1. A sensitive balance scale and 9 identical-looking coins are given. One of the 9 coins is counterfeit and slightly heavier than the others (not noticeably when weighed by hands, but noticeably when weighed by the scale). The task is to identify the counterfeit coin by a number of weighings. The minimum number of weighings that will be required to perform the task without the possibility of failure is:

1. 1
2. 2
3. 3
4. 4
5. 8

2. Suppose that you have won a door prize: one free play of Lotto 6/49. Out of the groups of 6 numbers shown below, which one would you rather play?

1. 1 2 3 4 5 6
2. 1 4 9 16 25 36
3. 2 3 5 7 11 13
4. 15 21 23 29 36 37
5. it does not matter which: they all have the same chance to win

3. Consider two 16-cup capacity plastic containers labelled "flour" and "sugar". The flour container contains 8 cups of pure flour and the sugar container contains 8 cups of pure ground sugar. Suppose that the flour and ground sugar have the same grain size, so that their volumes are additive when they are mixed (e.g. mixing 3 cups of flour and 2 cups of sugar yields exactly 5 cups of flour-sugar mixture). Now, take 1 cup of flour from the flour container, add it to the sugar container, and mix the contents of the sugar container well to get a uniformly blended flour-sugar mixture. Next, take a cup of the flour-sugar mixture from the sugar container and put it back into the flour container. At this point, which volume is larger: the volume of sugar in the flour container or the volume of flour in the sugar container?

1. the volume of sugar in the flour container
2. the two volumes are equal
3. 7/8 of a cup and 8/9 of a cup
4. the volume of flour in the sugar container
5. the information given is not enough to answer the question

4. Ann and Bill are both celebrating their birthday today. Two years from now Ann will be twice as old as Bill, while 3 years ago Ann was three times as old as Bill. How old is Bill now?

1. 6 years
2. 8 years
3. 11 years
4. 12 years

5. A farmer wants to ferry a (giant) cabbage, a goat, and a wolf across a river in a boat. The problem is that the boat is small: besides the farmer it can carry at most one of the cabbage, the goat, and the wolf. To make things worse, without the farmer's supervision the goat would chew on the cabbage, and the wolf would chew on the goat. What is the minimum number of river crossings the farmer must make to accomplish his goal without the possibility of damage to the cabbage or the goat? (This is not a trick question, so creative shortcuts, such as taping the animal's mouth, roping the cabbage to the goat's back, etc., are not to be considered.)

1. 5
2. 7
3. 9
4. 11
5. he cannot do it in any number of crossings

6. The decimal number 13 is equal to the binary number:

1. 1011
2. 1101
3. 1010
4. 1100
5. none of the above

7. 1 + 2 / 100 + 3 / 10000 is equal to:

1. 123 %
2. 1.23
3. 1.0203
4. 1.0023
5. none of the above

8. The value of the expression (a + b) ^3 / (a - b)^2 evaluated at a = 3 and b = -1 is:

1. 1/2
2. -1/16
3. 1
4. 8
5. 2

9. At a party: exactly 15 people drank some beer, exactly 12 people drank some wine, exactly 10 people drank both beer and wine, and exactly 18 people drank neither beer nor wine. The number of people at the party was:

1. 25
2. 30
3. 35
4. 40
5. none of the above

10. The angles of a triangle are in the ratio 3:4:5. The measure of the smallest angle is:

1. 90 degrees
2. 45 degrees
3. 36 degrees
4. 30 degrees

11. The sum of all odd integers from 1 to 99 inclusive is:

1. 2310
2. 2500
3. 3000
4. 3500

12. If the square root of a number is between 6 and 7, then its cube root must be between:

1. 2 and 3
2. 3 and 4
3. 4 and 5
4. 5 and 6

13. There are 4 people in a car; they are waiting for the driver. The average age of the 4 people in the car is 28 years. The driver arrives, gets in the car, and now the average age of the 5 people in the car is 30 years. How old is the driver?

1. 32
2. 38
3. 44
4. 50

14. Given that the equation x*x + A*x + B = 0 has exactly two solutions, x = 5 and x = -2, the value of A must be:

1. 10
2. 3
3. -3
4. -10

15. The largest possible area that a triangle can have, given that two if its sides must be 2 meters long each, is:

1. 3^(0.5) * 0.5 square meters
2. 3^(0.5) square meters
3. 2 square meters
4. 3 square meters

16. Two pennies are tossed. (Assume that each of the two faces of a penny has 50% probability to turn up on landing.) The probability of getting a double (two heads or two tails) is:

1. 1/4
2. 1/3
3. 1/2
4. 2/3

17. Three pennies are tossed. (Assume that each of the two faces of a penny has 50% probability to turn up on landing.) The probability of getting a triple (3 heads or 3 tails) is:

1. 1/4
2. 1/3
3. 1/2
4. 2/3

18. The least common multiple of 30, 126, 140, and 350 is:

1. 12600
2. 9450
3. 4200
4. 2100
5. 6300

19. The largest common divisor of 30, 126, 140, and 350 is:

1. 2
2. 6
3. 9
4. 14

20. P is a point in the plane with (x,y) coordinates (7,11). The equation of the line in the plane that passes through point P and perpendicular to the line y=x is:

1. 11x - 7y = 0
2. y - x = 4
3. x + y = 18
4. 11x + 7y = 154
5. none of the above