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# Point K = (A,0), Point G = (2A + 4, sqrt2A+ 9). Is the dista

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Point K = (A,0), Point G = (2A + 4, sqrt2A+ 9). Is the dista [#permalink]

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10 Jan 2013, 09:55
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Point K = (A,0), Point G = (2A + 4, $$\sqrt{2A+ 9}$$). Is the distance between point K and G prime?

(1) A^2 – 5A – 6 = 0
(2) A > 2
[Reveal] Spoiler: OA

Last edited by Bunuel on 29 Oct 2014, 08:37, edited 2 times in total.
Renamed the topic and edited the question.

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Re: Point K = (A,0), Point G = (2A + 4, sqrt2A+ 9). Is the dista [#permalink]

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10 Jan 2013, 16:51
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Point K = (A,0), Point G = (2A + 4, sqrt2A+ 9). Is the distance between point K and G prime?

The formula to calculate the distance between two points $$(x_1,y_1)$$ and $$(x_2,y_2)$$ is $$d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$$.

Hence, the distance between points G and K is $$d=\sqrt{(2A+4-A)^2+(\sqrt{2A+9}-0)^2}=\sqrt{(A+5)^2}=|A+5|$$

(1) A^2 – 5A – 6 = 0 --> $$(A-6)(A+1)=0$$ --> $$A=6$$ or $$A=-1$$ --> $$d=|A+5|=11=prime$$ or $$d=|A+5|=4\neq{prime}$$. Not sufficient.

(2) A > 2. If $$A=3$$, then $$d=|A+5|=8\neq{prime}$$ but if $$A=6$$, then $$d=|A+5|=11=prime$$. Not sufficient.

(1)+(2) Since from (2) A > 2, then from (1) $$A=6$$, thus $$d=|A+5|=11=prime$$. Sufficient.

Hope it's clear.
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Re: Point K = (A,0), Point G = (2A + 4, sqrt2A+ 9). Is the dista [#permalink]

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30 Mar 2017, 22:52
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sambam wrote:
Point K = (A,0), Point G = (2A + 4, $$\sqrt{2A+ 9}$$). Is the distance between point K and G prime?

(1) $$A^2 – 5A – 6 = 0$$
(2) $$A > 2$$

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Re: Point K = (A,0), Point G = (2A + 4, sqrt2A+ 9). Is the dista [#permalink]

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29 Oct 2014, 08:37
Hello from the GMAT Club BumpBot!

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Re: Point K = (A,0), Point G = (2A + 4, sqrt2A+ 9). Is the dista [#permalink]

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18 Jun 2016, 06:09
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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Re: Point K = (A,0), Point G = (2A + 4, sqrt2A+ 9). Is the dista [#permalink]

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30 Mar 2017, 23:29
ziyuen wrote:
sambam wrote:
Point K = (A,0), Point G = (2A + 4, $$\sqrt{2A+ 9}$$). Is the distance between point K and G prime?

(1) $$A^2 – 5A – 6 = 0$$
(2) $$A > 2$$

Edited. Thank you.
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Re: Point K = (A,0), Point G = (2A + 4, sqrt2A+ 9). Is the dista   [#permalink] 30 Mar 2017, 23:29
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