Which of the following statements are true?

Which of the following statements are true? [ with your own reasoning, of course! ]

1 This is a numbered list of twelve statements.
2 Exactly 3 of the last 6 statements are true.
3 Exactly 2 of the even-numbered statements are true.
4 If statement 5 is true, then statements 6 and 7 are both true.
5 The 3 preceding statements are all false.
6 Exactly 4 of the odd-numbered statements are true.
7 Either statement 2 or 3 is true, but not both.
8 If statement 7 is true, then 5 and 6 are both true.
9 Exactly 3 of the first 6 statements are true.
10 The next two statements are both true.
11 Exactly 1 of statements 7, 8 and 9 are true.
12 Exactly 4 of the preceding statements are true.





Ans.
1,8,10,11,12

Logic:

1 is anyways true.
Assume that 12 is true.So we are left with 3 more statements from 2 to 11 which can be true.
We put 10 as true which makes 11 true, 12 is already true(we have assumed).If 11 is true then either 7,8,9 should be true. Only 8 satisfies the condition.

Mirror puzzle

Imagine you are standing in front of a mirror, facing it. Raise your left hand. Raise your right hand. Look at your reflection. When you raise your left hand your reflection raises what appears to be his right hand. But when you tilt your head up, your reflection does too, and does not appear to tilt his/her head down. Why is it that the mirror appears to reverse left and right, but not up and down?






Ans.

Where lies the flaw in the logic?

You can imagine an arrow in flight, toward a target. For the arrow to reach the target, the arrow must first travel half of the overall distance from the starting point to the target. Next, the arrow must travel half of the remaining distance.

For example, if the starting distance was 10m, the arrow first travels 5m, then 2.5m.

If you extend this concept further, you can imagine the resulting distances getting smaller and smaller. Will the arrow ever reach the target?