8th Test - Miscellaneous

Analysis of results

1) If Joe is 1/4 as old as Jane will be in 4 years, how old is Joe if Jane is 12? _______4 years________

     Joe = 1/4 (Jane + 4), but Jane = 12, so Joe = 1/4 (12 + 4) = 4 years old

2) Bob can climb a rope at a rate of 3 feet per second. How long will it take him to climb an 18 foot rope?       ________6 sec_________

      Use unit cancelation:    18 ft / 3 ft/second = 6 seconds

3) If x$y = x � x/y, then what is 7$2? ___ 3 1/2 ___

   This is a common sort of problem on the continental math league tests.
   The $ represents some function that is defined. In this case we have
     7 - 7/2 = 3 1/2 or 3.5

4) There is a cage at the zoo that holds pigs and ducks. In the cage are 13 heads and 38 feet. How many pigs are there?   _____6 pigs______

    p + d = 13
   4p + 2d = 38
   4p + 2(13 - p) = 38
    4p - 2p = 12
    p = 6

5) Evaluate this expression (8 - 2) / (7 - 4) =   ___2_____

    6 / 3 = 6 divided by 2 = 2

6) If you flipped a set of 2 pennies 100 times, how many of those hundred times do you think both pennies would come up heads? ____25 times_____________

   There are 4 ways that 2 pennies can land: HH HT TH TT. HH will happen 1/4 of the time, so
    about25 times is expected.

7) What is the area of an L shape that is 5 inches high, 3 inches wide and 1 inch thick?
______7 square inches_______

Many drew the L, but still multiplies 5 x 3 to get 15, which is wrong.
   An L shape that is 5 inches high and 3 inches for the bottom part has area 7 square inches.

8) Find A and B if

      32
      AB
   + 59
---------
      99                    A=_0_   B= _8_
                               Almost everyone got this one.

9) I saw some ducks go by, but I did not count them. I did notice that there was 1 duck in front of 2 ducks, another duck behind 2 ducks, and there was a duck between 2 ducks. How many were there?
____3 ducks_____

Surprisingly only one person got this one. I thought it was relatively easy.
Each clause describes the position of one of 3 ducks. How could it be anything but 3?

10) How many seconds are in a day? _____84,400 seconds______

Use unit cancelation:
   24 hours/day * 60 minutes/hours * 60 seconds/minute = 84,400 seconds.
     A lot of people said that are only 1440 seconds in a day which does not make sense when you think about it.