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

It is currently 21 Nov 2019, 16:23

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 y is a positive integer, is square_root of y

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

Hide Tags

Find Similar Topics 
Retired Moderator
User avatar
Status: 2000 posts! I don't know whether I should feel great or sad about it! LOL
Joined: 04 Oct 2009
Posts: 954
Location: Peru
Schools: Harvard, Stanford, Wharton, MIT & HKS (Government)
WE 1: Economic research
WE 2: Banking
WE 3: Government: Foreign Trade and SMEs
If y is a positive integer, is square_root of y  [#permalink]

Show Tags

New post 30 Jun 2012, 03:46
1
15
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

58% (01:22) correct 42% (01:15) wrong based on 343 sessions

HideShow timer Statistics

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

(1) \(\sqrt{4y}\) is not an integer.
(2) \(\sqrt{5y}\) is an integer.

_________________
"Life’s battle doesn’t always go to stronger or faster men; but sooner or later the man who wins is the one who thinks he can."

My Integrated Reasoning Logbook / Diary: http://gmatclub.com/forum/my-ir-logbook-diary-133264.html

GMAT Club Premium Membership - big benefits and savings
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59236
Re: If y is a positive integer, is square_root of y  [#permalink]

Show Tags

New post 30 Jun 2012, 03:50
2
5
metallicafan wrote:
If y is a positive integer, is \(\sqrt{y}\) an integer?

(1) \(\sqrt{4y}\) is not an integer.
(2) \(\sqrt{5y}\) is an integer.


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

Note that as \(y\) is a positive integer then \(\sqrt{y}\) is either a positive integer or an irrational number. Also note that the question basically asks whether \(y\) is a perfect square.

(1) \(\sqrt{4*y}\) is not an integer --> \(\sqrt{4*y}=2*\sqrt{y}\neq{integer}\) --> \(\sqrt{y}\neq{integer}\). Sufficient.

(2) \(\sqrt{5*y}\) is an integer --> \(y\) can not be a prefect square because if it is, for example if \(y=x^2\) for some positive integer \(x\) then \(\sqrt{5*y}=\sqrt{5*x^2}=x\sqrt{5}\neq{integer}\). Sufficient.

Answer: D.

Similar questions:
if-x-is-a-positive-integer-is-sqrt-x-an-integer-88994.html
value-of-x-107195.html
number-prop-ds-106886.html
number-system-106606.html
odd-vs-even-trick-question-106562.html
quant-review-2nd-edition-ds-104421.html
algebra-ds-101464.html
i-cant-understand-how-the-oa-is-101475.html

Hope it helps.
_________________
General Discussion
Retired Moderator
User avatar
Status: 2000 posts! I don't know whether I should feel great or sad about it! LOL
Joined: 04 Oct 2009
Posts: 954
Location: Peru
Schools: Harvard, Stanford, Wharton, MIT & HKS (Government)
WE 1: Economic research
WE 2: Banking
WE 3: Government: Foreign Trade and SMEs
Re: If y is a positive integer, is square_root of y  [#permalink]

Show Tags

New post 30 Jun 2012, 04:08
Bunuel wrote:
metallicafan wrote:
If y is a positive integer, is \(\sqrt{y}\) an integer?

(1) \(\sqrt{4y}\) is not an integer.
(2) \(\sqrt{5y}\) is an integer.


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

Note that as \(y\) is a positive integer then \(\sqrt{y}\) is either a positive integer or an irrational number. Also note that the question basically asks whether \(y\) is a perfect square.

(1) \(\sqrt{4*y}\) is not an integer --> \(\sqrt{4*y}=2*\sqrt{y}\neq{integer}\) --> \(\sqrt{y}\neq{integer}\). Sufficient.

(2) \(\sqrt{5*y}\) is an integer --> \(y\) can not be a prefect square because if it is, for example if \(y=x^2\) for some positive integer \(x\) then \(\sqrt{5*y}=\sqrt{5*x^2}=x\sqrt{5}\neq{integer}\). Sufficient.

Answer: D.

Hope it helps.


Thank you Bunuel. I arrived to the same conclusion. However, I have a doubt:
Ok, we know that \(x\sqrt{5}\).
But how can we be so sure that x is not for example a a huge number like 10*10^10000000.... to make \(x\sqrt{5}\) a integer?
Maybe, I am forgeting a concept. Please, your help.
_________________
"Life’s battle doesn’t always go to stronger or faster men; but sooner or later the man who wins is the one who thinks he can."

My Integrated Reasoning Logbook / Diary: http://gmatclub.com/forum/my-ir-logbook-diary-133264.html

GMAT Club Premium Membership - big benefits and savings
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59236
Re: If y is a positive integer, is square_root of y  [#permalink]

Show Tags

New post 30 Jun 2012, 04:16
1
metallicafan wrote:
Bunuel wrote:
metallicafan wrote:
If y is a positive integer, is \(\sqrt{y}\) an integer?

(1) \(\sqrt{4y}\) is not an integer.
(2) \(\sqrt{5y}\) is an integer.


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

Note that as \(y\) is a positive integer then \(\sqrt{y}\) is either a positive integer or an irrational number. Also note that the question basically asks whether \(y\) is a perfect square.

(1) \(\sqrt{4*y}\) is not an integer --> \(\sqrt{4*y}=2*\sqrt{y}\neq{integer}\) --> \(\sqrt{y}\neq{integer}\). Sufficient.

(2) \(\sqrt{5*y}\) is an integer --> \(y\) can not be a prefect square because if it is, for example if \(y=x^2\) for some positive integer \(x\) then \(\sqrt{5*y}=\sqrt{5*x^2}=x\sqrt{5}\neq{integer}\). Sufficient.

Answer: D.

Hope it helps.


Thank you Bunuel. I arrived to the same conclusion. However, I have a doubt:
Ok, we know that \(x\sqrt{5}\).
But how can we be so sure that x is not for example a a huge number like 10*10^10000000.... to make \(x\sqrt{5}\) a integer?
Maybe, I am forgeting a concept. Please, your help.


The point is that \(\sqrt{5}\) is an irrational number, and the decimal representation of an irrational number never repeats or terminates (irrational numbers are not terminating decimals). So, \(integer*irrational\neq{integer}\) (no matter how large x is, \(x\sqrt{5}\) will never be an integer).

Hope it's clear.
_________________
Retired Moderator
User avatar
Status: 2000 posts! I don't know whether I should feel great or sad about it! LOL
Joined: 04 Oct 2009
Posts: 954
Location: Peru
Schools: Harvard, Stanford, Wharton, MIT & HKS (Government)
WE 1: Economic research
WE 2: Banking
WE 3: Government: Foreign Trade and SMEs
Re: If y is a positive integer, is square_root of y  [#permalink]

Show Tags

New post 30 Jun 2012, 18:22
Bunuel wrote:
The point is that \(\sqrt{5}\) is an irrational number, and the decimal representation of an irrational number never repeats or terminates (irrational numbers are not terminating decimals). So, \(integer*irrational\neq{integer}\) (no matter how large x is, \(x\sqrt{5}\) will never be an integer).

Hope it's clear.


Thank you Bunuel! An additional question: all the square roots (or roots in general) of prime numbers are irrational?
Thanks!
_________________
"Life’s battle doesn’t always go to stronger or faster men; but sooner or later the man who wins is the one who thinks he can."

My Integrated Reasoning Logbook / Diary: http://gmatclub.com/forum/my-ir-logbook-diary-133264.html

GMAT Club Premium Membership - big benefits and savings
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59236
Re: If y is a positive integer, is square_root of y  [#permalink]

Show Tags

New post 01 Jul 2012, 02:24
metallicafan wrote:
Bunuel wrote:
The point is that \(\sqrt{5}\) is an irrational number, and the decimal representation of an irrational number never repeats or terminates (irrational numbers are not terminating decimals). So, \(integer*irrational\neq{integer}\) (no matter how large x is, \(x\sqrt{5}\) will never be an integer).

Hope it's clear.


Thank you Bunuel! An additional question: all the square roots (or roots in general) of prime numbers are irrational?
Thanks!


Since no prime can be a perfect square (or perfect cube, ...), then \(\sqrt{prime}=irrational\).
_________________
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59236
Re: If y is a positive integer, is square_root of y  [#permalink]

Show Tags

New post 12 Jun 2013, 04:27
1
Manager
Manager
avatar
Joined: 08 May 2015
Posts: 88
GMAT 1: 630 Q39 V38
GMAT 2: 670 Q44 V38
GMAT 3: 750 Q49 V44
Re: If y is a positive integer, is square_root of y  [#permalink]

Show Tags

New post 13 Aug 2015, 15:04
Bunuel

What if y=125?

125 is an integer.

sqrt of 5*125 = sqrt of 625 = 25

This would make B insufficient.

Am I missing something here?
CEO
CEO
avatar
S
Joined: 20 Mar 2014
Posts: 2567
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Reviews Badge
Re: If y is a positive integer, is square_root of y  [#permalink]

Show Tags

New post 14 Aug 2015, 17:11
2
Mascarfi wrote:
Bunuel

What if y=125?

125 is an integer.

sqrt of 5*125 = sqrt of 625 = 25

This would make B insufficient.

Am I missing something here?


No, your calculations are fine and are consistent with the question. If you have y = 125, \(\sqrt{125}\) \(\neq\) Integer and thus get an unambiguous "no" making statement 2 sufficient. The original question is

"\(\sqrt{y}\) an integer?" So getting an unambiguous yes or no will be sufficient. Per Bunuel's solution, it is shown that y can not be a perfect square leading to \(\sqrt{y}\neq Integer\)

Hope this helps.
Manager
Manager
avatar
Joined: 08 May 2015
Posts: 88
GMAT 1: 630 Q39 V38
GMAT 2: 670 Q44 V38
GMAT 3: 750 Q49 V44
If y is a positive integer, is square_root of y  [#permalink]

Show Tags

New post 14 Aug 2015, 17:48
It's clear now. Completely forgot what the question was asking while looking at number 2. thanks
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13627
Re: If y is a positive integer, is square_root of y  [#permalink]

Show Tags

New post 09 Oct 2019, 03:52
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 Club Bot
Re: If y is a positive integer, is square_root of y   [#permalink] 09 Oct 2019, 03:52
Display posts from previous: Sort by

If y is a positive integer, is square_root of y

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





cron

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne