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

 It is currently 20 Jun 2019, 12:28

### 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

# If d is a positive integer, is d^1/2 an integer?

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

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 55732
If d is a positive integer, is d^1/2 an integer?  [#permalink]

### Show Tags

26 Feb 2014, 02:26
00:00

Difficulty:

5% (low)

Question Stats:

83% (00:58) correct 17% (01:04) wrong based on 684 sessions

### HideShow timer Statistics

The Official Guide For GMAT® Quantitative Review, 2ND Edition

If d is a positive integer, is $$\sqrt{d}$$ an integer?

(1) d is the square of an integer.
(2) $$\sqrt{d}$$ is the square of an integer.

Data Sufficiency
Question: 113
Category: Arithmetic Properties of numbers
Page: 161
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
1. Please provide your solutions to the questions;
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 55732
If d is a positive integer, is d^1/2 an integer?  [#permalink]

### Show Tags

26 Feb 2014, 02:26
SOLUTION

If d is a positive integer, is $$\sqrt{d}$$ an integer?

Given: $$d=integer$$.
Question: is $$\sqrt{d}=integer$$? or: is $$d$$ a perfect square: is $$d=integer^2$$?

(1) $$d$$ is the square of an integer --> $$d=integer^2$$ --> directly gives an answer. Sufficient.

(2) $$\sqrt{d}$$ is the square of an integer --> $$\sqrt{d}=integer^2=integer$$ (as square of an integer is an integer). Sufficient.

Answer: D.

Similar questions:
https://gmatclub.com/forum/if-n-p-q-p-a ... 01475.html
https://gmatclub.com/forum/if-d-is-a-po ... 09384.html
https://gmatclub.com/forum/if-x-is-a-po ... 65976.html
https://gmatclub.com/forum/if-d-is-a-po ... 67950.html
https://gmatclub.com/forum/if-z-is-a-po ... 01464.html
https://gmatclub.com/forum/if-y-is-a-po ... 08287.html
https://gmatclub.com/forum/if-sqrt-4a-i ... 06886.html
https://gmatclub.com/forum/what-is-the- ... 07195.html
https://gmatclub.com/forum/is-s-an-odd- ... 06562.html
_________________
Director
Joined: 25 Apr 2012
Posts: 668
Location: India
GPA: 3.21
WE: Business Development (Other)
Re: If d is a positive integer, is d^1/2 an integer?  [#permalink]

### Show Tags

26 Feb 2014, 04:15
1
1
If d is a positive integer, is $$\sqrt{d}$$ an integer?

(1) d is the square of an integer.
(2) $$\sqrt{d}$$ is the square of an integer.

Sol: Given d is a postive integer we need to check whether $$\sqrt{d}$$ = I where I is an integer

st1: Given d=a^2 where " a" is some postive integer then $$\sqrt{d}$$ =a which is an integer So St 1 is sufficent

St2: given $$\sqrt{d}$$ = b^2 where b is some integer so $$\sqrt{d}$$ is an integer.

Ans is D.

Note: • When the GMAT provides the square root sign for an even root, such as $$\sqrt{x}$$ or \sqrt{[4]{x}}, then the only accepted answer is the positive root.

That is, $$\sqrt{25}$$ , NOT +5 or -5. In contrast, the equation x^2=25 has TWO solutions, +5 and -5. Even roots have only a positive value on the GMAT.

• Odd roots will have the same sign as the base of the root. For example, $$\sqrt[3]{125} =5$$ and $$\sqrt[3]{-64} =-4$$.

Courtesy GMAT CLUB Math Book
_________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”
Manager
Joined: 25 Sep 2012
Posts: 237
Location: India
Concentration: Strategy, Marketing
GMAT 1: 660 Q49 V31
GMAT 2: 680 Q48 V34
Re: If d is a positive integer, is d^1/2 an integer?  [#permalink]

### Show Tags

27 Feb 2014, 06:39
A.) d = x^2
Therefore, root[d] = x
e.g. d= 16 then root[d] = 4

SUFFICIENT

B.) root[d] = x^2
square of an integer is an integer
e.g. 2^2 = 4, 3^2 = 9
e.g root[d] = 2^2 = 4

SUFFICIENT

Answer - D

Difficulty level - 550
Non-Human User
Joined: 09 Sep 2013
Posts: 11399
Re: If d is a positive integer, is d^1/2 an integer?  [#permalink]

### Show Tags

14 Sep 2018, 18:50
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 d is a positive integer, is d^1/2 an integer?   [#permalink] 14 Sep 2018, 18:50
Display posts from previous: Sort by

# If d is a positive integer, is d^1/2 an integer?

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

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