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Statement 2 gives us two values. Hence insufficient

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).

Statement 2 gives us two values. Hence insufficient

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).

Yes, you're right. I missed it. Sorry all.

It is indeed. Moral of the story- Read the question properly
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Hit kudos if my post helps you. You may send me a PM if you have any doubts about my solution or GMAT problems in general.

Preparation for final battel: GMAT PREP-1 750 Q50 V41 - Oct 16 2011 GMAT PREP-2 710 Q50 V36 - Oct 22 2011 ==> Scored 50 in Quant second time in a row MGMAT---- -1 560 Q28 V39 - Oct 29 2011 ==> Left Quant half done and continued with Verbal. Happy to see Q39

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.

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

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

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 \((x+y)^2\)

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 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

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.

D Both options are individually sufficient 1) adding both equations, (x+y)^2=100 Sufficient 2) (x+y)^2 =100 [*can't be the negative solution as it is a square] Sufficient

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)