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

It is currently 16 Aug 2018, 20:45

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 r,s and t are integers, is r+s =square root of t

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

Hide Tags

Senior Manager
Senior Manager
User avatar
P
Joined: 22 Feb 2018
Posts: 250
If r,s and t are integers, is r+s =square root of t  [#permalink]

Show Tags

New post 22 May 2018, 03:47
1
1
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

28% (00:58) correct 72% (01:15) wrong based on 138 sessions

HideShow timer Statistics

If \(r,s\) and \(t\) are integers, is \(r+s =\sqrt{t}\) ?

[1] \(r<-s\)

[2] \((r+s)^2=t\)

_________________

Good, good Let the kudos flow through you

Manager
Manager
User avatar
S
Joined: 28 Nov 2017
Posts: 145
Location: Uzbekistan
Premium Member
If r,s and t are integers, is r+s =square root of t  [#permalink]

Show Tags

New post Updated on: 31 May 2018, 21:58
2
Princ wrote:
If \(r,s\) and \(t\) are integers, is \(r+s =\sqrt{t}\) ?

[1] \(r<-s\)

[2] \((r+s)^2=t\)


(1) \(r<-s\)
\(r+s<0\). Since, \(\sqrt{t}\) is non-negative positive, answer is NO. Sufficient.

(2) \(|r+s|=\sqrt{t}\). Not sufficient.

Answer: A
_________________

Kindest Regards!
Tulkin.


Originally posted by Tulkin987 on 22 May 2018, 05:04.
Last edited by Tulkin987 on 31 May 2018, 21:58, edited 1 time in total.
Senior Manager
Senior Manager
User avatar
P
Joined: 22 Feb 2018
Posts: 250
Re: If r,s and t are integers, is r+s =square root of t  [#permalink]

Show Tags

New post 22 May 2018, 05:34
OA: A

Statement 1 : \(r<-s\)
\(r+s<0\)
\(\sqrt{t}\) can not be -ve.
So answer for is \(r+s=\sqrt{t}\) :no.
Statement 1 is alone sufficient.

Statement 2 : \((r+s)^2=t\)
\(|r+s|=\sqrt{t}\)

Case a :When \(r+s <0\)
Then statement 2 becomes \(-(r+s)=\sqrt{t}\)
Answer for is \(r+s=\sqrt{t}\) :no

Case b : When \({r+s}\geq{0}\),
then statement 2 becomes \(r+s=\sqrt{t}\).
answer for is \(r+s=\sqrt{t}\) :yes.
So statement 2 alone is insufficient.
_________________

Good, good Let the kudos flow through you

DS Forum Moderator
User avatar
P
Joined: 27 Oct 2017
Posts: 673
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Premium Member CAT Tests
Re: If r,s and t are integers, is r+s =square root of t  [#permalink]

Show Tags

New post 22 May 2018, 06:17
(1) \(r<-s\)
\(r+s<0\). So, r+s is negative. Since, \(\sqrt{t}\) is always NON NEGATIVE, answer is NO.
Sufficient.

(2) \(|r+s|=\sqrt{t}\).
Now \((r+s)\) can be equal to \(\sqrt{t}\) or -\(\sqrt{t}.\)
Not sufficient.

Answer: A
_________________

SC: Confusable words
All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory
Error log/Key Concepts
Combination Concept: Division into groups
Question of the Day (QOTD)
Free GMAT CATS

Intern
Intern
avatar
B
Joined: 24 Oct 2017
Posts: 48
Re: If r,s and t are integers, is r+s =square root of t  [#permalink]

Show Tags

New post 23 May 2018, 01:14
1
1
1
gmatbusters
LET t=36
ROOT36=+- 6
ROOT(t) can be either +ve or -ve
e-GMAT Representative
User avatar
P
Joined: 04 Jan 2015
Posts: 1894
Re: If r,s and t are integers, is r+s =square root of t  [#permalink]

Show Tags

New post 23 May 2018, 01:26
GYANENDRA88 wrote:
gmatbusters
LET t=36
ROOT36=+- 6
ROOT(t) can be either +ve or -ve


Let me clarify it with two specific cases:

    • If \(a^2\) = 16, then a = +4 or -4
It happens because from the equation \(a^2\) = 16, we can derive (a + 4)(a – 4) = 0, which gives us two values of a = +4 and -4
This can also be written as a = +\(\sqrt{16}\) or -\(\sqrt{16}\)
Now, \(\sqrt{16}\) = 4,
    Hence, the values of a = +4 or -4

    • If a = 16, then \(\sqrt{a}\) = \(\sqrt{16}\) = 4 always. Therefore \(\sqrt{a}\) is always positive.

Hope this clarifies your doubt.
_________________








Register for free sessions
Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Must Read Articles
Number Properties – Even Odd | LCM GCD
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets



| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Intern
Intern
avatar
B
Joined: 24 Oct 2017
Posts: 48
Re: If r,s and t are integers, is r+s =square root of t  [#permalink]

Show Tags

New post 23 May 2018, 01:58
EgmatQuantExpert
Thanks for your reply.
One can approach it in a different way-
let a=-6
t=a^2
root(t)=root(a^2)=-6
DS Forum Moderator
User avatar
P
Joined: 27 Oct 2017
Posts: 673
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Premium Member CAT Tests
Re: If r,s and t are integers, is r+s =square root of t  [#permalink]

Show Tags

New post 23 May 2018, 02:15
1
Hii
I am afraid your understanding is not correct.
If x² = 36, x = +/-6
But if x = \(\sqrt{36}\)
x = only 6.

The square root function gives only the positive value.


This is as per the definition of sqaure root function.

Please remember this concept, this is very important for GMAT.

If you have any further queries, feel free to tag me.

Happy Learning...

GYANENDRA88 wrote:
gmatbusters
LET t=36
ROOT36=+- 6
ROOT(t) can be either +ve or -ve

_________________

SC: Confusable words
All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory
Error log/Key Concepts
Combination Concept: Division into groups
Question of the Day (QOTD)
Free GMAT CATS

Intern
Intern
avatar
B
Joined: 24 Oct 2017
Posts: 48
Re: If r,s and t are integers, is r+s =square root of t  [#permalink]

Show Tags

New post 23 May 2018, 02:34
1
gmatbusters
Thanks for the reply
can you prove it mathematically that root36 is not equal to -6.
DS Forum Moderator
User avatar
P
Joined: 27 Oct 2017
Posts: 673
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Premium Member CAT Tests
Re: If r,s and t are integers, is r+s =square root of t  [#permalink]

Show Tags

New post 23 May 2018, 03:03
2
Hii
A function is a special relationship where each input has a single output.
So to define square root function, root function must give a unique answer. it has been defined as to be positive.. There is no reason for this.

See it like this, we say that the charge of electron is negative, actually it is defined to be negative. Scientists might have defined charge of electron to be positive and proton charge as negative. But who knows, God might be in favour of Proton that day.
:cool:
Similarly we say that numbers on the number line to left of zero is negative and to right of zero is positive. We could have defined the convention otherwise also. But it is defined like this. There is no explanation for this.
Hope it is clear now.


GYANENDRA88 wrote:
gmatbusters
Thanks for the reply
can you prove it mathematically that root36 is not equal to -6.

_________________

SC: Confusable words
All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory
Error log/Key Concepts
Combination Concept: Division into groups
Question of the Day (QOTD)
Free GMAT CATS

Senior Manager
Senior Manager
User avatar
P
Joined: 22 Feb 2018
Posts: 250
Re: If r,s and t are integers, is r+s =square root of t  [#permalink]

Show Tags

New post 23 May 2018, 05:20
1
The symbol √ does not mean square root. It means "principal square root", which is the positive square root.

From GMAT prespective , check out bunuel's comment

Quote:
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 positive 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 \(x=\sqrt{9}=3\).

Same matter has been discussed in below link
https://gmatclub.com/forum/square-root-always-positive-114114.html

You can also check below link from Manhattanprep :What’s the Deal with Square Roots on the GMAT?
https://www.manhattanprep.com/gmat/blog ... -the-gmat/
_________________

Good, good Let the kudos flow through you

DS Forum Moderator
User avatar
P
Joined: 27 Oct 2017
Posts: 673
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Premium Member CAT Tests
Re: If r,s and t are integers, is r+s =square root of t  [#permalink]

Show Tags

New post 31 May 2018, 08:33
Hi Tulkin987

We can not say that \(\sqrt{t}\) is positive, In fact \(\sqrt{t}\) is NON NEGATIVE.


Tulkin987 wrote:
Princ wrote:
If \(r,s\) and \(t\) are integers, is \(r+s =\sqrt{t}\) ?

[1] \(r<-s\)

[2] \((r+s)^2=t\)


(1) \(r<-s\)
\(r+s<0\). Since, \(\sqrt{t}\) is positive, answer is NO. Sufficient.

(2) \(|r+s|=\sqrt{t}\). Not sufficient.

Answer: A

_________________

SC: Confusable words
All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory
Error log/Key Concepts
Combination Concept: Division into groups
Question of the Day (QOTD)
Free GMAT CATS

Manager
Manager
User avatar
S
Joined: 28 Nov 2017
Posts: 145
Location: Uzbekistan
Premium Member
If r,s and t are integers, is r+s =square root of t  [#permalink]

Show Tags

New post 31 May 2018, 22:00
gmatbusters wrote:
Hi Tulkin987

We can not say that \(\sqrt{t}\) is positive, In fact \(\sqrt{t}\) is NON NEGATIVE.


Tulkin987 wrote:
Princ wrote:
If \(r,s\) and \(t\) are integers, is \(r+s =\sqrt{t}\) ?

[1] \(r<-s\)

[2] \((r+s)^2=t\)


(1) \(r<-s\)
\(r+s<0\). Since, \(\sqrt{t}\) is positive, answer is NO. Sufficient.

(2) \(|r+s|=\sqrt{t}\). Not sufficient.

Answer: A


Hi, gmatbusters! Corrected the mistake. Thanks :thumbup:
_________________

Kindest Regards!
Tulkin.

If r,s and t are integers, is r+s =square root of t &nbs [#permalink] 31 May 2018, 22:00
Display posts from previous: Sort by

If r,s and t are integers, is r+s =square root of t

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

Events & Promotions

PREV
NEXT


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®.