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Which number would be opposite to 1?

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posted Jun 19, 2014 by anonymous

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Thirty equally spaced points on the circumference of a circle are labelled in order with the numbers 1 to 30. Which number is diametrically opposite to 7?

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You have a weighing balance, which you can place weights on both sides of. You need to measure all weights between 1 and 1000.

For example if you have weights 1 and 3, you can measure test objects of weights 1, 3 or 4. You can also measure objects of weight 2, by placing 3 on one side and 1 on the side which contain the object to be weighed.

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Some cards from an ordinary pack of playing cards were laid out on a table with face upwards. I thought of one card there, The KING OF HEARTS. I announced that I would tell Mr. A the value and Mr. B the suit of my chosen card. I whispered to Mr. A that I had chosen a KING and whispered to Mr. B that I had chosen a HEART. Their subsequent discussion went as below:

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How many of those would be Diamonds?

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  1. What would be the coordinate of point P which divides the line joining A(-4,1) and B (17,10) in the ratio 1:2?
  2. What would be the length of OP where O is the origin (0,0)?
  3. In what ratio y axis divides the line segment AB?
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