GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 23 Jan 2020, 09:11

### 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

# If x and y are positive integers, what is the value of x^(1/2)+y^(1/2)

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

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 60627
If x and y are positive integers, what is the value of x^(1/2)+y^(1/2)  [#permalink]

### Show Tags

21 Oct 2015, 21:49
10
37
00:00

Difficulty:

15% (low)

Question Stats:

76% (01:16) correct 24% (01:24) wrong based on 1488 sessions

### HideShow timer Statistics

If x and y are positive integers, what is the value of $$\sqrt{x} + \sqrt{y}$$?

(1) x + y = 15
(2) $$\sqrt{xy}= 6$$

Kudos for a correct solution.

_________________
##### Most Helpful Community Reply
Retired Moderator
Joined: 29 Apr 2015
Posts: 815
Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE: Asset Management (Investment Banking)
If x and y are positive integers, what is the value of x^(1/2)+y^(1/2)  [#permalink]

### Show Tags

23 Oct 2015, 00:43
19
8
Bunuel wrote:
If x and y are positive integers, what is the value of $$\sqrt{x} + \sqrt{y}$$?

(1) x + y = 15
(2) $$\sqrt{xy}= 6$$

Kudos for a correct solution.

1) Gives you various single values for x and y. Therefore clearly insufficient.
2) If $$\sqrt{xy}= 6$$, then xy = 36 which can be built with 3*12 or 6*6 ... insufficient.

1+2) Here we know, x+y = 15 and xy = 36, hence x, or y are splitted up as 12 and 3. It does actually not matter if x is 3 or 12 or y is 3 or 12. The sum of $$\sqrt{x} + \sqrt{y}$$ will be the same.

Answer C.
##### General Discussion
Manager
Joined: 10 Aug 2015
Posts: 54
Concentration: General Management, Entrepreneurship
GMAT 1: 730 Q48 V42
Re: If x and y are positive integers, what is the value of x^(1/2)+y^(1/2)  [#permalink]

### Show Tags

23 Oct 2015, 05:42
6
2
To find the value of $$\sqrt{x} + \sqrt{y}$$ we need to know to have a value for x and a value for y.

Statement 1 : INSUFFICIENT
x + y = 15
We have different possible values for x and y:
x= 7 and y= 8
x= 9 and y= 6
x= 12 and y=3
All of these would yield different values for $$\sqrt{x} + \sqrt{y}$$. Since we can't find a unique value, the statement is not sufficient.

Statement 2 : INSUFFICIENT
If $$\sqrt{xy}=6$$ then $$(\sqrt{xy})^2=6^2$$ and $$xy=$$36.
Again, there are multiple values of x and y for which $$xy=36$$:
x=36 and y=1
x=6 and y=6
Since we can't find a unique value, the statement is not sufficient.

(1) + (2) = SUFFICIENT

We know that x+y = 15 and that xy=36, because x and y are positive integers we know that x=12 and y=3 OR x=3 and y=12 either way we will be able to calculate the value of $$\sqrt{x} + \sqrt{y}$$ because it will not change the result.

The answer is C.
Verbal Forum Moderator
Status: Greatness begins beyond your comfort zone
Joined: 08 Dec 2013
Posts: 2446
Location: India
Concentration: General Management, Strategy
Schools: Kelley '20, ISB '19
GPA: 3.2
WE: Information Technology (Consulting)
Re: If x and y are positive integers, what is the value of x^(1/2)+y^(1/2)  [#permalink]

### Show Tags

21 Oct 2015, 23:19
4
((x)^(1/2)+(y)^(1/2))^2 = x + y + 2 *(xy)^(1/2)

1. x+y= 15
Not sufficient

2.
(xy)^(1/2) = 6
Not sufficient

Combining 1 and 2, we get
x + y + 2 *(xy)^(1/2)= 15 + 2*6=27
=> ((x)^(1/2)+(y)^(1/2))^2 = 27
=> (x)^(1/2)+(y)^(1/2) =3*((3)^(1/2)

Sufficient
Answer C
_________________
When everything seems to be going against you, remember that the airplane takes off against the wind, not with it. - Henry Ford
The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long
Math Expert
Joined: 02 Sep 2009
Posts: 60627
Re: If x and y are positive integers, what is the value of x^(1/2)+y^(1/2)  [#permalink]

### Show Tags

19 Jan 2017, 02:25
1
malavika1 wrote:
Whenever we are given that for example, root(n) = something,

Can we always pretty much blindly conclude that n = (something)^2?

Or is there something we have to watch out for.

If we are given that say $$\sqrt{x}=y$$, then we can square and get x = y^2.
_________________
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9095
Location: United States (CA)
If x and y are positive integers, what is the value of x^(1/2)+y^(1/2)  [#permalink]

### Show Tags

20 Dec 2017, 07:45
1
1
Bunuel wrote:
If x and y are positive integers, what is the value of $$\sqrt{x} + \sqrt{y}$$?

(1) x + y = 15
(2) $$\sqrt{xy}= 6$$

We need to determine the value of √x + √y.

Statement One Alone:

x + y = 15

If x = 1 and y = 14, then √x + √y = 1 + √14. However, if x = 4 and y = 11, then √x + √y = 2 + √11. We see that we don’t have enough information to determine a unique value of √x + √y.

Statement one alone is not sufficient to answer the question.

Statement Two Alone:

√(xy) = 6

If x = 6 and y = 6, then √x + √y = 2√6. However, if x = 4 and y = 9, then √x + √y = 5. We see that we don’t have enough information to determine a unique value of √x + √y.

Statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Notice that (√x + √y)^2 = x + y + 2√(xy). From the two statements, we are given that x + y = 15 and √(xy) = 6, and thus (√x + √y)^2 = 15 + 2(6) = 27. Now, if we take the square root of both sides of the equation (√x + √y)^2 = 27, we have √x + √y = √27 = 3√3.

Answer: C
_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
181 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Math Expert
Joined: 02 Sep 2009
Posts: 60627
Re: If x and y are positive integers, what is the value of x^(1/2)+y^(1/2)  [#permalink]

### Show Tags

01 Jan 2018, 02:09
1
sushforgmat wrote:
GMATPrepNow wrote:
Bunuel wrote:
If x and y are positive integers, what is the value of $$\sqrt{x} + \sqrt{y}$$?

(1) x + y = 15
(2) $$\sqrt{xy}= 6$$

Kudos for a correct solution.

Target question: What is the value of √x + √y?

Statement 1: x + y = 15
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 14 and y = 1, in which case √x + √y = √14 + √1 = √14 + 1
Case b: x = 9 and y = 6, in which case √x + √y = √9 + √6 = 3 + √6
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: √(xy) = 6
In other words xy = 36
This statement doesn't FEEL sufficient either, so I'll TEST some values.
There are several values of x and y that satisfy statement 2. Here are two:
Case a: x = 1 and y = 36, in which case √x + √y = √1 + √36 = 1 + 6 = 7
Case b: x = 4 and y = 9, in which case √x + √y = √4 + √9 = 2 + 3 = 5
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that x + y = 15
Statement 2 tells us that √(xy) = 6
Recognize that (√x + √y)² = x + 2√(xy) + y
Rearrange to get: (√x + √y)² = 15 + 2(6)
Evaluate: (√x + √y)² = 27
So, √x + √y = √27
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer:

But, isn't √x + √y = ± √27 which would not result in a single solution for the question?

The square root of a number (generally even root of a number) is non-negative: 0 or positive. $$\sqrt[even]{nonnegative \ number}\geq 0$$. Thus, $$\sqrt{x} + \sqrt{y} = {nonnegative \ number} + {nonnegative \ number}= {nonnegative \ number}$$, so it cannot equal to a negative number.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 60627
Re: If x and y are positive integers, what is the value of x^(1/2)+y^(1/2)  [#permalink]

### Show Tags

12 Jan 2018, 05:00
1
bbg wrote:
I thought (1) alone was enough since if
x+y=15
I could do the squared root of each term
√x + √y = ± √15
Am I breaking some math rules?

Thank you in advance

If you take the square root from x + y = 15, you'll get $$\sqrt{x + y} = \sqrt{15}$$, which is NOT the same as $$\sqrt{x}+\sqrt{y} = \sqrt{15}$$. You see, generally, $$\sqrt{x + y} \neq \sqrt{x}+\sqrt{y}$$. For example, $$\sqrt{2 + 2} \neq \sqrt{2}+\sqrt{2}$$.
_________________
Marshall & McDonough Moderator
Joined: 13 Apr 2015
Posts: 1684
Location: India
Re: If x and y are positive integers, what is the value of x^(1/2)+y^(1/2)  [#permalink]

### Show Tags

21 Oct 2015, 22:54
(sqrt(x) + sqrt(y))^2 = x + y + 2(sqrt(xy))

Statement 1: Not Sufficient
Statement 2: Not Sufficient

Combining St1 and St2 we have the values for (x + y) and sqrt(xy) - Sufficient

Answer: C
Intern
Joined: 18 Jan 2017
Posts: 31
Re: If x and y are positive integers, what is the value of x^(1/2)+y^(1/2)  [#permalink]

### Show Tags

18 Jan 2017, 22:37
Whenever we are given that for example, root(n) = something,

Can we always pretty much blindly conclude that n = (something)^2?

Or is there something we have to watch out for.
Senior Manager
Joined: 21 Aug 2016
Posts: 254
Location: India
GPA: 3.9
WE: Information Technology (Computer Software)
Re: If x and y are positive integers, what is the value of x^(1/2)+y^(1/2)  [#permalink]

### Show Tags

19 Jan 2017, 03:44
Bunuel wrote:
malavika1 wrote:
Whenever we are given that for example, root(n) = something,

Can we always pretty much blindly conclude that n = (something)^2?

Or is there something we have to watch out for.

If we are given that say $$\sqrt{x}=y$$, then we can square and get x = y^2.

Sorry to post little unrelated post; where should we consider mode in GMAT. As I remember, in one of your post, you mentioned -- sqrt(x^2)=|x|
Math Expert
Joined: 02 Sep 2009
Posts: 60627
Re: If x and y are positive integers, what is the value of x^(1/2)+y^(1/2)  [#permalink]

### Show Tags

19 Jan 2017, 03:52
AR15J wrote:
Bunuel wrote:
malavika1 wrote:
Whenever we are given that for example, root(n) = something,

Can we always pretty much blindly conclude that n = (something)^2?

Or is there something we have to watch out for.

If we are given that say $$\sqrt{x}=y$$, then we can square and get x = y^2.

Sorry to post little unrelated post; where should we consider mode in GMAT. As I remember, in one of your post, you mentioned -- sqrt(x^2)=|x|

Not following you... What is your question?

P.S. Yes, $$\sqrt{x^2}=|x|$$.
_________________
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 4226
Location: Canada
If x and y are positive integers, what is the value of x^(1/2)+y^(1/2)  [#permalink]

### Show Tags

Updated on: 07 Sep 2018, 16:14
Top Contributor
1
Bunuel wrote:
If x and y are positive integers, what is the value of $$\sqrt{x} + \sqrt{y}$$?

(1) x + y = 15
(2) $$\sqrt{xy}= 6$$

Kudos for a correct solution.

Target question: What is the value of √x + √y?

Statement 1: x + y = 15
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 14 and y = 1, in which case √x + √y = √14 + √1 = √14 + 1
Case b: x = 9 and y = 6, in which case √x + √y = √9 + √6 = 3 + √6
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, read my article: http://www.gmatprepnow.com/articles/dat ... lug-values

Statement 2: √(xy) = 6
In other words xy = 36
This statement doesn't FEEL sufficient either, so I'll TEST some values.
There are several values of x and y that satisfy statement 2. Here are two:
Case a: x = 1 and y = 36, in which case √x + √y = √1 + √36 = 1 + 6 = 7
Case b: x = 4 and y = 9, in which case √x + √y = √4 + √9 = 2 + 3 = 5
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that x + y = 15
Statement 2 tells us that √(xy) = 6
Recognize that (√x + √y)² = x + 2√(xy) + y
Rearrange to get: (√x + √y)² = x + y + 2√(xy)
We get: (√x + √y)² = 15 + 2(6)
Evaluate: (√x + √y)² = 27
So, √x + √y = √27
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

RELATED VIDEO

_________________
Test confidently with gmatprepnow.com

Originally posted by GMATPrepNow on 01 Aug 2017, 12:29.
Last edited by GMATPrepNow on 07 Sep 2018, 16:14, edited 1 time in total.
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8445
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: If x and y are positive integers, what is the value of x^(1/2)+y^(1/2)  [#permalink]

### Show Tags

23 Dec 2017, 10:38
Bunuel wrote:
If x and y are positive integers, what is the value of $$\sqrt{x} + \sqrt{y}$$?

(1) x + y = 15
(2) $$\sqrt{xy}= 6$$

Kudos for a correct solution.

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 2 variables (x and y) and 0 equations, C is most likely to be the answer and so we should consider 1) & 2) first.

$$(\sqrt{x} + \sqrt{y})^2 = x + 2\sqrt{xy} + y = x + y + 2\sqrt{xy} = 15 + 2 \cdot 6 = 15 + 12 = 27$$.
Both conditions 1) & 2) are sufficient.

Since this is an integer question (one of the key question areas), we should also consider choices A and B by CMT 4(A).

Condition 1)
Since $$y = 15 - x$$, we have $$\sqrt{x} + \sqrt{y} = \sqrt{x} + \sqrt{15 - x}$$.
However, the condition 1) is not sufficient since we don't know $$x$$.

Condition 1)
Since $$xy = 36$$ and $$y = \frac{36}{x}$$, we have $$\sqrt{x} + \sqrt{y} = \sqrt{x} + \sqrt{\frac{36}{x}}$$.
However, the condition 1) is not sufficient since we don't know $$x$$.

Therefore, C is the answer.

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only \$79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Manager
Joined: 26 Dec 2017
Posts: 57
Location: India
Concentration: Technology, Marketing
WE: General Management (Internet and New Media)
Re: If x and y are positive integers, what is the value of x^(1/2)+y^(1/2)  [#permalink]

### Show Tags

01 Jan 2018, 02:04
GMATPrepNow wrote:
Bunuel wrote:
If x and y are positive integers, what is the value of $$\sqrt{x} + \sqrt{y}$$?

(1) x + y = 15
(2) $$\sqrt{xy}= 6$$

Kudos for a correct solution.

Target question: What is the value of √x + √y?

Statement 1: x + y = 15
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 14 and y = 1, in which case √x + √y = √14 + √1 = √14 + 1
Case b: x = 9 and y = 6, in which case √x + √y = √9 + √6 = 3 + √6
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: √(xy) = 6
In other words xy = 36
This statement doesn't FEEL sufficient either, so I'll TEST some values.
There are several values of x and y that satisfy statement 2. Here are two:
Case a: x = 1 and y = 36, in which case √x + √y = √1 + √36 = 1 + 6 = 7
Case b: x = 4 and y = 9, in which case √x + √y = √4 + √9 = 2 + 3 = 5
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that x + y = 15
Statement 2 tells us that √(xy) = 6
Recognize that (√x + √y)² = x + 2√(xy) + y
Rearrange to get: (√x + √y)² = 15 + 2(6)
Evaluate: (√x + √y)² = 27
So, √x + √y = √27
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer:

But, isn't √x + √y = ± √27 which would not result in a single solution for the question?
Manager
Joined: 26 Dec 2017
Posts: 57
Location: India
Concentration: Technology, Marketing
WE: General Management (Internet and New Media)
Re: If x and y are positive integers, what is the value of x^(1/2)+y^(1/2)  [#permalink]

### Show Tags

01 Jan 2018, 10:32
Bunuel wrote:
sushforgmat wrote:
GMATPrepNow wrote:
If x and y are positive integers, what is the value of $$\sqrt{x} + \sqrt{y}$$?

(1) x + y = 15
(2) $$\sqrt{xy}= 6$$

Kudos for a correct solution.

Target question: What is the value of √x + √y?

Statement 1: x + y = 15
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 14 and y = 1, in which case √x + √y = √14 + √1 = √14 + 1
Case b: x = 9 and y = 6, in which case √x + √y = √9 + √6 = 3 + √6
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: √(xy) = 6
In other words xy = 36
This statement doesn't FEEL sufficient either, so I'll TEST some values.
There are several values of x and y that satisfy statement 2. Here are two:
Case a: x = 1 and y = 36, in which case √x + √y = √1 + √36 = 1 + 6 = 7
Case b: x = 4 and y = 9, in which case √x + √y = √4 + √9 = 2 + 3 = 5
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that x + y = 15
Statement 2 tells us that √(xy) = 6
Recognize that (√x + √y)² = x + 2√(xy) + y
Rearrange to get: (√x + √y)² = 15 + 2(6)
Evaluate: (√x + √y)² = 27
So, √x + √y = √27
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer:

But, isn't √x + √y = ± √27 which would not result in a single solution for the question?

The square root of a number (generally even root of a number) is non-negative: 0 or positive. $$\sqrt[even]{nonnegative \ number}\geq 0$$. Thus, $$\sqrt{x} + \sqrt{y} = {nonnegative \ number} + {nonnegative \ number}= {nonnegative \ number}$$, so it cannot equal to a negative number.

With multiple books and reading a lot of content, I think I missed the basic point that you mentioned.
Thanks, Bunuel.
Intern
Joined: 17 Oct 2017
Posts: 2
Re: If x and y are positive integers, what is the value of x^(1/2)+y^(1/2)  [#permalink]

### Show Tags

12 Jan 2018, 04:03
I thought (1) alone was enough since if
x+y=15
I could do the squared root of each term
√x + √y = ± √15
Am I breaking some math rules?

Thank you in advance
IIMA, IIMC School Moderator
Joined: 04 Sep 2016
Posts: 1381
Location: India
WE: Engineering (Other)
If x and y are positive integers, what is the value of x^(1/2)+y^(1/2)  [#permalink]

### Show Tags

23 Jan 2018, 19:14
Bunuel chetan2u niks18 amanvermagmat

Quote:
If x and y are positive integers, what is the value of $$\sqrt{x} + \sqrt{y}$$?

(1) x + y = 15
(2) $$\sqrt{xy}= 6$$

I think we over complicated the solution.
Can we not simply approach q as : $$(a+b)^2$$ = $$a^2$$+ $$b^2$$ + 2 ab

Substitute $$\sqrt{a}$$ for a and $$\sqrt{b}$$ for b
only both statements together help in completing equation.

Is this method correct?
_________________
It's the journey that brings us happiness not the destination.

Feeling stressed, you are not alone!!
Retired Moderator
Joined: 25 Feb 2013
Posts: 1156
Location: India
GPA: 3.82
Re: If x and y are positive integers, what is the value of x^(1/2)+y^(1/2)  [#permalink]

### Show Tags

23 Jan 2018, 19:45
adkikani wrote:
Bunuel chetan2u niks18 amanvermagmat

Quote:
If x and y are positive integers, what is the value of $$\sqrt{x} + \sqrt{y}$$?

(1) x + y = 15
(2) $$\sqrt{xy}= 6$$

I think we over complicated the solution.
Can we not simply approach q as : $$(a+b)^2$$ = $$a^2$$+ $$b^2$$ + 2 ab

Substitute $$\sqrt{a}$$ for a and $$\sqrt{b}$$ for b
only both statements together help in completing equation.

Is this method correct?

Hi adkikani,

Yes it is perfectly fine and simpler. Square both sides and then take the square root of the resulting value and finally discard the negative value as x and y are positive

Posted from my mobile device
VP
Joined: 09 Mar 2016
Posts: 1223
If x and y are positive integers, what is the value of x^(1/2)+y^(1/2)  [#permalink]

### Show Tags

22 Apr 2018, 05:33
GMATPrepNow wrote:
Bunuel wrote:
If x and y are positive integers, what is the value of $$\sqrt{x} + \sqrt{y}$$?

(1) x + y = 15
(2) $$\sqrt{xy}= 6$$

Kudos for a correct solution.

Target question: What is the value of √x + √y?

Statement 1: x + y = 15
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 14 and y = 1, in which case √x + √y = √14 + √1 = √14 + 1
Case b: x = 9 and y = 6, in which case √x + √y = √9 + √6 = 3 + √6
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, read my article: http://www.gmatprepnow.com/articles/dat ... lug-values

Statement 2: √(xy) = 6
In other words xy = 36
This statement doesn't FEEL sufficient either, so I'll TEST some values.
There are several values of x and y that satisfy statement 2. Here are two:
Case a: x = 1 and y = 36, in which case √x + √y = √1 + √36 = 1 + 6 = 7
Case b: x = 4 and y = 9, in which case √x + √y = √4 + √9 = 2 + 3 = 5
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that x + y = 15
Statement 2 tells us that √(xy) = 6
Recognize that (√x + √y)² = x + 2√(xy) + y
Rearrange to get: (√x + √y)² = 15 + 2(6)
Evaluate: (√x + √y)² = 27
So, √x + √y = √27
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer:

RELATED VIDEO

hello there GMATPrepNow

can you please explain how you combine both statements to get answer

Statement 1 tells us that x + y = 15
Statement 2 tells us that √(xy) = 6

and then you say Recognize that (√x + √y)² = x + 2√(xy) + y

I dont recognize this pattern in either of the statements how can I recognize it looking at both statements where did you get this formula ?

I thought I should do square both sides of √(xy) = 6 so I am getting xy = 36 and also have x + y = 15 so I do something like this

x + y = 15 ---> x = 15-y and plug in here xy = 36

thank you in advance for taking time to explain and have a great gmat weekend
If x and y are positive integers, what is the value of x^(1/2)+y^(1/2)   [#permalink] 22 Apr 2018, 05:33

Go to page    1   2    Next  [ 25 posts ]

Display posts from previous: Sort by

# If x and y are positive integers, what is the value of x^(1/2)+y^(1/2)

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

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