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 funciton 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.