Geometry
Algebra
Probability
Word
Misc.
100
Seven cubes, whose volumes are 
, 
, 
, 
, 
, 
, and 
cubic units, are stacked vertically to form a tower in which the volumes of the cubes decrease from bottom to top. Except for the bottom cube, the bottom face of each cube lies completely on top of the cube below it. What is the total surface area of the tower (including the bottom) in square units?
B(658)
100
For the nonzero numbers a, b, and c, define (a, b, c) =a/c + b/c + c/a .
Find (2, 12, 9).
(A) 4 (B) 5 (C) 6 (D) 7 (E) 8
(C) 6
100
Four ordinary, six-sided, fair dice are tossed. What is the probability that the sum of the numbers on top is 5?
The total possibilities when we roll 4 fair 6-sided dice is 
We see that the only possible way for these dice to have a sum of 
is to have 
dice with ones on it and one dice with a 
on it. This can be done in 
ways. Thus, the probability is
100
Ike and Mike go into a sandwich shop with a total of 
to spend. Sandwiches cost 
each and soft drinks cost 
each. Ike and Mike plan to buy as many sandwiches as they can, and use any remaining money to buy soft drinks. Counting both sandwiches and soft drinks, how many items will they buy?
(D) 9
100
The numbers 3, 5, 7, a and b have an average (arithmetic mean) of 15. What is the average of a and b?
(C) 30
200
A cube has a volume of 729. Each of it sides are (x+2). Calculate the volume of a sphere with radius, x.
aakash
200
Compute the sum of all the roots of (2x + 3)(x − 4) + (2x + 3)(x − 6) = 0.
(A) 7/2 (B) 4 (C) 5 (D) 7 (E) 13
(A) 7/2
200
There are two cards; one is red on both sides and the other is red on one side and blue on the other. The cards have the same probability (1/2) of being chosen, and one is chosen and placed on the table. If the upper side of the card on the table is red, then the probability that the under-side is also red is
There are three red faces, and two are on the card that is completely red, so our answer is 
, which is 
.
200
Cindy was asked by her teacher to subtract 3 from a certain number and then divide the result by 9. Instead, she subtracted 9 and then divided the result by 3, giving an answer of 43. What would her answer have been had she worked the problem correctly?
(A) 15 (B) 34 (C) 43 (D) 51 (E) 138
(A) 15
200
What is the sum of all real numbers 
for which 
(C) 18
300
7. If an arc of 45◦ on circle A has the same length as an arc of 30◦ on circle B, then the ratio of the area of circle A to the area of circle B is
A. 4/9 B. 2/3 C. 5/6. D. 3/2. E. 9/4
A. 4/9
300
Both roots of the quadratic equation 
are prime numbers. The number of possible values of 
is
(B) 1
300
A person starting with 
and making 
bets, wins three times and loses three times, the wins and losses occurring in random order. The chance for a win is equal to the chance for a loss. If each wager is for half the money remaining at the time of the bet, then the final result is:
If the person wins the bet, the person has 
of the previous amount. If the person loses the bet, the person only has 
of the previous amount.
Because of the Commutative Property, the order of multiplying the multipliers does not matter. Thus, the person walks away with 
dollars, so the person loses 
. The answer is 
.
300
According to the standard convention for exponentiation,
If the order in which the exponentiations are performed is changed, how many other values are possible?
(B) 1
300
A driver travels for 2 hours at 60 miles per hour, during which her car gets 
miles per gallon of gasoline. She is paid $0.50 per mile, and her only expense is gasoline at $2.00 per gallon. What is her net rate of pay, in dollars per hour, after this expense?
E 26
400
The sides of a triangle have lengths of 15, 20, and 25. Find the length of the shortest altitude.
(A) 6 (B) 12 (C) 12.5 (D) 13 (E) 15
400
Given a + 1 = b + 2 = c + 3 = d + 4 = a + b + c + d + 5, then what is the value of a + b + c + d?
A) -1
B) −(10/3)
C) 12
D) 6
E) -2
a+1=a+b+c+d+5
b+2=a+b+c+d+5
c+3=a+b+c+d+5
d+4=a+b+c+d+5
Adding all the equations we get:
a+b+c+d+10=4(a+b+c+d)+20
Solving for (a+b+c+d) we get:
a+b+c+d=(-10/3)
400
Chloe chooses a real number uniformly at random from the interval 
. Independently, Laurent chooses a real number uniformly at random from the interval 
. What is the probability that Laurent's number is greater than Chloe's number?
Denote "winning" to mean "picking a greater number". There is a chance that Laurent chooses a number in the interval 
. In this case, Chloé cannot possibly win, since the maximum number she can pick is 
. Otherwise, if Laurent picks a number in the interval , with probability , then the two people are symmetric, and each has a chance of winning. Then, the total probability is: 
400
Aakash wants to store 30 computer files on floppy disks, each of which has a capacity of 1.44 megabytes (mb). Three of his files require 0.8 mb of memory each, 12 more require 0.7 mb each, and the remaining 15 require 0.4 mb each. No file can be split between floppy disks. What is the minimal number of floppy disks that will hold all the files?
(A) 12 (B) 13 (C) 14 (D) 15 (E) 16
B (13)
400
A sequence of numbers starts with , , and . The fourth number of the sequence is the sum of the previous three numbers in the sequence: 
. In the same way, every number after the fourth is the sum of the previous three numbers. What is the eighth number in the sequence?
(D) 68
500
What is the value of
(b) 9900
500
Using the digits 1, 2, 3, 4, 5, 6, 7, and 9, form 4 two-digit prime numbers, using each digit only once. What is the sum of the 4 prime numbers?
(E) 190
500
When 6fair standard 6-sided dice are thrown, the probability that the sum of the numbers on the top faces is 10can be written as
where n is a positive integer. What is n?
E 84
500
2. Mr. Earl E. Bird leaves his house for work at exactly 8:00 A.M. every morning. When he averages 40 miles per hour, he arrives at his workplace three minutes late. When he averages 60 miles per hour, he arrives three minutes early. At what average speed, in miles per hour, should Mr. Bird drive to arrive at his workplace precisely on time?
(A) 45 (B) 48 (C) 50 (D) 55 (E) 58
(B) 48
500
Austin and Temple are50 miles apart along Interstate 35. Bonnie drove from Austin to her daughter's house in Temple, averaging 60 miles per hour. Leaving the car with her daughter, Bonnie rode a bus back to Austin along the same route and averaged 40 miles per hour on the return trip. What was the average speed for the round trip, in miles per hour?
(B) 48