dmayhem93/agieval-sat-math huggingface dataset:
A group of 202 people went on an overnight camping trip, taking 60 tents with them. Some of the tents held 2 people each, and the rest held 4 people each. Assuming all the tents were filled to capacity and every person got to sleep in a tent, exactly how many of the tents were 2-person tents? Answer Choices: (A)30 (B)20 (C)19 (D)18 11
Answer index (0=A, 1=B, 2=C, 3=D): 2
If $\frac{2 a}{b}=\frac{1}{2}$, what is the value of $\frac{b}{a} ?$ Answer Choices: (A)$\frac{1}{8}$ (B)$\frac{1}{4}$ (C)2 (D)4
Answer index (0=A, 1=B, 2=C, 3=D): 3
Oil and gas production in a certain area dropped from 4 million barrels in 2000 to 1.9 million barrels in 2013. Assuming that the oil and gas production decreased at a constant rate, which of the following linear functions $f$ best models the production, in millions of barrels, $t$ years after the year 2000 ? Answer Choices: (A)$f(t)=\frac{21}{130} t+4$ (B)$f(t)=\frac{19}{130} t+4$ (C)$f(t)=-\frac{21}{130} t+4$ (D)$f(t)=-\frac{19}{130} t+4$
Answer index (0=A, 1=B, 2=C, 3=D): 2
$$\begin{aligned}& y=x^{2}+3 x-7 \\& y-5 x+8=0\end{aligned}$$How many solutions are there to the system of equations above? Answer Choices: (A)There are exactly 4 solutions. (B)There are exactly 2 solutions. (C)There is exactly 1 solution. (D)There are no solutions.
Answer index (0=A, 1=B, 2=C, 3=D): 2
$$\begin{aligned}& g(x)=2 x-1 \\& h(x)=1-g(x)\end{aligned}$$The functions $g$ and $h$ are defined above. What is the value of $h(0)$ ? Answer Choices: (A)-2 (B)0 (C)1 (D)2
Answer index (0=A, 1=B, 2=C, 3=D): 3
One pound of grapes costs $\$ 2$. At this rate, how many dollars will $c$ pounds of grapes cost? Answer Choices: (A)$2 c$ (B)$2+c$ (C)$\frac{2}{c}$ (D)$\frac{c}{2}$
Answer index (0=A, 1=B, 2=C, 3=D): 0
In a random sample of 200 cars of a particular model, 3 have a manufacturing defect. At this rate, how many of 10,000 cars of the same model will have a manufacturing defect? Answer Choices: (A)150 (B)200 (C)250 (D)300
Answer index (0=A, 1=B, 2=C, 3=D): 0
Two types of tickets were sold for a concert held at an amphitheater. Tickets to sit on a bench during the concert cost $\$ 75$ each, and tickets to sit on the lawn during the concert cost $\$ 40$ each. Organizers of the concert announced that 350 tickets had been sold and that $\$ 19,250$ had been raised through ticket sales alone. Which of the following systems of equations could be used to find the number of tickets for bench seats, $B$, and the number of tickets for lawn seats, $L$, that were sold for the concert? Answer Choices: (A)$(75 B)(40 L)=1,950$ $B+L=350$ (B)$40 B+75 L=19,250$ $B+L=350$ (C)$75 B+40 L=350$ $B+L=19,250$ (D)$75 B+40 L=19,250$ $B+L=350$
Answer index (0=A, 1=B, 2=C, 3=D): 3
In the $x y$-plane, the graph of which of the following equations is a line with a slope of 3 ? Answer Choices: (A)$y=\frac{1}{3} x$ (B)$y=x-3$ (C)$y=3 x+2$ (D)$y=6 x+3$
Answer index (0=A, 1=B, 2=C, 3=D): 2
$$x+1=\frac{2}{x+1}$$In the equation above, which of the following is a possible value of $x+1$ ? Answer Choices: (A)$1-\sqrt{2}$ (B)$\sqrt{2}$ (C)2 (D)4
Answer index (0=A, 1=B, 2=C, 3=D): 1
Roberto is an insurance agent who sells two types of policies: a $\$ 50,000$ policy and a $\$ 100,000$ policy. Last month, his goal was to sell at least 57 insurance policies. While he did not meet his goal, the total value of the policies he sold was over $\$ 3,000,000$. Which of the following systems of inequalities describes $x$, the possible number of $\$ 50,000$ policies, and $y$, the possible number of $\$ 100,000$ policies, that Roberto sold last month? Answer Choices: (A)$x+y<57$ $50,000 x+100,000 y<3,000,000$ (B)$x+y>57$ $50,000 x+100,000 y>3,000,000$ (C)$x+y<57$ $50,000 x+100,000 y>3,000,000$ (D)$x+y>57$ $50,000 x+100,000 y<3,000,000$
Answer index (0=A, 1=B, 2=C, 3=D): 2
$$\begin{aligned}& 2 x-y=8 \\& x+2 y=4\end{aligned}$$For the system of equations above, what is the value of $x+y$ ? Answer Choices: (A)-1 (B)4 (C)5 (D)20
Answer index (0=A, 1=B, 2=C, 3=D): 1
Which of the following is equivalent to $2\left(x^{2}-x\right)+3\left(x^{2}-x\right) ?$ Answer Choices: (A)$5 x^{2}-5 x$ (B)$5 x^{2}+5 x$ (C)$5 x$ (D)$5 x^{2}$
Answer index (0=A, 1=B, 2=C, 3=D): 0
Which of the following statements is true about the graph of the equation $2 y-3 x=-4$ in the $x y$-plane? Answer Choices: (A)It has a negative slope and a positive $y$-intercept. (B)It has a negative slope and a negative $y$-intercept. (C)It has a positive slope and a positive $y$-intercept. (D)It has a positive slope and a negative $y$-intercept.
Answer index (0=A, 1=B, 2=C, 3=D): 3
The front of a roller-coaster car is at the bottom of a hill and is 15 feet above the ground. If the front of the roller-coaster car rises at a constant rate of 8 feet per second, which of the following equations gives the height $h$, in feet, of the front of the roller-coaster car $s$ seconds after it starts up the hill? Answer Choices: (A)$h=8 s+15$ (B)$h=15 s+\frac{335}{8}$ (C)$h=8 s+\frac{335}{15}$ (D)$h=15 s+8$
Answer index (0=A, 1=B, 2=C, 3=D): 0
$$C=75 h+125$$The equation above gives the amount $C$, in dollars, an electrician charges for a job that takes $h$ hours. Ms. Sanchez and Mr. Roland each hired this electrician. The electrician worked 2 hours longer on Ms. Sanchez's job than on Mr. Roland's job. How much more did the electrician charge Ms. Sanchez than Mr. Roland? Answer Choices: (A)$\$ 75$ (B)$\$ 125$ (C)$\$ 150$ (D)$\$ 275$
Answer index (0=A, 1=B, 2=C, 3=D): 2
If $\frac{8}{x}=160$, what is the value of $x ?$ Answer Choices: (A)1,280 (B)80 (C)20 (D)0.05
Answer index (0=A, 1=B, 2=C, 3=D): 3
$$2 a x-15=3(x+5)+5(x-1)$$In the equation above, $a$ is a constant. If no value of $x$ satisfies the equation, what is the value of $a$ ? Answer Choices: (A)1 (B)2 (C)4 (D)8
Answer index (0=A, 1=B, 2=C, 3=D): 2
$$(a x+3)\left(5 x^{2}-b x+4\right)=20 x^{3}-9 x^{2}-2 x+12$$The equation above is true for all $x$, where $a$ and $b$ are constants. What is the value of $a b$ ? Answer Choices: (A)18 (B)20 (C)24 (D)40
Answer index (0=A, 1=B, 2=C, 3=D): 2
$$\frac{x}{x-3}=\frac{2 x}{2}$$Which of the following represents all the possible values of $x$ that satisfy the equation above? Answer Choices: (A)0 and 2 (B)0 and 4 (C)-4 and 4 (D)4
Answer index (0=A, 1=B, 2=C, 3=D): 1
$$\frac{1}{2 x+1}+5$$Which of the following is equivalent to the expression above for $x>0$ ? Answer Choices: (A)$\frac{2 x+5}{2 x+1}$ (B)$\frac{2 x+6}{2 x+1}$ (C)$\frac{10 x+5}{2 x+1}$ (D)$\frac{10 x+6}{2 x+1}$
Answer index (0=A, 1=B, 2=C, 3=D): 3
What is the set of all solutions to the equation $\sqrt{x+2}=-x ?$ Answer Choices: (A)$\{-1,2\}$ (B)$\{-1\}$ (C)$\{2\}$ (D)There are no solutions to the given equation.
Answer index (0=A, 1=B, 2=C, 3=D): 1
What value of $x$ satisfies the equation $3 x+3=27$ ? Answer Choices: (A)3 (B)8 (C)10 (D)27
Answer index (0=A, 1=B, 2=C, 3=D): 1
If $\frac{2 n}{5}=10$, what is the value of $2 n-1 ?$ Answer Choices: (A)24 (B)49 (C)50 (D)99
Answer index (0=A, 1=B, 2=C, 3=D): 1
$$\sqrt{x^{2}}=x$$Which of the following values of $x$ is NOT a solution to the equation above? Answer Choices: (A)-4 (B)0 (C)1 (D)3
Answer index (0=A, 1=B, 2=C, 3=D): 0
Washington High School randomly selected freshman, sophomore, junior, and senior students for a survey about potential changes to next year's schedule. Of students selected for the survey, $\frac{1}{4}$ were freshmen and $\frac{1}{3}$ were sophomores. Half of the remaining selected students were juniors. If336 students were selected for the survey, how many were seniors? Answer Choices: (A)240 (B)140 (C)120 (D)70
Answer index (0=A, 1=B, 2=C, 3=D): 3
Plant A is currently 20 centimeters tall, and Plant B is currently 12 centimeters tall. The ratio of the heights of Plant A to Plant B is equal to the ratio of the heights of Plant $\mathrm{C}$ to Plant D. If Plant $\mathrm{C}$ is 54 centimeters tall, what is the height of Plant $\mathrm{D}$, in centimeters? Answer Choices: (A)32.4 (B)44.0 (C)62.0 (D)90.0
Answer index (0=A, 1=B, 2=C, 3=D): 0
Biologists found a new species of pale shrimp at the world's deepest undersea vent, the Beebe Vent Field. The vent is 3.1 miles below the sea's surface.Approximately how many kilometers below the sea's surface is the vent? ( 1 kilometer $\approx 0.6214$ miles) Answer Choices: (A)2 (B)3 (C)4 (D)5
Answer index (0=A, 1=B, 2=C, 3=D): 3
A cargo helicopter delivers only 100-pound packages and 120-pound packages. For each delivery trip, the helicopter must carry at least 10 packages, and the total weight of the packages can be at most 1,100 pounds. What is the maximum number of 120-pound packages that the helicopter can carry per trip? Answer Choices: (A)2 (B)4 (C)5 (D)6
Answer index (0=A, 1=B, 2=C, 3=D): 2
A company purchased a machine valued at $\$ 120,000$. The value of the machine depreciates by the same amount each year so that after 10 years the value will be $\$ 30,000$. Which of the following equations gives the value, $v$, of the machine, in dollars, $t$ years after it was purchased for $0 \leq t \leq 10 ?$ Answer Choices: (A)$v=30,000-9,000 t$ (B)$v=120,000-9,000 t$ (C)$v=120,000+9,000 t$ (D)$v=120,000-30,000 t$
Answer index (0=A, 1=B, 2=C, 3=D): 1
Line $m$ in the $x y$-plane contains the points $(2,4)$ and $(0,1)$. Which of the following is an equation of line $m$ ? Answer Choices: (A)$y=2 x+3$ (B)$y=2 x+4$ (C)$y=\frac{3}{2} x+3$ (D)$y=\frac{3}{2} x+1$
Answer index (0=A, 1=B, 2=C, 3=D): 3
$$(4 x+4)(a x-1)-x^{2}+4$$In the expression above, $a$ is a constant. If the expression is equivalent to $b x$, where $b$ is a constant, what is the value of $b$ ? Answer Choices: (A)-5 (B)-3 (C)0 (D)12
Answer index (0=A, 1=B, 2=C, 3=D): 1
If $2 w+4 t=14$ and $4 w+5 t=25$, what is the value of $2 w+3 t ?$ Answer Choices: (A)6 (B)10 (C)13 (D)17
Answer index (0=A, 1=B, 2=C, 3=D): 2
Jennifer bought a box of Crunchy Grain cereal. The nutrition facts on the box state that a serving size of the cereal is $\frac{3}{4}$ cup and provides 210 calories, 50 of which are calories from fat. In addition, each serving of the cereal provides 180 milligrams of potassium, which is $5 \%$ of the daily allowance for adults.Q: If $p$ percent of an adult's daily allowance of potassium is provided by $x$ servings of Crunchy Grain cereal per day, which of the following expresses $p$ in terms of $x$ ? Answer Choices: (A)$p=0.5 x$ (B)$p=5 x$ (C)$p=(0.05)^{x}$ (D)$p=(1.05)^{x}$
Answer index (0=A, 1=B, 2=C, 3=D): 1
Jennifer bought a box of Crunchy Grain cereal. The nutrition facts on the box state that a serving size of the cereal is $\frac{3}{4}$ cup and provides 210 calories, 50 of which are calories from fat. In addition, each serving of the cereal provides 180 milligrams of potassium, which is $5 \%$ of the daily allowance for adults.Q: On Tuesday, Jennifer will mix Crunchy Grain cereal with Super Grain cereal for her breakfast. Super Grain cereal provides 240 calories per cup. If the total number of calories in one cup of Jennifer's mixture is 270, how much Super Grain cereal is in one cup of the mixture? Answer Choices: (A)$\frac{1}{8} \operatorname{cup}$ (B)$\frac{1}{4} \operatorname{cup}$ (C)$\frac{1}{3} \operatorname{cup}$ (D)$\frac{1}{2} \operatorname{cup}$
Answer index (0=A, 1=B, 2=C, 3=D): 1
The graph of the exponential function $h$ in the $x y$-plane, where $y=h(x)$, has a $y$-intercept of $d$, where $d$ is a positive constant. Which of the following could define the function $h$ ? Answer Choices: (A)$h(x)=-3(d)^{x}$ (B)$h(x)=3(x) d$ (C)$h(x)=d(-x)^{3}$ (D)$h(x)=d(3)^{x}$
Answer index (0=A, 1=B, 2=C, 3=D): 3
The weights, in pounds, for 15 horses in a stable were reported, and the mean, median, range, and standard deviation for the data were found. The horse with the lowest reported weight was found to actually weigh 10 pounds less than its reported weight. What value remains unchanged if the four values are reported using the corrected weight? Answer Choices: (A)Mean (B)Median (C)Range (D)Standard deviation
Answer index (0=A, 1=B, 2=C, 3=D): 1
Near the end of a US cable news show, the host invited viewers to respond to a poll on the show's website that asked, "Do you support the new federal policy discussed during the show?" At the end of the show, the host reported that $28 \%$ responded "Yes," and $70 \%$ responded "No." Which of the following best explains why the results are unlikely to represent the sentiments of the population of the United States? Answer Choices: (A)The percentages do not add up to $100 \%$, so any possible conclusions from the poll are invalid. (B)Those who responded to the poll were not a random sample of the population of the United States. (C)There were not $50 \%$ "Yes" responses and $50 \%$ "No" responses. (D)The show did not allow viewers enough time to respond to the poll.
Answer index (0=A, 1=B, 2=C, 3=D): 1
If $f(x)=5 x^{2}-3$ and $f(x+a)=5 x^{2}+30 x+42$, what is the value of $a$ ? Answer Choices: (A)-30 (B)$\quad-3$ (C)3 (D)30
Answer index (0=A, 1=B, 2=C, 3=D): 2
If $\sin x^{\circ}=a$, which of the following must be true for all values of $x$ ? Answer Choices: (A)$\cos x^{\circ}=a$ (B)$\sin \left(90^{\circ}-x^{\circ}\right)=a$ (C)$\cos \left(90^{\circ}-x^{\circ}\right)=a$ (D)$\sin \left(x^{2}\right)^{\circ}=a^{2}$
Answer index (0=A, 1=B, 2=C, 3=D): 2
$$h(x)=-16 x^{2}+100 x+10$$The quadratic function above models the height above the ground $h$, in feet, of a projectile $x$ seconds after it had been launched vertically. If $y=h(x)$ is graphed in the $x y$-plane, which of the following represents the real-life meaning of the positive $x$-intercept of the graph? Answer Choices: (A)The initial height of the projectile (B)The maximum height of the projectile (C)The time at which the projectile reaches its maximum height (D)The time at which the projectile hits the ground
Answer index (0=A, 1=B, 2=C, 3=D): 3
In the $x y$-plane, the graph of the polynomial function $f$ crosses the $x$-axis at exactly two points, $(a, 0)$ and $(b, 0)$, where $a$ and $b$ are both positive. Which of the following could define $f$ ? Answer Choices: (A)$f(x)=(x-a)(x-b)$ (B)$f(x)=(x+a)(x+b)$ (C)$f(x)=(x-a)(x+b)$ (D)$f(x)=x(x-a)(x-b)$
Answer index (0=A, 1=B, 2=C, 3=D): 0
If $y=3 x^{2}+6 x+2$ is graphed in the $x y$-plane, which of the following characteristics of the graph is displayed as a constant or coefficient in the equation? Answer Choices: (A)$y$-coordinate of the vertex (B)$x$-intercept $(\mathrm{s})$ (C)$y$-intercept (D)$x$-intercept of the line of symmetry
Answer index (0=A, 1=B, 2=C, 3=D): 2