In the xycoordinate plane, a line segment is drawn to join the points A (2, 1) and C(4, 3). If point B lies on line segment AC, is AB = BC?(1) The x-coordinate of point B is 3(2) The y-coordinate of point B is 2a)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 to answer the question asked.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 specific to the problem are needed.Correct answer is option 'D'. Can you explain this answer?

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In the xy–coordinate plane, a line segment is drawn to join the points A (2, 1) and C(4, 3). If point B lies on line segment AC, is AB = BC?

(1) The x-coordinate of point B is 3

(2) The y-coordinate of point B is 2

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 to answer the question asked.
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 specific to the problem are needed.

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

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In the xy–coordinate plane, a line segment is drawn to join the ...

Steps 1 & 2: Understand Question and Draw Inferences

The given information can be represented visually as under:

We need to find if AB = BC, that is, if B is the mid-point of AC?

From the figure, it is clear that the answer is YES only if:
- The x-coordinate of B = (mid-point between the x-coordinates of points A and C) = mid-point between (2 and
- AND, the y-coordinate of B = (mid-point between the y-coordinates of points A and C) = mid-point between
  - So, we see that the answer is YES if the coordinates of point B are (3, 2)
- Now, we are given that point B lies on the line segment AC.
  - Since we know the coordinates of both points A and C, we can find the equation of line segment AC:
    - Starting with the general equation: y = mx + c, where m is the slope of the line and c is the y-intercept
    - Since this line passes through point A (2, 1), we can write: 1 = 2m + c . . . (1)
    - And, since this line passes through point C(4, 3), we can write: 3 = 4m + c . . .(2)
    - (2) – (1): 2 = 2m
      - So, m = 1
    - From (1): 1 = 2 + c
      - So, c = -1
  - Therefore, the equation of line AC = y = x – 1
  - Since point B lies on line AC, it will satisfy this equation.
- So, if we know either the x-coordinate or the y-coordinate of point B, we will be able to find the other coordinate of point B using the equation of the line.
- Once we know both the x- and the y- coordinates of point B, the answer will be YES if these coordinates are (3, 2); else the answer will be NO
- Thus, in order to answer the question, we only need to know either the x- or the y-coordinate of point B

Step 3: Analyze Statement 1 independently

Statement 1 says that ‘The x-coordinate of point B is 3’

Since we know the x-coordinate of point B, using the equation of line AC (y = x – 1), we can find the y-coordinate of point B
Therefore, we can answer if the coordinates of point B are (3,2) or not
So, Statement 1 alone is sufficient to answer the question

Step 4: Analyze Statement 2 independently

Statement 2 says that ‘The y-coordinate of point B is 2’

Since we know the y-coordinate of point B, using the equation of line AC (y = x – 1), we can find the x-coordinate of point B
Therefore, we can answer if the coordinates of point B are (3,2) or not
So, Statement 2 alone is sufficient to answer the question

Step 5: Analyze Both Statements Together (if needed)

Since we’ve already arrived at a unique answer in Steps 3 and 4, this step is not required

Hence, the correct answer is Option D.

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Most Upvoted Answer

In the xy–coordinate plane, a line segment is drawn to join the ...

Given:
- Line segment AC joins points A(2, 1) and C(4, 3).
- Point B lies on line segment AC.

To Find:
- Whether AB = BC or not.

Statement 1:
- The x-coordinate of point B is 3.

Statement 2:
- The y-coordinate of point B is 2.

Analysis of Statement 1:
- The x-coordinate of point B is 3.
- This means that the x-coordinate of B lies between the x-coordinates of A and C.
- However, we do not have any information about the y-coordinate of B.
- Therefore, statement 1 alone is insufficient to determine whether AB = BC or not.

Analysis of Statement 2:
- The y-coordinate of point B is 2.
- This means that the y-coordinate of B lies between the y-coordinates of A and C.
- However, we do not have any information about the x-coordinate of B.
- Therefore, statement 2 alone is insufficient to determine whether AB = BC or not.

Analysis of Statements 1 and 2 together:
- Combining both statements, we know that the x-coordinate of B is 3 and the y-coordinate of B is 2.
- This means that B lies on the line segment AC and is equidistant from points A and C.
- Therefore, AB = BC.
- Hence, statements 1 and 2 together are sufficient to determine that AB = BC.

Conclusion:
- The answer is option (C) - BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
- The information from both statements is necessary to determine that AB = BC.

Answered by Talent Skill Learning · View profile

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In the xy–coordinate plane, a line segment is drawn to join the points A (2, 1) and C(4, 3). If point B lies on line segment AC, is AB = BC?(1) The x-coordinate of point B is 3(2) The y-coordinate of point B is 2a)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 to answer the question asked.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 specific to the problem are needed.Correct answer is option 'D'. Can you explain this answer?

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In the xy–coordinate plane, a line segment is drawn to join the points A (2, 1) and C(4, 3). If point B lies on line segment AC, is AB = BC?(1) The x-coordinate of point B is 3(2) The y-coordinate of point B is 2a)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 to answer the question asked.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 specific to the problem are needed.Correct 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 In the xy–coordinate plane, a line segment is drawn to join the points A (2, 1) and C(4, 3). If point B lies on line segment AC, is AB = BC?(1) The x-coordinate of point B is 3(2) The y-coordinate of point B is 2a)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 to answer the question asked.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 specific to the problem are needed.Correct 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 In the xy–coordinate plane, a line segment is drawn to join the points A (2, 1) and C(4, 3). If point B lies on line segment AC, is AB = BC?(1) The x-coordinate of point B is 3(2) The y-coordinate of point B is 2a)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 to answer the question asked.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 specific to the problem are needed.Correct answer is option 'D'. Can you explain this answer?.

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