Found problems: 63
2017-2018 SDML (Middle School), 1
Let $N = \frac{1}{3} + \frac{3}{5} + \frac{5}{7} + \frac{7}{9} + \frac{9}{11}$. What is the greatest integer which is less than $N$?
2017-2018 SDML (Middle School), 3
Evaluate the following expression: $$0 - 1 -2 + 3 - 4 + 5 + 6 + 7 - 8 + ... + 2000$$ The terms with minus signs are exactly the powers of two.
2014-2015 SDML (High School), 2
Sally is thinking of a positive four-digit integer. When she divides it by any one-digit integer greater than $1$, the remainder is $1$. How many possible values are there for Sally's four-digit number?
2016-2017 SDML (Middle School), 4
In a certain regular polygon, the measure of each interior angle is twice the measure of each exterior angle. How many sides does this regular polygon have?
2012-2013 SDML (Middle School), 12
For what digit $A$ is the numeral $1AA$ a perfect square in base-$5$ and a perfect cube in base-$6$?
$\text{(A) }0\qquad\text{(B) }1\qquad\text{(C) }2\qquad\text{(D) }3\qquad\text{(E) }4$
2016-2017 SDML (Middle School), 5
What is the measure in degrees of the acute angle formed by the hands of a $12$-hour clock at $3:20$ PM?
$\text{(A) }18\qquad\text{(B) }20\qquad\text{(C) }22\qquad\text{(D) }25\qquad\text{(E) }30$
2017-2018 SDML (Middle School), 5
If the sum of the slope and the $y$-intercept of a line is $3$, then through which point is the line guaranteed to pass?
2016-2017 SDML (Middle School), 3
A company that sells keychains has to pay $\mathdollar500$ in maintenance fees each day and then it pays each work $\mathdollar15$ an hour. Each worker makes $5$ keychains per hour, which are sold at $\mathdollar3.10$ each. What is the least number of workers the company has to hire in order to make a profit in an $8$-hour workday?
2016-2017 SDML (Middle School), 9
Let $N$ be the product of all odd primes less than $2^4$. What remainder does $N$ leave when divided by $2^4$?
$\text{(A) }5\qquad\text{(B) }7\qquad\text{(C) }9\qquad\text{(D) }11\qquad\text{(E) }13$
2017-2018 SDML (Middle School), 12
If $n$ is an integer such that $2 \leq n \leq 2017$, for how many values of $n$ is $\left(1 + \frac{1}{2}\right)\left(1 + \frac{1}{3}\right)\cdots\left(1 + \frac{1}{n}\right)$ equal to a positive integer?
$\mathrm{(A) \ } 0 \qquad \mathrm{(B) \ } 1 \qquad \mathrm {(C) \ } 1007 \qquad \mathrm{(D) \ } 1008 \qquad \mathrm{(E) \ } 2016$
2017-2018 SDML (Middle School), 8
Gorf the frog is standing on the first lily pad in a row of lily pads numbered from $1$ to $20$ from left to right. On a single jump, Gorf is able to jump either $1,2,$ or $3$ lily pads to the right. Unfortunately all the prime-numbered lily pads are contaminated with a deadly poison. How many sequences of jumps are there that allow Gorf to jump to the twentieth lily pad, while avoiding the poison?
2014-2015 SDML (Middle School), 7
Nine distinct digits appear in the decimal expansion of $2^{29}$. Which digit is missing?
2017-2018 SDML (Middle School), 2
How many ways are there to cover this region with dominoes?
[asy]
unitsize(20);
int[][] a = {
{999, 999, 000, 000, 000, 999, 999, 999},
{999, 999, 000, 888, 000, 999, 999, 999},
{999, 999, 000, 000, 000, 000, 000, 000},
{000, 000, 000, 888, 888, 000, 888, 000},
{000, 888, 000, 888, 888, 000, 000, 000},
{000, 000, 000, 000, 000, 000, 999, 999},
{999, 999, 999, 000, 888, 000, 999, 999},
{999, 999, 999, 000, 000, 000, 999, 999}};
for (int i = 0; i < 8; ++i) {
for (int j = 0; j < 8; ++j) {
if (a[j][i] != 999) draw((i, -j)--(i+1, -j)--(i+1, -j-1)--(i, -j-1)--cycle);
if (a[j][i] == 888) fill((i, -j)--(i+1, -j)--(i+1, -j-1)--(i, -j-1)--cycle);
}
}
[/asy]