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TheKingInTheNorth
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Point K = (A, 0), Point G = (2A + 4, (2A + 9)^(1/2)). Is the distance Updated on: 19 Aug 2018, 21:00
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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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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C
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Point K = (A, 0), Point G = (2A + 4, (2A + 9)^(1/2)). Is the distance 09 Jun 2017, 23:44
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abhisheknandy08
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
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What is Point G, it is not clear. Kindly check the question stem.
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Point K = (A, 0), Point G = (2A + 4, (2A + 9)^(1/2)). Is the distance 10 Jun 2017, 01:18
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Correct version of the question .
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pushpitkc
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Point K = (A, 0), Point G = (2A + 4, (2A + 9)^(1/2)). Is the distance 10 Jun 2017, 01:35
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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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Point K = (A, 0), Point G = (2A + 4, (2A + 9)^(1/2)). Is the distance 16 Jun 2017, 15:52
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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.

Posted from my mobile device
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Point K = (A, 0), Point G = (2A + 4, (2A + 9)^(1/2)). Is the distance 12 Oct 2019, 23:20
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TheKingInTheNorth
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
Show more

Distance between K and G = \(\sqrt{((2A + 9)^{1/2} - 0)^2 + (2A + 4 - A)^2}\)
= \(\sqrt{(2A + 9 + (A + 4)^2)}\)
= \(\sqrt{(2A + 9 + A^2 + 8A + 16)}\)
= \(\sqrt{(A^2 + 10A + 25)}\)
= \(\sqrt{(A + 5)^2}\)
= \(A + 5\)

(1) \(A^2 – 5A – 6 = 0\)
--> \(A^2 – 6A + A – 6 = 0\)
--> \(A(A - 6) + 1(A – 6) = 0\)
--> \((A - 6)(A + 1) = 0\)
--> A = 6 or -1
--> Two values are possible --> Insufficient

(2) \(A > 2\)
--> Infinite values are possible --> Insufficient

Combining (1) & (2),
--> \(A = 6 or -1\) & \(A > 2\)
--> \(A = 6\) only

--> Distance = \(A + 5 = 6 + 5 = 11\) --> Sufficient

IMO Option C
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Point K = (A, 0), Point G = (2A + 4, (2A + 9)^(1/2)). Is the distance 12 Oct 2019, 23:51
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TheKingInTheNorth
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
Show more

I suggest my students to use statements when you do not know how to proceed and this is one such scenario...

If you do not get hang of it or are short of time, --
There is one variable-A and if we know A, we can answer for sure.
Statement I gives two values of A as it is a quadratic equation. It may be possible that both lead to prime or non-prime, but in most cases it will not.
Statement II gives a range, so insuff
Combined, I says -1 and 6, II says>2, so a unique value C


Point K = (A, 0), Point G = (2A + 4, \(\sqrt{2A + 9}\))..
Two ways..

(I) Don't waste time finding an equation in variable here
We know that to know the distance here, we will require to know the value of A, so let us check the statements
(1) \(A^2 – 5A – 6 = 0...(A-6)(A+1)=0\) A =-1 or A=6..
A is -1.. \(K=(-1,0)\) and G\(=(2,\sqrt{7}\)...Distance = \(\sqrt{9+7}=\sqrt{16}=4\)..NO
A is 6.. \(K=(6,0)\) and G\(=(16,\sqrt{21}\)...Distance = \(\sqrt{100+21}=\sqrt{121}=11\).. Yes
Insuff

(2) A > 2
Clearly insuff. There may be cases where it is true and places where it may not be true.

Combined..ans is 11 and YES
Suff

C

(II) Simplify the question stem
Distance = \(\sqrt{(2A+4-A)^2+\sqrt{2A+9}^2}=\sqrt{A^2+10A+25}=\sqrt{(A+5)}^2=A+5\)
So, if A=2, 7 etc ans is YES and if A=3, 4 etc ans is NO
(1) A^2 – 5A – 6 = 0
A= -1 or 6
Insuff

(2) A > 2
Insuff

Combined A=6
Suff

C
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Point K = (A, 0), Point G = (2A + 4, (2A + 9)^(1/2)). Is the distance 13 Oct 2019, 07:39
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TheKingInTheNorth
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

I suggest my students to use statements when you do not know how to proceed and this is one such scenario...

If you do not get hang of it or are short of time, --
There is one variable-A and if we know A, we can answer for sure.
Statement I gives two values of A as it is a quadratic equation. It may be possible that both lead to prime or non-prime, but in most cases it will not.
Statement II gives a range, so insuff
Combined, I says 2 and 3, II says>2, so a unique value C


Point K = (A, 0), Point G = (2A + 4, \(\sqrt{2A + 9}\))..
Two ways..

(I) Don't waste time finding an equation in variable here
We know that to know the distance here, we will require to know the value of A, so let us check the statements
(1) \(A^2 – 5A – 6 = 0...(A-3)(A-2)=0\) A =2 or A=3..
A is 2.. \(K=(2,0)\) and G\(=(8,\sqrt{13}\)...Distance = \(\sqrt{36+13}=\sqrt{49}=7\)..Yes
A is 3.. \(K=(3,0)\) and G\(=(10,\sqrt{15}\)...Distance = \(\sqrt{49+15}=\sqrt{64}=8\).. No
Insuff

(2) A > 2
Clearly insuff. There may be cases where it is true and places where it may not be true.

Combined..ans is 3 and NO
Suff

C

(II) Simplify the question stem
Distance = \(\sqrt{(2A+4-A)^2+\sqrt{2A+9}^2}=\sqrt{A^2+10A+25}=\sqrt{(A+5)}^2=A+5\)
So, if A=2, 7 etc ans is YES and if A=3, 4 etc ans is NO
(1) A^2 – 5A – 6 = 0
A= 2 or 3
Insuff

(2) A > 2
Insuff

Combined A=3
Suff

C
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chetan2u
factorising is incorrect here. Mistakenly you have calculated (A-3) (A-2)
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Point K = (A, 0), Point G = (2A + 4, (2A + 9)^(1/2)). Is the distance 13 Oct 2019, 08:06
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chetan2u
TheKingInTheNorth
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

I suggest my students to use statements when you do not know how to proceed and this is one such scenario...

If you do not get hang of it or are short of time, --
There is one variable-A and if we know A, we can answer for sure.
Statement I gives two values of A as it is a quadratic equation. It may be possible that both lead to prime or non-prime, but in most cases it will not.
Statement II gives a range, so insuff
Combined, I says 2 and 3, II says>2, so a unique value C


Point K = (A, 0), Point G = (2A + 4, \(\sqrt{2A + 9}\))..
Two ways..

(I) Don't waste time finding an equation in variable here
We know that to know the distance here, we will require to know the value of A, so let us check the statements
(1) \(A^2 – 5A – 6 = 0...(A-3)(A-2)=0\) A =2 or A=3..
A is 2.. \(K=(2,0)\) and G\(=(8,\sqrt{13}\)...Distance = \(\sqrt{36+13}=\sqrt{49}=7\)..Yes
A is 3.. \(K=(3,0)\) and G\(=(10,\sqrt{15}\)...Distance = \(\sqrt{49+15}=\sqrt{64}=8\).. No
Insuff

(2) A > 2
Clearly insuff. There may be cases where it is true and places where it may not be true.

Combined..ans is 3 and NO
Suff

C

(II) Simplify the question stem
Distance = \(\sqrt{(2A+4-A)^2+\sqrt{2A+9}^2}=\sqrt{A^2+10A+25}=\sqrt{(A+5)}^2=A+5\)
So, if A=2, 7 etc ans is YES and if A=3, 4 etc ans is NO
(1) A^2 – 5A – 6 = 0
A= 2 or 3
Insuff

(2) A > 2
Insuff

Combined A=3
Suff

C
chetan2u
factorising is incorrect here. Mistakenly you have calculated (A-3) (A-2)
Show more

Thanks .. Yes, I calculated it for A^2-5A+6
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Point K = (A, 0), Point G = (2A + 4, (2A + 9)^(1/2)). Is the distance 13 Oct 2019, 10:03
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TheKingInTheNorth
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
Show more

Point K = (A, 0), Point G = (2A + 4, \(\sqrt{2A + 9}\)). Is the distance between point K and G prime?

Distance between K & G = \(\sqrt{(2A+4-A)^2 + (2A+9)} = \sqrt{(A+4)^2 + (2A+9)} = \sqrt{A^2 + 8A + 16 + 2A + 9} = \sqrt{A^2 + 10A + 25} = A+5\)
Q. A+5 is prime?

(1) A^2 – 5A – 6 = 0
(A-5/2)^2 = 6 + 25/4 = 49/4
A = 5/2 +- 7/2
A = 6 or -1
A + 5 = 11 or 4; 11 is prime but 4 is not a prime number
NOT SUFFICIENT

(2) A > 2
If A = 3; A+5 = 8 is not a prime number
If A = 6; A+5 = 11 is a prime number
NOT SUFFICIENT

(1) + (2)
(1) A^2 – 5A – 6 = 0
(A-5/2)^2 = 6 + 25/4 = 49/4
A = 5/2 +- 7/2
A = 6 or -1
A + 5 = 11 or 4; 11 is prime but 4 is not a prime number
(2) A > 2
A = 6; A+5 = 11 is a prime number
SUFFICIENT

IMO C
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Point K = (A, 0), Point G = (2A + 4, (2A + 9)^(1/2)). Is the distance 13 Nov 2019, 07:20
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\(Distance \ = \sqrt{A^2-6A+25}\)

\(Statement \ 1) \ \ (A-6)(A+1)=0 \implies A_1=6 \ (YES) \ A_2=-1 \ (NO)\)

\(Statement \ 2) \ \ A>2\)


\(Statement \ 1 \& \ 2) A=6 \ (YES)\)
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Point K = (A, 0), Point G = (2A + 4, (2A + 9)^(1/2)). Is the distance 18 Jul 2025, 20:21
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