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Point K = (A, 0), Point G = (2A + 4, (2A + 9)^(1/2)). Is the distance  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 67% (02:19) correct 33% (02:47) wrong based on 128 sessions

### HideShow timer Statistics 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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Originally posted by TheKingInTheNorth on 09 Jun 2017, 22:49.
Last edited by Bunuel on 19 Aug 2018, 21:00, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Point K = (A, 0), Point G = (2A + 4, (2A + 9)^(1/2)). Is the distance  [#permalink]

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abhisheknandy08 wrote:
Point K = (A, 0), Point G = 2A 4, 2A9. Is the distance between point K and G prime?
(1) A2 – 5A – 6 = 0
(2) A > 2

What is Point G, it is not clear. Kindly check the question stem.
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Re: Point K = (A, 0), Point G = (2A + 4, (2A + 9)^(1/2)). Is the distance  [#permalink]

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Correct version of the question .
Attachments Question.PNG [ 9.27 KiB | Viewed 1515 times ]

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Re: Point K = (A, 0), Point G = (2A + 4, (2A + 9)^(1/2)). Is the distance  [#permalink]

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Formula used:
Distance between points K(x1,y1) and G(x2,y2) = $$\sqrt{(x1 - x2)^2 + (y1 - y2)^2}$$

On analyzing statement 1 independently, we get A = 6,-1
When A=6, Points K(6,0) and G(16,$$\sqrt{21}$$) have a distance of 11(a prime number)
But if A=-1, Points K(-1,0) and G(2,$$\sqrt{7}$$) have a distance of 4(not a prime number)
Insufficient.

Similarly on analyzing statement 2 independently, using A = 3,6
Since we have got the distance, when A=6 to be prime.
Let analyze if A=3
Points K(3,0) and G(10,$$\sqrt{15}$$) have a distance of 8(not a prime number)
Insufficient.

But, on combining both the statements, we can clearly say A=6, which has a prime number as the distance between K and G.
Sufficient(Option C)
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Re: Point K = (A, 0), Point G = (2A + 4, (2A + 9)^(1/2)). Is the distance  [#permalink]

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In order to solve this question we need a restriction on the possibilities for X- statement 1 and 2 individual fail to provide criteria that allow us to narrow down a discrete value of "a" but statement 1 and 2 together allow us to factor the equation in one and asses one value of a.

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Re: Point K = (A, 0), Point G = (2A + 4, (2A + 9)^(1/2)). Is the distance  [#permalink]

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_________________ Re: Point K = (A, 0), Point G = (2A + 4, (2A + 9)^(1/2)). Is the distance   [#permalink] 19 Aug 2018, 21:01
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# Point K = (A, 0), Point G = (2A + 4, (2A + 9)^(1/2)). Is the distance  