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

 It is currently 18 Dec 2018, 21:51

### 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

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

## Events & Promotions

###### Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### Happy Christmas 20% Sale! Math Revolution All-In-One Products!

December 20, 2018

December 20, 2018

10:00 PM PST

11:00 PM PST

This is the most inexpensive and attractive price in the market. Get the course now!
• ### Key Strategies to Master GMAT SC

December 22, 2018

December 22, 2018

07:00 AM PST

09:00 AM PST

Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.

# If y is a positive integer is root(y) an integer?

Author Message
TAGS:

### Hide Tags

Director
Joined: 07 Jun 2004
Posts: 599
Location: PA
If y is a positive integer is root(y) an integer?  [#permalink]

### Show Tags

26 Jan 2011, 05:17
4
10
00:00

Difficulty:

55% (hard)

Question Stats:

60% (01:33) correct 40% (01:19) wrong based on 673 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

_________________

If the Q jogged your mind do Kudos me : )

Math Expert
Joined: 02 Sep 2009
Posts: 51285
If y is a positive integer is root(y) an integer?  [#permalink]

### Show Tags

26 Jan 2011, 05:37
4
6
rxs0005 wrote:
If y is a positive integer is root (y) an integer

S1 root( 4* y) is not an integer

S2 root( 5* y) is an integer

I do not agree with OA

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 --> $$y$$ cannot 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.

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
_________________
##### General Discussion
Director
Joined: 07 Jun 2004
Posts: 599
Location: PA

### Show Tags

26 Jan 2011, 05:47
thanks for the explanation the approach i took was

if y = 25 then root( 5* y) root(125) is an integer is valid and root(25) is an integer

if y = 20 then root( 5* y) root(100) is still an integer BUT root(20) is not an integer so i chose A

why is this approach wrong
_________________

If the Q jogged your mind do Kudos me : )

Math Expert
Joined: 02 Sep 2009
Posts: 51285

### Show Tags

26 Jan 2011, 06:08
rxs0005 wrote:
thanks for the explanation the approach i took was

if y = 25 then root( 5* y) root(125) is an integer is valid and root(25) is an integer

if y = 20 then root( 5* y) root(100) is still an integer BUT root(20) is not an integer so i chose A

why is this approach wrong

$$\sqrt{125}=5\sqrt{5}\approx{11.18}\neq{integer}$$.
_________________
Intern
Joined: 22 Sep 2010
Posts: 12

### Show Tags

27 Jan 2011, 01:49
nice explanation Bunuel, it was a bit tough for me too.
Retired Moderator
Joined: 05 Jul 2006
Posts: 1722
Re: If y is a positive integer, is root y an integer?  [#permalink]

### Show Tags

Updated on: 15 May 2013, 07:25
2
If y is a positive integer, is root y an integer?

(1) Root 4y is not an integer.
(2) Root 5y is an integer.

is y a perfect square?

1) 2 * sqrt y is not an integer .............. therefore sqrt y is not an integer and thus not a perfect square.......suff

2) y could be 1/5 or 5^3 for example still it can never be a perfect square .......suff

D

Originally posted by yezz on 15 May 2013, 07:19.
Last edited by yezz on 15 May 2013, 07:25, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 51285
Re: If y is a positive integer is root(y) an integer?  [#permalink]

### Show Tags

05 Jun 2013, 02:55
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

_________________
Intern
Joined: 20 Jun 2011
Posts: 44

### Show Tags

26 Nov 2013, 15:36
If $$y$$ is a positive integer is $$\sqrt{y}$$ an integer?

1) Means that we have $$\sqrt{4*y^{odd}}$$ --> $$\sqrt{y^{odd}} \neq {integer}$$ for $$y>1$$ If $$y = 1$$then statement is not true.

2) $$\sqrt{5y}$$ means that y has a $$5^{odd}$$ combination in its prime box, which means we have $$\sqrt{5^{odd}*y}$$, where y is some integer and $$\sqrt{5^{odd}*y} \neq {integer}$$

Both sufficient. D)
Manager
Joined: 25 Oct 2013
Posts: 150
Re: If y is a positive integer is root(y) an integer?  [#permalink]

### Show Tags

03 Feb 2014, 11:26
4
(1) $$\sqrt{4y}$$ is not an integer.

That is $$2\sqrt{y}$$ is not an integer => $$\sqrt{y}$$ is not an integer. Sufficient

(2) $$\sqrt{5y}$$ is an integer

let p be this integer.

$$\sqrt{5y} = p$$

then $$\sqrt{5}\sqrt{y}=p$$

or $$\sqrt{y} = \frac{p}{\sqrt{5}}$$

Now an integer divided by an irrational number cannot be integer. Sufficient

_________________

Click on Kudos if you liked the post!

Practice makes Perfect.

Non-Human User
Joined: 09 Sep 2013
Posts: 9206
Re: If y is a positive integer is root(y) an integer?  [#permalink]

### Show Tags

20 Feb 2018, 22:16
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.
_________________
Re: If y is a positive integer is root(y) an integer? &nbs [#permalink] 20 Feb 2018, 22:16
Display posts from previous: Sort by