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

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

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21 Oct 2015, 21:49
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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.
[Reveal] Spoiler: OA

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

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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

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

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21 Oct 2015, 23:19
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((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
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If x and y are positive integers, what is the value of x^(1/2)+y^(1/2) [#permalink]

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23 Oct 2015, 00:43
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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.

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

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23 Oct 2015, 05:42
2
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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.

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

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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.

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

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19 Jan 2017, 02:25
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Expert's post
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.
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Re: If x and y are positive integers, what is the value of x^(1/2)+y^(1/2) [#permalink]

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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|

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

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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, $$\sqrt{x^2}=|x|$$.
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Re: If x and y are positive integers, what is the value of x^(1/2)+y^(1/2) [#permalink]

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01 Aug 2017, 12:29
Expert's post
Top Contributor
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

[Reveal] Spoiler:
C

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Re: If x and y are positive integers, what is the value of x^(1/2)+y^(1/2)   [#permalink] 01 Aug 2017, 12:29
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