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Person A can complete a job in 2 hours. Person B can complete the same job in 10 hours. How long will it take them to finish together? | Step 1: Find each person's rate (fraction of job per hour).
A's rate = 1/2 of the job per hour
B's rate = 1/10 of the job per hour
Step 2: Combined rate = 1/2 + 1/10 = 10/(2×10) + 2/(2×10) = 12/20
Step 3: Time = 1 / (combined rate) = 20/12 = 1.67 hours
Answer: 1.67 hours | 1.67 hours | word_problems | medium | 8291b2daed3d |
Find the GCD (Greatest Common Divisor) of 17 and 39. | Use the Euclidean algorithm:
17 = 39 × 0 + 17
39 = 17 × 2 + 5
17 = 5 × 3 + 2
5 = 2 × 2 + 1
2 = 1 × 2 + 0
GCD(17, 39) = 1
Answer: 1 | 1 | number_theory | medium | 8fb43b22c1e4 |
A fair coin is flipped 4 times. What is the probability of getting all heads? | Step 1: Total possible outcomes = 2^4 = 16
Step 2: Count favorable outcomes for 'all heads': 1
Step 3: P(all heads) = 1/16 ≈ 0.062
Answer: 1/16 ≈ 6.2% | 1/16 | probability | medium | ba886b615c67 |
Solve: x² + 1x - 20 = 0 | Step 1: Use the quadratic formula: x = (-b ± √(b²-4ac)) / 2a
Here a=1, b=1, c=-20
Step 2: Calculate the discriminant.
b²-4ac = 1² - 4(1)(-20) = 1 - -80 = 81
Step 3: Find the roots.
x = (-1 ± √81) / 2
x = (-1 ± 9) / 2
x₁ = (-1 + 9) / 2 = 4
x₂ = (-1 - 9) / 2 = -5
Answer: x = 4 or x = -5 | 4 or -5 | algebra | medium | 7a70afc95238 |
Solve for x: 3x + 7 = -14 | Step 1: Subtract 7 from both sides.
3x + 7 - 7 = -14 - 7
3x = -21
Step 2: Divide both sides by 3.
x = -21 ÷ 3
x = -7
Answer: x = -7 | -7 | algebra | easy | 871459a5ed49 |
Solve for x: 11x + 1 = 67 | Step 1: Subtract 1 from both sides.
11x + 1 - 1 = 67 - 1
11x = 66
Step 2: Divide both sides by 11.
x = 66 ÷ 11
x = 6
Answer: x = 6 | 6 | algebra | easy | 20553742a9f1 |
A trader buys goods for $120 and sells them at a 15% profit. What is the selling price? | Step 1: Calculate the profit amount.
Profit = 15% × $120 = $18
Step 2: Selling Price = Cost Price + Profit
SP = $120 + $18 = $138
Answer: $138 | $138 | arithmetic | easy | 32b912e413cb |
How many liters of a 20% solution must be mixed with a 90% solution to obtain 10 liters of a 83% solution? | Step 1: Let x = liters of 20% solution; then (10 - x) = liters of 90% solution.
Step 2: Set up the equation for the amount of solute.
20x + 90(10 - x) = 83 × 10
20x + 900 - 90x = 830
-70x = 830 - 900
-70x = -70
x = -70 ÷ -70 = 1.0 liters
Step 3: 90% solution = 10 - 1.0 = 9.0 liters
Answer: 1.0 liters of 20... | 1.0L of 20% + 9.0L of 90% | word_problems | hard | 443d653771cb |
Find the GCD (Greatest Common Divisor) of 28 and 39. | Use the Euclidean algorithm:
28 = 39 × 0 + 28
39 = 28 × 1 + 11
28 = 11 × 2 + 6
11 = 6 × 1 + 5
6 = 5 × 1 + 1
GCD(28, 39) = 1
Answer: 1 | 1 | number_theory | medium | 084401b26a7b |
Calculate the compound interest on $1,000 at 7% per year, compounded annually, for 3 years. | Step 1: Use the formula A = P(1 + r/n)^(nt)
P = $1,000, r = 7% = 0.07, n = 1 (annually), t = 3 years
Step 2: Substitute values.
A = 1000 × (1 + 0.07/1)^(1×3)
A = 1000 × (1 + 0.07)^3
A = 1000 × 1.225043
A = $1,225.04
Step 3: Compound Interest = A - P = $1,225.04 - $1,000 = $225.04
Answer: Compound Interest ... | $225.04 | finance_math | medium | 400aa3b9e768 |
Solve: x² + 8x + 7 = 0 | Step 1: Use the quadratic formula: x = (-b ± √(b²-4ac)) / 2a
Here a=1, b=8, c=7
Step 2: Calculate the discriminant.
b²-4ac = 8² - 4(1)(7) = 64 - 28 = 36
Step 3: Find the roots.
x = (-8 ± √36) / 2
x = (-8 ± 6) / 2
x₁ = (-8 + 6) / 2 = -1
x₂ = (-8 - 6) / 2 = -7
Answer: x = -1 or x = -7 | -1 or -7 | algebra | medium | 3750d266b118 |
Solve: x² + 1x - 12 = 0 | Step 1: Use the quadratic formula: x = (-b ± √(b²-4ac)) / 2a
Here a=1, b=1, c=-12
Step 2: Calculate the discriminant.
b²-4ac = 1² - 4(1)(-12) = 1 - -48 = 49
Step 3: Find the roots.
x = (-1 ± √49) / 2
x = (-1 ± 7) / 2
x₁ = (-1 + 7) / 2 = 3
x₂ = (-1 - 7) / 2 = -4
Answer: x = 3 or x = -4 | 3 or -4 | algebra | medium | 37f2fa3d2934 |
Solve: x² - 6x = 0 | Step 1: Use the quadratic formula: x = (-b ± √(b²-4ac)) / 2a
Here a=1, b=-6, c=0
Step 2: Calculate the discriminant.
b²-4ac = -6² - 4(1)(0) = 36 - 0 = 36
Step 3: Find the roots.
x = (6 ± √36) / 2
x = (6 ± 6) / 2
x₁ = (6 + 6) / 2 = 6
x₂ = (6 - 6) / 2 = 0
Answer: x = 6 or x = 0 | 6 or 0 | algebra | medium | 4241951b3eaf |
Find the GCD (Greatest Common Divisor) of 58 and 42. | Use the Euclidean algorithm:
58 = 42 × 1 + 16
42 = 16 × 2 + 10
16 = 10 × 1 + 6
10 = 6 × 1 + 4
6 = 4 × 1 + 2
GCD(58, 42) = 2
Answer: 2 | 2 | number_theory | medium | d84db6f2202b |
How many liters of a 30% solution must be mixed with a 90% solution to obtain 10 liters of a 69% solution? | Step 1: Let x = liters of 30% solution; then (10 - x) = liters of 90% solution.
Step 2: Set up the equation for the amount of solute.
30x + 90(10 - x) = 69 × 10
30x + 900 - 90x = 690
-60x = 690 - 900
-60x = -210
x = -210 ÷ -60 = 3.5 liters
Step 3: 90% solution = 10 - 3.5 = 6.5 liters
Answer: 3.5 liters of ... | 3.5L of 30% + 6.5L of 90% | word_problems | hard | af9f3c6ddbd8 |
A trader buys goods for $300 and sells them at a 30% profit. What is the selling price? | Step 1: Calculate the profit amount.
Profit = 30% × $300 = $90
Step 2: Selling Price = Cost Price + Profit
SP = $300 + $90 = $390
Answer: $390 | $390 | arithmetic | easy | 938cc439e5a7 |
An item costing $250 is sold at a 5% loss. What is the selling price? | Step 1: Calculate the loss amount.
Loss = 5% × $250 = $12
Step 2: Selling Price = Cost Price - Loss
SP = $250 - $12 = $238
Answer: $238 | $238 | arithmetic | easy | c385d9b283ab |
Calculate the compound interest on $2,000 at 5% per year, compounded monthly, for 3 years. | Step 1: Use the formula A = P(1 + r/n)^(nt)
P = $2,000, r = 5% = 0.05, n = 12 (monthly), t = 3 years
Step 2: Substitute values.
A = 2000 × (1 + 0.05/12)^(12×3)
A = 2000 × (1 + 0.004167)^36
A = 2000 × 1.161472
A = $2,322.94
Step 3: Compound Interest = A - P = $2,322.94 - $2,000 = $322.94
Answer: Compound In... | $322.94 | finance_math | medium | 341aef680c9d |
Person A can complete a job in 6 hours. Person B can complete the same job in 5 hours. How long will it take them to finish together? | Step 1: Find each person's rate (fraction of job per hour).
A's rate = 1/6 of the job per hour
B's rate = 1/5 of the job per hour
Step 2: Combined rate = 1/6 + 1/5 = 5/(6×5) + 6/(6×5) = 11/30
Step 3: Time = 1 / (combined rate) = 30/11 = 2.73 hours
Answer: 2.73 hours | 2.73 hours | word_problems | medium | d74526482478 |
A product costs $250. It is on sale for 30% off. What is the discount amount? | Step 1: Calculate the discount.
Discount = 30% × $250 = 0.3 × 250 = $75
Step 2: The sale price would be $250 - $75 = $175
Answer: The discount is $75 | 75 | arithmetic | easy | c5e1110a1fc8 |
Two fair dice are rolled. What is the probability that the sum equals 7? | Step 1: Count outcomes that sum to the target by listing pairs.
(There are 36 total outcomes for two dice)
Step 2: For sum = 7: (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) → 6 outcomes
Step 3: P(sum=7) = 6/36 = 1/6 ≈ 0.167
Answer: 1/6 ≈ 16.7% | 1/6 | probability | medium | 214e094fdd98 |
Person A can complete a job in 4 hours. Person B can complete the same job in 8 hours. How long will it take them to finish together? | Step 1: Find each person's rate (fraction of job per hour).
A's rate = 1/4 of the job per hour
B's rate = 1/8 of the job per hour
Step 2: Combined rate = 1/4 + 1/8 = 8/(4×8) + 4/(4×8) = 12/32
Step 3: Time = 1 / (combined rate) = 32/12 = 2.67 hours
Answer: 2.67 hours | 2.67 hours | word_problems | medium | efcf8cc0d1eb |
A right triangle has one leg of 6 cm and hypotenuse of 10 cm. Find the other leg. | Step 1: Use the Pythagorean theorem: b² = c² - a²
b² = 10² - 6² = 100 - 36 = 64
Step 2: Take the square root.
b = √64 = 8 cm
Answer: 8 cm | 8 cm | geometry | easy | aa235638d9ae |
How many liters of a 50% solution must be mixed with a 70% solution to obtain 10 liters of a 63% solution? | Step 1: Let x = liters of 50% solution; then (10 - x) = liters of 70% solution.
Step 2: Set up the equation for the amount of solute.
50x + 70(10 - x) = 63 × 10
50x + 700 - 70x = 630
-20x = 630 - 700
-20x = -70
x = -70 ÷ -20 = 3.5 liters
Step 3: 70% solution = 10 - 3.5 = 6.5 liters
Answer: 3.5 liters of 50... | 3.5L of 50% + 6.5L of 70% | word_problems | hard | cd3954673e44 |
Find the median of: 74, 49, 41, 75, 83, 13, 85 | Step 1: Sort the values in ascending order.
13, 41, 49, 74, 75, 83, 85
Step 2: The median is the middle value (position 4 of 7).
Median = 74
Answer: 74 | 74 | statistics | easy | f73d789396a2 |
Car A leaves at 40 km/h. Car B starts 1 hour(s) later at 100 km/h. How long after Car B departs does it catch Car A? | Step 1: Find Car A's head start distance.
Head start = 40 km/h × 1 h = 40 km
Step 2: Find the rate at which Car B closes the gap.
Relative speed = 100 - 40 = 60 km/h
Step 3: Time to close the gap.
Time = 40 ÷ 60 = 0.67 hours
Answer: Car B catches Car A after 0.67 hours | 0.67 hours | word_problems | medium | bfedfbe54869 |
Calculate the area of a triangle with base 9 m and height 16 m. | Step 1: Use the formula: Area = (base × height) / 2
Area = (9 × 16) / 2 = 144 / 2 = 72.0 m²
Answer: 72.0 m² | 72.0 m² | geometry | easy | 2b31f52924b4 |
A right triangle has one leg of 12 cm and hypotenuse of 20 cm. Find the other leg. | Step 1: Use the Pythagorean theorem: b² = c² - a²
b² = 20² - 12² = 400 - 144 = 256
Step 2: Take the square root.
b = √256 = 16 cm
Answer: 16 cm | 16 cm | geometry | easy | 3bdb273cfc0d |
Car A leaves at 40 km/h. Car B starts 2 hour(s) later at 90 km/h. How long after Car B departs does it catch Car A? | Step 1: Find Car A's head start distance.
Head start = 40 km/h × 2 h = 80 km
Step 2: Find the rate at which Car B closes the gap.
Relative speed = 90 - 40 = 50 km/h
Step 3: Time to close the gap.
Time = 80 ÷ 50 = 1.6 hours
Answer: Car B catches Car A after 1.6 hours | 1.6 hours | word_problems | medium | 39f2931a1686 |
How many liters of a 30% solution must be mixed with a 70% solution to obtain 10 liters of a 47% solution? | Step 1: Let x = liters of 30% solution; then (10 - x) = liters of 70% solution.
Step 2: Set up the equation for the amount of solute.
30x + 70(10 - x) = 47 × 10
30x + 700 - 70x = 470
-40x = 470 - 700
-40x = -230
x = -230 ÷ -40 = 5.75 liters
Step 3: 70% solution = 10 - 5.75 = 4.25 liters
Answer: 5.75 liters... | 5.75L of 30% + 4.25L of 70% | word_problems | hard | 4efa6f9cb13d |
Find the area of a trapezoid with parallel sides of 6 m and 9 m, and height 5 m. | Step 1: Use the formula: Area = (a + b) / 2 × h
Area = (6 + 9) / 2 × 5 = 15 / 2 × 5 = 7.5 × 5 = 37.5 m²
Answer: 37.5 m² | 37.5 m² | geometry | medium | 630470737f02 |
Find the area of a trapezoid with parallel sides of 9 m and 20 m, and height 6 m. | Step 1: Use the formula: Area = (a + b) / 2 × h
Area = (9 + 20) / 2 × 6 = 29 / 2 × 6 = 14.5 × 6 = 87.0 m²
Answer: 87.0 m² | 87.0 m² | geometry | medium | 9c3a8539bc78 |
Solve for x: 14x + 12 = 96 | Step 1: Subtract 12 from both sides.
14x + 12 - 12 = 96 - 12
14x = 84
Step 2: Divide both sides by 14.
x = 84 ÷ 14
x = 6
Answer: x = 6 | 6 | algebra | easy | 3d743acd9cae |
A fair coin is flipped 3 times. What is the probability of getting exactly 2 heads? | Step 1: Total possible outcomes = 2^3 = 8
Step 2: Count favorable outcomes for 'exactly 2 heads': 3
Step 3: P(exactly 2 heads) = 3/8 ≈ 0.375
Answer: 3/8 ≈ 37.5% | 3/8 | probability | medium | b068b092fd11 |
Solve: x² + 3x - 4 = 0 | Step 1: Use the quadratic formula: x = (-b ± √(b²-4ac)) / 2a
Here a=1, b=3, c=-4
Step 2: Calculate the discriminant.
b²-4ac = 3² - 4(1)(-4) = 9 - -16 = 25
Step 3: Find the roots.
x = (-3 ± √25) / 2
x = (-3 ± 5) / 2
x₁ = (-3 + 5) / 2 = 1
x₂ = (-3 - 5) / 2 = -4
Answer: x = 1 or x = -4 | 1 or -4 | algebra | medium | 619f7d915830 |
How many liters of a 50% solution must be mixed with a 90% solution to obtain 10 liters of a 74% solution? | Step 1: Let x = liters of 50% solution; then (10 - x) = liters of 90% solution.
Step 2: Set up the equation for the amount of solute.
50x + 90(10 - x) = 74 × 10
50x + 900 - 90x = 740
-40x = 740 - 900
-40x = -160
x = -160 ÷ -40 = 4.0 liters
Step 3: 90% solution = 10 - 4.0 = 6.0 liters
Answer: 4.0 liters of ... | 4.0L of 50% + 6.0L of 90% | word_problems | hard | 3ebb78d93248 |
Find the median of: 87, 52, 89, 29, 90, 52, 63, 41, 25 | Step 1: Sort the values in ascending order.
25, 29, 41, 52, 52, 63, 87, 89, 90
Step 2: The median is the middle value (position 5 of 9).
Median = 52
Answer: 52 | 52 | statistics | easy | abca8f2e46ae |
A trader buys goods for $50 and sells them at a 5% profit. What is the selling price? | Step 1: Calculate the profit amount.
Profit = 5% × $50 = $2
Step 2: Selling Price = Cost Price + Profit
SP = $50 + $2 = $52
Answer: $52 | $52 | arithmetic | easy | db5f4ddfb7fb |
A trader buys goods for $200 and sells them at a 20% profit. What is the selling price? | Step 1: Calculate the profit amount.
Profit = 20% × $200 = $40
Step 2: Selling Price = Cost Price + Profit
SP = $200 + $40 = $240
Answer: $240 | $240 | arithmetic | easy | e4c4843c8f85 |
A right triangle has one leg of 27 cm and hypotenuse of 123 cm. Find the other leg. | Step 1: Use the Pythagorean theorem: b² = c² - a²
b² = 123² - 27² = 15129 - 729 = 14400
Step 2: Take the square root.
b = √14400 = 120 cm
Answer: 120 cm | 120 cm | geometry | easy | ea6a434cb014 |
Find the area of a rectangle with width 15 cm and height 20 cm. | Step 1: Use the formula: Area = width × height
Area = 15 × 20 = 300 cm²
Answer: 300 cm² | 300 cm² | geometry | easy | 91c9dc5e184f |
Calculate the compound interest on $10,000 at 8% per year, compounded monthly, for 5 years. | Step 1: Use the formula A = P(1 + r/n)^(nt)
P = $10,000, r = 8% = 0.08, n = 12 (monthly), t = 5 years
Step 2: Substitute values.
A = 10000 × (1 + 0.08/12)^(12×5)
A = 10000 × (1 + 0.006667)^60
A = 10000 × 1.489846
A = $14,898.46
Step 3: Compound Interest = A - P = $14,898.46 - $10,000 = $4,898.46
Answer: Co... | $4,898.46 | finance_math | medium | 8ff74500d14d |
Car A leaves at 50 km/h. Car B starts 1 hour(s) later at 90 km/h. How long after Car B departs does it catch Car A? | Step 1: Find Car A's head start distance.
Head start = 50 km/h × 1 h = 50 km
Step 2: Find the rate at which Car B closes the gap.
Relative speed = 90 - 50 = 40 km/h
Step 3: Time to close the gap.
Time = 50 ÷ 40 = 1.25 hours
Answer: Car B catches Car A after 1.25 hours | 1.25 hours | word_problems | medium | b6c349f719f3 |
Find the GCD (Greatest Common Divisor) of 46 and 46. | Use the Euclidean algorithm:
46 = 46 × 1 + 0
GCD(46, 46) = 46
Answer: 46 | 46 | number_theory | medium | 38b7960b009e |
Two fair dice are rolled. What is the probability that the sum equals 9? | Step 1: Count outcomes that sum to the target by listing pairs.
(There are 36 total outcomes for two dice)
Step 2: For sum = 7: (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) → 6 outcomes
Step 3: P(sum=7) = 6/36 = 1/6 ≈ 0.167
Answer: 1/6 ≈ 16.7% | 1/6 | probability | medium | 4d141c122986 |
Person A can complete a job in 3 hours. Person B can complete the same job in 10 hours. How long will it take them to finish together? | Step 1: Find each person's rate (fraction of job per hour).
A's rate = 1/3 of the job per hour
B's rate = 1/10 of the job per hour
Step 2: Combined rate = 1/3 + 1/10 = 10/(3×10) + 3/(3×10) = 13/30
Step 3: Time = 1 / (combined rate) = 30/13 = 2.31 hours
Answer: 2.31 hours | 2.31 hours | word_problems | medium | d139e2859728 |
How many liters of a 10% solution must be mixed with a 90% solution to obtain 10 liters of a 66% solution? | Step 1: Let x = liters of 10% solution; then (10 - x) = liters of 90% solution.
Step 2: Set up the equation for the amount of solute.
10x + 90(10 - x) = 66 × 10
10x + 900 - 90x = 660
-80x = 660 - 900
-80x = -240
x = -240 ÷ -80 = 3.0 liters
Step 3: 90% solution = 10 - 3.0 = 7.0 liters
Answer: 3.0 liters of ... | 3.0L of 10% + 7.0L of 90% | word_problems | hard | eb163af0b0af |
A fair coin is flipped 2 times. What is the probability of getting all heads? | Step 1: Total possible outcomes = 2^2 = 4
Step 2: Count favorable outcomes for 'all heads': 1
Step 3: P(all heads) = 1/4 ≈ 0.25
Answer: 1/4 ≈ 25.0% | 1/4 | probability | medium | 43da58ae8650 |
A trader buys goods for $150 and sells them at a 10% profit. What is the selling price? | Step 1: Calculate the profit amount.
Profit = 10% × $150 = $15
Step 2: Selling Price = Cost Price + Profit
SP = $150 + $15 = $165
Answer: $165 | $165 | arithmetic | easy | 3d885508c4f7 |
Person A can complete a job in 5 hours. Person B can complete the same job in 6 hours. How long will it take them to finish together? | Step 1: Find each person's rate (fraction of job per hour).
A's rate = 1/5 of the job per hour
B's rate = 1/6 of the job per hour
Step 2: Combined rate = 1/5 + 1/6 = 6/(5×6) + 5/(5×6) = 11/30
Step 3: Time = 1 / (combined rate) = 30/11 = 2.73 hours
Answer: 2.73 hours | 2.73 hours | word_problems | medium | 8fceff740dfc |
Person A can complete a job in 4 hours. Person B can complete the same job in 3 hours. How long will it take them to finish together? | Step 1: Find each person's rate (fraction of job per hour).
A's rate = 1/4 of the job per hour
B's rate = 1/3 of the job per hour
Step 2: Combined rate = 1/4 + 1/3 = 3/(4×3) + 4/(4×3) = 7/12
Step 3: Time = 1 / (combined rate) = 12/7 = 1.71 hours
Answer: 1.71 hours | 1.71 hours | word_problems | medium | f2e8013581ab |
A car travels at 65 km/h for 4 hours. How far does it travel? | Step 1: Use the formula: Distance = Speed × Time
Distance = 65 km/h × 4 h = 260 km
Answer: 260 km | 260 km | word_problems | easy | 88565c8aa94f |
Two fair dice are rolled. What is the probability that the sum equals 9? | Step 1: Count outcomes that sum to the target by listing pairs.
(There are 36 total outcomes for two dice)
Step 2: For sum = 7: (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) → 6 outcomes
Step 3: P(sum=7) = 6/36 = 1/6 ≈ 0.167
Answer: 1/6 ≈ 16.7% | 1/6 | probability | medium | 09efdd1a1405 |
A car travels at 65 km/h for 2.5 hours. How far does it travel? | Step 1: Use the formula: Distance = Speed × Time
Distance = 65 km/h × 2.5 h = 162.5 km
Answer: 162.5 km | 162.5 km | word_problems | easy | 9d016318d3b0 |
A car travels at 80 km/h for 1.5 hours. How far does it travel? | Step 1: Use the formula: Distance = Speed × Time
Distance = 80 km/h × 1.5 h = 120.0 km
Answer: 120.0 km | 120.0 km | word_problems | easy | 48d8c8c5f549 |
How many liters of a 50% solution must be mixed with a 80% solution to obtain 10 liters of a 64% solution? | Step 1: Let x = liters of 50% solution; then (10 - x) = liters of 80% solution.
Step 2: Set up the equation for the amount of solute.
50x + 80(10 - x) = 64 × 10
50x + 800 - 80x = 640
-30x = 640 - 800
-30x = -160
x = -160 ÷ -30 = 5.33 liters
Step 3: 80% solution = 10 - 5.33 = 4.67 liters
Answer: 5.33 liters... | 5.33L of 50% + 4.67L of 80% | word_problems | hard | 348298aa74d9 |
A right triangle has legs of length 9 cm and 12 cm. Find the hypotenuse. | Step 1: Use the Pythagorean theorem: c² = a² + b²
c² = 9² + 12² = 81 + 144 = 225
Step 2: Take the square root.
c = √225 = 15 cm
Answer: 15 cm | 15 cm | geometry | easy | bf59d001fc19 |
A right triangle has one leg of 6 cm and hypotenuse of 10 cm. Find the other leg. | Step 1: Use the Pythagorean theorem: b² = c² - a²
b² = 10² - 6² = 100 - 36 = 64
Step 2: Take the square root.
b = √64 = 8 cm
Answer: 8 cm | 8 cm | geometry | easy | f7d2f5918bce |
Car A leaves at 50 km/h. Car B starts 1 hour(s) later at 80 km/h. How long after Car B departs does it catch Car A? | Step 1: Find Car A's head start distance.
Head start = 50 km/h × 1 h = 50 km
Step 2: Find the rate at which Car B closes the gap.
Relative speed = 80 - 50 = 30 km/h
Step 3: Time to close the gap.
Time = 50 ÷ 30 = 1.67 hours
Answer: Car B catches Car A after 1.67 hours | 1.67 hours | word_problems | medium | f03a63b9af4d |
How many liters of a 30% solution must be mixed with a 80% solution to obtain 10 liters of a 73% solution? | Step 1: Let x = liters of 30% solution; then (10 - x) = liters of 80% solution.
Step 2: Set up the equation for the amount of solute.
30x + 80(10 - x) = 73 × 10
30x + 800 - 80x = 730
-50x = 730 - 800
-50x = -70
x = -70 ÷ -50 = 1.4 liters
Step 3: 80% solution = 10 - 1.4 = 8.6 liters
Answer: 1.4 liters of 30... | 1.4L of 30% + 8.6L of 80% | word_problems | hard | 3613acfef629 |
A card is drawn at random from a standard 52-card deck. What is the probability it is a spades? | Step 1: Count favorable outcomes.
There are 13 cards of each suit, so 13 spades.
Step 2: Total possible outcomes = 52
Step 3: P(spades) = 13/52 = 1/4 = 0.25
Answer: 1/4 = 25% | 1/4 = 25% | probability | easy | 8baddbc2f1b2 |
A product costs $1200. It is on sale for 20% off. What is the discount amount? | Step 1: Calculate the discount.
Discount = 20% × $1200 = 0.2 × 1200 = $240
Step 2: The sale price would be $1200 - $240 = $960
Answer: The discount is $240 | 240 | arithmetic | easy | ab268854794c |
Solve for x: 12x + 16 = 76 | Step 1: Subtract 16 from both sides.
12x + 16 - 16 = 76 - 16
12x = 60
Step 2: Divide both sides by 12.
x = 60 ÷ 12
x = 5
Answer: x = 5 | 5 | algebra | easy | ff27eade813f |
Calculate the area of a triangle with base 7 m and height 9 m. | Step 1: Use the formula: Area = (base × height) / 2
Area = (7 × 9) / 2 = 63 / 2 = 31.5 m²
Answer: 31.5 m² | 31.5 m² | geometry | easy | 4503bcfe6dc4 |
How many liters of a 30% solution must be mixed with a 70% solution to obtain 10 liters of a 38% solution? | Step 1: Let x = liters of 30% solution; then (10 - x) = liters of 70% solution.
Step 2: Set up the equation for the amount of solute.
30x + 70(10 - x) = 38 × 10
30x + 700 - 70x = 380
-40x = 380 - 700
-40x = -320
x = -320 ÷ -40 = 8.0 liters
Step 3: 70% solution = 10 - 8.0 = 2.0 liters
Answer: 8.0 liters of ... | 8.0L of 30% + 2.0L of 70% | word_problems | hard | 64e6a101cca6 |
A right triangle has one leg of 30 cm and hypotenuse of 78 cm. Find the other leg. | Step 1: Use the Pythagorean theorem: b² = c² - a²
b² = 78² - 30² = 6084 - 900 = 5184
Step 2: Take the square root.
b = √5184 = 72 cm
Answer: 72 cm | 72 cm | geometry | easy | 341ba9e8c378 |
Find the area of a rectangle with width 16 cm and height 19 cm. | Step 1: Use the formula: Area = width × height
Area = 16 × 19 = 304 cm²
Answer: 304 cm² | 304 cm² | geometry | easy | 820d27f3665b |
Person A can complete a job in 3 hours. Person B can complete the same job in 6 hours. How long will it take them to finish together? | Step 1: Find each person's rate (fraction of job per hour).
A's rate = 1/3 of the job per hour
B's rate = 1/6 of the job per hour
Step 2: Combined rate = 1/3 + 1/6 = 6/(3×6) + 3/(3×6) = 9/18
Step 3: Time = 1 / (combined rate) = 18/9 = 2.0 hours
Answer: 2.0 hours | 2.0 hours | word_problems | medium | 795e79b69069 |
A right triangle has legs of length 10 cm and 24 cm. Find the hypotenuse. | Step 1: Use the Pythagorean theorem: c² = a² + b²
c² = 10² + 24² = 100 + 576 = 676
Step 2: Take the square root.
c = √676 = 26 cm
Answer: 26 cm | 26 cm | geometry | easy | e3e525951a3c |
Person A can complete a job in 2 hours. Person B can complete the same job in 5 hours. How long will it take them to finish together? | Step 1: Find each person's rate (fraction of job per hour).
A's rate = 1/2 of the job per hour
B's rate = 1/5 of the job per hour
Step 2: Combined rate = 1/2 + 1/5 = 5/(2×5) + 2/(2×5) = 7/10
Step 3: Time = 1 / (combined rate) = 10/7 = 1.43 hours
Answer: 1.43 hours | 1.43 hours | word_problems | medium | a88b79f75576 |
Find the GCD (Greatest Common Divisor) of 24 and 31. | Use the Euclidean algorithm:
24 = 31 × 0 + 24
31 = 24 × 1 + 7
24 = 7 × 3 + 3
7 = 3 × 2 + 1
3 = 1 × 3 + 0
GCD(24, 31) = 1
Answer: 1 | 1 | number_theory | medium | 20afb1271e9d |
Solve for x: 6x + 5 = -19 | Step 1: Subtract 5 from both sides.
6x + 5 - 5 = -19 - 5
6x = -24
Step 2: Divide both sides by 6.
x = -24 ÷ 6
x = -4
Answer: x = -4 | -4 | algebra | easy | 07dc6629b7a5 |
62 is what percentage of 250? | Step 1: Divide the part by the whole.
62 ÷ 250 = 0.248
Step 2: Multiply by 100 to get percentage.
0.248 × 100 = 25%
Answer: 25% | 62 | arithmetic | easy | 8731f8922711 |
Solve for x: 4x + 3 = -37 | Step 1: Subtract 3 from both sides.
4x + 3 - 3 = -37 - 3
4x = -40
Step 2: Divide both sides by 4.
x = -40 ÷ 4
x = -10
Answer: x = -10 | -10 | algebra | easy | 9ca25d974323 |
Calculate the area of a triangle with base 19 m and height 15 m. | Step 1: Use the formula: Area = (base × height) / 2
Area = (19 × 15) / 2 = 285 / 2 = 142.5 m²
Answer: 142.5 m² | 142.5 m² | geometry | easy | af083b938773 |
Calculate the compound interest on $25,000 at 4% per year, compounded monthly, for 2 years. | Step 1: Use the formula A = P(1 + r/n)^(nt)
P = $25,000, r = 4% = 0.04, n = 12 (monthly), t = 2 years
Step 2: Substitute values.
A = 25000 × (1 + 0.04/12)^(12×2)
A = 25000 × (1 + 0.003333)^24
A = 25000 × 1.083143
A = $27,078.57
Step 3: Compound Interest = A - P = $27,078.57 - $25,000 = $2,078.57
Answer: Co... | $2,078.57 | finance_math | medium | aff09b48e431 |
Solve for x: 5x + 18 = -17 | Step 1: Subtract 18 from both sides.
5x + 18 - 18 = -17 - 18
5x = -35
Step 2: Divide both sides by 5.
x = -35 ÷ 5
x = -7
Answer: x = -7 | -7 | algebra | easy | 421139e481d7 |
An item costing $200 is sold at a 15% loss. What is the selling price? | Step 1: Calculate the loss amount.
Loss = 15% × $200 = $30
Step 2: Selling Price = Cost Price - Loss
SP = $200 - $30 = $170
Answer: $170 | $170 | arithmetic | easy | e12f47051381 |
240 is what percentage of 400? | Step 1: Divide the part by the whole.
240 ÷ 400 = 0.6
Step 2: Multiply by 100 to get percentage.
0.6 × 100 = 60%
Answer: 60% | 240 | arithmetic | easy | c06e39ef9400 |
Find the range of: 31, 34, 38, 41, 48, 51, 81, 89 | Step 1: Identify max and min values.
Max = 89, Min = 31
Step 2: Range = Max - Min = 89 - 31 = 58
Answer: 58 | 58 | statistics | easy | 25a8ac655e5a |
Find the area of a circle with radius 7 cm. Use π ≈ 3.14159. | Step 1: Use the formula: Area = π × r²
Area = 3.14159 × 7² = 3.14159 × 49 ≈ 153.94 cm²
Answer: ≈ 153.94 cm² | ≈ 153.94 cm² | geometry | easy | 02e392ae29f4 |
An item costing $100 is sold at a 40% loss. What is the selling price? | Step 1: Calculate the loss amount.
Loss = 40% × $100 = $40
Step 2: Selling Price = Cost Price - Loss
SP = $100 - $40 = $60
Answer: $60 | $60 | arithmetic | easy | b0ea389c2f07 |
Find the range of: 25, 27, 32, 91, 95 | Step 1: Identify max and min values.
Max = 95, Min = 25
Step 2: Range = Max - Min = 95 - 25 = 70
Answer: 70 | 70 | statistics | easy | 1b5bac0e7ec4 |
Find the area of a rectangle with width 13 cm and height 12 cm. | Step 1: Use the formula: Area = width × height
Area = 13 × 12 = 156 cm²
Answer: 156 cm² | 156 cm² | geometry | easy | aa2241e97db7 |
A right triangle has legs of length 18 cm and 80 cm. Find the hypotenuse. | Step 1: Use the Pythagorean theorem: c² = a² + b²
c² = 18² + 80² = 324 + 6400 = 6724
Step 2: Take the square root.
c = √6724 = 82 cm
Answer: 82 cm | 82 cm | geometry | easy | df680c190a7c |
Find the LCM (Least Common Multiple) of 38 and 32. | Step 1: Find GCD(38, 32) using Euclidean algorithm.
GCD = 2
Step 2: LCM = (a × b) / GCD
LCM = (38 × 32) / 2 = 1216 / 2 = 608
Answer: 608 | 608 | number_theory | medium | c3ef7495cc0c |
Calculate the compound interest on $1,000 at 6% per year, compounded quarterly, for 5 years. | Step 1: Use the formula A = P(1 + r/n)^(nt)
P = $1,000, r = 6% = 0.06, n = 4 (quarterly), t = 5 years
Step 2: Substitute values.
A = 1000 × (1 + 0.06/4)^(4×5)
A = 1000 × (1 + 0.015)^20
A = 1000 × 1.346855
A = $1,346.86
Step 3: Compound Interest = A - P = $1,346.86 - $1,000 = $346.86
Answer: Compound Intere... | $346.86 | finance_math | medium | e265c5761562 |
What is 30% of 80? | Step 1: Convert percentage to decimal: 30% = 0.3
Step 2: Multiply.
80 × 0.3 = 24
Answer: 24 | 24 | arithmetic | easy | 9adc27487d77 |
A trader buys goods for $80 and sells them at a 25% profit. What is the selling price? | Step 1: Calculate the profit amount.
Profit = 25% × $80 = $20
Step 2: Selling Price = Cost Price + Profit
SP = $80 + $20 = $100
Answer: $100 | $100 | arithmetic | easy | fb247a16b8ff |
Calculate the compound interest on $1,000 at 8% per year, compounded quarterly, for 2 years. | Step 1: Use the formula A = P(1 + r/n)^(nt)
P = $1,000, r = 8% = 0.08, n = 4 (quarterly), t = 2 years
Step 2: Substitute values.
A = 1000 × (1 + 0.08/4)^(4×2)
A = 1000 × (1 + 0.02)^8
A = 1000 × 1.171659
A = $1,171.66
Step 3: Compound Interest = A - P = $1,171.66 - $1,000 = $171.66
Answer: Compound Interest... | $171.66 | finance_math | medium | 45bb859153fd |
Solve: x² - 3x + 2 = 0 | Step 1: Use the quadratic formula: x = (-b ± √(b²-4ac)) / 2a
Here a=1, b=-3, c=2
Step 2: Calculate the discriminant.
b²-4ac = -3² - 4(1)(2) = 9 - 8 = 1
Step 3: Find the roots.
x = (3 ± √1) / 2
x = (3 ± 1) / 2
x₁ = (3 + 1) / 2 = 2
x₂ = (3 - 1) / 2 = 1
Answer: x = 2 or x = 1 | 2 or 1 | algebra | medium | 97227df469ba |
20 is what percentage of 50? | Step 1: Divide the part by the whole.
20 ÷ 50 = 0.4
Step 2: Multiply by 100 to get percentage.
0.4 × 100 = 40%
Answer: 40% | 20 | arithmetic | easy | 7bb134d06189 |
Solve: x² + 9x + 14 = 0 | Step 1: Use the quadratic formula: x = (-b ± √(b²-4ac)) / 2a
Here a=1, b=9, c=14
Step 2: Calculate the discriminant.
b²-4ac = 9² - 4(1)(14) = 81 - 56 = 25
Step 3: Find the roots.
x = (-9 ± √25) / 2
x = (-9 ± 5) / 2
x₁ = (-9 + 5) / 2 = -2
x₂ = (-9 - 5) / 2 = -7
Answer: x = -2 or x = -7 | -2 or -7 | algebra | medium | 4adf4451eb33 |
A card is drawn at random from a standard 52-card deck. What is the probability it is a diamonds? | Step 1: Count favorable outcomes.
There are 13 cards of each suit, so 13 diamonds.
Step 2: Total possible outcomes = 52
Step 3: P(diamonds) = 13/52 = 1/4 = 0.25
Answer: 1/4 = 25% | 1/4 = 25% | probability | easy | caea129a158d |
A right triangle has one leg of 27 cm and hypotenuse of 123 cm. Find the other leg. | Step 1: Use the Pythagorean theorem: b² = c² - a²
b² = 123² - 27² = 15129 - 729 = 14400
Step 2: Take the square root.
b = √14400 = 120 cm
Answer: 120 cm | 120 cm | geometry | easy | d637c5fceab3 |
Find the area of a rectangle with width 6 cm and height 17 cm. | Step 1: Use the formula: Area = width × height
Area = 6 × 17 = 102 cm²
Answer: 102 cm² | 102 cm² | geometry | easy | 31470b316b5c |
How many liters of a 20% solution must be mixed with a 60% solution to obtain 10 liters of a 48% solution? | Step 1: Let x = liters of 20% solution; then (10 - x) = liters of 60% solution.
Step 2: Set up the equation for the amount of solute.
20x + 60(10 - x) = 48 × 10
20x + 600 - 60x = 480
-40x = 480 - 600
-40x = -120
x = -120 ÷ -40 = 3.0 liters
Step 3: 60% solution = 10 - 3.0 = 7.0 liters
Answer: 3.0 liters of ... | 3.0L of 20% + 7.0L of 60% | word_problems | hard | 671296f1fbbd |
Person A can complete a job in 4 hours. Person B can complete the same job in 10 hours. How long will it take them to finish together? | Step 1: Find each person's rate (fraction of job per hour).
A's rate = 1/4 of the job per hour
B's rate = 1/10 of the job per hour
Step 2: Combined rate = 1/4 + 1/10 = 10/(4×10) + 4/(4×10) = 14/40
Step 3: Time = 1 / (combined rate) = 40/14 = 2.86 hours
Answer: 2.86 hours | 2.86 hours | word_problems | medium | 0912d45f8fbc |
A trader buys goods for $80 and sells them at a 12% profit. What is the selling price? | Step 1: Calculate the profit amount.
Profit = 12% × $80 = $9
Step 2: Selling Price = Cost Price + Profit
SP = $80 + $9 = $89
Answer: $89 | $89 | arithmetic | easy | 5037668cde61 |
A card is drawn at random from a standard 52-card deck. What is the probability it is a clubs? | Step 1: Count favorable outcomes.
There are 13 cards of each suit, so 13 clubs.
Step 2: Total possible outcomes = 52
Step 3: P(clubs) = 13/52 = 1/4 = 0.25
Answer: 1/4 = 25% | 1/4 = 25% | probability | easy | cf4a6677c759 |
End of preview. Expand in Data Studio
Math Reasoning SFT (100K)
100,000 math problems with detailed step-by-step solutions — ready for supervised fine-tuning of math reasoning models.
Dataset Description
100,000 problems across 8 mathematical categories and 3 difficulty levels:
Categories
| Category | Examples | Topics |
|---|---|---|
word_problems |
~23,100 | Rate/time/distance, work problems, mixture, meeting/catch-up |
arithmetic |
~15,400 | Percentages, profit/loss, ratios |
geometry |
~15,400 | Area (rectangle, triangle, circle, trapezoid), Pythagorean theorem |
algebra |
~15,200 | Linear equations, quadratic equations |
finance_math |
~7,800 | Compound interest (annual/quarterly/monthly compounding) |
number_theory |
~7,800 | GCD, LCM (Euclidean algorithm) |
probability |
~7,700 | Dice, cards, balls, coins |
statistics |
~7,600 | Mean, median, range |
Difficulty Distribution
| Level | Examples | Description |
|---|---|---|
easy |
~48,000 | Single-step or direct formula application |
medium |
~44,300 | Multi-step problems requiring setup |
hard |
~7,700 | Problems requiring simultaneous equations or complex setup |
Format
{
"problem": "A car travels at 60 km/h for 2.5 hours. How far does it travel?",
"solution": "Step 1: Use the formula: Distance = Speed × Time\n Distance = 60 km/h × 2.5 h = 150 km\n\nAnswer: 150 km",
"answer": "150 km",
"category": "word_problems",
"difficulty": "easy",
"id": "abc123"
}
Solution Structure
Every solution follows a consistent multi-step format:
- Formula identification — states the relevant formula or approach
- Substitution — plugs in the specific numbers
- Step-by-step calculation — shows intermediate results
- Final answer — clearly labeled
Answer:line
Use Case
- SFT for math reasoning capability in LLMs
- Training step-by-step problem solving behavior
- Curriculum learning: filter by
difficultyfor progressive training - Evaluation: held-out test sets for math benchmarks
- Chain-of-thought distillation
Filtering Examples
import json
# Load only medium/hard problems
with open("math-reasoning-sft-100k.jsonl") as f:
data = [json.loads(l) for l in f]
hard_algebra = [r for r in data if r["difficulty"] in ("medium","hard") and r["category"] == "algebra"]
License
Apache 2.0
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