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On the x-y coordinate plane, lines j and k intersect 30 May 2018, 07:05
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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

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On the x-y coordinate plane, lines j and k intersect 30 May 2018, 08:18
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Statement 1 is clearly sufficient as by substituting the value of x and y as 1 and -3 respectively, we can solve for a and b. Thus, a + b can be calculated.

Statement 2 gives an equation. If we try substituting the value of a in terms of b or vice versa, we cannot still solve because, the values of x and y are still unknown.

Hence, ans is A. IMO A.

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On the x-y coordinate plane, lines j and k intersect 30 May 2018, 09:28
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should be D,
from 1) after putting value of intersection point we can solve equations to get value of a and b and then a+b. sufficient

2)put a = b-3 in both equations for j and k and you can find a and b and then a+b. sufficient



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On the x-y coordinate plane, lines j and k intersect 30 May 2018, 09:31
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ravikumarmishra
should be D,
from 1) after putting value of intersection point we can solve equations to get value of a and b and then a+b. sufficient

2)put a = b-3 in both equations for j and k and you can find a and b and then a+b. sufficient



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my bad, it should be A, as you cannot solve 3 unknowns with 2 equations.


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On the x-y coordinate plane, lines j and k intersect 30 May 2018, 09:44
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Given: Eqn. of line j -> bx + ay = 5
Eqn. of line k -> 2bx - 3ay = -5
Lines j and k intersect at one point.

To find: Value of a + b

Approach:
1) Lines j and k intersect at (1, -3) => We have the point of intersection of line j and k, so we will get two eqns. with two unknowns a and b.
=> Sufficient

2) a - b = -3 Can't find the value of a + b Insufficient

Correct Answer= A
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On the x-y coordinate plane, lines j and k intersect 30 May 2018, 11:18
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GMATPrepNow
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

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Statement 1 :- Lines j and k intersect at (1, -3).

Use (1,-3) in the two given equation .
1st Equation:- bx + ay = 5
b - 3a = 5.

2nd Equation:- 2bx - 3ay = -5
2b(1) - 3a(-3) = -5
2b + 9a = -5.

Both the equation are in terms of a & b. On solving we can get the values of a & b.

Hence Sufficient.

Statement 2 :- a - b = -3.

a - b = -3
a = b+3.
1st Equation:- bx + ay = 5.
bx + (b+3)y = 5.
bx + by + 3y = 5.

2nd Equation:- 2bx - 3ay = -5
2bx - 3y(b+3) = -5
2bx - 3by -9y = -5

As you can see, we couldn't convert these two equation in two variable.
We have three unknown variable (x, b & y).
So we need three equation to find the values of a & b, thus a+b.

Hence Insufficient.

Ans - A.
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On the x-y coordinate plane, lines j and k intersect 23 Dec 2022, 04:12
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