = Integer

This is only possible when \(\sqrt{a} = Integer\)

(1) \(a\) is a positive integer

This is sufficient as per the given information - \(\sqrt{4a}\) = Integer

Hence, (1) =====> is SUFFICIENT

(2) \(a = n^6\), where n is an integer

As n is an integer and \(a = n^6\)

\(\sqrt{a} = \sqrt{n^6} = n^3\)

As n is integer, \(n^3\) will also be an integer.

Hence, (2) =====> is SUFFICIENT

Hence, Answer is D


Hi,
Nice explanation, just one question though-are we trying to say that number 2 multiplied by a sq. root can shall give an integer only when the sq root itself is an integer or to generalize, a sq root can when doubled always gives an integer? If Yes, can u please provide few examples for the same, If No, please explain why statement 1 is suff?

Thanx


Generally \(\sqrt{integer}\) is either an integer itself or an irrational number, it cannot be some reduced fraction like 1/2 or 2/3.

Similar questions to practice:
http://gmatclub.com/forum/if-x-is-a-pos ... 65976.html
http://gmatclub.com/forum/if-x-is-a-pos ... 88994.html
http://gmatclub.com/forum/what-is-the-v ... 07195.html
http://gmatclub.com/forum/if-sqrt-4a-is ... 06886.html
http://gmatclub.com/forum/if-8-0-5y-3-0 ... 06606.html
http://gmatclub.com/forum/is-s-an-odd-i ... 06562.html
http://gmatclub.com/forum/if-d-is-a-pos ... 04421.html
http://gmatclub.com/forum/if-z-is-a-pos ... 01464.html
http://gmatclub.com/forum/if-x-is-a-pos ... 01918.html
http://gmatclub.com/forum/if-y-is-a-pos ... 08287.html
https://gmatclub.com/forum/is-z-an-integer-191421.html
_________________
Intern
Intern
avatar
S
Joined: 16 Apr 2017
Posts: 45
Re: If (4a)^(1/2) integer, is (a)^(1/2) integer?  [#permalink]

Show Tags

New post 25 Jul 2017, 12:13
saurabhsavant wrote:
ydmuley wrote:
If is \(\sqrt{4a}\) integer, is \(\sqrt{a}\) integer?

\(\sqrt{4a}\) = Integer

This is only possible when \(\sqrt{a} = Integer\)

(1) \(a\) is a positive integer

This is sufficient as per the given information - \(\sqrt{4a}\) = Integer

Hence, (1) =====> is SUFFICIENT

(2) \(a = n^6\), where n is an integer

As n is an integer and \(a = n^6\)

\(\sqrt{a} = \sqrt{n^6} = n^3\)

As n is integer, \(n^3\) will also be an integer.

Hence, (2) =====> is SUFFICIENT

Hence, Answer is D


Hi,
Nice explanation, just one question though-are we trying to say that number 2 multiplied by a sq. root can shall give an integer only when the sq root itself is an integer or to generalize, a sq root can when doubled always gives an integer? If Yes, can u please provide few examples for the same, If No, please explain why statement 1 is suff?

Thanx



it is sufficient because \sqrt{4a} = \sqrt{4 * 1/4} = \sqrt{1} = 1(an integer)
however a = 1/4 so \sqrt{1/4} = 1/2 = not an integer, therefore statement 1 is sufficient,otherwise \sqrt{a} could be 1/2.
_________________
KUDOS please, if you like the post or if it helps :-)
GMAT Club Bot
Re: If (4a)^(1/2) integer, is (a)^(1/2) integer?   [#permalink] 25 Jul 2017, 12:13
Display posts from previous: Sort by

If (4a)^(1/2) integer, is (a)^(1/2) integer?

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.