sample_index
stringlengths 1
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| problem_index
stringlengths 1
3
| question
stringlengths 8
612
| image
imagewidth (px) 537
6.84k
| answer
stringclasses 7
values | choices
listlengths 2
6
| prompt
stringlengths 42
1.14k
|
|---|---|---|---|---|---|---|
3760
|
752
|
The figure above shows a triangular prism. If the volume of the prism is $\frac{81}{4}$, what is the value of $x$ ??
|
(A)
|
[
"3",
"4",
"5",
"6"
] |
The figure above shows a triangular prism. If the volume of the prism is $\frac{81}{4}$, what is the value of $x$ ??
Options:
(A) 3
(B) 4
(C) 5
(D) 6
|
|
3765
|
753
|
In the figure shown above, if all the water in the rectangular container is poured into the cylinder, the water level rises from $h$ inches to $(h+x)$ inches. Which of the following is the best approximation of the value of $x$ ??
|
(D)
|
[
"3",
"3.4",
"3.8",
"4.2"
] |
In the figure shown above, if all the water in the rectangular container is poured into the cylinder, the water level rises from $h$ inches to $(h+x)$ inches. Which of the following is the best approximation of the value of $x$ ??
Options:
(A) 3
(B) 3.4
(C) 3.8
(D) 4.2
|
|
3770
|
754
|
In the figure above, what is the value of x??
|
(C)
|
[
"A.35",
"B.40",
"C.50",
"D.65",
"E.130",
""
] |
In the figure above, what is the value of x??
Options:
(A) A.35
(B) B.40
(C) C.50
(D) D.65
(E) E.130
(F)
|
|
3775
|
755
|
What is the value of x^2 + y^2??
|
(A)
|
[
"A.21",
"B.27",
"C.33",
"D.\\sqrt{593} (approximately 24.35)",
"E.\\sqrt{611} (approximately 24.72)",
""
] |
What is the value of x^2 + y^2??
Options:
(A) A.21
(B) B.27
(C) C.33
(D) D.\sqrt{593} (approximately 24.35)
(E) E.\sqrt{611} (approximately 24.72)
(F)
|
|
3780
|
756
|
What is the value of a^2 + b^2??
|
(E)
|
[
"A.8",
"B.10",
"C.11",
"D.12",
"E.13",
""
] |
What is the value of a^2 + b^2??
Options:
(A) A.8
(B) B.10
(C) C.11
(D) D.12
(E) E.13
(F)
|
|
3785
|
757
|
In the figure above. What is the value of x??
|
(C)
|
[
"A.90",
"B.120",
"C.144",
"D.156",
"E.168",
""
] |
In the figure above. What is the value of x??
Options:
(A) A.90
(B) B.120
(C) C.144
(D) D.156
(E) E.168
(F)
|
|
3790
|
758
|
In triangle ABC above, the bisector of angle BAC is AD. The length of AB is equal to the length of AC. What is the measure of angle BAC??
|
(D)
|
[
"A.15*\\degree",
"B.30*\\degree",
"C.45*\\degree",
"D.60*\\degree",
"E.75*\\degree"
] |
In triangle ABC above, the bisector of angle BAC is AD. The length of AB is equal to the length of AC. What is the measure of angle BAC??
Options:
(A) A.15*\degree
(B) B.30*\degree
(C) C.45*\degree
(D) D.60*\degree
(E) E.75*\degree
|
|
3795
|
759
|
In the figure above. What is the value of y??
|
(A)
|
[
"A.65",
"B.70",
"C.75",
"D.80",
"E.85",
""
] |
In the figure above. What is the value of y??
Options:
(A) A.65
(B) B.70
(C) C.75
(D) D.80
(E) E.85
(F)
|
|
3800
|
760
|
Lines AB and AC are tangent to the circle. If M is the midpoint of segment AC and the measure of angle PMC equals the measure of angle MPC, what is the length, in terms of r, of segment PA??
|
(E)
|
[
"A.r + 1",
"B.2*r",
"C.r*\\sqrt{2}",
"D.r*\\sqrt{3}",
"E.r*\\sqrt{5}",
""
] |
Lines AB and AC are tangent to the circle. If M is the midpoint of segment AC and the measure of angle PMC equals the measure of angle MPC, what is the length, in terms of r, of segment PA??
Options:
(A) A.r + 1
(B) B.2*r
(C) C.r*\sqrt{2}
(D) D.r*\sqrt{3}
(E) E.r*\sqrt{5}
(F)
|
|
3805
|
761
|
In the triangle above, which of the following must be true??
|
(C)
|
[
"A.p=r",
"B.p<r",
"C.p>r",
"D.p=4",
"E.p>4",
""
] |
In the triangle above, which of the following must be true??
Options:
(A) A.p=r
(B) B.p<r
(C) C.p>r
(D) D.p=4
(E) E.p>4
(F)
|
|
3810
|
762
|
In the figure above if the area of triangle CAF is equal to the area of rectangle CDEF, what is the length of segment AD??
|
(C)
|
[
"A.7/2",
"B.5",
"C.7",
"D.15/2",
"E.15",
""
] |
In the figure above if the area of triangle CAF is equal to the area of rectangle CDEF, what is the length of segment AD??
Options:
(A) A.7/2
(B) B.5
(C) C.7
(D) D.15/2
(E) E.15
(F)
|
|
3815
|
763
|
In the figure above, the radii of four circles are 1, 2, 3, and 4, respectively. What is the ratio of the area of the small shaded ring to the area of the large shaded ring??
|
(D)
|
[
"2",
"4",
"5",
"7",
"7",
""
] |
In the figure above, the radii of four circles are 1, 2, 3, and 4, respectively. What is the ratio of the area of the small shaded ring to the area of the large shaded ring??
Options:
(A) 2
(B) 4
(C) 5
(D) 7
(E) 7
(F)
|
|
3820
|
764
|
If the perimeter of the rectangle above is 72, what is the value of x??
|
(C)
|
[
"A.9",
"B.15",
"C.18",
"D.21",
"E.36",
""
] |
If the perimeter of the rectangle above is 72, what is the value of x??
Options:
(A) A.9
(B) B.15
(C) C.18
(D) D.21
(E) E.36
(F)
|
|
3840
|
768
|
In rectangle ABCD above, the area of the shaded region is given by \\pi*l*w/4. If the area of the shaded region is 7*\\pi, what is the total area, to the nearest whole number, of the unshaded regions of rectangle ABCD ??
|
(B)
|
[
"A.4",
"B.6",
"C.8",
"D.9",
"E.10",
""
] |
In rectangle ABCD above, the area of the shaded region is given by \\pi*l*w/4. If the area of the shaded region is 7*\\pi, what is the total area, to the nearest whole number, of the unshaded regions of rectangle ABCD ??
Options:
(A) A.4
(B) B.6
(C) C.8
(D) D.9
(E) E.10
(F)
|
|
3845
|
769
|
What fraction of the area of the figure is shaded??
|
(B)
|
[
"A.3/8",
"B.1/4",
"C.1/8",
"D.1/10",
"E.1/16",
""
] |
What fraction of the area of the figure is shaded??
Options:
(A) A.3/8
(B) B.1/4
(C) C.1/8
(D) D.1/10
(E) E.1/16
(F)
|
|
3860
|
772
|
In the figure above, lines l and m are not parallel. Which of the following cannot be the value of x??
|
(B)
|
[
"A.89",
"B.90",
"C.91",
"D.92",
"E.93",
""
] |
In the figure above, lines l and m are not parallel. Which of the following cannot be the value of x??
Options:
(A) A.89
(B) B.90
(C) C.91
(D) D.92
(E) E.93
(F)
|
|
3865
|
773
|
In the figure above. What is the value of x??
|
(A)
|
[
"A.15",
"B.20",
"C.25",
"D.40",
"E.65",
""
] |
In the figure above. What is the value of x??
Options:
(A) A.15
(B) B.20
(C) C.25
(D) D.40
(E) E.65
(F)
|
|
3870
|
774
|
In the figure above, what is the value of x??
|
(A)
|
[
"A.72",
"B.70",
"C.68",
"D.66",
"E.64",
""
] |
In the figure above, what is the value of x??
Options:
(A) A.72
(B) B.70
(C) C.68
(D) D.66
(E) E.64
(F)
|
|
3885
|
777
|
In the figure above. What is the value of z??
|
(A)
|
[
"A.80",
"B.60",
"C.50",
"D.40",
"E.10",
""
] |
In the figure above. What is the value of z??
Options:
(A) A.80
(B) B.60
(C) C.50
(D) D.40
(E) E.10
(F)
|
|
3890
|
778
|
In the figure above. If AB = AO, what is the degree measure of angle ABO??
|
(D)
|
[
"A.15*\\degree",
"B.30*\\degree",
"C.45*\\degree",
"D.60*\\degree",
"E.90*\\degree",
""
] |
In the figure above. If AB = AO, what is the degree measure of angle ABO??
Options:
(A) A.15*\degree
(B) B.30*\degree
(C) C.45*\degree
(D) D.60*\degree
(E) E.90*\degree
(F)
|
|
3895
|
779
|
In the figure above, what is the value of x??
|
(C)
|
[
"A.45",
"B.50",
"C.65",
"D.75",
"E.It cannot be determined from the information given",
""
] |
In the figure above, what is the value of x??
Options:
(A) A.45
(B) B.50
(C) C.65
(D) D.75
(E) E.It cannot be determined from the information given
(F)
|
|
3900
|
780
|
In triangle ABC above, and D is the midpoint of AC. What is the length of BC??
|
(A)
|
[
"A.3*\\sqrt{3}",
"B.4*\\sqrt{2}",
"C.4*\\sqrt{3}",
"D.6*\\sqrt{2}",
"E.5*\\sqrt{3}",
""
] |
In triangle ABC above, and D is the midpoint of AC. What is the length of BC??
Options:
(A) A.3*\sqrt{3}
(B) B.4*\sqrt{2}
(C) C.4*\sqrt{3}
(D) D.6*\sqrt{2}
(E) E.5*\sqrt{3}
(F)
|
|
3905
|
781
|
In the figure above, CDE is an equilateral triangle and ABCE is a square with an area of 1. What is the perimeter of polygon ABCDE??
|
(B)
|
[
"A.4",
"B.5",
"C.6",
"D.7",
"E.8",
""
] |
In the figure above, CDE is an equilateral triangle and ABCE is a square with an area of 1. What is the perimeter of polygon ABCDE??
Options:
(A) A.4
(B) B.5
(C) C.6
(D) D.7
(E) E.8
(F)
|
|
3910
|
782
|
In triangle ABC above, AB = AC, E is the midpoint of line AB, and D is the midpoint of line AC. If AE = x, what is length BC??
|
(B)
|
[
"A.6",
"B.8",
"C.2*x",
"D.4*x",
"E.4*x^2",
""
] |
In triangle ABC above, AB = AC, E is the midpoint of line AB, and D is the midpoint of line AC. If AE = x, what is length BC??
Options:
(A) A.6
(B) B.8
(C) C.2*x
(D) D.4*x
(E) E.4*x^2
(F)
|
|
3915
|
783
|
What is the value of z??
|
(B)
|
[
"A.60",
"B.70",
"C.80",
"D.90",
"E.100",
""
] |
What is the value of z??
Options:
(A) A.60
(B) B.70
(C) C.80
(D) D.90
(E) E.100
(F)
|
|
3920
|
784
|
If the circumference of the large circle is 36 and the radius of the small circle is half of the radius of the large circle, what is the length of the darkened arc??
|
(D)
|
[
"A.10",
"B.8",
"C.6",
"D.4",
"E.2",
""
] |
If the circumference of the large circle is 36 and the radius of the small circle is half of the radius of the large circle, what is the length of the darkened arc??
Options:
(A) A.10
(B) B.8
(C) C.6
(D) D.4
(E) E.2
(F)
|
|
3925
|
785
|
In the figure above, a shaded polygon which has equal sides and equal angles is partially covered with a sheet of blank paper. If x + y = 80, how many sides does the polygon have??
|
(B)
|
[
"A.Ten",
"B.Nine",
"C.Eight",
"D.Seven",
"E.Six",
""
] |
In the figure above, a shaded polygon which has equal sides and equal angles is partially covered with a sheet of blank paper. If x + y = 80, how many sides does the polygon have??
Options:
(A) A.Ten
(B) B.Nine
(C) C.Eight
(D) D.Seven
(E) E.Six
(F)
|
|
3930
|
786
|
In the figure above. What is the radius of the smaller circle??
|
(B)
|
[
"A.1",
"B.2",
"C.4",
"D.8",
"E.16",
""
] |
In the figure above. What is the radius of the smaller circle??
Options:
(A) A.1
(B) B.2
(C) C.4
(D) D.8
(E) E.16
(F)
|
|
3935
|
787
|
In the figure above, the smaller circles are tangent to the larger circle at points A and C, and are tangent to each other at point B. What is the perimeter of the shaded region??
|
(D)
|
[
"A.6*\\pi",
"B.8*\\pi",
"C.9*\\pi",
"D.12*\\pi",
"E.15*\\pi",
""
] |
In the figure above, the smaller circles are tangent to the larger circle at points A and C, and are tangent to each other at point B. What is the perimeter of the shaded region??
Options:
(A) A.6*\pi
(B) B.8*\pi
(C) C.9*\pi
(D) D.12*\pi
(E) E.15*\pi
(F)
|
|
3940
|
788
|
In the diagram above, angle A is congruent to angle BED, and angle C is congruent to angle D. If the ratio of the length of AB to the length of EB is 5:1, and the area of the triangle BED is 5*a^2 + 10, what is the area of triangle ABC??
|
(D)
|
[
"A.5*a^2 + 10",
"B.25*a^2 + 50",
"C.25*a^2 + 100",
"D.125*a^2 + 250",
"E.cannot be determined",
""
] |
In the diagram above, angle A is congruent to angle BED, and angle C is congruent to angle D. If the ratio of the length of AB to the length of EB is 5:1, and the area of the triangle BED is 5*a^2 + 10, what is the area of triangle ABC??
Options:
(A) A.5*a^2 + 10
(B) B.25*a^2 + 50
(C) C.25*a^2 + 100
(D) D.125*a^2 + 250
(E) E.cannot be determined
(F)
|
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