Number Sense
Evaluate: 290+9+2+492+5+393+3 +0+1+5
1200
What is the sum of all integers x for which -30\leq x\leq 26?
-114
If \log_{25}(x-4)=\frac{1}{2} , find \frac{1}{\log_x3}.
2
What was the number 0 originally called?
Cipher
What is the sum of the roots of the polynomial x^2-17x+2 ?
5000
For how many different digits n is the two-digit number 6n divisible by n ? (The expression 6n should be interpreted as a two-digit integer with tens digit 6 and units digit n , not as 6 times n .)
6
Asha adds all the odd integers from 1 through 101, inclusive, and then subtracts all the even integers in that same range from her sum. What result does she obtain?
51
How many positive integers b have the property that \log_b 729 is a positive integer?
4
Where did Archimedes hail from?
Syracuse, Greece
What is the product of the roots of the polynomial x^2+3x-15 .
-15
How many two-digit prime numbers can be formed by choosing two different digits from the set {2,7,8,9} to be used as the tens digit and units digit?
4
To place the first paving stone in a path, Alex starts at the crate of stones, walks three feet, places the stone, and returns to the crate. For each subsequent stone, Alex walks two feet farther each way. Alex will place the first 50 stones in a path. After returning to the crate from placing the 50^{th} stone, what is the total distance Alex walked, in feet?
5200
Evaluate \log_{\sqrt{5}}125 \sqrt{5}.
7
Where were the Arabic numerals invented?
Let r_1, r_2, r_3 , be the the roots of x^3-6x^2+21x +a=0. Find all real numbers a such that the roots r_1, r_2, r_3 form an arithmetic sequence and are not all real.
-26
What is the least four-digit positive integer, with all different digits, that is divisible by each of its digits?
1236
The arithmetic mean of an odd number of consecutive odd integers is y. Find the sum of the smallest and largest of the integers in terms of y .
2y
Rewrite log_2 4\cdot \log_3 5 \cdot \log_4 6 \cdots \log_{62} 64 as a\log_b c, where a,b, and c are positive integers, b is prime, and c<100. Compute a+b+c.
How many sides does an "Enneadecagon" have?
19
Suppose that for some a,b,c we have a+b+c=6 , ab+ac+bc=5 and abc=-12. What is a^3+b^3+c^3 ?
90
If the least common multiple of A and B is 1575, and the ratio of A to B is 3:7, then what is their greatest common divisor?
75
If x and y are positive integers for which 3x+2y+xy=115+7x+6y, then what is x+y?
140
Consider the largest solution to the equation \log_{10x^2} 10+\log_{100x^3}10=-2. Find the value of \frac{1}{x^{12}}. writing your answer in decimal representation.
10000000
What is the only number that is twice the sum of its digits?
18
Find the sum of the roots, real and non-real, of the equation x^{2001}+(12-x)^{2001}=0, given that there are no multiple roots.
500