counting and probab
How many two-digit whole numbers are divisible by 14?
7
A number is selected at random from the first 20 positive integers. What is the probability that the number selected is an odd prime number? Express your answer as a percent.
35%
If the area of a 5-cm-by-5-cm square is decreased by 9 square cm to form a smaller square, what is the perimeter in centimeters of the new square?
16
Half of a third of x equals a fourth of y plus a fifth of y. If x = 27, what is the value of y?
10
What is the sum of all the integer values of x for which |3x – 3| < 13?
9
A set of 11 distinct positive integers has a mean of 8 and a range less than 12. What is the largest possible integer that could be a member of the set?
13
If n is a positive integer, what is the smallest value of n for which sqrt(8n/5) is an integer?
10
Right △ABC with legs AB = 3 cm and CB = 4 cm is rotated about one of its legs. What is the greatest possible number of cubic centimeters in the volume of the resulting solid? Express your answer to the nearest whole number.
50
Express this sum as a common fraction: .8 + .2 (both are repeating decimals: 0.8888888...+0.22222)
10/9
If the pattern shown continues, what is the letter in the 2010th position?
MATHLETEMATHLETEMATHLETE...
A
A state creates license plates that each contain two letters followed by three digits. The first letter must be a vowel (A, E, I, O, U), and duplicate letters and digits are allowed. How many different license plates are possible?
130000
What is the result when the greatest common factor of 6432 and 132 is increased by 11?
23
What is the equation of the line perpendicular to y=2x/3-1/3 at the point (−4, −3)? Express your answer in the form y = mx + b.
y=-3x/2-9
Anne was absent for the last algebra test. Her 19 classmates had a class average of exactly 77 points on this test. How many points must Anne score on this test to raise the class average by exactly one point?
97
The team had an easy trip to the MATHCOUNTS contest, but a detour on the way home made the return trip take twice as long. If the new route home (including the detour) was 50% longer than the original trip, and the average speed returning was 10 mi/h slower, what was the average speed of the team going to the contest?
40 mph
A drawer contains 5 pairs of white gloves, 7 pairs of black gloves and 4 pairs of gray gloves. Each pair of gloves has a right-handed glove and a left-handed glove. What is the minimum number of gloves you need to pull out of this drawer to be sure of having a matching pair of gloves?
17 gloves
Ivory writes down three two-digit numbers, each with units digit 7. The tens digit of the product of these three numbers is 5. What is the tens digit of the sum of the three numbers?
1
The line x + y = 5 intersects a rectangle with vertices at (0, 0), (0, 3), (8, 0) and (8, 3), dividing it into two regions as shown. What is the ratio of the area of the smaller region to the area of the larger region? Express your answer as a common fraction.
7/9
The Seat Shop makes 3-legged stools and 4-legged chairs, and each requires one seat. One day they used 6 seats and 20 legs. How many stools did they make?
4 stools
A medication's volume is listed as 0.25 grams. How many milligrams would that be?
250
A bag contains five red marbles, three blue marbles, and two green marbles. Six marbles are to be drawn from the bag, replacing each marble after it is drawn. What is the probability that two marbles of each color will be drawn? Express your answer as a common fraction.
81/1000
Kevin writes a sequence of numbers starting with 1, and repeatedly adding 1 until a multiple of 2 is reached. He then repeatedly adds 2 to this value until a multiple of 3 is reached, then adds 3 until he gets a multiple of 4, and so on. The first four terms are 1, 2, 4, 6. What will be the last term Kevin writes down before he adds 2000 for the first time?
3998000
The right triangle bounded by the x- and y-axes and the line 3x – y = 6 contains 2 lattice points in its interior. How many lattice points will be contained in the interior of the triangle bounded by the x- and y-axes and the line 3x – y = 24?
77
Amy has $5 in quarters, dimes, and nickels, where the total value in quarters is more than the total value of the dimes, and the total value of the dimes is more than the total value of the nickels. What is the maximum number of coins Amy could have?
55
Fido can chew a strip a rawhide at a rate of five inches per minute. Fluffy can chew a strip of rawhide at a rate of two inches per minute. Fluffy starts chewing on a long strip of rawhide, and six minutes later, Fido starts chewing on the other end. Each of them chews until all of the rawhide is gone, and in the end they have each consumed half of the original piece of rawhide. How long was the original strip of rawhide?
40 inches