question_id
int64 2
5k
| category
stringclasses 12
values | difficulty
stringclasses 3
values | question
stringlengths 10
89
| correct_answer
stringclasses 370
values | option_a
stringclasses 545
values | option_b
stringclasses 544
values | option_c
stringclasses 546
values | option_d
stringclasses 550
values | explanation
stringclasses 12
values |
|---|---|---|---|---|---|---|---|---|---|
4,939 |
combinatorics
|
hard
|
In how many ways can 5 books be arranged on a shelf if 2 specific books must be together?
|
48
|
24
|
60
|
48
|
120
|
Permutations and combinations
|
786 |
algebra
|
hard
|
Solve: x² + -14x + 49 = 0
|
x = 7 or x = 7
|
x = 6 or x = 8
|
x = 7 or x = 7
|
x = -7 or x = -7
|
x = 8 or x = 6
|
Algebraic manipulation and solving
|
2,129 |
calculus
|
easy
|
Find d/dx(x^5)
|
5x^4
|
x^4
|
x^5
|
5x^5
|
5x^4
|
Calculus differentiation and integration
|
1,133 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 5 and 12
|
13
|
11
|
14
|
13
|
12
|
Geometric calculation and spatial reasoning
|
2,026 |
fractions
|
hard
|
Simplify (2/3 + 1/6) × 3/5
|
1/2
|
1/2
|
2/2
|
1/3
|
0/2
|
Fraction arithmetic and simplification
|
719 |
algebra
|
hard
|
Solve: x² + -10x + 24 = 0
|
x = 4 or x = 6
|
x = 3 or x = 7
|
x = 4 or x = 6
|
x = -4 or x = -6
|
x = 5 or x = 5
|
Algebraic manipulation and solving
|
1,084 |
geometry
|
medium
|
What is the volume of a cube with side length 7?
|
343
|
343
|
378
|
323
|
358
|
Geometric calculation and spatial reasoning
|
3,102 |
probability
|
medium
|
Probability of drawing an ace from a standard deck
|
1/13
|
1/14
|
1/13
|
1/15
|
1/12
|
Probability calculation and expected value
|
947 |
geometry
|
easy
|
What is the area of a rectangle with length 5 and width 9?
|
45
|
53
|
45
|
48
|
40
|
Geometric calculation and spatial reasoning
|
1,403 |
statistics
|
medium
|
What is the mode of 6 4 6 6 5 4 6?
|
6
|
6
|
7
|
4
|
9
|
Statistical measure calculation
|
3,511 |
number_theory
|
medium
|
Find LCM of 12 and 16
|
48
|
48
|
53
|
38
|
63
|
Number theory and modular arithmetic
|
2,522 |
trigonometry
|
easy
|
Calculate tan(0°)
|
0
|
0
|
-1
|
undefined
|
1
|
Trigonometric functions and identities
|
1,043 |
geometry
|
medium
|
Find the area of a circle with radius 7 (use π ≈ 3.14)
|
153.94
|
155.74
|
153.94
|
151.44
|
157.14
|
Geometric calculation and spatial reasoning
|
2,862 |
trigonometry
|
hard
|
Solve sin(x) = 1/2 for 0° ≤ x ≤ 360°
|
x = 30° or 150°
|
x = 30° or 60°
|
x = 30° or 150°
|
x = 60° or 120°
|
x = 45° or 135°
|
Trigonometric functions and identities
|
295 |
arithmetic
|
hard
|
Calculate (6^3 × 2) ÷ 7
|
61
|
61
|
69
|
56
|
64
|
Standard arithmetic calculation
|
1,752 |
fractions
|
easy
|
Simplify 35/40
|
7/8
|
34/39
|
17/20
|
36/41
|
7/8
|
Fraction arithmetic and simplification
|
2,833 |
trigonometry
|
hard
|
Solve sin(x) = 1/2 for 0° ≤ x ≤ 360°
|
x = 30° or 150°
|
x = 30° or 60°
|
x = 30° or 150°
|
x = 60° or 120°
|
x = 45° or 135°
|
Trigonometric functions and identities
|
4,433 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
9
|
11
|
8
|
10
|
Vector operations and matrix calculations
|
1,687 |
fractions
|
easy
|
What is 1/2 + 1/4?
|
3/4
|
2/4
|
3/4
|
4/4
|
3/5
|
Fraction arithmetic and simplification
|
4,903 |
combinatorics
|
hard
|
In how many ways can 5 books be arranged on a shelf if 2 specific books must be together?
|
48
|
48
|
24
|
120
|
60
|
Permutations and combinations
|
752 |
algebra
|
hard
|
Solve: x² + -13x + 42 = 0
|
x = 7 or x = 6
|
x = 6 or x = 7
|
x = 7 or x = 6
|
x = -7 or x = -6
|
x = 8 or x = 5
|
Algebraic manipulation and solving
|
4,645 |
combinatorics
|
easy
|
How many ways to choose 2 items from 4 items?
|
6
|
8
|
5
|
6
|
4
|
Permutations and combinations
|
1,988 |
fractions
|
hard
|
Simplify (2/3 + 1/6) × 3/5
|
1/2
|
1/3
|
0/2
|
2/2
|
1/2
|
Fraction arithmetic and simplification
|
3,634 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
1
|
4
|
2
|
3
|
Number theory and modular arithmetic
|
1,948 |
fractions
|
hard
|
Simplify (2/3 + 1/6) × 3/5
|
1/2
|
0/2
|
1/2
|
2/2
|
1/3
|
Fraction arithmetic and simplification
|
1,191 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 7 and 24
|
25
|
24
|
26
|
23
|
25
|
Geometric calculation and spatial reasoning
|
264 |
arithmetic
|
medium
|
What is 10²?
|
100
|
100
|
90
|
115
|
108
|
Standard arithmetic calculation
|
1,886 |
fractions
|
medium
|
Divide 1 ÷ 5/7
|
7/5
|
7/5
|
5/7
|
7/6
|
8/5
|
Fraction arithmetic and simplification
|
716 |
algebra
|
hard
|
Solve: x² + -15x + 56 = 0
|
x = 7 or x = 8
|
x = 6 or x = 9
|
x = 7 or x = 8
|
x = -7 or x = -8
|
x = 8 or x = 7
|
Algebraic manipulation and solving
|
1,594 |
statistics
|
hard
|
Find the standard deviation of 2 4 6 8 (population)
|
2.24
|
2.94
|
2.24
|
1.74
|
2.54
|
Statistical measure calculation
|
3,114 |
probability
|
medium
|
Probability of drawing an ace from a standard deck
|
1/13
|
1/14
|
1/15
|
1/12
|
1/13
|
Probability calculation and expected value
|
3,006 |
probability
|
easy
|
What is the probability of getting heads on a fair coin flip?
|
1/2
|
1/4
|
1/3
|
1/2
|
2/3
|
Probability calculation and expected value
|
404 |
arithmetic
|
hard
|
Calculate (4^4 × 3) ÷ 9
|
85
|
80
|
93
|
85
|
88
|
Standard arithmetic calculation
|
4,611 |
combinatorics
|
easy
|
How many ways to choose 2 items from 4 items?
|
6
|
5
|
6
|
8
|
4
|
Permutations and combinations
|
611 |
algebra
|
medium
|
Find x: x² = 81
|
9
|
12
|
7
|
9
|
10
|
Algebraic manipulation and solving
|
4,423 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
10
|
8
|
9
|
11
|
Vector operations and matrix calculations
|
4,672 |
combinatorics
|
easy
|
How many ways can 4 people stand in a line?
|
24
|
24
|
6
|
8
|
16
|
Permutations and combinations
|
2,249 |
calculus
|
medium
|
What is d/dx(2x^4 - 6x + 1)?
|
8x^3 - 6
|
8x^3 - 6
|
8x^4 - 6
|
2x^3 - 6
|
8x^3 - 1
|
Calculus differentiation and integration
|
3,566 |
number_theory
|
medium
|
Find LCM of 12 and 16
|
48
|
53
|
63
|
48
|
38
|
Number theory and modular arithmetic
|
1,004 |
geometry
|
medium
|
What is the volume of a cube with side length 4?
|
64
|
44
|
79
|
64
|
99
|
Geometric calculation and spatial reasoning
|
4,303 |
linear_algebra
|
easy
|
Add vectors [2, 3] + [1, 4]
|
[3, 7]
|
[3, 6]
|
[2, 7]
|
[3, 7]
|
[4, 7]
|
Vector operations and matrix calculations
|
1,822 |
fractions
|
medium
|
Divide 4/7 ÷ 5/7
|
4/5
|
4/6
|
4/5
|
5/5
|
5/4
|
Fraction arithmetic and simplification
|
1,795 |
fractions
|
easy
|
Simplify 20/20
|
1/1
|
21/21
|
19/19
|
10/10
|
1/1
|
Fraction arithmetic and simplification
|
3,795 |
logic
|
easy
|
If all cats are mammals and Fluffy is a cat, then Fluffy is a:
|
mammal
|
pet
|
animal
|
mammal
|
cat
|
Logical reasoning and boolean operations
|
942 |
geometry
|
easy
|
What is the area of a rectangle with length 8 and width 5?
|
40
|
43
|
40
|
48
|
35
|
Geometric calculation and spatial reasoning
|
2,646 |
trigonometry
|
medium
|
Calculate sin²(x) + cos²(x)
|
1
|
1
|
2
|
sin(2x)
|
0
|
Trigonometric functions and identities
|
1,725 |
fractions
|
easy
|
Simplify 20/24
|
5/6
|
21/25
|
19/23
|
5/6
|
10/12
|
Fraction arithmetic and simplification
|
2,516 |
trigonometry
|
easy
|
Calculate tan(0°)
|
0
|
1
|
undefined
|
-1
|
0
|
Trigonometric functions and identities
|
1,345 |
statistics
|
easy
|
Find the median of 4 9 10 8 6 12 12
|
9
|
10
|
11
|
9
|
7
|
Statistical measure calculation
|
3,248 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
4.5
|
3.5
|
3
|
4
|
Probability calculation and expected value
|
3,847 |
logic
|
easy
|
True or False: 5 > 3 AND 2 < 4
|
True
|
Cannot determine
|
Depends on context
|
True
|
False
|
Logical reasoning and boolean operations
|
4,115 |
logic
|
hard
|
Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True
|
True
|
Depends on other variables
|
True
|
False
|
Cannot determine
|
Logical reasoning and boolean operations
|
104 |
arithmetic
|
easy
|
Find 12 × 12
|
144
|
149
|
144
|
141
|
146
|
Standard arithmetic calculation
|
3,051 |
probability
|
easy
|
How many outcomes when rolling a six-sided die?
|
6
|
6
|
5
|
8
|
7
|
Probability calculation and expected value
|
4,905 |
combinatorics
|
hard
|
In how many ways can 5 books be arranged on a shelf if 2 specific books must be together?
|
48
|
24
|
120
|
48
|
60
|
Permutations and combinations
|
3,446 |
number_theory
|
easy
|
What is the GCD of 12 and 18?
|
6
|
4
|
7
|
6
|
5
|
Number theory and modular arithmetic
|
3,181 |
probability
|
medium
|
Probability of rolling two sixes with two dice
|
1/36
|
1/35
|
1/30
|
1/32
|
1/36
|
Probability calculation and expected value
|
668 |
algebra
|
medium
|
Solve: 4x - 11 = 22
|
8
|
9
|
8
|
6
|
11
|
Algebraic manipulation and solving
|
3,780 |
logic
|
easy
|
True or False: 5 > 3 AND 2 < 4
|
True
|
Depends on context
|
False
|
Cannot determine
|
True
|
Logical reasoning and boolean operations
|
2,090 |
calculus
|
easy
|
Find d/dx(x^5)
|
5x^4
|
5x^5
|
x^4
|
5x^4
|
x^5
|
Calculus differentiation and integration
|
3,955 |
logic
|
medium
|
If P implies Q and P is true, what can we conclude about Q?
|
Q is true
|
P is false
|
Cannot determine
|
Q is true
|
Q is false
|
Logical reasoning and boolean operations
|
3,493 |
number_theory
|
medium
|
Find LCM of 12 and 16
|
48
|
63
|
38
|
53
|
48
|
Number theory and modular arithmetic
|
3,033 |
probability
|
easy
|
What is the probability of getting heads on a fair coin flip?
|
1/2
|
1/3
|
1/4
|
1/2
|
2/3
|
Probability calculation and expected value
|
4,788 |
combinatorics
|
medium
|
How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition?
|
60
|
75
|
60
|
50
|
125
|
Permutations and combinations
|
1,510 |
statistics
|
medium
|
Calculate the range of 5 17 4 19 13
|
15
|
18
|
16
|
15
|
13
|
Statistical measure calculation
|
3,266 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
3.5
|
3
|
4
|
4.5
|
Probability calculation and expected value
|
4,082 |
logic
|
hard
|
Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True
|
True
|
False
|
Depends on other variables
|
Cannot determine
|
True
|
Logical reasoning and boolean operations
|
1,855 |
fractions
|
medium
|
Divide 1 ÷ 1/3
|
3/1
|
4/1
|
3/1
|
1/3
|
3/2
|
Fraction arithmetic and simplification
|
3,474 |
number_theory
|
easy
|
What is the GCD of 14 and 21?
|
7
|
6
|
8
|
7
|
5
|
Number theory and modular arithmetic
|
1,615 |
statistics
|
hard
|
Find the standard deviation of 2 4 6 8 (population)
|
2.24
|
2.94
|
2.54
|
1.74
|
2.24
|
Statistical measure calculation
|
1,770 |
fractions
|
easy
|
What is 1/2 + 1/6?
|
2/3
|
2/4
|
1/3
|
3/3
|
2/3
|
Fraction arithmetic and simplification
|
1,081 |
geometry
|
medium
|
What is the volume of a cube with side length 6?
|
216
|
196
|
231
|
251
|
216
|
Geometric calculation and spatial reasoning
|
1,274 |
statistics
|
easy
|
Find the median of 15 3 12 8 15 11 20
|
12
|
10
|
12
|
14
|
13
|
Statistical measure calculation
|
3,604 |
number_theory
|
medium
|
Find LCM of 12 and 16
|
48
|
38
|
48
|
63
|
53
|
Number theory and modular arithmetic
|
3,746 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
3
|
1
|
4
|
2
|
Number theory and modular arithmetic
|
263 |
arithmetic
|
medium
|
What is 40% of 236?
|
94
|
99
|
104
|
94
|
89
|
Standard arithmetic calculation
|
2,098 |
calculus
|
easy
|
Find d/dx(x^4)
|
4x^3
|
4x^4
|
4x^3
|
x^3
|
x^4
|
Calculus differentiation and integration
|
3,251 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
3
|
4
|
3.5
|
4.5
|
Probability calculation and expected value
|
2,798 |
trigonometry
|
hard
|
Solve sin(x) = 1/2 for 0° ≤ x ≤ 360°
|
x = 30° or 150°
|
x = 30° or 60°
|
x = 30° or 150°
|
x = 60° or 120°
|
x = 45° or 135°
|
Trigonometric functions and identities
|
1,373 |
statistics
|
easy
|
What is the mean of 19 10 4 17 8 2 6 16?
|
10.2
|
8.2
|
12.2
|
10.2
|
11.2
|
Statistical measure calculation
|
1,177 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 8 and 15
|
17
|
15
|
17
|
18
|
16
|
Geometric calculation and spatial reasoning
|
329 |
arithmetic
|
hard
|
Calculate (3^4 × 2) ÷ 3
|
54
|
54
|
49
|
62
|
57
|
Standard arithmetic calculation
|
4,215 |
linear_algebra
|
easy
|
Calculate 5 × [2, 3]
|
[10, 15]
|
[9, 15]
|
[10, 14]
|
[11, 15]
|
[10, 15]
|
Vector operations and matrix calculations
|
2,493 |
calculus
|
hard
|
Find the derivative of sin(x²)
|
2x cos(x²)
|
cos(x²)
|
2x sin(x²)
|
cos(2x)
|
2x cos(x²)
|
Calculus differentiation and integration
|
3,402 |
number_theory
|
easy
|
Is 31 a prime number?
|
Yes
|
Cannot determine
|
Yes
|
No
|
Only if x>0
|
Number theory and modular arithmetic
|
3,280 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
4
|
3
|
4.5
|
3.5
|
Probability calculation and expected value
|
2,545 |
trigonometry
|
easy
|
What is sin(30°)?
|
0.5
|
0
|
-1
|
0.5
|
1
|
Trigonometric functions and identities
|
4,126 |
logic
|
hard
|
Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True
|
True
|
Cannot determine
|
True
|
False
|
Depends on other variables
|
Logical reasoning and boolean operations
|
2,027 |
fractions
|
hard
|
Simplify (2/3 + 1/6) × 3/5
|
1/2
|
0/2
|
1/2
|
1/3
|
2/2
|
Fraction arithmetic and simplification
|
1,971 |
fractions
|
hard
|
Simplify (2/3 + 1/6) × 3/5
|
1/2
|
0/2
|
1/3
|
2/2
|
1/2
|
Fraction arithmetic and simplification
|
1,090 |
geometry
|
medium
|
Find the area of a circle with radius 4 (use π ≈ 3.14)
|
50.27
|
50.27
|
52.07
|
53.47
|
47.77
|
Geometric calculation and spatial reasoning
|
3,024 |
probability
|
easy
|
How many outcomes when rolling a six-sided die?
|
6
|
8
|
6
|
7
|
5
|
Probability calculation and expected value
|
4,694 |
combinatorics
|
easy
|
How many ways to choose 2 items from 4 items?
|
6
|
8
|
4
|
5
|
6
|
Permutations and combinations
|
1,507 |
statistics
|
medium
|
What is the mode of 8 8 19 4 16 8 8?
|
8
|
9
|
8
|
6
|
11
|
Statistical measure calculation
|
951 |
geometry
|
easy
|
What is the area of a rectangle with length 10 and width 5?
|
50
|
50
|
58
|
45
|
53
|
Geometric calculation and spatial reasoning
|
1,347 |
statistics
|
easy
|
What is the mean of 6 12 7 18?
|
10.8
|
8.8
|
12.8
|
11.8
|
10.8
|
Statistical measure calculation
|
4,220 |
linear_algebra
|
easy
|
Calculate 3 × [2, 3]
|
[6, 9]
|
[7, 9]
|
[6, 8]
|
[6, 9]
|
[5, 9]
|
Vector operations and matrix calculations
|
2,921 |
probability
|
easy
|
How many outcomes when rolling a six-sided die?
|
6
|
7
|
5
|
8
|
6
|
Probability calculation and expected value
|
4,763 |
combinatorics
|
medium
|
How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition?
|
60
|
75
|
50
|
125
|
60
|
Permutations and combinations
|
4,462 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
5
|
6
|
4
|
3
|
Vector operations and matrix calculations
|
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