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 = -3a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'D'. Can you explain this answer?

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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

a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer the question asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed

Correct answer is option 'D'. Can you explain this answer?

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On the x-y coordinate plane, lines j and k intersect at one point.If t...

From the equation of line j, bx + ay = 5, we can rearrange it as ay = -bx + 5 and rewrite it as y = (-b/a)x + 5/a.

Similarly, from the equation of line k, 2bx - 3ay = -5, we can rearrange it as -3ay = -2bx - 5 and rewrite it as y = (-2b/-3a)x - 5/-3a, which simplifies to y = (2b/3a)x + 5/3a.

Comparing the equations of the lines, we can see that the slopes (-b/a and 2b/3a) must be equal for the lines to intersect at one point.

Now let's analyze the statements:

Statement (1) tells us that the lines j and k intersect at the point (1, -3). This means that the coordinates (x, y) = (1, -3) satisfy both equations. By substituting these values into the equations, we can form a system of equations:

a + b = 5 (from line j)
2b/3a - 3a = -5 (from line k)

From this system, we can solve for the values of a and b. Therefore, Statement (1) alone is sufficient to answer the question.

Statement (2) tells us that a - b = -3. While this provides a relationship between a and b, it does not give us enough information to determine their specific values. Therefore, Statement (2) alone is not sufficient to answer the question.

By combining both statements, we have the equations from Statement (1) and the relationship from Statement (2):

a + b = 5
a - b = -3

By solving this system of equations, we can find the values of a and b, and hence determine the value of a + b. Therefore, each statement alone is sufficient to answer the question.

Hence, the answer is (D): EACH statement ALONE is sufficient to answer the question asked.

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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 = -3a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'D'. Can you explain this answer?

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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 = -3a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'D'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about 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 = -3a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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 = -3a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'D'. Can you explain this answer?.

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