problem stringlengths 17 146 | solution stringlengths 72 380 | answer stringlengths 1 27 | category stringclasses 8
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Person A can complete a job in 3 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 = 1/3 of the job per hour
B's rate = 1/8 of the job per hour
Step 2: Combined rate = 1/3 + 1/8 = 8/(3×8) + 3/(3×8) = 11/24
Step 3: Time = 1 / (combined rate) = 24/11 = 2.18 hours
Answer: 2.18 hours | 2.18 hours | word_problems | medium | f7eae70c2b40 |
Find the area of a trapezoid with parallel sides of 6 m and 11 m, and height 10 m. | Step 1: Use the formula: Area = (a + b) / 2 × h
Area = (6 + 11) / 2 × 10 = 17 / 2 × 10 = 8.5 × 10 = 85.0 m²
Answer: 85.0 m² | 85.0 m² | geometry | medium | be01146abe67 |
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 | 95f3f8ccdf22 |
An item costing $80 is sold at a 20% loss. What is the selling price? | Step 1: Calculate the loss amount.
Loss = 20% × $80 = $16
Step 2: Selling Price = Cost Price - Loss
SP = $80 - $16 = $64
Answer: $64 | $64 | arithmetic | easy | fb5623b9749d |
How many liters of a 20% solution must be mixed with a 60% solution to obtain 10 liters of a 34% 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) = 34 × 10
20x + 600 - 60x = 340
-40x = 340 - 600
-40x = -260
x = -260 ÷ -40 = 6.5 liters
Step 3: 60% solution = 10 - 6.5 = 3.5 liters
Answer: 6.5 liters of ... | 6.5L of 20% + 3.5L of 60% | word_problems | hard | c594ebc44204 |
A car travels at 65 km/h for 5 hours. How far does it travel? | Step 1: Use the formula: Distance = Speed × Time
Distance = 65 km/h × 5 h = 325 km
Answer: 325 km | 325 km | word_problems | easy | 0a110a9cab33 |
Person A can complete a job in 5 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 = 1/5 of the job per hour
B's rate = 1/3 of the job per hour
Step 2: Combined rate = 1/5 + 1/3 = 3/(5×3) + 5/(5×3) = 8/15
Step 3: Time = 1 / (combined rate) = 15/8 = 1.88 hours
Answer: 1.88 hours | 1.88 hours | word_problems | medium | 3d2f20d7adee |
Car A leaves at 60 km/h. Car B starts 1.5 hour(s) later at 70 km/h. How long after Car B departs does it catch Car A? | Step 1: Find Car A's head start distance.
Head start = 60 km/h × 1.5 h = 90.0 km
Step 2: Find the rate at which Car B closes the gap.
Relative speed = 70 - 60 = 10 km/h
Step 3: Time to close the gap.
Time = 90.0 ÷ 10 = 9.0 hours
Answer: Car B catches Car A after 9.0 hours | 9.0 hours | word_problems | medium | 8aa7a086b114 |
Find the area of a trapezoid with parallel sides of 12 m and 16 m, and height 8 m. | Step 1: Use the formula: Area = (a + b) / 2 × h
Area = (12 + 16) / 2 × 8 = 28 / 2 × 8 = 14.0 × 8 = 112.0 m²
Answer: 112.0 m² | 112.0 m² | geometry | medium | 03796a2ba463 |
What is 40% of 120? | Step 1: Convert percentage to decimal: 40% = 0.4
Step 2: Multiply.
120 × 0.4 = 48
Answer: 48 | 48 | arithmetic | easy | 63affde415af |
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 | e48892d3c7ad |
A product costs $400. It is on sale for 30% off. What is the discount amount? | Step 1: Calculate the discount.
Discount = 30% × $400 = 0.3 × 400 = $120
Step 2: The sale price would be $400 - $120 = $280
Answer: The discount is $120 | 120 | arithmetic | easy | 61f40bb99a93 |
An item costing $50 is sold at a 15% loss. What is the selling price? | Step 1: Calculate the loss amount.
Loss = 15% × $50 = $7
Step 2: Selling Price = Cost Price - Loss
SP = $50 - $7 = $43
Answer: $43 | $43 | arithmetic | easy | fa39cd4b5e29 |
What is 10% of 120? | Step 1: Convert percentage to decimal: 10% = 0.1
Step 2: Multiply.
120 × 0.1 = 12
Answer: 12 | 12 | arithmetic | easy | 2a82605de9df |
Find the mean of: 14, 24, 33, 42, 56, 59, 89, 93, 99 | Step 1: Sum all values.
14 + 24 + 33 + 42 + 56 + 59 + 89 + 93 + 99 = 509
Step 2: Divide by the count of values (9).
Mean = 509 ÷ 9 = 56.56
Answer: 56.56 | 56.56 | statistics | easy | 3f3c4049a972 |
Find the LCM (Least Common Multiple) of 48 and 42. | Step 1: Find GCD(48, 42) using Euclidean algorithm.
GCD = 6
Step 2: LCM = (a × b) / GCD
LCM = (48 × 42) / 6 = 2016 / 6 = 336
Answer: 336 | 336 | number_theory | medium | 61b67d5acf81 |
What is 15% of 400? | Step 1: Convert percentage to decimal: 15% = 0.15
Step 2: Multiply.
400 × 0.15 = 60
Answer: 60 | 60 | arithmetic | easy | 3f9ff93e179d |
A fair six-sided die is rolled. What is the probability of rolling a 6? | Step 1: Identify favorable outcomes.
Rolling a 6: 1 outcome
Step 2: Total possible outcomes = 6
Step 3: Probability = favorable / total = 1/6 ≈ 0.167
Answer: 1/6 ≈ 16.7% | 1/6 | probability | medium | d5cb932e4652 |
How many liters of a 10% solution must be mixed with a 70% solution to obtain 10 liters of a 28% solution? | Step 1: Let x = liters of 10% solution; then (10 - x) = liters of 70% solution.
Step 2: Set up the equation for the amount of solute.
10x + 70(10 - x) = 28 × 10
10x + 700 - 70x = 280
-60x = 280 - 700
-60x = -420
x = -420 ÷ -60 = 7.0 liters
Step 3: 70% solution = 10 - 7.0 = 3.0 liters
Answer: 7.0 liters of ... | 7.0L of 10% + 3.0L of 70% | word_problems | hard | b16c822205cc |
A car travels at 70 km/h for 3.5 hours. How far does it travel? | Step 1: Use the formula: Distance = Speed × Time
Distance = 70 km/h × 3.5 h = 245.0 km
Answer: 245.0 km | 245.0 km | word_problems | easy | 6a7ccf965441 |
What is 40% of 50? | Step 1: Convert percentage to decimal: 40% = 0.4
Step 2: Multiply.
50 × 0.4 = 20
Answer: 20 | 20 | arithmetic | easy | b98ae5b6c877 |
60 is what percentage of 200? | Step 1: Divide the part by the whole.
60 ÷ 200 = 0.3
Step 2: Multiply by 100 to get percentage.
0.3 × 100 = 30%
Answer: 30% | 60 | arithmetic | easy | 51245eb84d1d |
A trader buys goods for $50 and sells them at a 20% profit. What is the selling price? | Step 1: Calculate the profit amount.
Profit = 20% × $50 = $10
Step 2: Selling Price = Cost Price + Profit
SP = $50 + $10 = $60
Answer: $60 | $60 | arithmetic | easy | abcf03cd0cdc |
An item costing $50 is sold at a 20% loss. What is the selling price? | Step 1: Calculate the loss amount.
Loss = 20% × $50 = $10
Step 2: Selling Price = Cost Price - Loss
SP = $50 - $10 = $40
Answer: $40 | $40 | arithmetic | easy | 1602d929f9b5 |
Find the GCD (Greatest Common Divisor) of 52 and 27. | Use the Euclidean algorithm:
52 = 27 × 1 + 25
27 = 25 × 1 + 2
25 = 2 × 12 + 1
2 = 1 × 2 + 0
GCD(52, 27) = 1
Answer: 1 | 1 | number_theory | medium | 987d5f592238 |
Calculate the compound interest on $1,000 at 10% per year, compounded quarterly, for 5 years. | Step 1: Use the formula A = P(1 + r/n)^(nt)
P = $1,000, r = 10% = 0.1, n = 4 (quarterly), t = 5 years
Step 2: Substitute values.
A = 1000 × (1 + 0.1/4)^(4×5)
A = 1000 × (1 + 0.025)^20
A = 1000 × 1.638616
A = $1,638.62
Step 3: Compound Interest = A - P = $1,638.62 - $1,000 = $638.62
Answer: Compound Interes... | $638.62 | finance_math | medium | a7f0563e5ed2 |
A right triangle has legs of length 6 cm and 8 cm. Find the hypotenuse. | Step 1: Use the Pythagorean theorem: c² = a² + b²
c² = 6² + 8² = 36 + 64 = 100
Step 2: Take the square root.
c = √100 = 10 cm
Answer: 10 cm | 10 cm | geometry | easy | bad6b00e56b8 |
How many liters of a 10% solution must be mixed with a 80% solution to obtain 10 liters of a 48% solution? | Step 1: Let x = liters of 10% solution; then (10 - x) = liters of 80% solution.
Step 2: Set up the equation for the amount of solute.
10x + 80(10 - x) = 48 × 10
10x + 800 - 80x = 480
-70x = 480 - 800
-70x = -320
x = -320 ÷ -70 = 4.57 liters
Step 3: 80% solution = 10 - 4.57 = 5.43 liters
Answer: 4.57 liters... | 4.57L of 10% + 5.43L of 80% | word_problems | hard | 19bbcdcaeaa6 |
A trader buys goods for $100 and sells them at a 10% profit. What is the selling price? | Step 1: Calculate the profit amount.
Profit = 10% × $100 = $10
Step 2: Selling Price = Cost Price + Profit
SP = $100 + $10 = $110
Answer: $110 | $110 | arithmetic | easy | ad9a8b04ad63 |
Solve for x: 9x + 17 = 17 | Step 1: Subtract 17 from both sides.
9x + 17 - 17 = 17 - 17
9x = 0
Step 2: Divide both sides by 9.
x = 0 ÷ 9
x = 0
Answer: x = 0 | 0 | algebra | easy | 0a23ad9459f3 |
An item costing $300 is sold at a 30% loss. What is the selling price? | Step 1: Calculate the loss amount.
Loss = 30% × $300 = $90
Step 2: Selling Price = Cost Price - Loss
SP = $300 - $90 = $210
Answer: $210 | $210 | arithmetic | easy | cbf4bcb637cf |
Find the LCM (Least Common Multiple) of 42 and 24. | Step 1: Find GCD(42, 24) using Euclidean algorithm.
GCD = 6
Step 2: LCM = (a × b) / GCD
LCM = (42 × 24) / 6 = 1008 / 6 = 168
Answer: 168 | 168 | number_theory | medium | 6db14dd33db1 |
Calculate the compound interest on $1,000 at 3% per year, compounded annually, for 3 years. | Step 1: Use the formula A = P(1 + r/n)^(nt)
P = $1,000, r = 3% = 0.03, n = 1 (annually), t = 3 years
Step 2: Substitute values.
A = 1000 × (1 + 0.03/1)^(1×3)
A = 1000 × (1 + 0.03)^3
A = 1000 × 1.092727
A = $1,092.73
Step 3: Compound Interest = A - P = $1,092.73 - $1,000 = $92.73
Answer: Compound Interest =... | $92.73 | finance_math | medium | fafd73622019 |
Car A leaves at 60 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 = 60 km/h × 1 h = 60 km
Step 2: Find the rate at which Car B closes the gap.
Relative speed = 90 - 60 = 30 km/h
Step 3: Time to close the gap.
Time = 60 ÷ 30 = 2.0 hours
Answer: Car B catches Car A after 2.0 hours | 2.0 hours | word_problems | medium | 8580088f927e |
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 | 321f81845eba |
Solve for x: 14x + 2 = 86 | Step 1: Subtract 2 from both sides.
14x + 2 - 2 = 86 - 2
14x = 84
Step 2: Divide both sides by 14.
x = 84 ÷ 14
x = 6
Answer: x = 6 | 6 | algebra | easy | 6f4cfe0b117b |
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 | 167355038f79 |
Calculate the compound interest on $2,000 at 10% per year, compounded monthly, for 5 years. | Step 1: Use the formula A = P(1 + r/n)^(nt)
P = $2,000, r = 10% = 0.1, n = 12 (monthly), t = 5 years
Step 2: Substitute values.
A = 2000 × (1 + 0.1/12)^(12×5)
A = 2000 × (1 + 0.008333)^60
A = 2000 × 1.645309
A = $3,290.62
Step 3: Compound Interest = A - P = $3,290.62 - $2,000 = $1,290.62
Answer: Compound I... | $1,290.62 | finance_math | medium | 58fa907ceddb |
Calculate the compound interest on $10,000 at 10% per year, compounded quarterly, for 5 years. | Step 1: Use the formula A = P(1 + r/n)^(nt)
P = $10,000, r = 10% = 0.1, n = 4 (quarterly), t = 5 years
Step 2: Substitute values.
A = 10000 × (1 + 0.1/4)^(4×5)
A = 10000 × (1 + 0.025)^20
A = 10000 × 1.638616
A = $16,386.16
Step 3: Compound Interest = A - P = $16,386.16 - $10,000 = $6,386.16
Answer: Compoun... | $6,386.16 | finance_math | medium | b74394e755bd |
Solve for x: 2x + 15 = 21 | Step 1: Subtract 15 from both sides.
2x + 15 - 15 = 21 - 15
2x = 6
Step 2: Divide both sides by 2.
x = 6 ÷ 2
x = 3
Answer: x = 3 | 3 | algebra | easy | a827b010fe4b |
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 | 6e3d934c560a |
Calculate the compound interest on $25,000 at 8% per year, compounded monthly, for 5 years. | Step 1: Use the formula A = P(1 + r/n)^(nt)
P = $25,000, r = 8% = 0.08, n = 12 (monthly), t = 5 years
Step 2: Substitute values.
A = 25000 × (1 + 0.08/12)^(12×5)
A = 25000 × (1 + 0.006667)^60
A = 25000 × 1.489846
A = $37,246.14
Step 3: Compound Interest = A - P = $37,246.14 - $25,000 = $12,246.14
Answer: C... | $12,246.14 | finance_math | medium | 118566f9a715 |
Solve: x² - 2x - 3 = 0 | Step 1: Use the quadratic formula: x = (-b ± √(b²-4ac)) / 2a
Here a=1, b=-2, c=-3
Step 2: Calculate the discriminant.
b²-4ac = -2² - 4(1)(-3) = 4 - -12 = 16
Step 3: Find the roots.
x = (2 ± √16) / 2
x = (2 ± 4) / 2
x₁ = (2 + 4) / 2 = 3
x₂ = (2 - 4) / 2 = -1
Answer: x = 3 or x = -1 | 3 or -1 | algebra | medium | a77d9267cbfb |
Person A can complete a job in 6 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 = 1/6 of the job per hour
B's rate = 1/8 of the job per hour
Step 2: Combined rate = 1/6 + 1/8 = 8/(6×8) + 6/(6×8) = 14/48
Step 3: Time = 1 / (combined rate) = 48/14 = 3.43 hours
Answer: 3.43 hours | 3.43 hours | word_problems | medium | d7826582daf7 |
A bag contains 8 red balls and 7 blue balls. One ball is drawn at random. What is the probability it is red? | Step 1: Total balls = 8 + 7 = 15
Step 2: Favorable outcomes (red balls) = 8
Step 3: P(red) = 8/15 ≈ 0.533
Answer: 8/15 ≈ 53.3% | 8/15 | probability | easy | dec8f77b2c9b |
Solve: x² + 1x - 42 = 0 | Step 1: Use the quadratic formula: x = (-b ± √(b²-4ac)) / 2a
Here a=1, b=1, c=-42
Step 2: Calculate the discriminant.
b²-4ac = 1² - 4(1)(-42) = 1 - -168 = 169
Step 3: Find the roots.
x = (-1 ± √169) / 2
x = (-1 ± 13) / 2
x₁ = (-1 + 13) / 2 = 6
x₂ = (-1 - 13) / 2 = -7
Answer: x = 6 or x = -7 | 6 or -7 | algebra | medium | 3738738a81f4 |
Calculate the compound interest on $25,000 at 3% per year, compounded annually, for 3 years. | Step 1: Use the formula A = P(1 + r/n)^(nt)
P = $25,000, r = 3% = 0.03, n = 1 (annually), t = 3 years
Step 2: Substitute values.
A = 25000 × (1 + 0.03/1)^(1×3)
A = 25000 × (1 + 0.03)^3
A = 25000 × 1.092727
A = $27,318.17
Step 3: Compound Interest = A - P = $27,318.17 - $25,000 = $2,318.17
Answer: Compound ... | $2,318.17 | finance_math | medium | 0af3b1346a55 |
Calculate the compound interest on $5,000 at 6% per year, compounded quarterly, for 3 years. | Step 1: Use the formula A = P(1 + r/n)^(nt)
P = $5,000, r = 6% = 0.06, n = 4 (quarterly), t = 3 years
Step 2: Substitute values.
A = 5000 × (1 + 0.06/4)^(4×3)
A = 5000 × (1 + 0.015)^12
A = 5000 × 1.195618
A = $5,978.09
Step 3: Compound Interest = A - P = $5,978.09 - $5,000 = $978.09
Answer: Compound Intere... | $978.09 | finance_math | medium | 4ad9ac8516fc |
A car travels at 30 km/h for 5 hours. How far does it travel? | Step 1: Use the formula: Distance = Speed × Time
Distance = 30 km/h × 5 h = 150 km
Answer: 150 km | 150 km | word_problems | easy | c0cd37452067 |
Find the LCM (Least Common Multiple) of 49 and 14. | Step 1: Find GCD(49, 14) using Euclidean algorithm.
GCD = 7
Step 2: LCM = (a × b) / GCD
LCM = (49 × 14) / 7 = 686 / 7 = 98
Answer: 98 | 98 | number_theory | medium | 75197c733613 |
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 | ec77c1524477 |
Calculate the compound interest on $5,000 at 7% per year, compounded monthly, for 10 years. | Step 1: Use the formula A = P(1 + r/n)^(nt)
P = $5,000, r = 7% = 0.07, n = 12 (monthly), t = 10 years
Step 2: Substitute values.
A = 5000 × (1 + 0.07/12)^(12×10)
A = 5000 × (1 + 0.005833)^120
A = 5000 × 2.009661
A = $10,048.31
Step 3: Compound Interest = A - P = $10,048.31 - $5,000 = $5,048.31
Answer: Comp... | $5,048.31 | finance_math | medium | b9ce6a130dd5 |
An item costing $300 is sold at a 25% loss. What is the selling price? | Step 1: Calculate the loss amount.
Loss = 25% × $300 = $75
Step 2: Selling Price = Cost Price - Loss
SP = $300 - $75 = $225
Answer: $225 | $225 | arithmetic | easy | 2c636fde65d0 |
Calculate the area of a triangle with base 9 m and height 15 m. | Step 1: Use the formula: Area = (base × height) / 2
Area = (9 × 15) / 2 = 135 / 2 = 67.5 m²
Answer: 67.5 m² | 67.5 m² | geometry | easy | 0a3b76948b7e |
Solve for x: 11x + 15 = -29 | Step 1: Subtract 15 from both sides.
11x + 15 - 15 = -29 - 15
11x = -44
Step 2: Divide both sides by 11.
x = -44 ÷ 11
x = -4
Answer: x = -4 | -4 | algebra | easy | 328cfe1ebb3c |
A bag contains 6 red balls and 3 blue balls. One ball is drawn at random. What is the probability it is red? | Step 1: Total balls = 6 + 3 = 9
Step 2: Favorable outcomes (red balls) = 6
Step 3: P(red) = 6/9 ≈ 0.667
Answer: 6/9 ≈ 66.7% | 6/9 | probability | easy | e73efa443218 |
Person A can complete a job in 6 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 = 1/6 of the job per hour
B's rate = 1/10 of the job per hour
Step 2: Combined rate = 1/6 + 1/10 = 10/(6×10) + 6/(6×10) = 16/60
Step 3: Time = 1 / (combined rate) = 60/16 = 3.75 hours
Answer: 3.75 hours | 3.75 hours | word_problems | medium | 8a5f3c2a4581 |
An item costing $50 is sold at a 10% loss. What is the selling price? | Step 1: Calculate the loss amount.
Loss = 10% × $50 = $5
Step 2: Selling Price = Cost Price - Loss
SP = $50 - $5 = $45
Answer: $45 | $45 | arithmetic | easy | 743c28b4a77d |
A fair coin is flipped 2 times. What is the probability of getting exactly 2 heads? | Step 1: Total possible outcomes = 2^2 = 4
Step 2: Count favorable outcomes for 'exactly 2 heads': 1
Step 3: P(exactly 2 heads) = 1/4 ≈ 0.25
Answer: 1/4 ≈ 25.0% | 1/4 | probability | medium | e2c4f3002361 |
A trader buys goods for $80 and sells them at a 15% profit. What is the selling price? | Step 1: Calculate the profit amount.
Profit = 15% × $80 = $12
Step 2: Selling Price = Cost Price + Profit
SP = $80 + $12 = $92
Answer: $92 | $92 | arithmetic | easy | a3297a622c17 |
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 | ba31d9facc55 |
Find the median of: 96, 35, 48, 51, 43, 79, 51, 97, 50 | Step 1: Sort the values in ascending order.
35, 43, 48, 50, 51, 51, 79, 96, 97
Step 2: The median is the middle value (position 5 of 9).
Median = 51
Answer: 51 | 51 | statistics | easy | 6374d6240396 |
Car A leaves at 60 km/h. Car B starts 1.5 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 = 60 km/h × 1.5 h = 90.0 km
Step 2: Find the rate at which Car B closes the gap.
Relative speed = 100 - 60 = 40 km/h
Step 3: Time to close the gap.
Time = 90.0 ÷ 40 = 2.25 hours
Answer: Car B catches Car A after 2.25 hours | 2.25 hours | word_problems | medium | 11c47b951a91 |
A fair six-sided die is rolled. What is the probability of rolling a 4? | Step 1: Identify favorable outcomes.
Rolling a 4: 1 outcome
Step 2: Total possible outcomes = 6
Step 3: Probability = favorable / total = 1/6 ≈ 0.167
Answer: 1/6 ≈ 16.7% | 1/6 | probability | medium | 524d1d1c4a3d |
Calculate the compound interest on $1,000 at 7% per year, compounded monthly, for 10 years. | Step 1: Use the formula A = P(1 + r/n)^(nt)
P = $1,000, r = 7% = 0.07, n = 12 (monthly), t = 10 years
Step 2: Substitute values.
A = 1000 × (1 + 0.07/12)^(12×10)
A = 1000 × (1 + 0.005833)^120
A = 1000 × 2.009661
A = $2,009.66
Step 3: Compound Interest = A - P = $2,009.66 - $1,000 = $1,009.66
Answer: Compou... | $1,009.66 | finance_math | medium | 78f12007ffa0 |
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 | 0c493967799c |
Person A can complete a job in 4 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 = 1/4 of the job per hour
B's rate = 1/6 of the job per hour
Step 2: Combined rate = 1/4 + 1/6 = 6/(4×6) + 4/(4×6) = 10/24
Step 3: Time = 1 / (combined rate) = 24/10 = 2.4 hours
Answer: 2.4 hours | 2.4 hours | word_problems | medium | ee9e2b9ad6a4 |
Find the mean of: 13, 39, 66, 76, 85, 90, 93, 96, 99 | Step 1: Sum all values.
13 + 39 + 66 + 76 + 85 + 90 + 93 + 96 + 99 = 657
Step 2: Divide by the count of values (9).
Mean = 657 ÷ 9 = 73.0
Answer: 73.0 | 73.0 | statistics | easy | 3d79143722e1 |
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 | 09e601e54fc6 |
Solve: x² + 2x - 35 = 0 | Step 1: Use the quadratic formula: x = (-b ± √(b²-4ac)) / 2a
Here a=1, b=2, c=-35
Step 2: Calculate the discriminant.
b²-4ac = 2² - 4(1)(-35) = 4 - -140 = 144
Step 3: Find the roots.
x = (-2 ± √144) / 2
x = (-2 ± 12) / 2
x₁ = (-2 + 12) / 2 = 5
x₂ = (-2 - 12) / 2 = -7
Answer: x = 5 or x = -7 | 5 or -7 | algebra | medium | 28bc1ebf27c0 |
Calculate the compound interest on $1,000 at 6% per year, compounded annually, for 10 years. | Step 1: Use the formula A = P(1 + r/n)^(nt)
P = $1,000, r = 6% = 0.06, n = 1 (annually), t = 10 years
Step 2: Substitute values.
A = 1000 × (1 + 0.06/1)^(1×10)
A = 1000 × (1 + 0.06)^10
A = 1000 × 1.790848
A = $1,790.85
Step 3: Compound Interest = A - P = $1,790.85 - $1,000 = $790.85
Answer: Compound Intere... | $790.85 | finance_math | medium | fa1512408601 |
A right triangle has legs of length 3 cm and 4 cm. Find the hypotenuse. | Step 1: Use the Pythagorean theorem: c² = a² + b²
c² = 3² + 4² = 9 + 16 = 25
Step 2: Take the square root.
c = √25 = 5 cm
Answer: 5 cm | 5 cm | geometry | easy | 757b90d2950d |
Solve for x: 2x + 3 = -11 | Step 1: Subtract 3 from both sides.
2x + 3 - 3 = -11 - 3
2x = -14
Step 2: Divide both sides by 2.
x = -14 ÷ 2
x = -7
Answer: x = -7 | -7 | algebra | easy | 44228fa56586 |
Calculate the compound interest on $2,000 at 4% per year, compounded quarterly, for 5 years. | Step 1: Use the formula A = P(1 + r/n)^(nt)
P = $2,000, r = 4% = 0.04, n = 4 (quarterly), t = 5 years
Step 2: Substitute values.
A = 2000 × (1 + 0.04/4)^(4×5)
A = 2000 × (1 + 0.01)^20
A = 2000 × 1.22019
A = $2,440.38
Step 3: Compound Interest = A - P = $2,440.38 - $2,000 = $440.38
Answer: Compound Interest... | $440.38 | finance_math | medium | 4b02b1ab8a7d |
Find the area of a circle with radius 9 cm. Use π ≈ 3.14159. | Step 1: Use the formula: Area = π × r²
Area = 3.14159 × 9² = 3.14159 × 81 ≈ 254.47 cm²
Answer: ≈ 254.47 cm² | ≈ 254.47 cm² | geometry | easy | 2cac95f58245 |
Solve for x: 11x + 12 = 12 | Step 1: Subtract 12 from both sides.
11x + 12 - 12 = 12 - 12
11x = 0
Step 2: Divide both sides by 11.
x = 0 ÷ 11
x = 0
Answer: x = 0 | 0 | algebra | easy | 30b6998c144d |
How many liters of a 10% solution must be mixed with a 70% solution to obtain 10 liters of a 53% solution? | Step 1: Let x = liters of 10% solution; then (10 - x) = liters of 70% solution.
Step 2: Set up the equation for the amount of solute.
10x + 70(10 - x) = 53 × 10
10x + 700 - 70x = 530
-60x = 530 - 700
-60x = -170
x = -170 ÷ -60 = 2.83 liters
Step 3: 70% solution = 10 - 2.83 = 7.17 liters
Answer: 2.83 liters... | 2.83L of 10% + 7.17L of 70% | word_problems | hard | fa1f97efec4c |
Find the range of: 22, 36, 41, 48, 52, 58, 85, 86, 90 | Step 1: Identify max and min values.
Max = 90, Min = 22
Step 2: Range = Max - Min = 90 - 22 = 68
Answer: 68 | 68 | statistics | easy | a4ebe9d00d4c |
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 | 7958ee251d50 |
Find the range of: 25, 44, 45, 86, 95, 96, 98, 99, 99 | Step 1: Identify max and min values.
Max = 99, Min = 25
Step 2: Range = Max - Min = 99 - 25 = 74
Answer: 74 | 74 | statistics | easy | ab54bb214e58 |
Two trains start from cities 350 km apart, heading toward each other. Train A travels at 40 km/h and Train B at 70 km/h. How long until they meet? | Step 1: Find the combined speed (they approach each other).
Combined speed = 40 + 70 = 110 km/h
Step 2: Time = Distance ÷ Combined Speed
Time = 350 ÷ 110 = 3.18 hours
Answer: They meet after 3.18 hours | 3.18 hours | word_problems | medium | 7d9176f3e8e8 |
Find the LCM (Least Common Multiple) of 10 and 23. | Step 1: Find GCD(10, 23) using Euclidean algorithm.
GCD = 1
Step 2: LCM = (a × b) / GCD
LCM = (10 × 23) / 1 = 230 / 1 = 230
Answer: 230 | 230 | number_theory | medium | 2bddb6ad4d3a |
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 | fbf0daf8ca30 |
Calculate the compound interest on $1,000 at 7% per year, compounded quarterly, for 5 years. | Step 1: Use the formula A = P(1 + r/n)^(nt)
P = $1,000, r = 7% = 0.07, n = 4 (quarterly), t = 5 years
Step 2: Substitute values.
A = 1000 × (1 + 0.07/4)^(4×5)
A = 1000 × (1 + 0.0175)^20
A = 1000 × 1.414778
A = $1,414.78
Step 3: Compound Interest = A - P = $1,414.78 - $1,000 = $414.78
Answer: Compound Inter... | $414.78 | finance_math | medium | 7cd6c804c3bc |
Solve: x² + 1x = 0 | Step 1: Use the quadratic formula: x = (-b ± √(b²-4ac)) / 2a
Here a=1, b=1, c=0
Step 2: Calculate the discriminant.
b²-4ac = 1² - 4(1)(0) = 1 - 0 = 1
Step 3: Find the roots.
x = (-1 ± √1) / 2
x = (-1 ± 1) / 2
x₁ = (-1 + 1) / 2 = 0
x₂ = (-1 - 1) / 2 = -1
Answer: x = 0 or x = -1 | 0 or -1 | algebra | medium | 565bf44d104b |
Solve for x: 14x + 16 = -26 | Step 1: Subtract 16 from both sides.
14x + 16 - 16 = -26 - 16
14x = -42
Step 2: Divide both sides by 14.
x = -42 ÷ 14
x = -3
Answer: x = -3 | -3 | algebra | medium | 86a9e501e226 |
A trader buys goods for $500 and sells them at a 25% profit. What is the selling price? | Step 1: Calculate the profit amount.
Profit = 25% × $500 = $125
Step 2: Selling Price = Cost Price + Profit
SP = $500 + $125 = $625
Answer: $625 | $625 | arithmetic | easy | f5e78c8edf0f |
Solve for x: 7x + 18 = 46 | Step 1: Subtract 18 from both sides.
7x + 18 - 18 = 46 - 18
7x = 28
Step 2: Divide both sides by 7.
x = 28 ÷ 7
x = 4
Answer: x = 4 | 4 | algebra | medium | 82b867c15577 |
Find the LCM (Least Common Multiple) of 29 and 35. | Step 1: Find GCD(29, 35) using Euclidean algorithm.
GCD = 1
Step 2: LCM = (a × b) / GCD
LCM = (29 × 35) / 1 = 1015 / 1 = 1015
Answer: 1015 | 1015 | number_theory | medium | c36ad7cd6860 |
A bag contains 6 red balls and 6 blue balls. One ball is drawn at random. What is the probability it is red? | Step 1: Total balls = 6 + 6 = 12
Step 2: Favorable outcomes (red balls) = 6
Step 3: P(red) = 6/12 ≈ 0.5
Answer: 6/12 ≈ 50.0% | 6/12 | probability | easy | 8f5c1fec71e8 |
Find the mean of: 24, 30, 42, 57, 81 | Step 1: Sum all values.
24 + 30 + 42 + 57 + 81 = 234
Step 2: Divide by the count of values (5).
Mean = 234 ÷ 5 = 46.8
Answer: 46.8 | 46.8 | statistics | easy | 678129992ae8 |
Calculate the compound interest on $10,000 at 6% per year, compounded annually, for 2 years. | Step 1: Use the formula A = P(1 + r/n)^(nt)
P = $10,000, r = 6% = 0.06, n = 1 (annually), t = 2 years
Step 2: Substitute values.
A = 10000 × (1 + 0.06/1)^(1×2)
A = 10000 × (1 + 0.06)^2
A = 10000 × 1.1236
A = $11,236.0
Step 3: Compound Interest = A - P = $11,236.0 - $10,000 = $1,236.0
Answer: Compound Inter... | $1,236.0 | finance_math | medium | 5f1e98480ca1 |
Solve for x: 11x + 12 = 34 | Step 1: Subtract 12 from both sides.
11x + 12 - 12 = 34 - 12
11x = 22
Step 2: Divide both sides by 11.
x = 22 ÷ 11
x = 2
Answer: x = 2 | 2 | algebra | easy | c1a3594f713e |
Calculate the area of a triangle with base 10 m and height 9 m. | Step 1: Use the formula: Area = (base × height) / 2
Area = (10 × 9) / 2 = 90 / 2 = 45.0 m²
Answer: 45.0 m² | 45.0 m² | geometry | easy | 4935e14c1f2e |
How many liters of a 10% solution must be mixed with a 90% solution to obtain 10 liters of a 65% 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) = 65 × 10
10x + 900 - 90x = 650
-80x = 650 - 900
-80x = -250
x = -250 ÷ -80 = 3.12 liters
Step 3: 90% solution = 10 - 3.12 = 6.88 liters
Answer: 3.12 liters... | 3.12L of 10% + 6.88L of 90% | word_problems | hard | 27c266612840 |
A right triangle has one leg of 28 cm and hypotenuse of 100 cm. Find the other leg. | Step 1: Use the Pythagorean theorem: b² = c² - a²
b² = 100² - 28² = 10000 - 784 = 9216
Step 2: Take the square root.
b = √9216 = 96 cm
Answer: 96 cm | 96 cm | geometry | easy | 0f99bc163726 |
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 | f8c109b511e3 |
How many liters of a 30% solution must be mixed with a 70% solution to obtain 10 liters of a 55% 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) = 55 × 10
30x + 700 - 70x = 550
-40x = 550 - 700
-40x = -150
x = -150 ÷ -40 = 3.75 liters
Step 3: 70% solution = 10 - 3.75 = 6.25 liters
Answer: 3.75 liters... | 3.75L of 30% + 6.25L of 70% | word_problems | hard | f565cb9df326 |
Solve for x: 5x + 14 = 29 | Step 1: Subtract 14 from both sides.
5x + 14 - 14 = 29 - 14
5x = 15
Step 2: Divide both sides by 5.
x = 15 ÷ 5
x = 3
Answer: x = 3 | 3 | algebra | medium | e0c57656e3a5 |
Find the median of: 88, 21, 22, 64, 72, 45, 23, 17 | Step 1: Sort the values in ascending order.
17, 21, 22, 23, 45, 64, 72, 88
Step 2: The median is the middle value (position 5 of 8).
Median = 45
Answer: 45 | 45 | statistics | easy | 89d68ec95c57 |
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