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Challenge question: On the x-y coordinate plane, lines j and

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Challenge question: On the x-y coordinate plane, lines j and

by Brent@GMATPrepNow » Wed May 30, 2018 5:49 am

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Challenge question

On the x-y coordinate plane, lines j and k intersect at one point.
If the equation of line j is bx + ay = 5, and the equation of line k is 2bx - 3ay = -5, what is the value of a + b?

(1) Lines j and k intersect at (1, -3).
(2) a - b = -3


Answer A
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by GMATGuruNY » Wed May 30, 2018 7:08 am

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Brent@GMATPrepNow wrote:Challenge question

On the x-y coordinate plane, lines j and k intersect at one point.
If the equation of line j is bx + ay = 5, and the equation of line k is 2bx - 3ay = -5, what is the value of a + b?

(1) Lines j and k intersect at (1, -3).
(2) a - b = -3
Statement 1:
Substituting x=1 and y=-3 into the equations for lines j and k, we get:
Line j:
b(1) - a(-3) = 5
b + 3a = 5.
Line k:
2b(1) - 3a(-3) = -5
2b + 9a = -5.
The two equations in green can be solved for a and b.
Thus, the value of a+b can be determined.
SUFFICIENT.

Statement 2: a = b+3
Case 1: b=1 and a=4
Substituting b=1 and a=4 into the equations for lines j and k, we get:
Line j:
1x + 4y = 5
x + 4y = 5
Line k:
2(1)(x) - 3(4)y = -5
2x - 12y = -5.
The two equations in blue can be solved to determine the intersection for j and k.
In this case, a+b = 4+1 = 5.

Case 2: b=2 and a=5
Substituting b=2 and a=5 into the equations for lines j and k, we get:
Line j:
2x + 5y = 5.
Line k:
2(2)(x) - 3(5)y = -5
4x - 15y = -5.
The two equations in red can be solved to determine the intersection for j and k.
In this case, a+b = 5+2 = 7.

Since a+b can be different values, INSUFFICIENT.

The correct answer is A.
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