Commuting, Bus and Train

A woman can commute either by train or by bus. If she goes to work on the train in the morning, she comes home on the bus in the afternoon; and if she comes home in the afternoon on the train, it means that she took the bus that morning. During x days the woman rode the train 9 times and rode the bus 8 times in the morning and 15 times in the afternoon. Find x.

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Total Growth

There are 351 students in the 8th grade at Thomas Jefferson High School. Of these, 176 are boys. During the school year the boys grew an average of 3 inches in height, and the girls grew an average of 0.75 inches (they had done their major growing in 6th and 7th grades). If all the 8th grade students were lying stretched out in a straight line, head-to-feet, on the playground, on the last day of school, how much longer would that line be than it would have been on the first day of school that year?

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Agatha the Cow

A certain breed of cow has its first calf on its second birthday and another on every birthday thereafter. All calves are female. Stella’s cousin Jeroen (Ye-roon’) is the proud owner of such a cow; her name is Agatha. Agatha was born on New Year’s Day 2005. If Jeroen keeps Agatha and all of her calves and their calves (and so on) that are born before the Summer Olympic games in August 2012, how big will his herd be?

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Mixed Sticks

This picture represents a bunch of sticks lying on top of a black table. You are looking directly down on the sticks, which are all square in section; that is, their thickness (which you can’t see) is exactly equal to their width, which is shown.

You will notice right away that some of these sticks rest directly on the table and are therefore level—as are certain other sticks which rest on them. Bearing this in mind, answer the following questions:


  1. Make a small cross (x) on each level stick.
  2. Draw an arrow pointing towards the lower end of each sloping stick. Which sticks are they?
  3. Which level stick is highest above the table?
  4. Which stick slopes the most?
  5. Which stick slopes the least
  6. Does Stick G touch Stick A?
  7. Does Stick B touch Stick H?
  8. Does Stick M touch Stick A?
  9. If stick C were long enough to reach over to Stick B, would it touch B?
  10. If a short stick were placed directly under Stick G, touching A and E, would it touch Stick B? Would it touch Stick D?
  11. Are Sticks A and B parallel?
  12. Are Sticks K and M parallel?

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