It is currently 20 Apr 2018, 03:31

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

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

Hide Tags

Intern
Intern
avatar
B
Joined: 29 Jan 2017
Posts: 47
If p is a positive integer is √p a positive integer? [#permalink]

Show Tags

New post 19 Dec 2017, 22:16
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

45% (01:03) correct 55% (01:18) wrong based on 29 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
[Reveal] Spoiler: OA
DS Forum Moderator
avatar
G
Joined: 22 Aug 2013
Posts: 1019
Location: India
Premium Member CAT Tests
Re: If p is a positive integer is √p a positive integer? [#permalink]

Show Tags

New post 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.

Hence A answer
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 44573
Re: If p is a positive integer is √p a positive integer? [#permalink]

Show Tags

New post 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.

Answer: A.

Hope it's clear.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | 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?
Extra-hard Quant Tests with Brilliant Analytics

Re: If p is a positive integer is √p a positive integer?   [#permalink] 19 Dec 2017, 23:34
Display posts from previous: Sort by

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

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


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