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

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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.

Answer: C.

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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Re: Point K = (A,0), Point G = (2A + 4, sqrt2A+ 9). Is the dista   [#permalink] 29 Oct 2014, 08:37
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