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

 It is currently 21 May 2019, 21:59

### 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

# If p is a positive integer is √p a positive integer?

Author Message
TAGS:

### Hide Tags

Intern
Joined: 29 Jan 2017
Posts: 44
If p is a positive integer is √p a positive integer?  [#permalink]

### Show Tags

19 Dec 2017, 22:16
5
00:00

Difficulty:

75% (hard)

Question Stats:

44% (01:39) correct 56% (02:06) wrong based on 71 sessions

### HideShow timer Statistics

If p is a positive integer is √p a positive integer?

1) p is n percentage of n where n is a positive integer
2) p/100 is a positive integer
Retired Moderator
Joined: 22 Aug 2013
Posts: 1443
Location: India
Re: If p is a positive integer is √p a positive integer?  [#permalink]

### Show Tags

19 Dec 2017, 22:49
(1) p is n% of n, this means p = n/100 * n = (n^2)/100
Here n is a positive integer, so n^2 is a perfect square. And n^2 must be divisible by 100, because then only p will be an integer. Now if we take square root both sides, we have
√p = √(n^2)/ √100 = n/10
Since n^2 is divisible by 100, this means n must be divisible by 10. So √p is an integer. Sufficient.

(2) p is divisible by 100.
If p = 400, then √p = 20 is an integer.
If p = 300, then √p = 10 √3, is not an integer. So Insufficient.

Math Expert
Joined: 02 Sep 2009
Posts: 55231
Re: If p is a positive integer is √p a positive integer?  [#permalink]

### Show Tags

19 Dec 2017, 23:34
If p is a positive integer is √p a positive integer?

(1) p is n percentage of n where n is a positive integer --> p = n/100*n = (n/10)^2. Now, n is an integer, so n/10 is either an integer or a fraction but since p is an integer and fraction^2 cannot be an integer, then n/10 can only be an integer, thus p = (n/10)^2 = integer^2. Sufficient.

(2) p/100 is a positive integer. If p = 100, then the answer is YES but if p = 200, then the answer is NO. Not sufficient.

Hope it's clear.
_________________
Intern
Joined: 21 Nov 2017
Posts: 1
If p is a positive integer is √p a positive integer?  [#permalink]

### Show Tags

12 Sep 2018, 02:44
amanvermagmat wrote:
(1) p is n% of n, this means p = n/100 * n = (n^2)/100
Here n is a positive integer, so n^2 is a perfect square. And n^2 must be divisible by 100, because then only p will be an integer. Now if we take square root both sides, we have
√p = √(n^2)/ √100 = n/10
Since n^2 is divisible by 100, this means n must be divisible by 10. So √p is an integer. Sufficient.

(2) p is divisible by 100.
If p = 400, then √p = 20 is an integer.
If p = 300, then √p = 10 √3, is not an integer. So Insufficient.

Why are we not considering -n/10 as a possible root of n^2/100, in which case p would be negative and give a NO to the "is p a positive integer" question?

That would make Statement 1 insufficient.
If p is a positive integer is √p a positive integer?   [#permalink] 12 Sep 2018, 02:44
Display posts from previous: Sort by