Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 15 Jul 2019, 23:23 ### 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.  # M01-19

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 56234

### Show Tags

sanjay1810 wrote:
Hi Bunuel,

Can you please elaborate on how st 2 is not sufficient ?

x - y = 9
( \sqrt{x} + \sqrt{y} ) ( \sqrt{x} - \sqrt{y} ) = 9 = 9 . 1 OR 3. 3
Since it's given the x> y >0, sum of two numbers cannot be equal to difference of the same two numbers. So 3,3 is out. So 9, 1 is still left.
Both numbers positive, one greater than the other,
so
\sqrt{x} + \sqrt{y} = 9
\sqrt{x} - \sqrt{y} = 1
this can be solved and we get the ans which obviously i wrong as per OA.

What's wrong here and why is 2 not sufficient?

Thanks.

You are assuming that $$\sqrt{x} + \sqrt{y}$$ and $$\sqrt{x} - \sqrt{y}$$ are integers, which is not given. Why cannot $$\sqrt{x} + \sqrt{y}$$ be 81 and $$\sqrt{x} - \sqrt{y}$$ be 1/9? x - y = 9 has infinitely many solutions, so you cannot get the single numerical value of $$\sqrt{x} - \sqrt{y}$$
_________________
Intern  B
Joined: 19 Nov 2012
Posts: 28

### Show Tags

Bunuel wrote:

You are assuming that $$\sqrt{x} + \sqrt{y}$$ and $$\sqrt{x} - \sqrt{y}$$ are integers, which is not given. Why cannot $$\sqrt{x} + \sqrt{y}$$ be 81 and $$\sqrt{x} - \sqrt{y}$$ be 1/9? x - y = 9 has infinitely many solutions, so you cannot get the single numerical value of $$\sqrt{x} - \sqrt{y}$$

Fell for the trap. Thanks Bunuel as always for the quick response - eye opener!
Manager  S
Joined: 02 Mar 2018
Posts: 65
Location: India
GMAT 1: 640 Q51 V26 GPA: 3.1

### Show Tags

How do we solve the equation from √x-√y=2

Originally posted by gsingh0711 on 31 Jul 2018, 16:20.
Last edited by gsingh0711 on 01 Aug 2018, 05:18, edited 1 time in total.
Math Expert V
Joined: 02 Sep 2009
Posts: 56234

### Show Tags

gsingh0711 wrote:
How do we solve the quation from √−y√=2

Please learn how to format math formulae: https://gmatclub.com/forum/rules-for-po ... l#p1096628
_________________
Manager  S
Joined: 02 Mar 2018
Posts: 65
Location: India
GMAT 1: 640 Q51 V26 GPA: 3.1

### Show Tags

Bunuel wrote:
gsingh0711 wrote:
How do we solve the quation from √−y√=2

Please learn how to format math formulae: https://gmatclub.com/forum/rules-for-po ... l#p1096628

Thanks for sharing the link. Hope the expression is decipherable now. please clarify my doubt pertaining to the question.
Intern  S
Joined: 30 Apr 2018
Posts: 34
Location: India
Concentration: Finance, General Management
GMAT 1: 760 Q51 V42 GPA: 4
WE: Engineering (Computer Software)

### Show Tags

Hi Bunuel,
for the second statement, could you please let me know how the below approach is incorrect
Statement 2: x -y =9
This can be expanded as
$$(\sqrt{x} + \sqrt{y})(\sqrt{x} - \sqrt{y})$$ = 9
The Right Hand Side can be either -3 * -3, -1 * -9, 1*9, 3*3
Since it is already given that both x and y are positive, we are left with only 3*3 and 1*9. Also, since the sum and difference of two numbers cannot be the same unless one or both are 0, 3*3 is also eliminated. Hence, we are left with 9*1 thereby, giving us a solution
$$(\sqrt{x} + \sqrt{y})$$ = 9 and
$$(\sqrt{x} - \sqrt{y})$$ = 1
Math Expert V
Joined: 02 Sep 2009
Posts: 56234

### Show Tags

aroraishita02 wrote:
Hi Bunuel,
for the second statement, could you please let me know how the below approach is incorrect
Statement 2: x -y =9
This can be expanded as
$$(\sqrt{x} + \sqrt{y})(\sqrt{x} - \sqrt{y})$$ = 9
The Right Hand Side can be either -3 * -3, -1 * -9, 1*9, 3*3
Since it is already given that both x and y are positive, we are left with only 3*3 and 1*9. Also, since the sum and difference of two numbers cannot be the same unless one or both are 0, 3*3 is also eliminated. Hence, we are left with 9*1 thereby, giving us a solution
$$(\sqrt{x} + \sqrt{y})$$ = 9 and
$$(\sqrt{x} - \sqrt{y})$$ = 1

Check here: https://gmatclub.com/forum/m01-183530-20.html#p2083627
_________________ Re: M01-19   [#permalink] 02 Sep 2018, 21:28

Go to page   Previous    1   2   [ 27 posts ]

Display posts from previous: Sort by

# M01-19

Moderators: chetan2u, Bunuel  