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2,700 | In a certain sequence of numbers, the first number is $1$, and, for all $n\ge 2$, the product of the first $n$ numbers in the sequence is $n^2$. The sum of the third and the fifth numbers in the sequence is | \frac{61}{16} | 89.0625 |
2,701 | The product $(8)(888\dots8)$, where the second factor has $k$ digits, is an integer whose digits have a sum of $1000$. What is $k$? | 991 | 55.46875 |
2,702 | The symbol $|a|$ means $+a$ if $a$ is greater than or equal to zero, and $-a$ if a is less than or equal to zero; the symbol $<$ means "less than";
the symbol $>$ means "greater than."
The set of values $x$ satisfying the inequality $|3-x|<4$ consists of all $x$ such that: | $-1<x<7$ | 0 |
2,703 | Frieda the frog begins a sequence of hops on a $3 \times 3$ grid of squares, moving one square on each hop and choosing at random the direction of each hop-up, down, left, or right. She does not hop diagonally. When the direction of a hop would take Frieda off the grid, she "wraps around" and jumps to the opposite edge. For example if Frieda begins in the center square and makes two hops "up", the first hop would place her in the top row middle square, and the second hop would cause Frieda to jump to the opposite edge, landing in the bottom row middle square. Suppose Frieda starts from the center square, makes at most four hops at random, and stops hopping if she lands on a corner square. What is the probability that she reaches a corner square on one of the four hops? | \frac{13}{16} | 0.78125 |
2,704 | Parallelogram $ABCD$ has area $1,\!000,\!000$. Vertex $A$ is at $(0,0)$ and all other vertices are in the first quadrant. Vertices $B$ and $D$ are lattice points on the lines $y = x$ and $y = kx$ for some integer $k > 1$, respectively. How many such parallelograms are there? (A lattice point is any point whose coordinates are both integers.) | 784 | 41.40625 |
2,705 | In $\triangle ABC$, point $F$ divides side $AC$ in the ratio $1:2$. Let $E$ be the point of intersection of side $BC$ and $AG$ where $G$ is the midpoints of $BF$. The point $E$ divides side $BC$ in the ratio | 1/3 | 0 |
2,706 | All the numbers $1, 2, 3, 4, 5, 6, 7, 8, 9$ are written in a $3\times3$ array of squares, one number in each square, in such a way that if two numbers are consecutive then they occupy squares that share an edge. The numbers in the four corners add up to $18$. What is the number in the center? | 7 | 59.375 |
2,707 | $\frac{1}{1+\frac{1}{2+\frac{1}{3}}}=$ | \frac{7}{10} | 60.15625 |
2,708 | The mean of three numbers is $10$ more than the least of the numbers and $15$ less than the greatest. The median of the three numbers is $5$. What is their sum? | 30 | 82.8125 |
2,709 | What is the radius of a circle inscribed in a rhombus with diagonals of length $10$ and $24$? | \frac{60}{13} | 44.53125 |
2,710 | A month with $31$ days has the same number of Mondays and Wednesdays. How many of the seven days of the week could be the first day of this month? | 3 | 40.625 |
2,711 | Ana and Bonita were born on the same date in different years, $n$ years apart. Last year Ana was $5$ times as old as Bonita. This year Ana's age is the square of Bonita's age. What is $n?$ | 12 | 91.40625 |
2,712 | For any three real numbers $a$, $b$, and $c$, with $b\neq c$, the operation $\otimes$ is defined by:
\[\otimes(a,b,c)=\frac{a}{b-c}\]
What is $\otimes(\otimes(1,2,3),\otimes(2,3,1),\otimes(3,1,2))$? | -\frac{1}{4} | 95.3125 |
2,713 | If $m>0$ and the points $(m,3)$ and $(1,m)$ lie on a line with slope $m$, then $m=$ | \sqrt{3} | 93.75 |
2,714 | The first AMC $8$ was given in $1985$ and it has been given annually since that time. Samantha turned $12$ years old the year that she took the seventh AMC $8$. In what year was Samantha born? | 1979 | 98.4375 |
2,715 | Let $ABCD$ be an isosceles trapezoid with $AD=BC$ and $AB<CD.$ Suppose that the distances from $A$ to the lines $BC,CD,$ and $BD$ are $15,18,$ and $10,$ respectively. Let $K$ be the area of $ABCD.$ Find $\sqrt2 \cdot K.$ | 270 | 0 |
2,716 | What is $\frac{2+4+6}{1+3+5} - \frac{1+3+5}{2+4+6}$? | \frac{7}{12} | 94.53125 |
2,717 | Menkara has a $4 \times 6$ index card. If she shortens the length of one side of this card by $1$ inch, the card would have area $18$ square inches. What would the area of the card be in square inches if instead she shortens the length of the other side by $1$ inch? | 20 | 81.25 |
2,718 | Mr. Patrick teaches math to $15$ students. He was grading tests and found that when he graded everyone's test except Payton's, the average grade for the class was $80$. After he graded Payton's test, the test average became $81$. What was Payton's score on the test? | 95 | 64.0625 |
2,719 | A circle with area $A_1$ is contained in the interior of a larger circle with area $A_1+A_2$. If the radius of the larger circle is $3$, and if $A_1 , A_2, A_1 + A_2$ is an arithmetic progression, then the radius of the smaller circle is | \sqrt{3} | 89.84375 |
2,720 | Given square $ABCD$ with side $8$ feet. A circle is drawn through vertices $A$ and $D$ and tangent to side $BC$. The radius of the circle, in feet, is: | 5 | 60.15625 |
2,721 | The sum of three numbers is $20$. The first is four times the sum of the other two. The second is seven times the third. What is the product of all three? | 28 | 93.75 |
2,722 | On a trip from the United States to Canada, Isabella took $d$ U.S. dollars. At the border she exchanged them all, receiving $10$ Canadian dollars for every $7$ U.S. dollars. After spending $60$ Canadian dollars, she had $d$ Canadian dollars left. What is the sum of the digits of $d$? | 5 | 85.15625 |
2,723 | Ed and Ann both have lemonade with their lunch. Ed orders the regular size. Ann gets the large lemonade, which is 50% more than the regular. After both consume $\frac{3}{4}$ of their drinks, Ann gives Ed a third of what she has left, and 2 additional ounces. When they finish their lemonades they realize that they both drank the same amount. How many ounces of lemonade did they drink together? | 40 | 31.25 |
2,724 | For how many integers $x$ is the point $(x, -x)$ inside or on the circle of radius $10$ centered at $(5, 5)$? | 11 | 96.875 |
2,725 | The area of polygon $ABCDEF$, in square units, is | 46 | 0 |
2,726 | Suppose that on a parabola with vertex $V$ and a focus $F$ there exists a point $A$ such that $AF=20$ and $AV=21$. What is the sum of all possible values of the length $FV?$ | \frac{40}{3} | 16.40625 |
2,727 | Two medians of a triangle with unequal sides are $3$ inches and $6$ inches. Its area is $3 \sqrt{15}$ square inches. The length of the third median in inches, is: | 3\sqrt{6} | 42.1875 |
2,728 | A rectangular box measures $a \times b \times c$, where $a$, $b$, and $c$ are integers and $1\leq a \leq b \leq c$. The volume and the surface area of the box are numerically equal. How many ordered triples $(a,b,c)$ are possible? | 10 | 85.15625 |
2,729 | A sample consisting of five observations has an arithmetic mean of $10$ and a median of $12$. The smallest value that the range (largest observation minus smallest) can assume for such a sample is | 5 | 7.8125 |
2,730 | Let $ABC$ be an equilateral triangle. Extend side $\overline{AB}$ beyond $B$ to a point $B'$ so that $BB'=3 \cdot AB$. Similarly, extend side $\overline{BC}$ beyond $C$ to a point $C'$ so that $CC'=3 \cdot BC$, and extend side $\overline{CA}$ beyond $A$ to a point $A'$ so that $AA'=3 \cdot CA$. What is the ratio of the area of $\triangle A'B'C'$ to the area of $\triangle ABC$? | 16:1 | 0 |
2,731 | On a trip from the United States to Canada, Isabella took $d$ U.S. dollars. At the border she exchanged them all, receiving $10$ Canadian dollars for every $7$ U.S. dollars. After spending $60$ Canadian dollars, she had $d$ Canadian dollars left. What is the sum of the digits of $d$? | 5 | 84.375 |
2,732 | A bug travels from A to B along the segments in the hexagonal lattice pictured below. The segments marked with an arrow can be traveled only in the direction of the arrow, and the bug never travels the same segment more than once. How many different paths are there? | 2400 | 0 |
2,733 | Let $n$ be the number of pairs of values of $b$ and $c$ such that $3x+by+c=0$ and $cx-2y+12=0$ have the same graph. Then $n$ is: | 2 | 96.09375 |
2,734 | Sides $AB$, $BC$, $CD$ and $DA$ of convex quadrilateral $ABCD$ are extended past $B$, $C$, $D$ and $A$ to points $B'$, $C'$, $D'$ and $A'$, respectively. Also, $AB = BB' = 6$, $BC = CC' = 7$, $CD = DD' = 8$ and $DA = AA' = 9$. The area of $ABCD$ is $10$. The area of $A'B'C'D'$ is | 114 | 0 |
2,735 | Let $a$, $b$, and $c$ be positive integers with $a \ge b \ge c$ such that
$a^2-b^2-c^2+ab=2011$ and
$a^2+3b^2+3c^2-3ab-2ac-2bc=-1997$.
What is $a$? | 253 | 48.4375 |
2,736 | Three distinct vertices of a cube are chosen at random. What is the probability that the plane determined by these three vertices contains points inside the cube? | \frac{4}{7} | 51.5625 |
2,737 | The figure is constructed from $11$ line segments, each of which has length $2$. The area of pentagon $ABCDE$ can be written as $\sqrt{m} + \sqrt{n}$, where $m$ and $n$ are positive integers. What is $m + n ?$ | 23 | 0 |
2,738 | $A$ and $B$ together can do a job in $2$ days; $B$ and $C$ can do it in four days; and $A$ and $C$ in $2\frac{2}{5}$ days.
The number of days required for A to do the job alone is: | 3 | 94.53125 |
2,739 | A wooden cube $n$ units on a side is painted red on all six faces and then cut into $n^3$ unit cubes. Exactly one-fourth of the total number of faces of the unit cubes are red. What is $n$? | 4 | 82.8125 |
2,740 | An isosceles right triangle with legs of length $8$ is partitioned into $16$ congruent triangles as shown. The shaded area is | 20 | 21.09375 |
2,741 | The least positive integer with exactly $2021$ distinct positive divisors can be written in the form $m \cdot 6^k$, where $m$ and $k$ are integers and $6$ is not a divisor of $m$. What is $m+k?$ | 58 | 14.0625 |
2,742 | The stronger Goldbach conjecture states that any even integer greater than 7 can be written as the sum of two different prime numbers. For such representations of the even number 126, the largest possible difference between the two primes is | 100 | 35.15625 |
2,743 | Using only the paths and the directions shown, how many different routes are there from $\text{M}$ to $\text{N}$? | 6 | 18.75 |
2,744 | Find the area of the smallest region bounded by the graphs of $y=|x|$ and $x^2+y^2=4$. | \pi | 3.90625 |
2,745 | Cozy the Cat and Dash the Dog are going up a staircase with a certain number of steps. However, instead of walking up the steps one at a time, both Cozy and Dash jump. Cozy goes two steps up with each jump (though if necessary, he will just jump the last step). Dash goes five steps up with each jump (though if necessary, he will just jump the last steps if there are fewer than 5 steps left). Suppose that Dash takes 19 fewer jumps than Cozy to reach the top of the staircase. Let $s$ denote the sum of all possible numbers of steps this staircase can have. What is the sum of the digits of $s$? | 13 | 68.75 |
2,746 | Which triplet of numbers has a sum NOT equal to 1? | 1.1 + (-2.1) + 1.0 | 0 |
2,747 | A grocer stacks oranges in a pyramid-like stack whose rectangular base is $5$ oranges by $8$ oranges. Each orange above the first level rests in a pocket formed by four oranges below. The stack is completed by a single row of oranges. How many oranges are in the stack? | 100 | 31.25 |
2,748 | What is the product of $\frac{3}{2} \times \frac{4}{3} \times \frac{5}{4} \times \cdots \times \frac{2006}{2005}$? | 1003 | 100 |
2,749 | A regular hexagon has side length 6. Congruent arcs with radius 3 are drawn with the center at each of the vertices, creating circular sectors as shown. The region inside the hexagon but outside the sectors is shaded as shown What is the area of the shaded region? | 54\sqrt{3}-18\pi | 0 |
2,750 | An $n$-digit positive integer is cute if its $n$ digits are an arrangement of the set $\{1,2,...,n\}$ and its first $k$ digits form an integer that is divisible by $k$, for $k = 1,2,...,n$. For example, $321$ is a cute $3$-digit integer because $1$ divides $3$, $2$ divides $32$, and $3$ divides $321$. How many cute $6$-digit integers are there? | 4 | 0 |
2,751 | The population of Nosuch Junction at one time was a perfect square. Later, with an increase of $100$, the population was one more than a perfect square. Now, with an additional increase of $100$, the population is again a perfect square.
The original population is a multiple of: | 7 | 36.71875 |
2,752 | At the beginning of the school year, $50\%$ of all students in Mr. Well's class answered "Yes" to the question "Do you love math", and $50\%$ answered "No." At the end of the school year, $70\%$ answered "Yes" and $30\%$ answered "No." Altogether, $x\%$ of the students gave a different answer at the beginning and end of the school year. What is the difference between the maximum and the minimum possible values of $x$? | 60 | 24.21875 |
2,753 | The sum of six consecutive positive integers is 2013. What is the largest of these six integers? | 338 | 89.84375 |
2,754 | The fourth power of $\sqrt{1+\sqrt{1+\sqrt{1}}}$ is | 3+2\sqrt{2} | 65.625 |
2,755 | A point $(x,y)$ in the plane is called a lattice point if both $x$ and $y$ are integers. The area of the largest square that contains exactly three lattice points in its interior is closest to | 5.0 | 0.78125 |
2,756 | What expression is never a prime number when $p$ is a prime number? | $p^2+26$ | 0 |
2,757 | Given points $P(-1,-2)$ and $Q(4,2)$ in the $xy$-plane; point $R(1,m)$ is taken so that $PR+RQ$ is a minimum. Then $m$ equals: | -\frac{2}{5} | 35.15625 |
2,758 | The measure of angle $ABC$ is $50^\circ$, $\overline{AD}$ bisects angle $BAC$, and $\overline{DC}$ bisects angle $BCA$. The measure of angle $ADC$ is | 115^\circ | 85.15625 |
2,759 | A set of teams held a round-robin tournament in which every team played every other team exactly once. Every team won $10$ games and lost $10$ games; there were no ties. How many sets of three teams $\{A, B, C\}$ were there in which $A$ beat $B$, $B$ beat $C$, and $C$ beat $A$? | 385 | 40.625 |
2,760 | In $\triangle ABC, AB = 13, BC = 14$ and $CA = 15$. Also, $M$ is the midpoint of side $AB$ and $H$ is the foot of the altitude from $A$ to $BC$.
The length of $HM$ is | 6.5 | 45.3125 |
2,761 | Eight spheres of radius 1, one per octant, are each tangent to the coordinate planes. What is the radius of the smallest sphere, centered at the origin, that contains these eight spheres? | 1+\sqrt{3} | 11.71875 |
2,762 | A circle of radius $r$ is concentric with and outside a regular hexagon of side length $2$. The probability that three entire sides of hexagon are visible from a randomly chosen point on the circle is $1/2$. What is $r$? | $3\sqrt{2}+\sqrt{6}$ | 0 |
2,763 | Two numbers whose sum is $6$ and the absolute value of whose difference is $8$ are roots of the equation: | x^2-6x-7=0 | 92.1875 |
2,764 | How many four-digit whole numbers are there such that the leftmost digit is odd, the second digit is even, and all four digits are different? | 1400 | 97.65625 |
2,765 | If $\frac{x^2-bx}{ax-c}=\frac{m-1}{m+1}$ has roots which are numerically equal but of opposite signs, the value of $m$ must be: | \frac{a-b}{a+b} | 85.15625 |
2,766 | In how many ways can $47$ be written as the sum of two primes? | 0 | 78.90625 |
2,767 | A right rectangular prism whose surface area and volume are numerically equal has edge lengths $\log_{2}x, \log_{3}x,$ and $\log_{4}x.$ What is $x?$ | 576 | 52.34375 |
2,768 | If $2^a+2^b=3^c+3^d$, the number of integers $a,b,c,d$ which can possibly be negative, is, at most: | 0 | 69.53125 |
2,769 | In the $xy$-plane, the segment with endpoints $(-5,0)$ and $(25,0)$ is the diameter of a circle. If the point $(x,15)$ is on the circle, then $x=$ | 10 | 96.09375 |
2,770 | How many sets of two or more consecutive positive integers have a sum of $15$? | 2 | 3.125 |
2,771 | Find the sum of the digits in the answer to
$\underbrace{9999\cdots 99}_{94\text{ nines}} \times \underbrace{4444\cdots 44}_{94\text{ fours}}$
where a string of $94$ nines is multiplied by a string of $94$ fours. | 846 | 100 |
2,772 | There are $20$ students participating in an after-school program offering classes in yoga, bridge, and painting. Each student must take at least one of these three classes, but may take two or all three. There are $10$ students taking yoga, $13$ taking bridge, and $9$ taking painting. There are $9$ students taking at least two classes. How many students are taking all three classes? | 3 | 91.40625 |
2,773 | Sarah places four ounces of coffee into an eight-ounce cup and four ounces of cream into a second cup of the same size. She then pours half the coffee from the first cup to the second and, after stirring thoroughly, pours half the liquid in the second cup back to the first. What fraction of the liquid in the first cup is now cream? | \frac{2}{5} | 52.34375 |
2,774 | The sum of the digits of a two-digit number is subtracted from the number. The units digit of the result is $6$. How many two-digit numbers have this property? | 10 | 73.4375 |
2,775 | Let $M$ be the midpoint of side $AB$ of triangle $ABC$. Let $P$ be a point on $AB$ between $A$ and $M$, and let $MD$ be drawn parallel to $PC$ and intersecting $BC$ at $D$. If the ratio of the area of triangle $BPD$ to that of triangle $ABC$ is denoted by $r$, then | r=\frac{1}{2} | 11.71875 |
2,776 | While Steve and LeRoy are fishing 1 mile from shore, their boat springs a leak, and water comes in at a constant rate of 10 gallons per minute. The boat will sink if it takes in more than 30 gallons of water. Steve starts rowing towards the shore at a constant rate of 4 miles per hour while LeRoy bails water out of the boat. What is the slowest rate, in gallons per minute, at which LeRoy can bail if they are to reach the shore without sinking? | 8 | 85.9375 |
2,777 | In a circle with center $O$ and radius $r$, chord $AB$ is drawn with length equal to $r$ (units). From $O$, a perpendicular to $AB$ meets $AB$ at $M$. From $M$ a perpendicular to $OA$ meets $OA$ at $D$. In terms of $r$ the area of triangle $MDA$, in appropriate square units, is: | \frac{r^2\sqrt{3}}{32} | 6.25 |
2,778 | A parking lot has 16 spaces in a row. Twelve cars arrive, each of which requires one parking space, and their drivers chose spaces at random from among the available spaces. Auntie Em then arrives in her SUV, which requires 2 adjacent spaces. What is the probability that she is able to park? | \frac{17}{28} | 5.46875 |
2,779 | Triangle $ABC$ with $AB=50$ and $AC=10$ has area $120$. Let $D$ be the midpoint of $\overline{AB}$, and let $E$ be the midpoint of $\overline{AC}$. The angle bisector of $\angle BAC$ intersects $\overline{DE}$ and $\overline{BC}$ at $F$ and $G$, respectively. What is the area of quadrilateral $FDBG$? | 75 | 8.59375 |
2,780 | The Fibonacci sequence $1,1,2,3,5,8,13,21,\ldots$ starts with two 1s, and each term afterwards is the sum of its two predecessors. Which one of the ten digits is the last to appear in the units position of a number in the Fibonacci sequence? | 6 | 94.53125 |
2,781 | The difference between a $6.5\%$ sales tax and a $6\%$ sales tax on an item priced at $\$20$ before tax is | $0.10 | 0 |
2,782 | If $\angle A = 60^\circ$, $\angle E = 40^\circ$ and $\angle C = 30^\circ$, then $\angle BDC =$ | 50^\circ | 11.71875 |
2,783 | In the complex plane, let $A$ be the set of solutions to $z^{3}-8=0$ and let $B$ be the set of solutions to $z^{3}-8z^{2}-8z+64=0.$ What is the greatest distance between a point of $A$ and a point of $B?$ | $2\sqrt{21}$ | 0 |
2,784 | \dfrac{1}{10} + \dfrac{9}{100} + \dfrac{9}{1000} + \dfrac{7}{10000} = | 0.1997 | 67.96875 |
2,785 | The rectangle shown has length $AC=32$, width $AE=20$, and $B$ and $F$ are midpoints of $\overline{AC}$ and $\overline{AE}$, respectively. The area of quadrilateral $ABDF$ is | 320 | 66.40625 |
2,786 | Find the least positive integer $n$ for which $\frac{n-13}{5n+6}$ is a non-zero reducible fraction. | 84 | 51.5625 |
2,787 | Let $ABCD$ be a trapezoid with $AB \parallel CD$, $AB=11$, $BC=5$, $CD=19$, and $DA=7$. Bisectors of $\angle A$ and $\angle D$ meet at $P$, and bisectors of $\angle B$ and $\angle C$ meet at $Q$. What is the area of hexagon $ABQCDP$? | $30\sqrt{3}$ | 0 |
2,788 | The sum of two angles of a triangle is $\frac{6}{5}$ of a right angle, and one of these two angles is $30^{\circ}$ larger than the other. What is the degree measure of the largest angle in the triangle? | 72 | 85.9375 |
2,789 | Loki, Moe, Nick and Ott are good friends. Ott had no money, but the others did. Moe gave Ott one-fifth of his money, Loki gave Ott one-fourth of his money and Nick gave Ott one-third of his money. Each gave Ott the same amount of money. What fractional part of the group's money does Ott now have? | \frac{1}{4} | 96.09375 |
2,790 | $\frac{10^7}{5\times 10^4}=$ | 200 | 82.8125 |
2,791 | If $y=x+\frac{1}{x}$, then $x^4+x^3-4x^2+x+1=0$ becomes: | $x^2(y^2+y-6)=0$ | 0 |
2,792 | Two right circular cones with vertices facing down as shown in the figure below contain the same amount of liquid. The radii of the tops of the liquid surfaces are $3$ cm and $6$ cm. Into each cone is dropped a spherical marble of radius $1$ cm, which sinks to the bottom and is completely submerged without spilling any liquid. What is the ratio of the rise of the liquid level in the narrow cone to the rise of the liquid level in the wide cone? | 4:1 | 0 |
2,793 | What is equal to $\sqrt{9-6\sqrt{2}}+\sqrt{9+6\sqrt{2}}$? | $2\sqrt{6}$ | 0 |
2,794 | A telephone number has the form \text{ABC-DEF-GHIJ}, where each letter represents a different digit. The digits in each part of the number are in decreasing order; that is, $A > B > C$, $D > E > F$, and $G > H > I > J$. Furthermore, $D$, $E$, and $F$ are consecutive even digits; $G$, $H$, $I$, and $J$ are consecutive odd digits; and $A + B + C = 9$. Find $A$. | 8 | 57.8125 |
2,795 | Some marbles in a bag are red and the rest are blue. If one red marble is removed, then one-seventh of the remaining marbles are red. If two blue marbles are removed instead of one red, then one-fifth of the remaining marbles are red. How many marbles were in the bag originally? | 22 | 80.46875 |
2,796 | Vertex $E$ of equilateral $\triangle{ABE}$ is in the interior of unit square $ABCD$. Let $R$ be the region consisting of all points inside $ABCD$ and outside $\triangle{ABE}$ whose distance from $AD$ is between $\frac{1}{3}$ and $\frac{2}{3}$. What is the area of $R$? | \frac{3-\sqrt{3}}{9} | 0 |
2,797 | Let $ABCD$ be a parallelogram with $\angle{ABC}=120^\circ$, $AB=16$ and $BC=10$. Extend $\overline{CD}$ through $D$ to $E$ so that $DE=4$. If $\overline{BE}$ intersects $\overline{AD}$ at $F$, then $FD$ is closest to | 3 | 3.90625 |
2,798 | Consider the set of all fractions $\frac{x}{y}$, where $x$ and $y$ are relatively prime positive integers. How many of these fractions have the property that if both numerator and denominator are increased by $1$, the value of the fraction is increased by $10\%$? | 1 | 36.71875 |
2,799 | Let points $A = (0,0)$, $B = (1,2)$, $C = (3,3)$, and $D = (4,0)$. Quadrilateral $ABCD$ is cut into equal area pieces by a line passing through $A$. This line intersects $\overline{CD}$ at point $\left (\frac{p}{q}, \frac{r}{s} \right )$, where these fractions are in lowest terms. What is $p + q + r + s$? | 58 | 2.34375 |
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