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Lines 3x + 4ky + 6 = 0, and kx -3y +9 = 0 intersect in the second quad

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KarunMendiratta
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Lines 3x + 4ky + 6 = 0, and kx -3y +9 = 0 intersect in the second quad [#permalink] New post   09 Aug 2021, 06:32
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SUPER HARD

Lines \(3x + 4ky + 6 = 0\), and \(kx -3y +9 = 0\) intersect in the second quadrant

Quantity A
Quantity B
Number of possible integral values of \(k\)
4


A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
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A
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Re: Lines 3x + 4ky + 6 = 0, and kx -3y +9 = 0 intersect in the second quad [#permalink] New post   10 Aug 2021, 17:51
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two lines cross in the second quadrant, and they have different slopes (-/+ve), various intercepts (-6,9).
for x=0, equations become 4ky=-6 and 3y=9 and if y=-6, then k=1/4; for y=3, kx=0 or x=0 again.
for y=0, equations become 3x=-6 and kx=-9 resulting in -2k=-9, k=9/2

integral of k is along the line between two intercepts and possible cross points or 9/2-1/4= 17/4, which is greater than 4

Answer must be A


KarunMendiratta wrote:
SUPER HARD

Lines \(3x + 4ky + 6 = 0\), and \(kx -3y +9 = 0\) intersect in the second quadrant

Quantity A
Quantity B
Number of possible integral values of \(k\)
4


A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
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Re: Lines 3x + 4ky + 6 = 0, and kx -3y +9 = 0 intersect in the second quad [#permalink] New post   16 Oct 2023, 09:45
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Re: Lines 3x + 4ky + 6 = 0, and kx -3y +9 = 0 intersect in the second quad [#permalink]
16 Oct 2023, 09:45
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