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

It is currently 17 Jan 2019, 05:52

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 in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
  • The winning strategy for a high GRE score

     January 17, 2019

     January 17, 2019

     08:00 AM PST

     09:00 AM PST

    Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL.
  • Free GMAT Strategy Webinar

     January 19, 2019

     January 19, 2019

     07:00 AM PST

     09:00 AM PST

    Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

If m and n are both positive, what is the value of m*root(n)

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

Hide Tags

 
Intern
Intern
avatar
Joined: 04 May 2009
Posts: 13
If m and n are both positive, what is the value of m*root(n)  [#permalink]

Show Tags

New post 16 May 2009, 11:26
2
9
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

63% (00:49) correct 37% (01:05) wrong based on 646 sessions

HideShow timer Statistics

If m and n are both positive, what is the value of \(m*\sqrt{n}\)?

(1) \(\frac{m*n}{\sqrt{n}}=10\)
(2) \(\frac{m^2*n}{2}=50\)

I thought I was doing well understanding the difference between taking a square root and unsquaring a variable. Then I ran into the following DS problem:

If m and n are both positive, what is the value of \(m\sqrt{n}\) ?

1.\(\frac{m*n} {\sqrt{n}}\)= 10 (this is sufficient, no problem there)
2. \(m^2*n = 100\)

For statement 2, the explanation in the book says that we take the positive square root of both sides to obtain m√n = 10. If -10 is not a solution here, then (2) would indeed be suffcient.

But how is that different from saying we are unsquaring (m√n)^2, which would yield m√n = 10, -10 ?

As an example, the number properties guide in mgmt claims that x^2 = 4 has two solutions, x=2 and x=-2. That makes sense and I'm just not seeing what's different here.
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 52230
If m and n are both positive, what is the value of m*root(n)  [#permalink]

Show Tags

New post 30 Apr 2010, 00:34
2
6
Merged similar topics.

achan wrote:
If m and n are both positive, what is the value of \(m*\sqrt{n}\)?

(1) \(\frac{m*n}{\sqrt{n}}=10\)

(2) \(\frac{m^2*n}{2}=50\)

The textbook answer says (D) but the Square root of choice (2) will give us +/- 10.
Should we ignore -10 and conclude that (2) also gives us the answer


Theory:

GMAT is dealing only with Real Numbers: Integers, Fractions and Irrational Numbers.

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, \(\sqrt{25}=5\), 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 \(\sqrt[3]{-64} =-4\).


Back to the original question:

If m and n are both positive, what is the value of \(m*\sqrt{n}\)?

(1) \(\frac{m*n}{\sqrt{n}}=10\) --> reduce by \(\sqrt{n}\) --> \(m*\sqrt{n}=10\). Sufficient.

(2) \(\frac{m^2*n}{2}=50\) --> \((m*\sqrt{n})^2=100\) --> \(m*\sqrt{n}=10\) or \(m*\sqrt{n}=-10\). BUT since m and n are both positive (given) \(m*\sqrt{n}\) cannot equal to -10. Hence only one solution is valid: \(m*\sqrt{n}=10\). Sufficient.

Answer: D.

Hope it helps.
_________________

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

General Discussion
Director
Director
User avatar
Joined: 01 Apr 2008
Posts: 768
Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014
Re: DS Problem - "unsquaring" vs taking a square root  [#permalink]

Show Tags

New post 27 Sep 2009, 20:35
1
This is a specific concept about GMAT.

If you know that the sign of the variable inside the square root is positive then ALWAYS ignore the negative value.
Intern
Intern
avatar
Joined: 23 Sep 2009
Posts: 8
Location: uzbekistan
Schools: Chicago booth,Dartmouth,Duke
Re: DS Problem - "unsquaring" vs taking a square root  [#permalink]

Show Tags

New post 31 Dec 2009, 03:37
for this problem:

m^2*n=100
m^2=100\n
m=sqrt(100\n)

since no number is -ve when sqrt the answer is d
Manager
Manager
avatar
Joined: 29 Apr 2010
Posts: 60
Tricky DS question  [#permalink]

Show Tags

New post Updated on: 30 Apr 2010, 00:15
If m and n are both positive, what is the value of \(m*\sqrt{n}\)?

(1) \(\frac{m*n}{\sqrt{n}}=10\)

(2) \(\frac{m^2*n}{2}=50\)

The textbook answer says (D) but the Square root of choice (2) will give us +/- 10.
Should we ignore -10 and conclude that (2) also gives us the answer

Originally posted by achan on 29 Apr 2010, 23:57.
Last edited by Bunuel on 30 Apr 2010, 00:15, edited 3 times in total.
Formating
Manager
Manager
User avatar
Joined: 17 Mar 2014
Posts: 228
Location: India
Concentration: Operations, Strategy
GMAT 1: 670 Q48 V35
GPA: 3.19
WE: Information Technology (Computer Software)
GMAT ToolKit User
If m and n are both positive, what is the value of m*root(n)  [#permalink]

Show Tags

New post 14 Jun 2015, 06:22
Bunuel wrote:
Merged similar topics.

achan wrote:
If m and n are both positive, what is the value of \(m*\sqrt{n}\)?

(1) \(\frac{m*n}{\sqrt{n}}=10\)

(2) \(\frac{m^2*n}{2}=50\)

The textbook answer says (D) but the Square root of choice (2) will give us +/- 10.
Should we ignore -10 and conclude that (2) also gives us the answer


Theory:

GMAT is dealing only with Real Numbers: Integers, Fractions and Irrational Numbers.

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, \(\sqrt{25}=5\), 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 \(\sqrt[3]{-64} =-4\).


Back to the original question:

If m and n are both positive, what is the value of \(m*\sqrt{n}\)?

(1) \(\frac{m*n}{\sqrt{n}}=10\) --> reduce by \(\sqrt{n}\) --> \(m*\sqrt{n}=10\). Sufficient.

(2) \(\frac{m^2*n}{2}=50\) --> \((m*\sqrt{n})^2=100\) --> \(m*\sqrt{n}=10\) or \(m*\sqrt{n}=-10\). BUT since m and n are both positive (given) \(m*\sqrt{n}\) cannot equal to -10. Hence only one solution is valid: \(m*\sqrt{n}=10\). Sufficient.

Answer: D.

Hope it helps.


Bunuel ,
If they had not provided that m and n both are positive then also statement B alone would be sufficient right ??
I mean when question stem itself provides sqaure root sign , we should consider only POSITIVE root right ??
_________________

Press +1 Kudos if you find this Post helpful :)

Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7197
Re: If m and n are both positive, what is the value of m*root(n)  [#permalink]

Show Tags

New post 14 Jun 2015, 06:28
adityadon wrote:
Bunuel wrote:
Merged similar topics.

achan wrote:
If m and n are both positive, what is the value of \(m*\sqrt{n}\)?

(1) \(\frac{m*n}{\sqrt{n}}=10\)

(2) \(\frac{m^2*n}{2}=50\)

The textbook answer says (D) but the Square root of choice (2) will give us +/- 10.
Should we ignore -10 and conclude that (2) also gives us the answer


Theory:

GMAT is dealing only with Real Numbers: Integers, Fractions and Irrational Numbers.

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, \(\sqrt{25}=5\), 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 \(\sqrt[3]{-64} =-4\).


Back to the original question:

If m and n are both positive, what is the value of \(m*\sqrt{n}\)?

(1) \(\frac{m*n}{\sqrt{n}}=10\) --> reduce by \(\sqrt{n}\) --> \(m*\sqrt{n}=10\). Sufficient.

(2) \(\frac{m^2*n}{2}=50\) --> \((m*\sqrt{n})^2=100\) --> \(m*\sqrt{n}=10\) or \(m*\sqrt{n}=-10\). BUT since m and n are both positive (given) \(m*\sqrt{n}\) cannot equal to -10. Hence only one solution is valid: \(m*\sqrt{n}=10\). Sufficient.

Answer: D.

Hope it helps.


Bunuel ,
If they had not provided that m and n both are positive then also statement B alone would be sufficient right ??
I mean when question stem itself provides sqaure root sign , we should consider only POSITIVE root right ??


Hi,
the answer in that case will not B..
statement two will give you two values for m one +ive and other -ive..
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Intern
Intern
User avatar
Joined: 16 Jul 2015
Posts: 40
GMAT 1: 580 Q37 V33
GMAT 2: 580 Q39 V31
GMAT 3: 560 Q40 V28
GMAT 4: 580 Q37 V32
GMAT 5: 680 Q45 V37
GMAT 6: 690 Q47 V37
Re: If m and n are both positive, what is the value of m*root(n)  [#permalink]

Show Tags

New post 06 Jul 2016, 02:38
Please help clarify my doubt for statement 2.it says that m^2n=2*50
So basically,m^2*n=100,wherein there can be three possibilities
10^2 *1=100
5^2 *4=100,or
2^2 *25=100
Then how can we determine that it is the first scenario only??? please correct my concept if I am wrong
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 52230
Re: If m and n are both positive, what is the value of m*root(n)  [#permalink]

Show Tags

New post 06 Jul 2016, 02:59
bhamini1 wrote:
Please help clarify my doubt for statement 2.it says that m^2n=2*50
So basically,m^2*n=100,wherein there can be three possibilities
10^2 *1=100
5^2 *4=100,or
2^2 *25=100
Then how can we determine that it is the first scenario only??? please correct my concept if I am wrong


The question asks to find the value of \(m*\sqrt{n}\). In all cases you consider there the value of \(m*\sqrt{n}\) is the same: 10.
_________________

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

Current Student
User avatar
Joined: 18 Oct 2014
Posts: 843
Location: United States
GMAT 1: 660 Q49 V31
GPA: 3.98
GMAT ToolKit User
Re: If m and n are both positive, what is the value of m*root(n)  [#permalink]

Show Tags

New post 06 Jul 2016, 10:42
1
gb82 wrote:
If m and n are both positive, what is the value of \(m*\sqrt{n}\)?

(1) \(\frac{m*n}{\sqrt{n}}=10\)
(2) \(\frac{m^2*n}{2}=50\)



(1) \(\frac{m*n}{\sqrt{n}}=10\)

Multiply both numerator and denominator by \sqrt{n}

we will get \(m*\sqrt{n}\)= 10

(2) \(\frac{m^2*n}{2}=50\)

\frac{m^2*n}{2}= 100
Squaring both sides \(m*\sqrt{n}\)= 10

D is the answer
_________________

I welcome critical analysis of my post!! That will help me reach 700+

Manager
Manager
avatar
G
Joined: 27 Jan 2016
Posts: 138
Schools: ISB '18
GMAT 1: 700 Q50 V34
Re: If m and n are both positive, what is the value of m*root(n)  [#permalink]

Show Tags

New post 31 Oct 2017, 10:18
1) msqrt(n) = 10
2) m2n = 100
square root on both sides
msqrt(n) = 10
Answer :D
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 9416
Premium Member
Re: If m and n are both positive, what is the value of m*root(n)  [#permalink]

Show Tags

New post 19 Dec 2018, 23:28
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: If m and n are both positive, what is the value of m*root(n) &nbs [#permalink] 19 Dec 2018, 23:28
Display posts from previous: Sort by

If m and n are both positive, what is the value of m*root(n)

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


Copyright

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