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Middle School Math Quiz

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Post by indophile Fri Jun 24, 2011 3:02 pm

From a math magazine. Have fun.

1. After a typist had completed ten letters and addressed the ten corresponding envelopes, a careless intern inserted the letters in the envelope at random, one letter per envelope. What is the probability that exactly nine letters were inserted in the proper envelopes?

2. In a certain tournament, a player must be defeated 3 times to be eliminated. If 512 contestants enter the tournament, what is the greatest number of games that could be played?

3. A bicyclist riding against the wind averages 10 mph travelling from A to B, but with the wind averages 15 mph returning from B to A. How many miles per hour is his average speed for the trip?

4. What is the number of real numbers X such that 25|x| = x-squared + 144?

5. How many integers x in {1,2,3,4,……99,100} satisfy that x-squared + x-cubed is the square of an integer?

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Post by Mosquito Fri Jun 24, 2011 3:19 pm

1. 0. There have to be atleast 2 incorrect insertions.
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Post by Mosquito Fri Jun 24, 2011 3:23 pm

5. 3,8,15,24,35,48,63,80,99. For this condition to satisfy, x+1 has to be a perfect square.
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Post by Mosquito Fri Jun 24, 2011 3:25 pm

3. 12 miles/hour.
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Post by indophile Fri Jun 24, 2011 3:41 pm

PseudoIntellectual wrote:

Your answers to 1, 3, 5 are all correct. However, for 5 instead of writing down the actual numbers that satisfy the conditions you should have said 9 (the number of numbers that satify the condition:-)

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Post by Mosquito Fri Jun 24, 2011 4:34 pm

4. 4 . Quadratic equation has 2 real numbers as a soln and since it is absolute, their negative will be a solution too.
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Post by indophile Fri Jun 24, 2011 9:51 pm

PseudoIntellectual wrote:4. 4 . Quadratic equation has 2 real numbers as a soln and since it is absolute, their negative will be a solution too.
Yes. 9,16, -9, -16.

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Post by indophile Sat Jun 25, 2011 10:16 am

Answer for # 2lly out of the tournment

There are 512 players. So 511 players must be defeated 3 times each to be totally out of the tournament. The most the ultimate winner can be defeated is 2 times.
So the greatest number of games that can be played = 511x3 + 2 = 1535.

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