There are three parallel straight lines. Two points A and B are marked on the first line, points C and D are marked on the second lines and points E and F are marked on the third line. Each of these six points can move to any position on its respective st

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Q: 88 (IAS/2006)
There are three parallel straight lines. Two points A and B are marked on the first line, points C and D are marked on the second lines and points E and F are marked on the third line. Each of these six points can move to any position on its respective straight line. Consider the following statements:
I. The maximum number of triangles that can be drawn by joining these points is 18.
II. The maximum number of triangles that can be drawn by joining these points is zero.
Which of the statements given above is/are correct?

question_subject: 

Logic/Reasoning

question_exam: 

IAS

stats: 

0,2,5,2,2,3,0

keywords: 

{'triangles': [0, 0, 1, 1], 'parallel straight lines': [0, 0, 1, 0], 'respective straight line': [0, 0, 1, 0], 'maximum number': [1, 0, 1, 2], 'third line': [0, 0, 1, 0], 'second lines': [0, 0, 1, 0], 'points': [0, 0, 1, 3], 'first line': [1, 0, 2, 0], 'position': [3, 2, 7, 11]}

The question is regarding the number of triangles that can be formed by joining points on three parallel straight lines.

Option 1 suggests that up to 18 triangles can be formed, but this is incorrect. A triangle requires three points that are not all in a line. Since all the points are on parallel lines, they will always be in a line and a triangle can never be formed.

Option 2 proposes that no triangles can be formed. This is in fact correct, as explained above, no matter where the points are moved along their respective parallel lines, they will always be in a line and cannot form a triangle.

Option 3 suggests that both the above statements are correct which we already established isn`t true, since only the second statement is correct.

Option 4 suggests neither of the statements are correct which is also not true because the second statement is correct.

Thus, the correct answer is option 2: only the second statement is correct. No triangles can be formed with points on parallel lines.