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

It is currently 16 Oct 2019, 07:24

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 √m is an integer, what is the value of √m?

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58378
If √m is an integer, what is the value of √m?  [#permalink]

Show Tags

New post 21 Sep 2018, 01:35
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

56% (00:59) correct 44% (01:06) wrong based on 148 sessions

HideShow timer Statistics

CEO
CEO
User avatar
D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2977
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Reviews Badge
If √m is an integer, what is the value of √m?  [#permalink]

Show Tags

New post 21 Sep 2018, 01:46
Bunuel wrote:
If √m is an integer, what is the value of √m?

(1) 13 ≤ m ≤ 16
(2) 3 ≤ √m ≤ 4


Given: \(√m = Integer\)

Question: what is the value of √m?

Statement 1: 13 ≤ m ≤ 16

i.e. \(√13 ≤ √m ≤ √16\)

i.e. \(3.6 ≤ √m ≤ 4\)

Only possible integer value of \(√m = 4\)
i.e. m = 16
SUFFICIENT

Statement 2: \(3 ≤ √m ≤ 4\)

i.e. m may be 9 or 16 and \(√m\) may be 3 or 4 hence

NOT SUFFICIENT

Answer: Option A
_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
e-GMAT Representative
User avatar
V
Joined: 04 Jan 2015
Posts: 3074
Re: If √m is an integer, what is the value of √m?  [#permalink]

Show Tags

New post 22 Sep 2018, 03:45
1

Solution



Given:
    • √m is an integer

To find:
    • The value of √m

Analysing Statement 1
From the information given in statement 1, 13 ≤ m ≤ 16.

    • As √m is an integer, m must be a perfect square.
In the given range 13 ≤ m ≤ 16, only one perfect square exists, which is 16.

Therefore, we can find unique value of √m.

Hence, statement 1 is sufficient.

Analysing Statement 2
From the information given in statement 2, 3 ≤ √m ≤ 4.
    • From this statement, we can say √m can be either 3 or 4.

Hence, statement 2 is not sufficient.

The correct answer is option A.

Answer: A
_________________
Intern
Intern
avatar
S
Joined: 03 Apr 2017
Posts: 44
Re: If √m is an integer, what is the value of √m?  [#permalink]

Show Tags

New post 22 Sep 2018, 09:45
But root m could be both +4 and -4. We wont get a unique solution. Why is A sufficient?
Intern
Intern
avatar
B
Joined: 04 Jun 2018
Posts: 15
Location: India
Schools: German MBA (I)
GMAT 1: 660 Q48 V31
Reviews Badge
If √m is an integer, what is the value of √m?  [#permalink]

Show Tags

New post 29 Jan 2019, 11:01
mitrakaushi wrote:
But root m could be both +4 and -4. We wont get a unique solution. Why is A sufficient?


I have the same confusion. Bunuel, Could you please clarify ?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58378
Re: If √m is an integer, what is the value of √m?  [#permalink]

Show Tags

New post 29 Jan 2019, 11:34
2
shaanaa22 wrote:
mitrakaushi wrote:
But root m could be both +4 and -4. We wont get a unique solution. Why is A sufficient?


I have the same confusion. Bunuel, Could you please clarify ?



\(\sqrt{...}\) is the square root sign, a function (called the principal square root function), which cannot give negative result. So, this sign (\(\sqrt{...}\)) always means non-negative square root.

Image
The graph of the function f(x) = √x

Notice that it's defined for non-negative numbers and is producing non-negative results.

TO SUMMARIZE:
When the GMAT provides the square root sign for an even root, such as a square root, fourth root, etc. then the only accepted answer is the non-negative root. That is:

\(\sqrt{9} = 3\), NOT +3 or -3;
\(\sqrt[4]{16} = 2\), NOT +2 or -2;

Notice that in contrast, the equation \(x^2 = 9\) has TWO solutions, +3 and -3. Because \(x^2 = 9\) means that \(x =-\sqrt{9}=-3\) or \(x=\sqrt{9}=3\).
_________________
Intern
Intern
avatar
B
Joined: 04 Jun 2018
Posts: 15
Location: India
Schools: German MBA (I)
GMAT 1: 660 Q48 V31
Reviews Badge
Re: If √m is an integer, what is the value of √m?  [#permalink]

Show Tags

New post 30 Jan 2019, 08:52
Bunuel wrote:
shaanaa22 wrote:
mitrakaushi wrote:
But root m could be both +4 and -4. We wont get a unique solution. Why is A sufficient?


I have the same confusion. Bunuel, Could you please clarify ?



\(\sqrt{...}\) is the square root sign, a function (called the principal square root function), which cannot give negative result. So, this sign (\(\sqrt{...}\)) always means non-negative square root.

Image
The graph of the function f(x) = √x

Notice that it's defined for non-negative numbers and is producing non-negative results.

TO SUMMARIZE:
When the GMAT provides the square root sign for an even root, such as a square root, fourth root, etc. then the only accepted answer is the non-negative root. That is:

\(\sqrt{9} = 3\), NOT +3 or -3;
\(\sqrt[4]{16} = 2\), NOT +2 or -2;

Notice that in contrast, the equation \(x^2 = 9\) has TWO solutions, +3 and -3. Because \(x^2 = 9\) means that \(x =-\sqrt{9}=-3\) or \(x=\sqrt{9}=3\).



Thank you so much for the response, Bunuel! It was really helpful.
GMAT Club Bot
Re: If √m is an integer, what is the value of √m?   [#permalink] 30 Jan 2019, 08:52
Display posts from previous: Sort by

If √m is an integer, what is the value of √m?

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





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