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Hence, we have two possible solutions, therefore Statement 1 is insufficient

Statement 2 : \(Y\) is not equal to zero But, X could be equal to zero or be the reciprocal of Y, therefore, statement 2 would fall under the same scenarios as statement 1

Hence, we have two possible solutions, therefore Statement 2 is insufficient

Both Statement 1 & 2 together confirms that \(X & Y\) both are not equal to zero, therefore, they have to be reciprocals and since statement gives us the value of \(X=-1/2\), we can also the value of \(Y=-2/1\) (Reciprocal of X) and thereafter we can find the value of \(X + Y = -1/2 + -2/1 = -5/2\)

Hence, both together are sufficient, therefore C is the correct Answer!

Re: If √(xy) = xy, what is the value of x + y? [#permalink]

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15 Oct 2014, 21:26

1

This post received KUDOS

Bunuel wrote:

Tough and Tricky questions: Algebra.

If √(xy) = xy, what is the value of x + y?

(1) x = -1/2 (2) y is not equal to 0

I did something similar to DMMK, except for one thing: I know \(\sqrt{n}\) = \(n\) only when \(n\) = 0 or \(n\) = 1. For all other values of \(n\), the two would not be equal. Knowing this made it much simpler to plug in the statements. I just had to determine if from the statement(s) provided, can I rule out xy = 0 or xy=1.

Stament 1: Knowing that x = -1/2, y could equal 0 or -2, and still make the premise true. Either value of y would make x + y a different value. Therefore, it is insufficient.

Statement 2: Knowing that y is not equal to 0, x could equal zero or the inverse of y, and still make the premise true. Either value of x would make x + y a different value. Therefore, it is insufficient.

Now to evaluate both statements together.

The reason we rejected statement 1 by itself was because y could equal one of two possible values. Statement 2 eliminates one of those options. Therefore y must equal -2. And therefore both statements together are sufficient to answer "what is the value of x+y."

Re: If √(xy) = xy, what is the value of x + y? [#permalink]

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15 Nov 2015, 12:31

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Statement 1: x = -1/2 From the given equation (i), we can have two different values of y. Hence two different values of x + y INSUFFICIENT

Statement 2: y is not equal to 0 No information about x INSUFFICIENT

Combining Statement 1 and Statement 2: x = -1/2 and y is not equal to 0 From (i), xy cannot be 0 since both x and y are not = 0 Hence xy = 1 y = -2 x + y = \(-\frac{5}{2}\) SUFFICIENT

Re: If √(xy) = xy, what is the value of x + y? [#permalink]

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14 Apr 2017, 06:13

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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