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
Difficulty level: 700+
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Challenge question: On the x-y coordinate plane, lines j and
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Statement 1: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
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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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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