1
Sample question. (20) Simplify:
27
4
18
4
2
Ans: 3
JV1.1. (30) The height of my tv screen is 3/4 its width. If the diagonal is 30 inches, what is the
width in inches?
Ans: 24
JV1.2. (20) 8 teams play in a tournament in which teams are eliminated only after losing two
games. What is the largest number of games that could be played?
Ans: 15
JV1.3. (30) My stock increased in value 20% the first year and 30% the second. What is the total
percentage increase?
Ans: 56 or 56%
JV1.4 (20) Calculate: 100  99  98  97  96  ...  81  80
Ans: 90
JV1.5. (30) My final grade is the average of 3 midterms plus the final, with the final being given
twice the weight of each of the other 3 exams. I scored 88, 86, and 92 on the three midterms.
What do I need to score on the final so my average is 90?
Ans: 92
JV1.6 (30) If I flip a fair coin three times, what is the probability of getting at least one head?
Ans: 7/8
JV1.7 (30)The product of three consecutive odd integers is 315. What is the smallest of the
three integers?
Ans: 5
JV1.8 (30)What is the greatest common divisor of 108 and 360?
Ans: 36
1
1
1
1
JV1.9. (20) Calculate (1  )(1  )(1  )...(1  )
2
3
4
10
Ans: 1/10
JV1.10 (30) What is x if 2-(x-(3-x)) = 1?
Ans: 2
JV1.11. (20) Calculate: 1 + 3 + 5 + 7 + ... + 19
Ans: 100
JV1.12 (30) The volume of a pyramid with a square base and a height of 5 inches is 15 cubic
inches. What is the length in inches of the side of the base?
Ans: 3
2
JV2.1 (30) How many hours is it from 3 am Sunday to 7 p.m Friday?
Ans: 136
JV2.2 (30) One faucet can fill a tub in 20 minutes, another in 30 minutes. How long will it take
to fill if both faucets are used?
Ans: 12 min.
JV2.3 (40) Find the values of x which give a positive integer solutions to: 5x + 8y = 76
Ans: 4, 12
JV2.4 (30) The first term of a sequence is 1. Thereafter, each term is the sum of all preceding
terms. What is the 8-th term? Ans: 64
JV2.5 (30) What will the following computer program print?
x=2
while x < 100
x = x+3
end while
print x
Ans: 101
JV2.6 (40) Solve for y: x 2  y 2  16, x 2  12  7 x
Ans: 0,  7
JV2.7 (30) Express the infinite decimal .363636... as a reduced fraction.
Ans: 4/11
JV2.8 (40) Perform the base eight addition: 336eight  454eight  ????eight
Ans: 1012 or 1012eight
JV2.9 (20) By what factor is the volume of a cylinder increased if its height is doubled and its
diameter is tripled?
Ans: 18
JV2.10 (30) The squares of two consecutive positive odd integers differ by 48. What is their
sum?
Ans: 24
JV2.11 (30) An equilateral triangle of side 12 is inscribed in a circle. What is its radius?
Ans: 2
JV2.12 (20) If I roll two dice, what is the probability the product of the numbers is even?
Ans: 3/4
3
JV3.1 (30) If you correctly fill out a 9 by 9 Sudoku puzzle, what is the sum of all the numbers?
Ans. 405
JV3.2 (30) A swimming pool is 20 feet wide, 30 feet long, and 8 feet deep. How many hours
will it take to fill it with a hose with capacity 1/2 cubic foot per minute?
Ans: 160
JV3.3 (30) Solve for x: | | x  2 | 3 |  4
Ans: -5, 9
JV3.4 (20) If I roll three dice what is the probability the sum of the three numbers is even?
Ans: 1/2
JV3.5 (30) What is the average of the set of odd numbers which are greater than 4 and less than
22?
Ans 13
JV3.6 (30) Two positive numbers differ by 4; their squares differ by 36. What is their sum?
Ans: 9
JV3.7 (30) Give the value of x for a positive integer solution of 4x + 7y = 30.
Ans: 4
JV3.8 (20) A line is perpendicular to y  5  2 x and crosses it on the y-axis. Give its equation
x
in the form y = mx + b.
Ans: y   5
2
JV3.9 (30) Express
5
as an infinite repeating decimal.
27
Ans: .185185… or .185
JV3.10 (30) Do the base five multiplication: 34 five  21 five  ??? five
Ans: 1314 or 1314 five
JV3.11 (30) A cone has diameter equal to its height. Its volume is 18 in3 . What is its height?
Ans: 6 in
JV3.12 (20) What is the interior angle, in degrees, of a regular dodecagon.
Ans: 150
4
JV4.1 (30) Four lines can divide the plane into how many regions at most?
Ans: 11
JV4.2. (30) Four consecutive even integers add up to 284. What is the smallest of the four?
Ans 68
JV4.3 (20) We break a decagon into triangles by joining vertices. How many triangles do we
get? Ans: 7
JV4.4 (30) How many different ways are there to arrange the letters {a, b, c, d} so that b is
immediately to the right of a? Ans: 6
JV4.5 (30) If the two digits of a number are reversed the number is increased by 18. What is
the largest number it could be?
Ans: 79
JV4.6 (30) A swimming pool is circular in shape. I swim from one side 10 feet and touch the
wall. I turn 90 degrees and swim 24 feet again touching the wall. What is the diameter of the
pool?
Ans: 26 feet
JV4.7 (20) What is the total surface area of a hemisphere of radius 2?
Ans: 12
JV4.8 (45) How many ways can I make a total of 50 cents if I have only quarters, dimes and
nickels? Ans: 10
JV4.9 (45) A cone has radius 3 inches and height 4 inches. What is the area of the slanted part?
Ans: 15
JV4.10 (45) What is the largest integer n such that
20!
is an integer?
6n
Ans: 8
JV4.11 (30) What is the probability I draw two socks of the same color if I draw randomly from
a drawer with 4 grey socks and 3 black socks? Ans: 3/7
JV4.12 (30) Perform the base four division:
3300 four
12 four
 ??? four
Ans: 220 or 220 four