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Is the distance prime

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Is the distance prime

by Layo » Fri Aug 26, 2011 2:03 am
Point K = (A,0). Point G = (2A+4, root(2A+9))
Is the distance between point K and G prime?
(1) A^2 - 5A - 6 = 0
(2) A > 2
OA C

edit: sorry guys, i fixed the typo
Last edited by Layo on Fri Aug 26, 2011 9:41 am, edited 1 time in total.
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Source: — Data Sufficiency |
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by sumgb » Fri Aug 26, 2011 3:42 am
(1) A2 - 5A - 6 = 0
i understand it's a quadratic and you mean A^2
but
2A+4, root(2A+9)
does this mean 2^A?

pls use ^ symbol to represent powers. thanks
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by prateek_guy2004 » Fri Aug 26, 2011 7:42 am
yes little difficult to understand.....
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by n@resh » Fri Aug 26, 2011 8:00 am
Layo wrote:Point K = (A,0). Point G = (2A+4, root(2A+9))
Is the distance between point K and G prime?
(1) A2 - 5A - 6 = 0
(2) A > 2
ANS: C!
As per given we have distance between K and G = +(A + 5) or -(A+5) but as distance always +ive we consider A+5.
from stmt 1: A = 6 or -1. that leads to us: KG = 11(prime) or 4(not prime)

not sufficient!

statemnt 2: A>2, any value i.e. A can be 3,4,5...etc which leads to distances like 8,9,10,11...etc clearly not sufficient.

combine 2 statments: A = 6 or -1 and A>2 .... Hence A = 6 is the only possible value which leads to a prime number.

Answer is C!
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by gmatboost » Fri Aug 26, 2011 8:36 am
I think the question is:
Point K = (A,0). Point G = (2A+4, root(2A+9))
Is the distance between point K and G prime?
(1) A^2 - 5A - 6 = 0
(2) A > 2
Distance is sqrt( [x_1-x_2]^2 + [y_1-y_2]^2 )

D = sqrt( [2A + 4 - A]^2 + [root(2A+9) - 0]^2 )
D = sqrt( [A + 4]^2 + [root(2A+9)]^2 )
D = sqrt( A^2 + 8A + 16 + 2A + 9)
D = sqrt( A^2 + 10A + 25)
Note that A^2 + 10A + 25 = (A + 5)^2
D = |a+5| since we need D to be positive

(1) A^2 - 5A - 6 = 0
(A - 6)(A + 1) = 0
A = 6 or A = -1
D = 11 or D = 4
Insufficient since 11 is prime, 4 is not

(2) A > 2
Insufficient

Combined
[spoiler]Sufficient (D = 11)[/spoiler]
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by Layo » Fri Aug 26, 2011 9:44 am
Thank you all for responses, now its clear for me.
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by force5 » Fri Aug 26, 2011 12:36 pm
Yes C....
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