Last visit was: 15 Jul 2024, 14:09 It is currently 15 Jul 2024, 14:09
Toolkit
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

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.

# Is √(x + y) an integer?

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94354
Own Kudos [?]: 641117 [2]
Given Kudos: 85011
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 6020
Own Kudos [?]: 13785 [1]
Given Kudos: 125
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Senior Manager
Joined: 03 May 2020
Posts: 266
Own Kudos [?]: 299 [2]
Given Kudos: 675
Location: India
Concentration: Marketing, Strategy
GMAT 1: 700 Q47 V39
Senior Moderator - Masters Forum
Joined: 19 Jan 2020
Posts: 3128
Own Kudos [?]: 2810 [2]
Given Kudos: 1511
Location: India
GPA: 4
WE:Analyst (Internet and New Media)
Is √(x + y) an integer? [#permalink]
2
Kudos
To find: √x+y = an integer?

Statement 1: X^3 = 64
=> X = 4 {what about Y?}
(Insufficient)

Statement 2: X^2 = Y-3
There can be many values for both X and Y here ranging from positive to negative (Insufficient).

Statement 1&2 : X^2 = Y-3 & X = 4
(4)^2 = Y-3
16+3 = Y
19 = Y
Putting Value of X and Y in √x+y
√4+19 = √23 (not an integer)
(Sufficient)

IMO C

Posted from my mobile device
Senior Manager
Joined: 12 Dec 2015
Posts: 464
Own Kudos [?]: 545 [1]
Given Kudos: 84
Re: Is √(x + y) an integer? [#permalink]
1
Kudos
Is $$\sqrt{x + y}$$ an integer?

(1) $$x^3 = 64$$--> insuff: x=4, if y=0, then $$\sqrt{x + y}$$ = $$\sqrt{4 + 0}$$=2 --> yes, but if y=1, then $$\sqrt{x + y}$$ = $$\sqrt{4 + 1}$$=$$\sqrt{5}$$ --> no

(2) $$x^2 = y – 3$$ --> insuff: y=x^2+3, $$\sqrt{x + y}$$ = $$\sqrt{x + x^2+3}$$ =$$\sqrt{(x+1/2)^2+3-1/2^2}$$ =$$\sqrt{(x+1/2)^2+11/4}$$, if x=2, $$\sqrt{(x+1/2)^2+11/4}$$ = 3, if x =4, $$\sqrt{(x+1/2)^2+11/4}$$ not equant to integer

combining (1) & (2)=>
from (1) x=4
y=4^2+3=19
so $$\sqrt{x + y}$$ = $$\sqrt{4 + 19}$$= $$\sqrt{23}$$ --> yes, $$\sqrt{x + y}$$ is not an integer
Manager
Joined: 24 Sep 2013
Posts: 164
Own Kudos [?]: 109 [0]
Given Kudos: 40
Location: Saudi Arabia
GPA: 3.8
WE:Project Management (Energy and Utilities)
Re: Is √(x + y) an integer? [#permalink]
sqrt( x+y) = integer ?
x+y = int^2
it means x+y must be a integer who is perfect square.
x=? ; y=?

Statement 1: x^3 = 64
=> x = 4
Not Sufficient

Statement 2: x^2 = y - 3
Not Sufficient.

Statement 1 & Statement 2 :

From (1) ; x=4
From (2) ; y = 4^2 + 3 = 16+3 = 19
sqrt(4+19) is not an integer
Sufficient

Manager
Joined: 24 May 2018
Posts: 96
Own Kudos [?]: 101 [1]
Given Kudos: 35
Location: India
Concentration: General Management, Human Resources
WE:Engineering (Energy and Utilities)
Re: Is √(x + y) an integer? [#permalink]
1
Kudos
From statement 1,
We get x=4,
Hence, insufficient.

From statement 2,
x^2=y-3
Let, y=12, we get x= 3 and -3
Again putting values of x and y, 3 and 12 respectively we get sqrt(x+y) = sqrt(15) (not an integer)
Putting x and y, -3 and 12 respectively we get sqrt(x+y) = 3 (integer)
Hence, insufficient.

Combining,
Putting x as 4 on statement 2 we get y= 19
Thus sqrt(x+y) = sqrt(19) not an integer.

Combining works and we get no the sqrt(x+y) is not an integer.

Hence, IMO ans is C.

Posted from my mobile device
Stern School Moderator
Joined: 26 May 2020
Status:Spirited
Posts: 632
Own Kudos [?]: 540 [1]
Given Kudos: 219
Concentration: General Management, Technology
WE:Analyst (Computer Software)
Re: Is √(x + y) an integer? [#permalink]
1
Kudos
Bunuel wrote:
Is $$\sqrt{x + y}$$ an integer?

(1) $$x^3 = 64$$

(2) $$x^2 = y – 3$$

imo C .

(1) $$x^3 = 64$$

No info about y .. so insufficient .

(2) $$x^2 = y – 3$$

2 variables unknown.. No info .. so insufficient .

Combining 1 and 2 .. we can find x and y and can find whether $$\sqrt{x + y}$$ is integer or not ..

So ans is C
Intern
Joined: 21 Oct 2019
Posts: 22
Own Kudos [?]: 3 [0]
Given Kudos: 189
Re: Is √(x + y) an integer? [#permalink]
What if we substitute y=x^2-3 in the question ?
Then we know for sure that sq.root(x+(x^2)-3)!=integer
Can someone help me out here please ?
Stern School Moderator
Joined: 26 May 2020
Status:Spirited
Posts: 632
Own Kudos [?]: 540 [1]
Given Kudos: 219
Concentration: General Management, Technology
WE:Analyst (Computer Software)
Is √(x + y) an integer? [#permalink]
1
Kudos
Anush56 wrote:
What if we substitute y=x^2-3 in the question ?
Then we know for sure that sq.root(x+(x^2)-3)!=integer
Can someone help me out here please ?

Anush56

Even if we substitute $$(y=x^2 + 3)$$ in $$\sqrt{(x+y)}$$

K = $$\sqrt{x + (x^2 + 3) }$$

if x = 2 ,then K = 3 = integer .

if x = 0.5 ,then K = $$\frac{ 6}{4 }$$ is not an integer

So option B is insufficient

Hope it helps..
Senior Manager
Joined: 05 Aug 2019
Posts: 317
Own Kudos [?]: 286 [0]
Given Kudos: 130
Location: India
GMAT 1: 600 Q50 V22
GMAT 2: 670 Q50 V28 (Online)
GPA: 4
Re: Is √(x + y) an integer? [#permalink]
Kindly see the attachment.
Combined statements are sufficient.
C
Attachments

1.PNG [ 25.55 KiB | Viewed 5496 times ]

Non-Human User
Joined: 09 Sep 2013
Posts: 33980
Own Kudos [?]: 851 [0]
Given Kudos: 0
Re: Is (x + y) an integer? [#permalink]
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: Is (x + y) an integer? [#permalink]
Moderator:
Math Expert
94354 posts