Modular Arithmetic
What is 61 mod 7?
5 or -2
How many three-letter words can you make from the letters of PEARL?
60
Choosing a random number between 1 and 10, what is the probability of choosing a number less than 20?
1.0
What is the mean of the set of numbers:
{1, 2, 7, 7, 19, 2, 4}
(add them up and divide by the number of numbers)
6
What is the perimeter of the square with area 9 cm2?
12cm
if it is 7:00PM now, what time will it be in 970 hours?
5:00 AM
How many ways can you rearrange the letters of the word SASSAFRASS?
5040
1/6
What is the MEDIAN of the set of numbers:
{1, 2, 7, 7, 19, 2, 4}
(write them in increasing order and find the middle number)
4
If 5 zips equal 4 squawks, and 3 squawks equal 5 bangs, how many zips equal
12 bangs?
16 zips
What is the last digit of 12^1000?
6
In how many ways is it possible to seat seven people at a round table?
720
In a bag, there are 12 purple, 7 green, 11 blue and 3 pink marbles. If you select two marbles at random from the bag, without replacement, what is the
probability that you will choose first a pink marble and then a purple marble? Express your answer as a common fraction
3/88
100
A bicycle that originally cost $200 is on sale for $140. By what percent was the
price reduced?
30%
1 modulo 3 and
0 modulo 7
48
In how many ways is it possible to seat seven people at a round table if Alex and Bob cannot sit together?
600
Five distinct integers from 1 to 10 are chosen, and five distinct integers from 11 to 20 are chosen. No two numbers differ by exactly 10. What is the probability that the sum of all chosen numbers is greater than 110?
0
The mean, median, and unique mode of the positive integers {3,4,5,6,6,7,x} are all equal. What is the value of x?
11
Triangle ABC has an area of 40 units2. Point D is on side AC, and AD:DC = 3:1.
What is the area of triangle BDC?
10 units2
How many positive three-digit integers have a remainder of 2 when divided by 6, a
remainder of 5 when divided by 9, and a remainder of 7 when divided by 11?
5
A bug starts at a vertex of an equilateral triangle. On each move, it randomly selects one of the two vertices where it is not currently located, and crawls along a side of the triangle to that vertex. Find the probability that the bug moves to its starting vertex on its tenth move.
171/512
If two standard, fair 6-sided dice are rolled, what is the probability that the product of the two numbers rolled is a perfect square? Express your answer as a common
fraction.
2/9
The mean of a set of five different positive integers is 15. The median is 18. What
is the maximum possible value of the largest of these five integers?
35
A water tank in the shape of a rectangular prism has
dimensions of 10 feet by 3 feet by 2 feet and is oriented with
the top and bottom surfaces being level. At 11:00 a.m., the
water level is at 70% of the tank’s height. The water begins
draining from the bottom of the tank at a constant rate. At
noon the water level is down to 40% of the tank’s height. At
1:00 p.m., how many cubic feet of water are left in the tank?
6 cubic feet