Unnamed: 0
int64 0
40.3k
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stringlengths 10
5.15k
| ground_truth
stringlengths 1
1.22k
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float64 0
100
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|---|---|---|---|
2,200 | Two integers have a sum of 26. When two more integers are added to the first two integers the sum is 41. Finally when two more integers are added to the sum of the previous four integers the sum is 57. What is the minimum number of odd integers among the 6 integers? | 1 | 94.53125 |
2,201 | The number of circular pipes with an inside diameter of $1$ inch which will carry the same amount of water as a pipe with an inside diameter of $6$ inches is: | 36 | 93.75 |
2,202 | In our number system the base is ten. If the base were changed to four you would count as follows:
$1,2,3,10,11,12,13,20,21,22,23,30,\ldots$ The twentieth number would be: | 110 | 99.21875 |
2,203 | A refrigerator is offered at sale at $250.00 less successive discounts of 20% and 15%. The sale price of the refrigerator is: | 77\% of 250.00 | 0 |
2,204 | There are four more girls than boys in Ms. Raub's class of $28$ students. What is the ratio of number of girls to the number of boys in her class? | 4 : 3 | 2.34375 |
2,205 | $\frac{2^1+2^0+2^{-1}}{2^{-2}+2^{-3}+2^{-4}}$ equals | 8 | 89.84375 |
2,206 | A ball with diameter 4 inches starts at point A to roll along the track shown. The track is comprised of 3 semicircular arcs whose radii are $R_1 = 100$ inches, $R_2 = 60$ inches, and $R_3 = 80$ inches, respectively. The ball always remains in contact with the track and does not slip. What is the distance the center of the ball travels over the course from A to B? | 238\pi | 0.78125 |
2,207 | The decimal representation of \(\frac{1}{20^{20}}\) consists of a string of zeros after the decimal point, followed by a 9 and then several more digits. How many zeros are in that initial string of zeros after the decimal point? | 26 | 35.9375 |
2,208 | The number of solutions to \{1,~2\} \subseteq~X~\subseteq~\{1,~2,~3,~4,~5\}, where $X$ is a subset of \{1,~2,~3,~4,~5\} is | 6 | 0 |
2,209 | Suppose one of the eight lettered identical squares is included with the four squares in the T-shaped figure outlined. How many of the resulting figures can be folded into a topless cubical box? | 6 | 4.6875 |
2,210 | For any real value of $x$ the maximum value of $8x - 3x^2$ is: | \frac{16}{3} | 96.875 |
2,211 | Steve's empty swimming pool will hold $24,000$ gallons of water when full. It will be filled by $4$ hoses, each of which supplies $2.5$ gallons of water per minute. How many hours will it take to fill Steve's pool? | 40 | 96.875 |
2,212 | The taxi fare in Gotham City is $2.40 for the first $\frac{1}{2}$ mile and additional mileage charged at the rate $0.20 for each additional 0.1 mile. You plan to give the driver a $2 tip. How many miles can you ride for $10? | 3.3 | 72.65625 |
2,213 | To be continuous at $x = -1$, the value of $\frac{x^3 + 1}{x^2 - 1}$ is taken to be: | -\frac{3}{2} | 76.5625 |
2,214 | Let $n=x-y^{x-y}$. Find $n$ when $x=2$ and $y=-2$. | -14 | 93.75 |
2,215 | Triangle $ABC$ is inscribed in a circle. The measure of the non-overlapping minor arcs $AB$, $BC$ and $CA$ are, respectively, $x+75^{\circ} , 2x+25^{\circ},3x-22^{\circ}$. Then one interior angle of the triangle is: | $61^{\circ}$ | 0 |
2,216 | Distinct points $A$, $B$, $C$, and $D$ lie on a line, with $AB=BC=CD=1$. Points $E$ and $F$ lie on a second line, parallel to the first, with $EF=1$. A triangle with positive area has three of the six points as its vertices. How many possible values are there for the area of the triangle? | 3 | 82.8125 |
2,217 | Two candles of the same length are made of different materials so that one burns out completely at a uniform rate in $3$ hours and the other in $4$ hours. At what time P.M. should the candles be lighted so that, at 4 P.M., one stub is twice the length of the other? | 1:36 | 39.0625 |
2,218 | The smallest sum one could get by adding three different numbers from the set $\{ 7,25,-1,12,-3 \}$ is | 3 | 96.09375 |
2,219 | If $xy = b$ and $\frac{1}{x^2} + \frac{1}{y^2} = a$, then $(x + y)^2$ equals: | $b(ab + 2)$ | 0 |
2,220 | Let $m$ be a positive integer and let the lines $13x+11y=700$ and $y=mx-1$ intersect in a point whose coordinates are integers. Then m can be: | 6 | 90.625 |
2,221 | It takes Clea 60 seconds to walk down an escalator when it is not moving, and 24 seconds when it is moving. How many seconds would it take Clea to ride the escalator down when she is not walking? | 40 | 95.3125 |
2,222 | On a trip to the beach, Anh traveled 50 miles on the highway and 10 miles on a coastal access road. He drove three times as fast on the highway as on the coastal road. If Anh spent 30 minutes driving on the coastal road, how many minutes did his entire trip take? | 80 | 83.59375 |
2,223 | $\triangle BAD$ is right-angled at $B$. On $AD$ there is a point $C$ for which $AC=CD$ and $AB=BC$. The magnitude of $\angle DAB$ is: | $60^{\circ}$ | 0 |
2,224 | The units digit of $3^{1001} 7^{1002} 13^{1003}$ is | 3 | 0 |
2,225 | What is the value of the product \[
\left(\frac{1\cdot3}{2\cdot2}\right)\left(\frac{2\cdot4}{3\cdot3}\right)\left(\frac{3\cdot5}{4\cdot4}\right)\cdots\left(\frac{97\cdot99}{98\cdot98}\right)\left(\frac{98\cdot100}{99\cdot99}\right)?
\] | \frac{50}{99} | 90.625 |
2,226 | How many non-congruent right triangles with positive integer leg lengths have areas that are numerically equal to $3$ times their perimeters? | 7 | 0 |
2,227 | A town's population increased by $1,200$ people, and then this new population decreased by $11\%$. The town now had $32$ less people than it did before the $1,200$ increase. What is the original population? | 10000 | 82.03125 |
2,228 | The increasing sequence $3, 15, 24, 48, \ldots$ consists of those positive multiples of 3 that are one less than a perfect square. What is the remainder when the 1994th term of the sequence is divided by 1000? | 935 | 0 |
2,229 | The set of points satisfying the pair of inequalities $y>2x$ and $y>4-x$ is contained entirely in quadrants: | I and II | 0 |
2,230 | The sum $2\frac{1}{7} + 3\frac{1}{2} + 5\frac{1}{19}$ is between | $10\frac{1}{2} \text{ and } 11$ | 0 |
2,231 | Toothpicks of equal length are used to build a rectangular grid as shown. If the grid is 20 toothpicks high and 10 toothpicks wide, then the number of toothpicks used is | 430 | 39.0625 |
2,232 | If $x$ is the cube of a positive integer and $d$ is the number of positive integers that are divisors of $x$, then $d$ could be | 202 | 0 |
2,233 | What is \(\sum^{100}_{i=1} \sum^{100}_{j=1} (i+j) \)? | 1{,}010{,}000 | 0 |
2,234 | A bag contains only blue balls and green balls. There are $6$ blue balls. If the probability of drawing a blue ball at random from this bag is $\frac{1}{4}$, then the number of green balls in the bag is | 18 | 100 |
2,235 | What is the value of $2-(-2)^{-2}$? | \frac{7}{4} | 97.65625 |
2,236 | A child builds towers using identically shaped cubes of different colors. How many different towers with a height 8 cubes can the child build with 2 red cubes, 3 blue cubes, and 4 green cubes? (One cube will be left out.) | 1260 | 44.53125 |
2,237 | The graphs of $y = -|x-a| + b$ and $y = |x-c| + d$ intersect at points $(2,5)$ and $(8,3)$. Find $a+c$. | 10 | 54.6875 |
2,238 | Suppose $n^{*}$ means $\frac{1}{n}$, the reciprocal of $n$. For example, $5^{*}=\frac{1}{5}$. How many of the following statements are true?
i) $3^*+6^*=9^*$
ii) $6^*-4^*=2^*$
iii) $2^*\cdot 6^*=12^*$
iv) $10^*\div 2^* =5^*$ | 2 | 84.375 |
2,239 | How many of the first $2018$ numbers in the sequence $101, 1001, 10001, 100001, \dots$ are divisible by $101$? | 505 | 66.40625 |
2,240 | $\log p+\log q=\log(p+q)$ only if: | p=\frac{q}{q-1} | 3.90625 |
2,241 | What is the reciprocal of $\frac{1}{2}+\frac{2}{3}$? | \frac{6}{7} | 90.625 |
2,242 | A cell phone plan costs $20$ dollars each month, plus $5$ cents per text message sent, plus $10$ cents for each minute used over $30$ hours. In January Michelle sent $100$ text messages and talked for $30.5$ hours. How much did she have to pay? | 28.00 | 40.625 |
2,243 | An isosceles triangle is a triangle with two sides of equal length. How many of the five triangles on the square grid below are isosceles?
[asy] for(int a=0; a<12; ++a) { draw((a,0)--(a,6)); } for(int b=0; b<7; ++b) { draw((0,b)--(11,b)); } draw((0,6)--(2,6)--(1,4)--cycle,linewidth(3)); draw((3,4)--(3,6)--(5,4)--cycle,linewidth(3)); draw((0,1)--(3,2)--(6,1)--cycle,linewidth(3)); draw((7,4)--(6,6)--(9,4)--cycle,linewidth(3)); draw((8,1)--(9,3)--(10,0)--cycle,linewidth(3)); [/asy] | 4 | 91.40625 |
2,244 | The value of $10^{\log_{10}7}$ is: | 7 | 91.40625 |
2,245 | If the ratio of the legs of a right triangle is $1: 2$, then the ratio of the corresponding segments of the hypotenuse made by a perpendicular upon it from the vertex is: | 1: 4 | 76.5625 |
2,246 | If $\frac{x}{y}=\frac{3}{4}$, then the incorrect expression in the following is: | $\frac{1}{4}$ | 0 |
2,247 | A convex polyhedron $Q$ has vertices $V_1,V_2,\ldots,V_n$, and $100$ edges. The polyhedron is cut by planes $P_1,P_2,\ldots,P_n$ in such a way that plane $P_k$ cuts only those edges that meet at vertex $V_k$. In addition, no two planes intersect inside or on $Q$. The cuts produce $n$ pyramids and a new polyhedron $R$. How many edges does $R$ have? | 300 | 32.8125 |
2,248 | What is the value of
1-(-2)-3-(-4)-5-(-6)? | 5 | 51.5625 |
2,249 | Points $P$ and $Q$ are both in the line segment $AB$ and on the same side of its midpoint. $P$ divides $AB$ in the ratio $2:3$,
and $Q$ divides $AB$ in the ratio $3:4$. If $PQ=2$, then the length of $AB$ is: | 70 | 98.4375 |
2,250 | If $x=\frac{1-i\sqrt{3}}{2}$ where $i=\sqrt{-1}$, then $\frac{1}{x^2-x}$ is equal to | -1 | 88.28125 |
2,251 | Eight people are sitting around a circular table, each holding a fair coin. All eight people flip their coins and those who flip heads stand while those who flip tails remain seated. What is the probability that no two adjacent people will stand? | \frac{47}{256} | 20.3125 |
2,252 | What describes the set of values of $a$ for which the curves $x^2+y^2=a^2$ and $y=x^2-a$ in the real $xy$-plane intersect at exactly 3 points? | a>\frac{1}{2} | 47.65625 |
2,253 | If $f(2x)=\frac{2}{2+x}$ for all $x>0$, then $2f(x)=$ | \frac{8}{4+x} | 94.53125 |
2,254 | Let $x$ be chosen at random from the interval $(0,1)$. What is the probability that $\lfloor\log_{10}4x\rfloor - \lfloor\log_{10}x\rfloor = 0$? Here $\lfloor x\rfloor$ denotes the greatest integer that is less than or equal to $x$. | \frac{1}{6} | 14.0625 |
2,255 | Toothpicks are used to make a grid that is $60$ toothpicks long and $32$ toothpicks wide. How many toothpicks are used altogether? | 3932 | 32.03125 |
2,256 | In $\triangle ABC$, $E$ is the midpoint of side $BC$ and $D$ is on side $AC$.
If the length of $AC$ is $1$ and $\measuredangle BAC = 60^\circ, \measuredangle ABC = 100^\circ, \measuredangle ACB = 20^\circ$ and
$\measuredangle DEC = 80^\circ$, then the area of $\triangle ABC$ plus twice the area of $\triangle CDE$ equals | \frac{\sqrt{3}}{8} | 1.5625 |
2,257 | A number of students from Fibonacci Middle School are taking part in a community service project. The ratio of $8^{\text{th}}$-graders to $6^{\text{th}}$-graders is $5:3$, and the the ratio of $8^{\text{th}}$-graders to $7^{\text{th}}$-graders is $8:5$. What is the smallest number of students that could be participating in the project? | 89 | 93.75 |
2,258 | Circles with centers $P, Q$ and $R$, having radii $1, 2$ and $3$, respectively, lie on the same side of line $l$ and are tangent to $l$ at $P', Q'$ and $R'$, respectively, with $Q'$ between $P'$ and $R'$. The circle with center $Q$ is externally tangent to each of the other two circles. What is the area of triangle $PQR$? | \sqrt{6}-\sqrt{2} | 46.875 |
2,259 | A high school basketball game between the Raiders and Wildcats was tied at the end of the first quarter. The number of points scored by the Raiders in each of the four quarters formed an increasing geometric sequence, and the number of points scored by the Wildcats in each of the four quarters formed an increasing arithmetic sequence. At the end of the fourth quarter, the Raiders had won by one point. Neither team scored more than $100$ points. What was the total number of points scored by the two teams in the first half? | 34 | 17.96875 |
2,260 | Consider the $12$-sided polygon $ABCDEFGHIJKL$, as shown. Each of its sides has length $4$, and each two consecutive sides form a right angle. Suppose that $\overline{AG}$ and $\overline{CH}$ meet at $M$. What is the area of quadrilateral $ABCM$? | 88/5 | 0.78125 |
2,261 | The sum to infinity of the terms of an infinite geometric progression is $6$. The sum of the first two terms is $4\frac{1}{2}$. The first term of the progression is: | 9 or 3 | 0 |
2,262 | Several sets of prime numbers, such as $\{7,83,421,659\}$ use each of the nine nonzero digits exactly once. What is the smallest possible sum such a set of primes could have? | 207 | 77.34375 |
2,263 | What is the largest number of solid $2 \times 2 \times 1$ blocks that can fit in a $3 \times 2 \times 3$ box? | 4 | 10.9375 |
2,264 | Let $S$ be the set $\{1,2,3,...,19\}$. For $a,b \in S$, define $a \succ b$ to mean that either $0 < a - b \le 9$ or $b - a > 9$. How many ordered triples $(x,y,z)$ of elements of $S$ have the property that $x \succ y$, $y \succ z$, and $z \succ x$? | 855 | 84.375 |
2,265 | $\frac{16+8}{4-2}=$ | 12 | 38.28125 |
2,266 | In how many ways can $345$ be written as the sum of an increasing sequence of two or more consecutive positive integers? | 6 | 0 |
2,267 | A closed box with a square base is to be wrapped with a square sheet of wrapping paper. The box is centered on the wrapping paper with the vertices of the base lying on the midlines of the square sheet of paper, as shown in the figure on the left. The four corners of the wrapping paper are to be folded up over the sides and brought together to meet at the center of the top of the box, point $A$ in the figure on the right. The box has base length $w$ and height $h$. What is the area of the sheet of wrapping paper?
[asy] size(270pt); defaultpen(fontsize(10pt)); filldraw(((3,3)--(-3,3)--(-3,-3)--(3,-3)--cycle),lightgrey); dot((-3,3)); label("$A$",(-3,3),NW); draw((1,3)--(-3,-1),dashed+linewidth(.5)); draw((-1,3)--(3,-1),dashed+linewidth(.5)); draw((-1,-3)--(3,1),dashed+linewidth(.5)); draw((1,-3)--(-3,1),dashed+linewidth(.5)); draw((0,2)--(2,0)--(0,-2)--(-2,0)--cycle,linewidth(.5)); draw((0,3)--(0,-3),linetype("2.5 2.5")+linewidth(.5)); draw((3,0)--(-3,0),linetype("2.5 2.5")+linewidth(.5)); label('$w$',(-1,-1),SW); label('$w$',(1,-1),SE); draw((4.5,0)--(6.5,2)--(8.5,0)--(6.5,-2)--cycle); draw((4.5,0)--(8.5,0)); draw((6.5,2)--(6.5,-2)); label("$A$",(6.5,0),NW); dot((6.5,0)); [/asy] | 2(w+h)^2 | 0.78125 |
2,268 | The letters $\text{A}$, $\text{J}$, $\text{H}$, $\text{S}$, $\text{M}$, $\text{E}$ and the digits $1$, $9$, $8$, $9$ are "cycled" separately as follows and put together in a numbered list:
\[\begin{tabular}[t]{lccc} & & AJHSME & 1989 \ & & & \ 1. & & JHSMEA & 9891 \ 2. & & HSMEAJ & 8919 \ 3. & & SMEAJH & 9198 \ & & ........ & \end{tabular}\]
What is the number of the line on which $\text{AJHSME 1989}$ will appear for the first time? | 12 | 82.8125 |
2,269 | A six place number is formed by repeating a three place number; for example, $256256$ or $678678$, etc. Any number of this form is always exactly divisible by: | 1001 | 70.3125 |
2,270 | What is the maximum value of $n$ for which there is a set of distinct positive integers $k_1, k_2, \dots, k_n$ for which
\[k_1^2 + k_2^2 + \dots + k_n^2 = 2002?\] | 16 | 3.125 |
2,271 | Let $\angle ABC = 24^\circ$ and $\angle ABD = 20^\circ$. What is the smallest possible degree measure for $\angle CBD$? | 4 | 98.4375 |
2,272 | In unit square $ABCD,$ the inscribed circle $\omega$ intersects $\overline{CD}$ at $M,$ and $\overline{AM}$ intersects $\omega$ at a point $P$ different from $M.$ What is $AP?$ | \frac{\sqrt{5}}{10} | 46.09375 |
2,273 | Six bags of marbles contain $18, 19, 21, 23, 25$ and $34$ marbles, respectively. One bag contains chipped marbles only. The other $5$ bags contain no chipped marbles. Jane takes three of the bags and George takes two of the others. Only the bag of chipped marbles remains. If Jane gets twice as many marbles as George, how many chipped marbles are there? | 23 | 81.25 |
2,274 | The number of points equidistant from a circle and two parallel tangents to the circle is: | 3 | 24.21875 |
2,275 | Kate bakes a $20$-inch by $18$-inch pan of cornbread. The cornbread is cut into pieces that measure $2$ inches by $2$ inches. How many pieces of cornbread does the pan contain? | 90 | 99.21875 |
2,276 | Horses $X, Y$ and $Z$ are entered in a three-horse race in which ties are not possible. The odds against $X$ winning are $3:1$ and the odds against $Y$ winning are $2:3$, what are the odds against $Z$ winning? (By "odds against $H$ winning are $p:q$" we mean the probability of $H$ winning the race is $\frac{q}{p+q}$.) | 17:3 | 90.625 |
2,277 | Externally tangent circles with centers at points $A$ and $B$ have radii of lengths $5$ and $3$, respectively. A line externally tangent to both circles intersects ray $AB$ at point $C$. What is $BC$? | 12 | 60.9375 |
2,278 | In the figure below, $3$ of the $6$ disks are to be painted blue, $2$ are to be painted red, and $1$ is to be painted green. Two paintings that can be obtained from one another by a rotation or a reflection of the entire figure are considered the same. How many different paintings are possible?
[asy]
size(100);
pair A, B, C, D, E, F;
A = (0,0);
B = (1,0);
C = (2,0);
D = rotate(60, A)*B;
E = B + D;
F = rotate(60, A)*C;
draw(Circle(A, 0.5));
draw(Circle(B, 0.5));
draw(Circle(C, 0.5));
draw(Circle(D, 0.5));
draw(Circle(E, 0.5));
draw(Circle(F, 0.5));
[/asy] | 12 | 7.8125 |
2,279 | Vertex $E$ of equilateral $\triangle ABE$ is in the interior of square $ABCD$, and $F$ is the point of intersection of diagonal $BD$ and line segment $AE$. If length $AB$ is $\sqrt{1+\sqrt{3}}$ then the area of $\triangle ABF$ is | \frac{\sqrt{3}}{2} | 37.5 |
2,280 | In an $h$-meter race, Sunny is exactly $d$ meters ahead of Windy when Sunny finishes the race. The next time they race, Sunny sportingly starts $d$ meters behind Windy, who is at the starting line. Both runners run at the same constant speed as they did in the first race. How many meters ahead is Sunny when Sunny finishes the second race? | \frac {d^2}{h} | 60.9375 |
2,281 | Call a $7$-digit telephone number $d_1d_2d_3-d_4d_5d_6d_7$ memorable if the prefix sequence $d_1d_2d_3$ is exactly the same as either of the sequences $d_4d_5d_6$ or $d_5d_6d_7$ (possibly both). Assuming that each $d_i$ can be any of the ten decimal digits $0, 1, 2, \ldots, 9$, the number of different memorable telephone numbers is | 19990 | 3.125 |
2,282 | Mr. Harman needs to know the combined weight in pounds of three boxes he wants to mail. However, the only available scale is not accurate for weights less than $100$ pounds or more than $150$ pounds. So the boxes are weighed in pairs in every possible way. The results are $122$, $125$ and $127$ pounds. What is the combined weight in pounds of the three boxes? | 187 | 57.03125 |
2,283 | If $\frac{m}{n}=\frac{4}{3}$ and $\frac{r}{t}=\frac{9}{14}$, the value of $\frac{3mr-nt}{4nt-7mr}$ is: | -\frac{11}{14} | 85.9375 |
2,284 | $2\left(1-\frac{1}{2}\right) + 3\left(1-\frac{1}{3}\right) + 4\left(1-\frac{1}{4}\right) + \cdots + 10\left(1-\frac{1}{10}\right)=$ | 45 | 99.21875 |
2,285 | If $x$ and $\log_{10} x$ are real numbers and $\log_{10} x<0$, then: | $0<x<1$ | 0 |
2,286 | A softball team played ten games, scoring $1,2,3,4,5,6,7,8,9$, and $10$ runs. They lost by one run in exactly five games. In each of the other games, they scored twice as many runs as their opponent. How many total runs did their opponents score? | 45 | 37.5 |
2,287 | The number halfway between $\frac{1}{6}$ and $\frac{1}{4}$ is | \frac{5}{24} | 96.875 |
2,288 | Circles $A, B,$ and $C$ each have radius 1. Circles $A$ and $B$ share one point of tangency. Circle $C$ has a point of tangency with the midpoint of $\overline{AB}.$ What is the area inside circle $C$ but outside circle $A$ and circle $B?$ | 2 | 35.9375 |
2,289 | The number $10!$ ($10$ is written in base $10$), when written in the base $12$ system, ends with exactly $k$ zeros. The value of $k$ is | 4 | 86.71875 |
2,290 | Segments $AD=10$, $BE=6$, $CF=24$ are drawn from the vertices of triangle $ABC$, each perpendicular to a straight line $RS$, not intersecting the triangle. Points $D$, $E$, $F$ are the intersection points of $RS$ with the perpendiculars. If $x$ is the length of the perpendicular segment $GH$ drawn to $RS$ from the intersection point $G$ of the medians of the triangle, then $x$ is: | \frac{40}{3} | 95.3125 |
2,291 | Sara makes a staircase out of toothpicks as shown:
[asy] size(150); defaultpen(linewidth(0.8)); path h = ellipse((0.5,0),0.45,0.015), v = ellipse((0,0.5),0.015,0.45); for(int i=0;i<=2;i=i+1) { for(int j=0;j<=3-i;j=j+1) { filldraw(shift((i,j))*h,black); filldraw(shift((j,i))*v,black); } } [/asy]
This is a 3-step staircase and uses 18 toothpicks. How many steps would be in a staircase that used 180 toothpicks? | 12 | 35.9375 |
2,292 | Chandra pays an on-line service provider a fixed monthly fee plus an hourly charge for connect time. Her December bill was $12.48, but in January her bill was $17.54 because she used twice as much connect time as in December. What is the fixed monthly fee? | 6.24 | 0 |
2,293 | Travis has to babysit the terrible Thompson triplets. Knowing that they love big numbers, Travis devises a counting game for them. First Tadd will say the number $1$, then Todd must say the next two numbers ($2$ and $3$), then Tucker must say the next three numbers ($4$, $5$, $6$), then Tadd must say the next four numbers ($7$, $8$, $9$, $10$), and the process continues to rotate through the three children in order, each saying one more number than the previous child did, until the number $10,000$ is reached. What is the $2019$th number said by Tadd? | 5979 | 3.125 |
2,294 | A right triangle has perimeter $32$ and area $20$. What is the length of its hypotenuse? | \frac{59}{4} | 11.71875 |
2,295 | Three runners start running simultaneously from the same point on a 500-meter circular track. They each run clockwise around the course maintaining constant speeds of 4.4, 4.8, and 5.0 meters per second. The runners stop once they are all together again somewhere on the circular course. How many seconds do the runners run? | 2500 | 50 |
2,296 | Tony works $2$ hours a day and is paid $\$0.50$ per hour for each full year of his age. During a six month period Tony worked $50$ days and earned $\$630$. How old was Tony at the end of the six month period? | 13 | 82.8125 |
2,297 | If $\log_8{3}=p$ and $\log_3{5}=q$, then, in terms of $p$ and $q$, $\log_{10}{5}$ equals | \frac{3pq}{1+3pq} | 78.125 |
2,298 | How many sequences of $0$s and $1$s of length $19$ are there that begin with a $0$, end with a $0$, contain no two consecutive $0$s, and contain no three consecutive $1$s? | 65 | 93.75 |
2,299 | Andy the Ant lives on a coordinate plane and is currently at $(-20, 20)$ facing east (that is, in the positive $x$-direction). Andy moves $1$ unit and then turns $90^{\circ}$ left. From there, Andy moves $2$ units (north) and then turns $90^{\circ}$ left. He then moves $3$ units (west) and again turns $90^{\circ}$ left. Andy continues his progress, increasing his distance each time by $1$ unit and always turning left. What is the location of the point at which Andy makes the $2020$th left turn? | $(-1030, -990)$ | 0 |
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