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On a graph the four corners of a certain quadrilateral are (a,5), (b,5), (a,0) and (b,0). If a + c = 12, a < b and both a and b are positive values then what is the area of the quadrilateral?
(1) b + c = 6
(2) The quadrilateral is a rectangle.
  • 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 'A'. Can you explain this answer?
Verified Answer
On a graph the four corners of a certain quadrilateral are (a,5), (b,5...
Given information:
  • The four corners of the quadrilateral are (a,5), (b,5), (a,0), and (b,0).
  • a + c = 12.
  • a < b and both a and b are positive values.
We need to find the area of the quadrilateral.
Statement 1: b + c = 6
Statement 1 alone is sufficient to answer the question.
Explanation:
The coordinates of the four corners of the quadrilateral are (a,5), (b,5), (a,0), and (b,0). From the given information, we can deduce that the quadrilateral has two sides of length b - a and two sides of length 5.
Since the opposite sides of a rectangle are equal in length, if the quadrilateral is a rectangle, then b - a = 5.
From statement 1, we have b + c = 6. Since a + c = 12, subtracting the equations gives b - a = 6 - 12 = -6. However, it is given that both a and b are positive values, so the quadrilateral cannot be a rectangle.
Therefore, statement 1 alone is sufficient to determine that the quadrilateral is not a rectangle, which means the quadrilateral is not necessarily a parallelogram. Without knowing the specific shape of the quadrilateral, we cannot determine its area.
Hence, the correct answer is (A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
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Most Upvoted Answer
On a graph the four corners of a certain quadrilateral are (a,5), (b,5...
Given information:
  • The four corners of the quadrilateral are (a,5), (b,5), (a,0), and (b,0).
  • a + c = 12.
  • a < b and both a and b are positive values.
We need to find the area of the quadrilateral.
Statement 1: b + c = 6
Statement 1 alone is sufficient to answer the question.
Explanation:
The coordinates of the four corners of the quadrilateral are (a,5), (b,5), (a,0), and (b,0). From the given information, we can deduce that the quadrilateral has two sides of length b - a and two sides of length 5.
Since the opposite sides of a rectangle are equal in length, if the quadrilateral is a rectangle, then b - a = 5.
From statement 1, we have b + c = 6. Since a + c = 12, subtracting the equations gives b - a = 6 - 12 = -6. However, it is given that both a and b are positive values, so the quadrilateral cannot be a rectangle.
Therefore, statement 1 alone is sufficient to determine that the quadrilateral is not a rectangle, which means the quadrilateral is not necessarily a parallelogram. Without knowing the specific shape of the quadrilateral, we cannot determine its area.
Hence, the correct answer is (A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
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On a graph the four corners of a certain quadrilateral are (a,5), (b,5), (a,0) and (b,0). If a + c = 12, a < b and both a and b are positive values then what is the area of the quadrilateral?(1) b + c = 6(2) The quadrilateral is a rectangle.a)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 'A'. Can you explain this answer?
Question Description
On a graph the four corners of a certain quadrilateral are (a,5), (b,5), (a,0) and (b,0). If a + c = 12, a < b and both a and b are positive values then what is the area of the quadrilateral?(1) b + c = 6(2) The quadrilateral is a rectangle.a)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 'A'. 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 a graph the four corners of a certain quadrilateral are (a,5), (b,5), (a,0) and (b,0). If a + c = 12, a < b and both a and b are positive values then what is the area of the quadrilateral?(1) b + c = 6(2) The quadrilateral is a rectangle.a)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 'A'. 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 a graph the four corners of a certain quadrilateral are (a,5), (b,5), (a,0) and (b,0). If a + c = 12, a < b and both a and b are positive values then what is the area of the quadrilateral?(1) b + c = 6(2) The quadrilateral is a rectangle.a)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 'A'. Can you explain this answer?.
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