What is the value of (x + y)^2?

Question

(1) x^2 − xy = 28 and 3xy + y^2 = 72.

(2) (x + y)^4 = 10,000

hashjax · Answer

How can you solve with A? I was inclining more towards E.

blink005 · Answer

Add equations in 1

x^2 − xy = 28 & 3xy + y^2 = 72.

x^2+2xy+y^2=100
(x+y)^2=100

Sufficient

Makes sense?

Statement 2 gives us two values. Hence insufficient

GMATPill · Answer

Actually statement 2 gives only 1 value.

(x + y)^2 = 100

it cannot = -100
because the left side is a square - which means the right side must be a positive number and cannot be negative.

If the square weren't there - then you can say there are 2 possible values: +100 and -100. But since the question asks for what (x+y)^2 is - we know that it must be the positive version.

Therefore, either (1) or (2) would work. Answer would be (D).

ajaysamp · Answer

Let x+y = -10, then (x+y)^4 = 10000. So A it is.

Cheers,

AJ

Posted from my mobile device

blink005 · Answer

Yes, you're right. I missed it. Sorry all. It is indeed. Moral of the story- Read the question properly :-)

heman2402 · Answer

"D"

1. X^2 - XY = 28
 Y^2 + 3XY = 72
________________
X^2 + Y^2 + 2XY = 100

=> (X + Y)^2 = 100
SUFFICIENT.

2. (X + Y)^4 = 10,000 
 => ((X+Y)^2)^2 = ((10)^2)^2
 => (X+Y)^2 = 100
SUFFICIENT

reatsaint · Answer

(1) Add both the eq. 
(2) (x + y)^4 = 10,000 means (x + y)^2 can be 100 or -100, but (x + y)^2 being a square we can have only 100. 
Hence Ans = D

Bunuel · Answer

What is the value of (x + y)^2?

(1) x^2 − xy = 28 and 3xy + y^2 = 72.

Sum the equations: x^2 + 2xy + y^2 = 100 --> (x + y)^2 = 100. Sufficient.

(2) (x + y)^4 = 10,000 --> take the square root: (x + y)^2 = 100. Sufficient. Notice that (x + y)^2 cannot be -100 because the square of a number cannot be negative.

Answer: D.

xnthic · Answer

Bunuel  , a basic question if you don't mind clarifying;

For (x + y)^4 , you can simply take the square root .... but hypothetically if (x + y)^2 = 10,000 you can't simply take the square root? you'll have to FOIL it out?

For example, I've seen some Qs where if (x + y)^2 = 100 .... (x + y) does not equal +- 10, it's x^2 + 2xy + y^2 = 100

But (x + y)^4, you're able to simply take the square root?

Just really confused about this concept. Appreciate all the help. thank you

abhimahna · Answer

Let me try help you out.

See, I have  (x + y)^4 = 10000

Now, if take the fourth root of the above equation, we will get (x+y) = 10 or (x+y) = - 10

So, we have two values for (x+y).

But NOTICE, the question stem asks the value of  (x + y)^2 , so whichever value of (x+y) when squared will always give 100.

Hence, we have a single value of (x+y) => The statement is sufficient.

Even if we had  (x + y)^2 = 10000 , we would have got the value of (x+y) either equal to 100 and -100. But remember question is   NOT   asking you the value of (x+y), it is asking the value of  (x+y)^2

I hope its clear now.

xnthic · Answer

Thanks for clarifying ! I definitely get the answer and logic.

However, related to this about a basic math concept. My question is simply: in other math situations, is it allowed to simply take square root (x + y)^2 which gives +-10 OR is that not allowed and you'd have to foil out the algebraic expression?

Thanks for the help !

Posted from my mobile device

abhimahna · Answer

Yes, it is allowed to take the square root on both the sides of the equation. But make sure both signs(+ and -) are considered. Go through the below link to get more clarity on this concept. https://www.purplemath.com/modules/solvquad2.htm

nayakr1127 · Answer

D
Both options are individually sufficient
1) adding both equations, 
(x+y)^2=100
Sufficient
2) (x+y)^2 =100 
 
Sufficient

Sent from my HTC One E9PLUS dual sim using  GMAT Club Forum mobile app

Joc456 · Answer

What is the value of (x + y)^2?

(1) x^2 − xy = 28 and 3xy + y^2 = 72.

(2) (x + y)^4 = 10,000

(1) x^2 − xy = 28 and 3xy + y^2 = 72.

I first factored out (x+y)²=x²_2xy+y²

x²-xy=28
x²=28+xy

3xy + y² = 72.

y²=72-3xy

if we substitute the values back into the equation we get

28+xy+2xy+72-3xy

From here the variables cancel out and we get =100

(2) (x + y)^4 = 10,000
Take the square root of both sides
(x+y)²=100

D

amanvermagmat · Answer

We need to find (x + y)^2. And (x + y)^2 = x^2 + y^2 + 2xy

(1) We are given two equations:
x^2 − xy = 28 and 3xy + y^2 = 72. If we add these two equations, we get: x^2 - xy + 3xy + y^2 = 28+72 OR x^2 + y^2 + 2xy = 100. This is sufficient.

(2) (x + y)^4 = 10,000 Or ((x + y)^2)^2 = (100)^2 
This gives us (x + y)^2 = 100 
This is also sufficient. (We should note that though 10000 is also the square of -100, we cannot write -100 on RHS as LHS is (x + y)^2, and square of anything cannot be negative)

Hence  D answer

Basshead · Answer

(1) Add the two equations together:

x^2 + 2xy + y^2 = 100

(x+y)^2 = 100

SUFFICIENT.

(2)  (x+y)^4 = 10,000

(x+y)^2 = 100

SUFFICIENT.

Answer is D.

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What is the value of (x + y)^2?

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