niryuu/sni-each-converted huggingface dataset:
If a, b, and x are positive integers and \(\triangle(a,x,b)\) is defined as the number of possible different triangles with sides of lengths a, b, and x, what is the value of \(\triangle(2,x,7)\)?
(A)2 (B)3 (C)4 (D)5 (E)6
Output: B
Two cylindrical tanks have the same height, but the radius of one tank equals the diameter of the other. If the volume of the larger is \(k\%\) more than the volume of the smaller, \(k\) =
(A)50 (B)100 (C)200 (D)300 (E)400
Output: D
How many lines can be drawn from one vertex of a cube to the other vertices of the cube, such that the lines are not parallel to any edge of the cube?
(A)4 (B)6 (C)7 (D)24 (E)42
Output: A
A square, stained-glass window pane is composed of 36 individual squares of colored glass. Some individual squares are red and others are blue. Which of the following is NOT a possible ratio of red to blue squares in the window?
(A)1 : 35 (B)1 : 7 (C)2 : 7 (D)5 : 7 (E)4 : 5
Output: B
If \(d\) is the length of a diagonal of a square, what does \(d^2\) represent?
(A)the area of the square (B)twice the area of the square (C)\(\frac { 1 } { 2 } \) the area of the square (D)4 times the area of the square (E)\(\frac { 1 } { 4 } \) the area of the square
Output: B
What is the y-intercept of the linear equation \(3y - 33x = 12\)?
(A)\(-4\) (B)\(-2\) (C)0 (D)3 (E)4
Output: E
Points L, M, and N lie in a plane. If the distance between L and M is 4, and the distance between M and N is 9, which of the following could be the distance between L and N? I. 5 II. 8 III. 13
(A)I only (B)II only (C)III only (D)I and III (E)I, II and III
Output: E
What is the area of a circle that is circumscribed around a square that has sides of length 6?
(A)\(6\pi\) (B)\(18\pi\) (C)\(18 \sqrt { 2 } \pi\) (D)\(36\pi\) (E)\(72\pi\)
Output: B
If the circumference of a circle is equal to the perimeter of a square whose sides are \(7t\), what is the radius of the circle?
(A)1 (B)2 (C)4 (D)\(\pi\) (E)\(2\pi\)
Output: B
If \(c(x) = x^2 - 6\), how many times does the graph of \(c(x)\) cross the x-axis?
(A)0 (B)1 (C)2 (D)3 (E)4
Output: C
In square PQRS, point T is the midpoint of side \(\overline { QR } \). If the area of PQRS is 3, what is the area of quadrilateral PQTS ?
(A)\(\frac { 3 } { 2 } \) (B)2 (C)\(\frac { 9 } { 4 } \) (D)\(\frac { 3 \sqrt { 3 } } { 2 } \) (E)\(2 \sqrt { 3 } \)
Output: C
If the perimeter of equilateral triangle E equals the perimeter of square S, what is the ratio of the length of a side of square S to the length of a side of triangle E?
(A)1:1 (B)2:3 (C)3:4 (D)4:3 (E)2:1
Output: C
The center of a circle is at the origin of a rectangular coordinate plane. If the points \((-3,0)\), \((0,3)\), and \((3,0)\) are on the circumference of the circle, what is the probability that a randomly selected point from within the circle will fall within the triangle formed by those three points?
(A)\(\frac{1}{4}\) (B)\(\frac{1}{\pi}\) (C)\(\frac{1}{3}\) (D)\(\frac{\pi}{4}\) (E)\(\frac{\pi}{3}\)
Output: B
What is the area of the quadrilateral whose vertices are at (1, 1), (5, 1), (5, 5) and (3, 5)?
(A)8 (B)12 (C)16 (D)24 (E)10 + 2\(\sqrt { 2 } \)
Output: B
In a standard coordinate plane, if Q is the point \((1,5)\), R is the point \((1,1)\), and S is the point \((4,1)\), what is the length of QS?
(A)3 (B)4 (C)5 (D)6 (E)7
Output: C
If the graph of the function g in the xy-plane contains the points (0,4), (-2,0), and (2,0), which of the following could be true? I. The graph of g is a parabola. II. The graph of g has a maximum value. III. The graph of g is a line.
(A)I only (B)II only (C)III only (D)I and II only (E)I, II, and III
Output: D
In \(\triangle { EFG } \), the length of \(\overline { EF } \) is 9 and the length of \(\overline { EG } \) is 12. Each of the following could be the length of side \(\overline { FG } \) EXCEPT
(A)20 (B)16 (C)8 (D)4 (E)2
Output: E
What is the y-intercept of the line that passes through the points \((1, 21)\) and \((4, 42)\)?
(A)0 (B)7 (C)9 (D)14 (E)19
Output: D
Three lines intersect within a circle. What is the greatest number of separate, non-overlapping regions that can be formed inside the circle by the intersection of the lines?
(A)Four (B)Five (C)Six (D)Seven (E)Eight or more
Output: D
What is the maximum number of points of intersection between a square and a circle?
(A)less than 4 (B)4 (C)6 (D)8 (E)more than 8
Output: D
A(-3,2) B(1,2) C(6,-1) The coordinates of points A, B and C in the xy- plane are given above. What is the area of \(\triangle { ABC } \) ?
(A)6 (B)8 (C)10 (D)12 (E)18
Output: A
What is the equation of the line that passes through the points \((3,4)\) and \((-1,5)\)?
(A)\(x + 4y = 19\) (B)\(3x + 4y = 19\) (C)\(3x + 4y = 20\) (D)\(4x + y = 19\) (E)\(4x + y = 20\)
Output: A
Jim has identical drinking glasses each in the shape of a right circular cylinder with internal diameter of 3 inches. He pours milk from a gallon jug into each glass until it is full. If the height of milk in each glass is about 6 inches, what is the largest number of full milk glasses that he can pour from one gallon of milk? (Note: There are 231 cubic inches in 1 gallon.)
(A)2 (B)4 (C)5 (D)6
Output: C
\begin{gather} x^2 + y^2 + 4x - 2y = -1 \end{gather} The equation of a circle in the xy-plane is shown above. What is the radius of the circle?
(A)2 (B)3 (C)4 (D)9
Output: A
Let the lengths of the sides of a triangle be represented by \(x + 3\), \(2x - 3\), and \(3x - 5\). If the perimeter of the triangle is 25, what is the length of the shortest side?
(A)5 (B)7 (C)8 (D)10 (E)It cannot be determined from the information given
Output: B
In the xy-plane, the equation of line l is \(y = 3x + 2\). If line m is the reflection of line l in the y-axis, what is the equation of line m?
(A)\(y = -3x + 2\) (B)\(y = -3x - 2\) (C)\(y = 3x - 2\) (D)\(y = \frac{1}{3}x + 2\) (E)\(y = -\frac{1}{3}x + 2\)
Output: A
A rectangle has a perimeter equal to the circumference of a circle of radius 3. If the width of the rectangle is 3, what is its length?
(A)\(3\pi - 3\) (B)\(4.5\pi - 3\) (C)\(6\pi - 6\) (D)\(9\pi - 3\) (E)\(9\pi - 6\)
Output: A
If a rectangular solid that has a width of 8, a length of 8 and a height of 16 is divided into 16 identical cubes, what is the length of the edge of one of the cubes?
(A)2 (B)3 (C)4 (D)6 (E)8
Output: C
Let P and Q be points 2 inches apart, and let A be the area, in square inches, of a circle that passes through P and Q. Which of the following is the set of all possible values of A?
(A)\(0 < A\) (B)\(0 < A \leq \pi\) (C)\(A = \pi\) (D)\(A > \pi\) (E)\(A \geq \pi\)
Output: E
A line segment joining two points on the circumference of a circle is 1 inch from the center of the circle at its closest point. If the circle has a 2-inch radius, what is the length of the line segment?
(A)1 (B)\(\sqrt{3}\) (C)2 (D)\(2\sqrt{3}\) (E)\(4\sqrt{3}\)
Output: D
The length and width of a certain rectangle are both decreased by 50 percent. If the length and width of the new rectangle are then increased by 40 percent, the area of resulting rectangle is what percent less than the area of the original rectangle?
(A)10\% (B)45\% (C)49\% (D)51\% (E)90\%
Output: D
What is the measure, in degrees, of the smaller angle formed by the hour hand and the minute hand of a clock at 11:20?
(A)120 (B)130 (C)135 (D)140 (E)150
Output: D
A line passes through the points (0, a) and (b, O). Which of the following is the slope of the line?
(A)\(-\frac { a } { b } \) (B)\(-\frac { b } { a } \) (C)\(\frac { a } { b } \) (D)\(\frac { b } { a } \) (E)\(\frac { a } { ab } \)
Output: A
What is the volume, in cubic inches, of a cube whose surface area is 60 square inches?
(A)\(10\sqrt { 10 } \) (B)\(15\sqrt { 15 } \) (C)\(60\sqrt { 60 } \) (D)1000 (E)3375
Output: A
What is the diameter of a circle whose area is A?
(A)\(2\sqrt { \frac { A } { \pi } } \) (B)\(\sqrt { \frac { A } { \pi } } \) (C)\(\frac { A } { 2\pi } \) (D)\(\frac { A } { \pi } \) (E)\(\frac { 2\sqrt { A } } { \pi } \)
Output: A
Line l has an undefined slope and contains the point \((-2,3)\). Which of the following points is also on line l?
(A)\((0, 3)\) (B)\((5, 5)\) (C)\((0, 0)\) (D)\((3, -2)\) (E)\((-2, 5)\)
Output: E
If a square and an equilateral triangle have equal perimeters, what is the ratio of the area of the triangle to the area of the square?
(A)\(\frac { 4\sqrt { 3 } } { 9 } \) (B)\(\frac { 4 } { 9 } \) (C)\(\frac { 3 } { 4 } \) (D)\(\frac { 1 } { 1 } \) (E)\(\frac { 4 } { 3 } \)
Output: A
The earth makes one complete rotation about its axis every 24 hours. Assuming it rotates at a constant rate, through how many degrees would Goannaville, Australia rotate from 1:00 PM on January 2 to 4:00 PM on January 3?
(A)202 degrees (B)250 degrees (C)350 degrees (D)363 degrees (E)405 degrees
Output: E
If the lengths of the sides of a certain triangle are a, b, and c, which of the following statements could be true?
(A)\(c = b + a\) (B)\(c = b - a\) (C)\(c = 2a + b\) (D)\(c + 2 = a + b + 3\) (E)\(c + 3 = a + b + 2\)
Output: E
A right circular cylinder vase with an inner base radius of 6 inches is filled with water to a height of 20 inches. After a smaller solid right circular cylinder with base radius of 4 inches is then completely submerged in the water, the height of water is 24 inches. What is the height, in inches, of smaller cylinder?
(A)8 (B)9 (C)10 (D)11 (E)12
Output: B
The length of a playground is 3 feet more than its width. If the length of the playground is 13 feet, what is the area of the playground in square feet?
(A)93 (B)130 (C)145 (D)153 (E)160
Output: B
What is the perimeter of a triangle with vertices \((-1, 1)\), \((5, 1)\), and \((2, 5)\)?
(A)16 (B)13 (C)\(6 + 2\sqrt{7}\) (D)11 (E)\(6 + 2\sqrt{5}\)
Output: A
A 1,000 square meter parcel of land is bought for \$300,000 and then divided into five equally sized plots. The first four plots are then sold at a price of \$320 per square meter. If the overall profit is to be at least 20\%, what is the minimum selling price of the fifth plot?
(A)\$64,000 (B)\$68,000 (C)\$80,000 (D)\$96,000 (E)\$104,000
Output: E
If the circumference of circle I is equal to the diameter of circle II, what is the ratio of the area of circle II to the area of circle I?
(A)\(\frac { 1 } { \pi^2 } \) (B)\(\sqrt { \pi } \) (C)\(\pi\) (D)\(\pi^2\) (E)\(4\pi^2\)
Output: D
In a coordinate plane, if points C\((2, 5)\), D\((-1, 2)\), and E\((x, y)\) lie on line l, which of the following could be the coordinates of point E?
(A)\((0, 1)\) (B)\((1, 1)\) (C)\((0, 2)\) (D)\((1, 3)\) (E)\((1, 4)\)
Output: E
In \(\triangle { ABC } \) two sides, AB and BC are equal. Side AC has a length of 5, and the perimeter of \(\triangle { ABC } \) is 13. If the measure of angle ABC is \(x\), which of the following must be true about \(x\)?
(A)\(x < 60\) (B)\(60 < x < 90\) (C)\(x = 90\) (D)\(x > 90\) (E)It cannot be determined from the information given.
Output: B
In rectangle EFGH, \(\overline { EF } \perp \overline { EH } \) and GH = 4. Which of the following could be the length of \(\overline { EG } \)?
(A)1 (B)2 (C)3 (D)4 (E)5
Output: E
If a rectangular rug measures 72 inches by 96 inches, what is its area in square feet? (1 foot = 12 inches)
(A)864 (B)576 (C)336 (D)144 (E)48
Output: E
If the average (arithmetic mean) of the measures of two angles of a quadrilateral is 60 degrees, what is the average of the measures of the other two angles?
(A)\(60\degree\) (B)\(90\degree\) (C)\(120\degree\) (D)\(180\degree\) (E)\(240\degree\)
Output: C
C, D, and E are points on a line, in that order. If the length of segment CE is 30, and the length of segment CD is twice the length of DE, what is the length of segment CD?
(A)10 (B)15 (C)20 (D)25 (E)30
Output: C
Points A, B, C, and D lie on the line in that order. If \(AB = 2BC = 3CD = k\) and \(CD = 6\), what is the distance from A to C?
(A)27 (B)33 (C)38 (D)42 (E)54
Output: A
If the perimeter of a regular polygon is 21, which of the following could be the length of one side of the polygon?
(A)6 (B)5 (C)4 (D)3 (E)2
Output: D
Points A, B and C are three vertices of a triangle. The location of point X is such that AX = BX. Which of the following could be true? I. X is on \(\overline { AB } \) II. X is inside \(\triangle { ABC } \) III. X is outside \(\triangle { ABC } \)
(A)I only (B)III only (C)I and II only (D)II and III only (E)I, II and III
Output: E
If the length of one side of a triangle is 6 and the length of another side is 2, which of the following CANNOT be the length of the third side of the triangle?
(A)5 (B)6 (C)7 (D)7.5 (E)8
Output: E
In square \(ABCD\), vertex \(A\) is at (-1, -1) and vertex \(C\) is at (4, 2). What is the area of square \(ABCD\)?
(A)9 (B)15 (C)17 (D)25 (E)34
Output: C
A circular grass field has a circumference of \(120\sqrt { \pi } \) meters. If Eric can mow 400 square meters of grass per hour, how many hours will he take to mow the entire field?
(A)4 (B)5 (C)6 (D)8 (E)9
Output: E
In a certain polygon, all of the angles are equal and all of the sides are of equal length. Point Q is a vertex of the polygon. If four diagonals can be drawn from point Q to the other vertices of the polygon, how many sides does the polygon have?
(A)Eight (B)Seven (C)Six (D)Five (E)Four
Output: B
A triangle has a perimeter of 16 and one side of length 4. If the lengths of the other two sides are equal, what is the length of each of the other two sides?
(A)5 (B)6 (C)7 (D)8 (E)9
Output: B
If A is point (-4, 1) and B is point (2, 1) what is the area of the circle that has \(\overline { AB } \) as a diameter?
(A)\(3\pi\) (B)\(6\pi\) (C)\(9\pi\) (D)\(12\pi\) (E)\(36\pi\)
Output: C
The graph of \(y = x - 2\) is drawn on a set of coordinate axes. If the graph of \(y = x + 7\) is then drawn on the same axes, how does the second graph compare to the first?
(A)The second graph will be 9 units above the first. (B)The second graph will be 3 units above the first. (C)The second graph will be 5 units bellow the first. (D)The second graph will be 9 units bellow the first. (E)The second graph will have a greater slope than the first.
Output: A
Which of the following is the distance between the points (7, 3) and (11, 0) in the xy-coordinate plane?
(A)4 (B)5 (C)6 (D)7 (E)8
Output: B
Square ABCD in the coordinate plane has points A(1,3), B(5,7) and C(9,3). Which of the following could be the coordinates of point D?
(A)(3,1) (B)(3,-3) (C)(5,-1) (D)(5,3) (E)(7,-5)
Output: C
Which of the following could be the lengths of the sides of a triangle?
(A)3, 5 and 8 (B)3, 6 and 10 (C)4, 5 and 2 (D)5, 9 and 15 (E)10, 20 and 8
Output: C
A frame 2 inches wide is placed around a rectangular picture with dimensions 8 inches by 12 inches. What is the area of the frame in square inches?
(A)44 (B)96 (C)128 (D)144 (E)168
Output: B
In the xy-plane, the parabola with equation y = (x - 11)^2 intersects the line with equation y = 25 at two points, A and B. What is the length of \overline{AB}?
(A)10 (B)12 (C)14 (D)16
Output: A
A rectangular box is 4 inches long, 10 inches wide, and 15 inches high. If exactly 60 smaller identical rectangular boxes can be stored perfectly in this larger box, which of the following could be the dimensions, in inches, of these smaller boxes?
(A)2 by 5 by 6 (B)3 by 4 by 6 (C)3 by 5 by 6 (D)4 by 5 by 6 (E)5 by 6 by 12
Output: A
The volume of a cylinder whose height is 4 and whose radius is 2 is how many times the volume of a cylinder whose height is 2 and whose radius is 4?
(A)\(\frac { 1 } { 4 } \) (B)\(\frac { 1 } { 2 } \) (C)1 (D)2 (E)4
Output: B
Lines l and m and two circles lie in a plane. If l passes through the center of the two circles and m is perpendicular to l, which of the following could NOT be the number of points at which m intersects the circles?
(A)0 (B)1 (C)2 (D)4 (E)5
Output: E
The length of the diagonal of a square is \(j + 3\). Which of the following represents the area of the square?
(A)\(j^2 + 9\) (B)\(j^2 + 6j + 9\) (C)\((j^2 + 9) \sqrt { 2 } \) (D)\(\frac { j^2 + 9 } { 2 } \) (E)\(\frac { j^2 + 6j + 9 } { 2 } \)
Output: E
In \(\triangle { XYZ } \), the length of \(\overline { XY } \) is 5 and the length of \(\overline { YZ } \) is 18. Which of the following could not be the length of \(\overline { ZX } \)?
(A)12.5 (B)13.5 (C)15 (D)16 (E)16.5
Output: A
A square and an equilateral triangle each have sides of length 5. What is the ratio of the area of the square to the area of the triangle?
(A)\(\frac { 4 } { 3 } \) (B)\(\frac { 16 } { 9 } \) (C)\(\frac { \sqrt { 3 } } { 4 } \) (D)\(\frac { 4\sqrt { 3 } } { 3 } \) (E)\(\frac { 16\sqrt { 3 } } { 9 } \)
Output: D
The hypotenuse of an isosceles triangle has endpoints (4, 3) and (9, 8). What is the length of one of the legs of the triangle?
(A)3 (B)5 (C)7 (D)9 (E)11
Output: B
Both \(\triangle { ABC } \) and \(\triangle { AED } \) are equilateral. If \(AD = \frac { 2 } { 3 } DC\), then the perimeter of \(\triangle { AED } \) is what fraction of the perimeter of \(\triangle { ABC } \)?
(A)\(\frac { 1 } { 3 } \) (B)\(\frac { 2 } { 5 } \) (C)\(\frac { 3 } { 5 } \) (D)\(\frac { 2 } { 3 } \) (E)\(\frac { 4 } { 5 } \)
Output: B
Container A and container B are right circular cylinders. Container A has a radius of 4 inches and a height of 5 inches while container B has a radius of 2 inches and a height of 10 inches. Sarah pours equal amounts of oil into both containers and finds that the height of the oil in container A is 2 inches. What is the height of the oil in container B ?
(A)8 inches (B)8.5 inches (C)9 inches (D)9.5 inches (E)10 inches
Output: A
What is the slope of a line with the equation \(y + 3 = 5(x - 2)\) ?
(A)7 (B)5 (C)3 (D)10 (E)13
Output: B
Some clay is shaped into a sphere with a radius of 2 inches. If more clay is added to the original sphere so that the radius is increased by 4 inches, then the volume of the new sphere is how many times greater than the volume of the original sphere?
(A)3 (B)8 (C)27 (D)64 (E)208
Output: C
Line l has a slope of 1 and contains the point \((1,2)\). Which of the following points is also on line l?
(A)\((1, 1)\) (B)\((2, 2)\) (C)\((1, 3)\) (D)\((0, 2)\) (E)\((2, 3)\)
Output: E
Six lines intersect at one point to form 12 equal angles that are non-overlapping. What is the measure, in degrees, of one of these angles?
(A)15 (B)20 (C)30 (D)45 (E)60
Output: C
A rectangle is twice as long as it is wide. If the width is a, what is the length of a diagonal?
(A)\(a\sqrt { 2 } \) (B)\(a\sqrt { 3 } \) (C)\(a\sqrt { 5 } \) (D)\(3a\) (E)\(5a\)
Output: C
A circle with radius r is inscribed in a square. If a point within the square is randomly selected, what is the probability that the point will not be within the circle?
(A)\(\frac { \pi } { 4 } \) (B)\(\frac { \pi - 4 } { 4 } \) (C)\(\frac { 4 - \pi } { 4 } \) (D)\(\pi r\) (E)\(4r\)
Output: C
In the xy-coordinate plane, the center of a circle is at ( 4, 0) and a point on the circle is at (7, 4). What is the area of the circle?
(A)\(4 \pi\) (B)\(9 \pi\) (C)\(16 \pi\) (D)\(25 \pi\) (E)\(36 \pi\)
Output: D
If A is at (3, -1) and B is at (5, 6) what is the slope of the perpendicular bisector of segment \(\overline { AB } \) ?
(A)\(-\frac { 7 } { 2 } \) (B)\(-\frac { 2 } { 5 } \) (C)\(-\frac { 2 } { 7 } \) (D)\(\frac { 2 } { 7 } \) (E)\(\frac { 2 } { 5 } \)
Output: C
If \(A, B, C\), and \(D\) lie on the same straight line, and if \(AC = 2CD = 3BD\), what is the value of the ratio \(\frac { BC } { CD } \)?
(A)\(\frac { 1 } { 6 } \) (B)\(\frac { 1 } { 3 } \) (C)\(\frac { 1 } { 2 } \) (D)\(\frac { 5 } { 3 } \) (E)It cannot be determined from the information given
Output: E
Two sides of a right triangle are 5 and 6. Which of the following could be the length of the third side? I. \(\sqrt { 11 } \) II. \(\sqrt { 31 } \) III. \(\sqrt { 61 } \)
(A)I only (B)III only (C)I and II only (D)I and III only (E)I, II, and III
Output: D
A line in the xy-plane passes through the origin and has a slope of \frac{1}{7}. Which of the following points lies on the line?
(A)(0, 7) (B)(1, 7) (C)(7, 7) (D)(14, 2)
Output: D
In the xy-plane, a line contains the points (-3,7), (1,-3) and (3, t). What is the value of t ?
(A)-13 (B)-11 (C)-10 (D)-9 (E)-8
Output: E
R, S and T are points with RT = 2RS. Which of the following could be true? I. R, S and T are the vertices of a right triangle. II. R, S and T are three of the vertices of a square. III. R, S and T all lie on the circumference of a circle.
(A)I only (B)III only (C)I and II only (D)I and III only (E)I, II, and III
Output: D
A rectangular swimming pool has a volume of 8,640 cubic feet. If its length is 60 feet and its depth is 6 feet, what is the width of the pool in feet?
(A)16 (B)19 (C)24 (D)28 (E)36
Output: C
Which of the following equation defines the line in the xy coordinate system above?
(A)\(y = - \frac { 1 } { 3 } x - 2\) (B)\(y = - \frac { 1 } { 2 } x - 3\) (C)\(y = - 2x - 3\) (D)\(y = - 2x + 3\) (E)\(y = -3x - 2\)
Output: A
What is the volume, in cubic inches, of a cube whose total surface area is 216 square inches?
(A)6 (B)18 (C)36 (D)216 (E)1296
Output: D
A fire fighter with a 52-foot ladder approaches a burning building, which rests on level ground. If the top of the ladder must be at least 48 feet above ground level, what is the maximum possible distance, in feet, from the exact middle of the ladder to the wall of the building?
(A)0 (B)5 (C)10 (D)15 (E)20
Output: C
Three lines, \(\ell_1\), \(\ell_2\) and \(\ell_3\), intersect as shown. What is the value of \(m\) ?
(A)115 (B)120 (C)125 (D)130 (E)145
Output: B
A certain flag has a length that is 2 times its width. What is the width of a flag that has an area of 100?
(A)5 (B)\(5\sqrt { 2 } \) (C)10 (D)\(10\sqrt { 2 } \) (E)20
Output: B
The measures of the angles of a triangle, in degrees, can be expressed by the ratio 4:5:6. What is the sum of the measures of the largest and smallest angles?
(A)80 (B)100 (C)120 (D)140 (E)160
Output: C
If the surface area of a cube is \(150x^2\), what is the volume of the cube?
(A)\(8x^3\) (B)\(27x^3\) (C)\(64x^3\) (D)\(125x^3\) (E)\(150x^3\)
Output: D
The length of a line segment with endpoints L and P is a positive integer less than 24. N is the midpoint of \(\overline { LP } \), M is the midpoint of \(\overline { LN } \) and O is the midpoint of \(\overline { NP } \). Which of the following could be the distance between M and P?
(A)18 (B)17 (C)16 (D)15 (E)14
Output: D
What is the greatest number of pieces that can result from slicing a spherical orange with three straight cuts?
(A)5 (B)6 (C)7 (D)8 (E)9
Output: D
In a certain triangle, the measure of the largest angle is 40 degrees more than the measure of the middle-sized angle. If the measure of the smallest angle is 20 degrees, what is the degree measure of the largest angle?
(A)60 (B)80 (C)100 (D)120 (E)160
Output: C
If point \(M(a,b)\) is the midpoint of the line segment connecting point \(A(5,10)\) and point \(B(15,4)\), what is the value of \(a + b\)?
(A)5 (B)6 (C)7 (D)8 (E)9
Output: A
\begin{gather} nA = 360 \end{gather} The measure A, in degrees, of an exterior angle of a regular polygon is related to the number of sides, n, of the polygon by the formula above. If the measure of an exterior angle of a regular polygon is greater than 50 degrees, what is the greatest number of sides it can have?
(A)5 (B)6 (C)7 (D)8
Output: C
For any point on line \(\ell\), the product of the x-coordinate and the y-coordinate is less than or equal to zero. Which of the following could be the equation of line \(\ell\) ?
(A)\(y = -2\) (B)\(x = -2\) (C)\(y = -2x\) (D)\(y = -2x - 2\) (E)\(y = 2x - 2\)
Output: C
A rectangular box is constructed from ten square tiles, each of which has a perimeter of 24 centimeters. If the box is formed so that the tiles do not overlap, what is the volume of the box in cubic centimeters?
(A)432 (B)288 (C)240 (D)216 (E)36
Output: A
If A (2, -1) and B (4, 7) are the endpoints of a diameter of a circle, what is the area of the circle?
(A)\(16\pi\) (B)\(17\pi\) (C)\(18\pi\) (D)\(144\pi\) (E)\(1156\pi\)
Output: B
Which of the following has the same area as a circle with an area of \(16\pi\)?
(A)A circle with a radius of \(4\pi\) (B)A circle with a circumference of \(32\pi\) (C)A circle with a radius of 8 (D)A circle with a diameter of 4 (E)A circle with a circumference of \(8\pi\)
Output: E
In the standard x, y-coordinate plane, the center of circle O is the origin. If circle O has an area of \(25 \pi\), each of the following points lies on the circumference of the circle EXCEPT
(A)\((5, 0)\) (B)\((4, -4)\) (C)\((3, 4)\) (D)\((-3, 4)\) (E)\((-4, 3)\)
Output: B
The perimeter of square A is 4 times the perimeter of square B. If the perimeter of square B is given to be 18, then what is the length of a single side of square A?
(A)4.5 (B)18 (C)22 (D)48 (E)72
Output: B
If the length of one side of a triangle is 5, which of the following CANNOT be the lengths of the other two sides of the triangle?
(A)3 and 3 (B)3 and 5 (C)7 and 8 (D)7 and 3 (E)7 and 12
Output: E
If one angle in a right triangle is \(20\degree\), which of the following is the degree measure of another angle in the triangle?
(A)30 (B)40 (C)50 (D)60 (E)70
Output: E
What is the area of the circle whose center is at O (2, -2) and that passes through point P (3, 3)?
(A)\(2\pi\) (B)\(6\pi\) (C)\(10\pi\) (D)\(25\pi\) (E)\(26\pi\)
Output: E
The lengths of two sides of a triangle are \((x - 2)\) and \((x + 2)\), where \(x > 2\). Which of the following ranges includes all and only the possible values of the third side y?
(A)\(0 < y < x\) (B)\(0 < y < 2x\) (C)\(2 < y < x\) (D)\(4 < y < x\) (E)\(4 < y < 2x\)
Output: E
In \(\triangle { ABC } \), \(\overline { AB } = \overline { BC } \) and \(\overline { AB } \perp \overline { BC } \). If \(\overline { BC } = 10\), what is the area of the triangle?
(A)\(10 \sqrt { 2 } \) (B)25 (C)50 (D)\(50 \sqrt { 2 } \) (E)100
Output: C
If seven different lines lie in a plane, what is the greatest possible number of intersections?
(A)18 (B)20 (C)21 (D)22 (E)30
Output: C
If m is an integer and m, m + 1, and m + 2 are the lengths of the sides of a triangle, which of the following could be the value of m? I. 1 II. 10 III. 100
(A)I only (B)II only (C)III only (D)II and III only (E)I, II, and III
Output: D
The midpoint of segment \(\overline { PQ } \) is F , and the length of \(\overline { FQ } \) is \(3m\). What is the length of \(\overline { PQ } \) in terms of \( m\) ?
(A)\(\frac { 3 } { 2 } m\) (B)\(3m\) (C)\(4m\) (D)\(\frac { 9 } { 2 } m\) (E)\(6m\)
Output: E
A rectangular solid that has a width of 8, a length of 8, and a height of 12 is divided into 12 cubes, each of equal volume. What is the length of the edge of one of these cubes?
(A)4 (B)6 (C)8 (D)12 (E)64
Output: A
A rectangular box is 24 inches long, 10 inches wide, and 15 inches high. If exactly 60 smaller identical rectangular boxes can be stored perfectly in this larger box, which of the following could be the dimensions, in inches, of these smaller boxes?
(A)\(2 \times 5 \times 6\) (B)\(3 \times 4 \times 6\) (C)\(3 \times 5 \times 6\) (D)\(4 \times 5 \times 6\) (E)\(5 \times 6 \times 12\)
Output: A
\(A\) (5, 1) lies on a circle whose center is \(O\) (1, 5). If \(AB\) is a diameter, what are the coordinates of \(B\) ?
(A)(3, 3) (B)(6, 6) (C)(-1, 5) (D)(-1, 10) (E)(-3, 9)
Output: E
Lines m and n are parallel. If lines m and n are cut by three different transversals, what is the least number of points of intersection that can occur among the five lines?
(A)3 (B)4 (C)5 (D)6 (E)8
Output: B
Right triangle A has base b, height h, and area x. Rectangle B has length 2b and width 2h. What is the area of rectangle B in terms of x ?
(A)2x (B)4x (C)6x (D)7x (E)8x
Output: E
Points E and F lie in the xy-coordinate plane at (0,10) and (6,0), respectively. Which of the following is the midpoint of \(\overline { EF } \) ?
(A)(5,3) (B)(3,5) (C)(3,10) (D)(10,3) (E)(6,10)
Output: B
Points Q, R, and S lie on \(\overline { XZ } \) in such a way that Q is the midpoint of \(\overline { XZ } \), R is the midpoint of \(\overline { XQ } \) and S is the mid point of \(\overline { QZ } \). If QS = 4, what is length of RZ?
(A)8 (B)12 (C)16 (D)20 (E)24
Output: B
What is the length of each of the five equal sides of a regular pentagon if the perimeter of the pentagon is equal to the perimeter of a square whose area is 25?
(A)4 (B)5 (C)10 (D)20 (E)25
Output: A
Points P, Q, R, S, and T lie on a line in that order. If PR = 6 and PQ = QR = RS = ST, then PT =
(A)3 (B)6 (C)9 (D)12 (E)24
Output: D
If a rectangle of perimeter 12 has a width that is 2 less than its length, what is its area?
(A)6 (B)8 (C)10 (D)20 (E)35
Output: B
If the lengths of two sides of a triangle are 9 and 15, which of the following CANNOT be the length of the third side?
(A)5 (B)9 (C)10 (D)15 (E)20
Output: A
On the xy-coordinate plane, moving the graph of \(y = x - 5\) three units upward would result in the graph of which of the following functions?
(A)\(y = x - 8\) (B)\(y = x - 3\) (C)\(y = x - 2\) (D)\(y = x + 3\) (E)\(y = x + 5\)
Output: C
Points J, K, and L lie on a circle whose center is point O. If \(\overline {JK}\) passes through O, which of the following is true about triangle LOK?
(A)All three angles are less then 90 degrees. (B)One angle measures exactly 90 degrees. (C)At least one angle is greater than 90 degrees. (D)At least two of the angles have the same measure. (E)\(\overline {KO} = \overline{KL}\)
Output: D
If the legs of right triangle \(PQR\) have lengths 5 and 12, what is the perimeter of a right triangle with each side twice the length of its corresponding side in \(\triangle { PQR } \) ?
(A)12 (B)20 (C)30 (D)42 (E)60
Output: D
A triangle has vertices at points A, B, and C, which are located at (1, 0), (-3, 0), and (0, 5) respectively. What is the distance from the midpoint of \(\overline { AB } \) to point C ?
(A)3 (B)5 (C)\(\sqrt { 26 } \) (D)\(\sqrt { 29 } \) (E)\(\frac { \sqrt { 26 } + \sqrt { 34 } } { 2 } \)
Output: C
If lines \(\overline { BC } \) and \(\overline { BD } \) are each perpendicular to line \(\overline { AB } \), which of the following must be true?
(A)\(\overline { AB } \perp \overline { CD } \) (B)\(\overline { AB } \perp \overline { AC } \) (C)\(\overline { AC } \perp \overline { AD } \) (D)\(\overline { AB } \parallel \overline { CD } \) (E)\(\overline { BC } \perp \overline { BD } \)
Output: A
The measures of the three angles of a triangle are in the ratio of 5:5:10, and the length of the longest side is 10. From this information, which of the following can be determined? I. The area of the triangle II. The perimeter of the triangle III. The length of each of the three altitudes
(A)I only (B)II only (C)III only (D)I and II only (E)I, II, and III
Output: E