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How many triangles can be formed using 8 points in a given plane?
(1) A triangle is formed by joining 3 distinct points in the plane
(2) Out of 8 given points, three are collinear
(2) Out of 8 given points, three are collinear
- 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 'B'. Can you explain this answer?
Most Upvoted Answer
How many triangles can be formed using 8 points in a given plane?(1) A...
Statement (1):
A triangle is formed by joining 3 distinct points in the plane.
This statement alone is not sufficient to determine the number of triangles that can be formed using 8 points. It only tells us that a triangle can be formed by joining 3 distinct points, but it does not provide any information about the total number of points or their arrangement in the plane.
Statement (2):
Out of 8 given points, three are collinear.
This statement alone is not sufficient to determine the number of triangles that can be formed using 8 points. It only tells us that three points are collinear, but it does not provide any information about the remaining 5 points or their arrangement in the plane.
Combined statements (1) and (2):
By combining the two statements, we can determine the number of triangles that can be formed using 8 points in a given plane.
If three points are collinear, they cannot form a triangle. Therefore, in order to form a triangle, we need to choose 3 points out of the remaining 5 points that are not collinear.
The total number of triangles that can be formed can be calculated using the combination formula:
C(n,r) = n! / (r!(n-r)!)
Where n is the total number of points and r is the number of points to be chosen to form a triangle.
In this case, n = 5 (as 3 points are collinear) and r = 3.
C(5,3) = 5! / (3!(5-3)!) = 5! / (3!2!) = (5x4x3x2x1) / (3x2x1x2x1) = 10
Therefore, the number of triangles that can be formed using 8 points in a given plane is 10.
Conclusion:
From the analysis above, we can conclude that statement (2) alone is sufficient to answer the question asked, but statement (1) alone is not sufficient. Therefore, the correct answer is option B.
A triangle is formed by joining 3 distinct points in the plane.
This statement alone is not sufficient to determine the number of triangles that can be formed using 8 points. It only tells us that a triangle can be formed by joining 3 distinct points, but it does not provide any information about the total number of points or their arrangement in the plane.
Statement (2):
Out of 8 given points, three are collinear.
This statement alone is not sufficient to determine the number of triangles that can be formed using 8 points. It only tells us that three points are collinear, but it does not provide any information about the remaining 5 points or their arrangement in the plane.
Combined statements (1) and (2):
By combining the two statements, we can determine the number of triangles that can be formed using 8 points in a given plane.
If three points are collinear, they cannot form a triangle. Therefore, in order to form a triangle, we need to choose 3 points out of the remaining 5 points that are not collinear.
The total number of triangles that can be formed can be calculated using the combination formula:
C(n,r) = n! / (r!(n-r)!)
Where n is the total number of points and r is the number of points to be chosen to form a triangle.
In this case, n = 5 (as 3 points are collinear) and r = 3.
C(5,3) = 5! / (3!(5-3)!) = 5! / (3!2!) = (5x4x3x2x1) / (3x2x1x2x1) = 10
Therefore, the number of triangles that can be formed using 8 points in a given plane is 10.
Conclusion:
From the analysis above, we can conclude that statement (2) alone is sufficient to answer the question asked, but statement (1) alone is not sufficient. Therefore, the correct answer is option B.
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How many triangles can be formed using 8 points in a given plane?(1) A...
Statement (1): A triangle is formed by joining 3 distinct points in the plane.
This statement tells us that a triangle is formed by selecting 3 distinct points among the given 8 points. However, it does not provide us with information about the arrangement or positioning of these points. Therefore, statement (1) alone is not sufficient to determine the number of triangles that can be formed.
Statement (2): Out of 8 given points, three are collinear.
This statement tells us that three of the given 8 points lie on the same line. If three points are collinear, they cannot form a triangle since a triangle requires three non-collinear points. Therefore, if three points are collinear among the 8 given points, no triangle can be formed.
From statement (2) alone, we can conclude that the number of triangles that can be formed is zero since there are three collinear points.
Therefore, statement (2) alone is sufficient to answer the question. The answer is (B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
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How many triangles can be formed using 8 points in a given plane?(1) A triangle is formed by joining 3 distinct points in the plane(2) Out of 8 given points, three are collineara)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 'B'. Can you explain this answer?
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How many triangles can be formed using 8 points in a given plane?(1) A triangle is formed by joining 3 distinct points in the plane(2) Out of 8 given points, three are collineara)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 'B'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about How many triangles can be formed using 8 points in a given plane?(1) A triangle is formed by joining 3 distinct points in the plane(2) Out of 8 given points, three are collineara)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 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many triangles can be formed using 8 points in a given plane?(1) A triangle is formed by joining 3 distinct points in the plane(2) Out of 8 given points, three are collineara)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 'B'. Can you explain this answer?.
How many triangles can be formed using 8 points in a given plane?(1) A triangle is formed by joining 3 distinct points in the plane(2) Out of 8 given points, three are collineara)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 'B'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about How many triangles can be formed using 8 points in a given plane?(1) A triangle is formed by joining 3 distinct points in the plane(2) Out of 8 given points, three are collineara)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 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many triangles can be formed using 8 points in a given plane?(1) A triangle is formed by joining 3 distinct points in the plane(2) Out of 8 given points, three are collineara)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 'B'. Can you explain this answer?.
Solutions for How many triangles can be formed using 8 points in a given plane?(1) A triangle is formed by joining 3 distinct points in the plane(2) Out of 8 given points, three are collineara)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 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
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