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What is the value of xy? (1) x^2 + 4√2x + 8 = 0 (2) y^2 − 12y + 36 =0

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Bunuel
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What is the value of xy? (1) x^2 + 4√2x + 8 = 0 (2) y^2 − 12y + 36 =0 [#permalink] New post  10 Sep 2021, 01:30
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What is the value of xy ?


(1) \(x^2 + 4√2*x + 8 = 0\)

(2) \(y^2 − 12y + 36 = 0\)




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What is the value of xy? (1) x^2 + 4√2x + 8 = 0 (2) y^2 − 12y + 36 =0 [#permalink] New post  10 Sep 2021, 06:59
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Bunuel wrote:
What is the value of xy ?

(1) \(x^2 + 4√2*x + 8 = 0\)

(2) \(y^2 − 12y + 36 = 0\)



Statement 1:

Note this is a square, as the square root of 8 is \(2\sqrt{2}\). Then there is a single value of x. Since we don't know y, this is insufficient.

Statement 2:

Similar to above, insufficient.

Combined:

We know both x and y. Sufficient.

Ans: C
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What is the value of xy? (1) x^2 + 4√2x + 8 = 0 (2) y^2 − 12y + 36 =0 [#permalink] New post  10 Sep 2021, 07:18
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Find out xy

1. x^2+4√2∗x+8=0
We do not know y, so insufficient unless x=0, which is not the case here

=> (x+2√2)^2=0
=> x=-2√2

2. y^2−12y+36=0
We do not know x, so insufficient unless y=0, which is not the case here

=> (y-6)^2=0
=> y=6

Now we know x and y so xy=6*-2√2

IMO C is the answer
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Re: What is the value of xy? (1) x^2 + 4√2x + 8 = 0 (2) y^2 − 12y + 36 =0 [#permalink] New post  10 Sep 2021, 08:38
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(1) \(x^2 + 4√2*x + 8 = 0\)
<=> \((x + 2√2)^{2}\) = 0
<=> x = -2√2
but we have no clues of y ==> insufficient

(2) \(y^2 − 12y + 36 = 0\)
<=> \((y - 6)^{2} = 0\)
<=> y = 6
but we have no clues of x ==> insufficient

Combine (1) & (2), we have xy = -2√2 * 6
=> sufficient
=> IMO: C
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Re: What is the value of xy? (1) x^2 + 4√2x + 8 = 0 (2) y^2 − 12y + 36 =0 [#permalink] New post  11 Sep 2021, 00:49
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Bunuel wrote:
What is the value of xy?


(1) \(x^2 + 4\sqrt{2}x + 8 = 0\)

(2) \(y^2 − 12y + 36 = 0\)



(1) \(x^2 + 4\sqrt{2}x + 8 = 0\)
=> \((x+2\sqrt{2})^2 = 0\)
=> x = \(-2\sqrt{2}\)
Don't know the value of y
=> Insufficiency

(2) \(y^2 − 12y + 36 = 0\)
=> \((y-6)^2=0\)
=> \( y = 6\)
Don't know the value of x
=> Insufficiency

(1) & (2) => xy = \(-12\sqrt{2}\)
=> Sufficiency

=> Choice C
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Re: What is the value of xy? (1) x^2 + 4√2x + 8 = 0 (2) y^2 − 12y + 36 =0 [#permalink] New post  11 Sep 2021, 00:53
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Need x and y.

Statement (1)
It is of the form \((a^2+b^2)=a^2+2ab+b^2\) where b is \(2\sqrt{2}\). So x can be determined, but no info of y. Insufficient.

Statement (2)
Just like statement (1), you can determine y but not x. Again insufficient.

Combine (1) and (2)
You get distinct values of x and y which can be multiplied to find xy.

Answer C
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Re: What is the value of xy? (1) x^2 + 4√2x + 8 = 0 (2) y^2 − 12y + 36 =0 [#permalink]
11 Sep 2021, 00:53
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