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[ { "content": "How many ways can 3 friends be arranged around a circular dinner table?\n\n['A)A)16', 'B)B)2', 'C)C)96', 'D)D)120', 'E)E)720']", "role": "user", "uuid": "7818cdca-1055-46c5-a72a-d8749fc746be" }, { "content": "The number of arrangements of n distinct objects in a row is given by n!n!.\nThe number of arrangements of n distinct objects in a circle is given by (n−1)!(n−1)!.\nThe difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have:\nn!n=(n−1)!n!n=(n−1)!.\nSo, the answer is (3 - 1)! = 2! = 2.\nAnswer: B.", "role": "assistant", "uuid": "b5a5421b-bbdb-486d-8bf4-ff512d58e0ab" } ]

{ "coherence": 2.53, "complexity": 1.49, "correctness": 2.25, "helpfulness": 2.18, "instruction-following": 2.51, "safety": 3.82, "verbosity": 1.41, "verbosity-coeff": -0.1349 }

[ { "content": "In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?\n\n['A)210', 'B)209', 'C)212', 'D)211', 'E)200']", "role": "user", "uuid": "e998bb17-2ad2-4ed6-9417-cd3fc8859301" }, { "content": "In a group of 6 boys and 4 girls, four children are to be selected such that at least one boy should be there.\nHence we have 4 options as given below\nWe can select 4 boys ...(option 1)\nNumber of ways to this = 6C4\nWe can select 3 boys and 1 girl ...(option 2)\nNumber of ways to this = 6C3 × 4C1\nWe can select 2 boys and 2 girls ...(option 3)\nNumber of ways to this = 6C2 × 4C2\nWe can select 1 boy and 3 girls ...(option 4)\nNumber of ways to this = 6C1 × 4C3\nTotal number of ways\n= 6C4 + 6C3 × 4C1 + 6C2 × 4C2 + 6C1 × 4C3\n= 6C2 + 6C3 × 4C1 + 6C2 × 4C2 + 6C1 × 4C1[∵ nCr = nC(n-r)]\n= 15 + 80 + 90 + 24\n= 209\nB", "role": "assistant", "uuid": "2364d332-2666-49b9-b0e3-f3d98d106ccd" } ]

{ "coherence": 2.88, "complexity": 2.18, "correctness": 2.27, "helpfulness": 2.29, "instruction-following": 3.15, "safety": 5.24, "verbosity": 1.74, "verbosity-coeff": -0.1917 }

[ { "content": "A company has a job to prepare certain number of cans and there are three machines A, B and C for this job. A can complete the job in 3 days, B can complete the job in 4 days and C can complete the job in 6 days. How many days the company will it take to complete the job if all the machines are used simultaneously?\n\n['A)4 days', 'B)4/3 days', 'C)3 days', 'D)12days', 'E)14 days']", "role": "user", "uuid": "b113b86a-122f-4571-b3cb-ca754e6b3f62" }, { "content": "Let the total number of cans to be prepared be 12.\nThe number of cans prepared by A in 1 day = 4.\nThe number of cans prepared by B in 1 day = 3.\nThe number of cans prepared by C in 1 day = 2.\nThus, the total number of cans that can be prepared by all the machines working simultaneously in a single day = 9.\nTherefore, the number of days taken to complete the whole work = 12/9 = 4/3 days.\nANSWER:B", "role": "assistant", "uuid": "abfea46c-298b-4d75-b288-066478f48f21" } ]

{ "coherence": 2.9, "complexity": 1.55, "correctness": 2.78, "helpfulness": 3.02, "instruction-following": 3.95, "safety": 5.44, "verbosity": 1.61, "verbosity-coeff": -0.1562 }

[ { "content": "What is the smallest positive integer K such that the product of 1575 x K is a perfect square?\n\n['A)7', 'B)9', 'C)15', 'D)25', 'E)63']", "role": "user", "uuid": "4251d136-d073-43ed-854e-6c2394642b8c" }, { "content": "perfect square, is just an integer that can be written as the square of some other integer. For example 16=4^2, is a perfect square.\nNow, 1575 = 3^2 * 5^2 * 7, so if k=7 then 1575 k = (3 * 5 * 7)^2, which is a perfect square (basically the least positive value of k must complete only the power of 7 to even power as powers of other primes are already even).\nAnswer: A.", "role": "assistant", "uuid": "1787cb15-6eb1-4dc4-8afe-79331076d4c9" } ]

{ "coherence": 2.45, "complexity": 1.39, "correctness": 1.56, "helpfulness": 1.7, "instruction-following": 1.71, "safety": 4.81, "verbosity": 1.1, "verbosity-coeff": -0.2363 }

[ { "content": "College T has 1000 students. Of the 210 students majoring in one or more of the sciences,135 are majoring in Chemistry and 155 are majoring in Biology. If at least 30 of the students are not majoring in either Chemistry or Biology, then the number of students majoring in both Chemistry and Biology could be any number from?\n\n['A)110 to 135', 'B)110 to 130', 'C)130', 'D)110', 'E)105']", "role": "user", "uuid": "329badcb-8041-481a-97f3-84cc06133e05" }, { "content": "Total = Chemistry + Biology - Both + Neither\n210 = 135 + 155 - Both + N\nWe know that N (Neither) must be at least 30, so set N=30 and solve:\n210 = 135 + 155 - Both + 30\n210 = 320 - Both\nBoth = 110\nEven if you're not sure whether 110 is the highest or lowest Both could possibly be, it doesn't matter, because you know it's a boundary point of the range.\nBoth can not be greater than 135, because even if every chemistry major was also a biology major, there are only 135 chemistry majors total. A the solution.", "role": "assistant", "uuid": "32a8e517-8604-4f68-a7ba-d8dc9ba2f620" } ]

{ "coherence": 2.84, "complexity": 1.05, "correctness": 2.31, "helpfulness": 2.41, "instruction-following": 2.64, "safety": 5.01, "verbosity": 1.1, "verbosity-coeff": -0.1626 }

[ { "content": "Each student at a certain business school is assigned a 3-digit student identification number. The first digit of the identification number cannot be zero, and the last digit of the identification number must be prime. How many different student identification numbers can the school create?\n\n['A)9,000', 'B)3,600', 'C)2,700', 'D)360', 'E)1,944']", "role": "user", "uuid": "19f41b7e-58f6-4a7a-9093-9c4dbf9b0842" }, { "content": "The identification number is of the form _ _ _ _\n1. First digit cannot be 0\n2. Middle digits can be anything\n3. Last digit has to be prime - 2, 3, 5, 7\nWe can have the following number of possibilities for each space\n__ __ __ __\n9 10 4\nTotal cases = 360\nAnswer : D", "role": "assistant", "uuid": "b7321789-c567-48f2-8e3a-d6a7bd5ed10f" } ]

{ "coherence": 2.2, "complexity": 1.27, "correctness": 2.14, "helpfulness": 2.29, "instruction-following": 2.84, "safety": 5.91, "verbosity": 0.96, "verbosity-coeff": -0.2372 }

[ { "content": "Two pipes A and B can separately fill a tank in 16 and 10 minutes respectively. A third pipe C can drain off 60 liters of water per minute. If all the pipes are opened, the tank can be filled in 10 minutes. What is the capacity of the tank?\n\n['A)590 liters', 'B)960 liters', 'C)740 liters', 'D)560 liters', 'E)580 liters']", "role": "user", "uuid": "c4fc0d2e-6a29-440d-bdf1-cf3fb0cd0260" }, { "content": "1/16 + 1/10 - 1/x\n= 1/10\nx = 12\n16 * 60 = 960\nAnswer:B", "role": "assistant", "uuid": "7e580cc4-0a63-4a23-8c34-b4a78921a989" } ]

{ "coherence": 2.12, "complexity": 1.73, "correctness": 1.73, "helpfulness": 2.06, "instruction-following": 2.23, "safety": 6.38, "verbosity": 0.82, "verbosity-coeff": -0.1465 }

[ { "content": "The greatest number by which the product of three consecutive multiples of 5 is always\n\n['A)54', 'B)81', 'C)750', 'D)243', 'E)None of these']", "role": "user", "uuid": "7f8e42af-f77e-4b0c-b213-c5f9c1d57487" }, { "content": "Explanation:\n5*10*15 = 750\nOption C", "role": "assistant", "uuid": "ef5338e2-b4cd-4e11-b2ab-faab618c8e04" } ]

{ "coherence": 2.74, "complexity": 1.39, "correctness": 2.43, "helpfulness": 2.57, "instruction-following": 2.62, "safety": 4.62, "verbosity": 0.63, "verbosity-coeff": -0.1157 }

[ { "content": "When n is divided by 19 , the remainder is 6. When n is divided by 11, the quotient is equal to Z, and the remainder is equal to 6. Z must be divisible by which of the following numbers?\n\n['A)3', 'B)7', 'C)10', 'D)13', 'E)nineteen']", "role": "user", "uuid": "21dbbee1-23e8-44c4-9ae3-b173c49d7b1d" }, { "content": "N = 19 q + 6\nN = 11 z + 6\nEquating\n19 Q + 6 = 11z+6\n11z=19q\n11z/19 = q\nsince q is an integer Z must be divisible by 19.\nANSWER:E", "role": "assistant", "uuid": "6b93a0a1-d51d-46f0-8738-825e243986e2" } ]

{ "coherence": 2.86, "complexity": 2.06, "correctness": 2.33, "helpfulness": 2.41, "instruction-following": 2.61, "safety": 4.62, "verbosity": 1.27, "verbosity-coeff": -0.1568 }

[ { "content": "The sum of two numbers is 64, and one of them is 12 more than the other. What are the two numbers?\n\n['A)26-38', 'B)50-34', 'C)60-24', 'D)42-42', 'E)21-63']", "role": "user", "uuid": "338ca8c2-6516-46d7-955c-34b2d6325543" }, { "content": "In this problem, we are asked to find two numbers. Therefore, we must let x be one of them. Let x, then, be the first number.\nWe are told that the other number is 12 more, x + 12.\nThe problem states that their sum is 64:\nword problem = 64\nThe line over x + 12 is a grouping symbol called a vinculum. It saves us writing parentheses.\nWe have:\n2x = 64 − 12\n= 52.\nx = 52/2\n= 26.\nThis is the first number. Therefore the other number is\nx + 12 = 26 + 12 = 38.\nThe sum of 26 + 38 is 64.\nA", "role": "assistant", "uuid": "1a54003d-00d6-4108-9029-059c4012d421" } ]

{ "coherence": 2.31, "complexity": 1.67, "correctness": 1.79, "helpfulness": 1.86, "instruction-following": 2.41, "safety": 3.99, "verbosity": 1.74, "verbosity-coeff": -0.1846 }

[ { "content": "If f(y)=y^2 and y is a positive integer, which of the following CANNOT be the value of f(f(y))?\n\n['A)1', 'B)144', 'C)81', 'D)16', 'E)256']", "role": "user", "uuid": "5d10e1cd-dccd-4af7-994f-a646aa064983" }, { "content": "f(y)=y^2\nf(f(y)) = (y^2)^2\n=y^4\nA. 1 , y=1\nD. 16 , y=2\nC. 81 , y=3\nB. 144\nf(y)=12\nSquare root of 12 is not a positive integer . Hence 144 can not be the value of f(f(y)) .\nE. 256 , y=4\nAnswer B", "role": "assistant", "uuid": "8e5f4cf8-970b-4529-aeca-d1e75545e7f7" } ]

{ "coherence": 2.45, "complexity": 1.78, "correctness": 1.47, "helpfulness": 1.6, "instruction-following": 2.14, "safety": 4.97, "verbosity": 1.39, "verbosity-coeff": -0.2304 }

[ { "content": "A military garrison in a wild frontier has 600 men who have provisions to last 20 weeks. At the end of 6 weeks they are joined by another 300 men. How long will the provisions last?\n\n['A)13 1/3', 'B)9 1/3', 'C)11 3/3', 'D)12 1/2', 'E)12 3/4']", "role": "user", "uuid": "c9e5787f-b1f5-47a4-a531-fbd6c35ff879" }, { "content": "Total provisions=600*20*7=84000\nProvisions used for in 6 weeks=6*7*600=25200\nremaining provisions=58800\nremaining provisions need to be split between 900(600+300) people.\nNumber of provisions per person= 58800/900\nwe need to find the answer in terms of weeks=(58800/900)/7=9 1/3\nAnswer:B", "role": "assistant", "uuid": "7b32726b-c51f-40fa-a4a3-a01d9fe1bcfc" } ]

{ "coherence": 2.96, "complexity": 1.55, "correctness": 2.7, "helpfulness": 2.78, "instruction-following": 3.5, "safety": 5.44, "verbosity": 1.61, "verbosity-coeff": -0.1138 }

[ { "content": "Four of the five parts numbered (a), (b), (c), (d) and (e) in the following equation are exactly, equal. Which of the parts is not equal to the other four? The number of that part is the answer.\n\n['A)375.789 + 41.28 – 115.249', 'B)6.45 × 120.8 – 477.34', 'C)1015.71 – 738.416 + 24.526', 'D)853.12 + 109.73 – 661.03', 'E)132.8 × 3.5 – 152.98']", "role": "user", "uuid": "f2ff0e11-d5a6-4d92-8576-44c9ecab5b63" }, { "content": "Others are equal to 301.82.\nAnswer E", "role": "assistant", "uuid": "3db12e60-f188-4af4-ae0d-1fcf7741ac82" } ]

{ "coherence": 2.37, "complexity": 0.75, "correctness": 1.73, "helpfulness": 1.79, "instruction-following": 2.08, "safety": 4.7, "verbosity": 0.59, "verbosity-coeff": -0.1145 }

[ { "content": "The length of the rectangular field is double its width. Inside the field there is square shaped pond 8m long. If the area of the pond is 1/2 of the area of the field. What is the length of the field?\n\n['A)13', 'B)16', 'C)34', 'D)43', 'E)42']", "role": "user", "uuid": "eb8b0f9f-d83e-4ccc-b3fe-c3c1c4b8e9cb" }, { "content": "Explanation:\nA/2 = 8 * 8 => A = 8 * 8 * 2\nx * 2x = 8 * 8 * 2\nx = 8 => 2x = 16\nAnswer: Option B", "role": "assistant", "uuid": "b699813b-19e7-48ac-ab42-8837a7da392a" } ]

{ "coherence": 2.88, "complexity": 1.52, "correctness": 2.59, "helpfulness": 2.74, "instruction-following": 2.92, "safety": 5.48, "verbosity": 0.43, "verbosity-coeff": -0.1294 }

[ { "content": "If each edge of cube increased by 15%, the percentage increase in\n\n['A)30.25', 'B)32.25', 'C)38.25', 'D)37.25', 'E)41.25']", "role": "user", "uuid": "b3cfb1ed-e3f2-411c-8278-00222d02dae8" }, { "content": "100 × (115)/100 × (115)/100 = 132.25 => 32.25%\nAnswer is B.", "role": "assistant", "uuid": "a539265e-801b-4412-be45-d2fa1f6bc87e" } ]

{ "coherence": 2.74, "complexity": 1.23, "correctness": 2.12, "helpfulness": 2.31, "instruction-following": 2.84, "safety": 4.11, "verbosity": 0.96, "verbosity-coeff": -0.1187 }

[ { "content": "In a coconut grove, (x + 2) trees yield 60 nuts per year, x trees yield 120 nuts per year and (x – 2) trees yield 180 nuts per year. If the average yield per year per tree be 100, find x.\n\n['A)3', 'B)4', 'C)5', 'D)6', 'E)None of the above']", "role": "user", "uuid": "e3770665-d888-4758-96a6-ff4859307e33" }, { "content": "(x+2)×60+x×120+(x−2)×180/(x+2)+x+(x−2)=100\n⇒ 360x−240/3x = 100\n⇒ 60x = 240 ⇒ x = 4\nAnswer E", "role": "assistant", "uuid": "cefd7c25-2b7c-40ce-b67c-0272ec67ef76" } ]

{ "coherence": 2.39, "complexity": 1.94, "correctness": 1.49, "helpfulness": 1.4, "instruction-following": 2.1, "safety": 4.03, "verbosity": 0.87, "verbosity-coeff": -0.1238 }

[ { "content": "Two trains each 150m in length each, are running on two parallel lines in opposite directions. If one goes at the speed of 95km/h while the other travels at 85km/h. how long will it take for them to pass each other completely.\n\n['A)25 sec', 'B)23 sec', 'C)34 sec', 'D)22 sec', 'E)6 sec']", "role": "user", "uuid": "94e008f3-0f73-4998-a12d-11ebc8499ca8" }, { "content": "Explanation:\nD = 150 m + 150 m = 300 m\nRS = 95 + 85 = 180 * 5/18 = 50\nT = 300 * 1/50 = 6 sec\nAnswer: Option E", "role": "assistant", "uuid": "ded74bac-c583-4773-b001-1587f185429c" } ]

{ "coherence": 2.64, "complexity": 1.79, "correctness": 2.41, "helpfulness": 2.49, "instruction-following": 3.21, "safety": 4.58, "verbosity": 1.37, "verbosity-coeff": -0.0924 }

[ { "content": "Pipe A can fill a tank in 9 hours. Due to a leak at the bottom, it takes 12 hours for the pipe A to fill the tank. In what time can the leak alone empty the full tank?\n\n['A)36', 'B)88', 'C)18', 'D)26', 'E)12']", "role": "user", "uuid": "ee529521-1be1-4417-8af7-56123956cd0b" }, { "content": "Let the leak can empty the full tank in x hours 1/9 - 1/x = 1/12\n=> 1/x = 1/9 - 1/12 = 1/12\n=> x = 36. Answer:A", "role": "assistant", "uuid": "15346b7f-4c03-443c-a4e2-9c8fdc8496fc" } ]

{ "coherence": 2.72, "complexity": 1.51, "correctness": 2.41, "helpfulness": 2.41, "instruction-following": 2.84, "safety": 5.24, "verbosity": 1.29, "verbosity-coeff": -0.1427 }

[ { "content": "A train 360 m long runs with a speed of 45 km/hr. What time will it take to pass a platform of 390 m long?\n\n['A)38 sec', 'B)35 sec', 'C)44 sec', 'D)40 sec', 'E)60 sec']", "role": "user", "uuid": "84e69b63-3f35-49a6-a654-c609f5a7ccb5" }, { "content": "Explanation:\nSpeed = 45 km/hr = 45×(10/36) m/s\n= 150/12 = 50/4 = 25/2 m/s\nTotal distance = length of the train + length of the platform\n= 360 + 390 = 750 meter\nTime taken to cross the platform = 750/(25/2) = 750×2/25 = 60 seconds\nAnswer: Option E", "role": "assistant", "uuid": "ebd97f13-02fd-4f3e-8555-6f42488a5366" } ]

{ "coherence": 2.59, "complexity": 2.35, "correctness": 2.18, "helpfulness": 2.47, "instruction-following": 3.05, "safety": 4.77, "verbosity": 1.59, "verbosity-coeff": -0.1143 }

[ { "content": "A certain company expects quarterly earnings of $0.80 per share of stock, half of which will be distributed as dividends to shareholders while the rest will be used for research and development. If earnings are greater than expected , shareholders will receive an additional $0.04 per share for each additional $0.10 of per share earnings. If quarterly earnings are $1.10 per share, what will be the dividend paid to a person who owns 100 shares of the company's stock?\n\n['A)$92', 'B)$96', 'C)$52', 'D)$120', 'E)$240']", "role": "user", "uuid": "5b4bf1fa-6e6a-4f00-8fea-8e46820b12cd" }, { "content": "EPS Actual> EPS expected.\neach gets and additional .12 per share.\nThus .52*100 --> $52\nanswer is C", "role": "assistant", "uuid": "91310a40-1c89-4133-a9db-d55ffcb2b7f0" } ]

{ "coherence": 2.49, "complexity": 0.16, "correctness": 2.06, "helpfulness": 2.21, "instruction-following": 1.8, "safety": 4.93, "verbosity": 0.45, "verbosity-coeff": -0.1616 }

[ { "content": "A patient was given a bottle of tablets by the doctor and he was asked to take five tablets in a gap of 30 minutes.\nIn how much time will he be able to take all the five tablets?\n\n['A)1 Hour.', 'B)2 Hour.', 'C)3 Hour.', 'D)None', 'E)Cannot be determined']", "role": "user", "uuid": "30198e7a-9004-48c5-b877-1569ccec81ec" }, { "content": "Suppose he takes the first tablet at 8:00 pm. Then the second will be consumed by him at 8:30, third at 9:00, fourth at 9:30 and fifth at 10:00.\nTime = 2 hour\nAnswer B", "role": "assistant", "uuid": "bfbca751-b82a-47ac-b0e8-ee788a6ffb14" } ]

{ "coherence": 2.9, "complexity": 0.97, "correctness": 2.55, "helpfulness": 2.72, "instruction-following": 2.92, "safety": 4.7, "verbosity": 1.24, "verbosity-coeff": -0.0954 }

[ { "content": "An amount of Rs. 3000 becomes Rs. 3600 in four years at simple interest. If the rate of interest was 1% more, then what was be the total amount?\n\n['A)3729', 'B)2799', 'C)3720', 'D)2884', 'E)2881']", "role": "user", "uuid": "3b9475b9-3a3c-4cd7-ad88-88fe634ac5a6" }, { "content": "A = P(1 + TR/100)\n=> 3600 = 3000[1 + (4 * R)/100] => R = 5%\nNow R = 6%\n=> A = 3000[1 + (4 * 6)/100] = Rs. 3720.\nAnswer:C", "role": "assistant", "uuid": "b872b93d-f5d9-4c55-ab28-ab76250f515a" } ]

{ "coherence": 2.8, "complexity": 1.65, "correctness": 2.64, "helpfulness": 2.92, "instruction-following": 4.32, "safety": 4.7, "verbosity": 1.38, "verbosity-coeff": -0.1201 }

[ { "content": "Certain stocks in April were 10% less than they were in May and 20% Lesser than they were in June. What was the percentage decrease in the stocks from May to June?\n\n['A)5%', 'B)10%', 'C)20%', 'D)28%', 'E)50%']", "role": "user", "uuid": "4221cdf1-1b6f-4252-af2f-12798522bd75" }, { "content": "Let stocks value in Feb = 100 => In Jan = 90 and March = 90 * 80/100 = 72\nThus, percent decrease in stocks from Feb to March = 100 - 72 = 28%\nHence Answer is D", "role": "assistant", "uuid": "6aa2ea07-0110-4bd9-a5be-ea623b18cc89" } ]

{ "coherence": 2.51, "complexity": 1.94, "correctness": 1.89, "helpfulness": 1.74, "instruction-following": 1.78, "safety": 5.09, "verbosity": 0.95, "verbosity-coeff": -0.1254 }

[ { "content": "The product of a and b is equal to 1 more than twice the sum of a and b. If b = 7, what is the value of b - a?\n\n['A)2', 'B)5', 'C)4', 'D)24', 'E)35']", "role": "user", "uuid": "d338eaf5-4590-4691-8d6a-a3ebe57b3a42" }, { "content": "ab= 1 + 2(a+b)\n7a= 1+2a +14\n5a= 15\na=3\nb-a= 7-3=4\nC is the answer", "role": "assistant", "uuid": "09bcd03c-52a3-42b4-8c7a-72db8ac4c650" } ]

{ "coherence": 3.35, "complexity": 1.77, "correctness": 3, "helpfulness": 2.98, "instruction-following": 3.07, "safety": 5.16, "verbosity": 0.98, "verbosity-coeff": -0.1993 }

[ { "content": "A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 16 cm. What is the length of the wire?\n\n['A)9', 'B)8', 'C)7', 'D)6', 'E)4']", "role": "user", "uuid": "2e913109-f00d-41be-92c2-8a4affddeb52" }, { "content": "Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere.\nπ(16)2 * h = (4/3)π (12)3 => h = 9 cm\nAnswer: A", "role": "assistant", "uuid": "2b0d19ec-d37b-4c65-a8f6-d94a2744e856" } ]

{ "coherence": 2.96, "complexity": 1.19, "correctness": 2.39, "helpfulness": 2.68, "instruction-following": 3.72, "safety": 5.52, "verbosity": 0.79, "verbosity-coeff": -0.1324 }

[ { "content": "Two friends want to buy a snack. They combine their money and find they have $4.15, consisting of quarters, dimes, and nickels. If they have 37 coins and the number of quarters is half the number of nickels, how many quarters do they have?\n\n['A)9', 'B)10', 'C)11', 'D)12', 'E)13']", "role": "user", "uuid": "65f66d4a-8a66-43f9-9215-c50cb88b0919" }, { "content": "Let x be the number of quarters. Then 2x is the number of nickels.\n(1) 25x + 10x + 10D = 415. Then 7x + 2D = 83\n(2) 3x + D = 37. Then 6x + 2D = 74\nLet's subtract equation (2) from equation (1).\nx = 9\nThe answer is A.", "role": "assistant", "uuid": "90a56426-9461-45cc-9f2e-4f763837ce8c" } ]

{ "coherence": 2.7, "complexity": 1.49, "correctness": 1.56, "helpfulness": 1.87, "instruction-following": 2.21, "safety": 4.66, "verbosity": 0.33, "verbosity-coeff": -0.1337 }

[ { "content": "A dishonest shopkeeper deceives by 15% at the time of purchase of article and also 15% at the time of sale.Find out the profit percentage\nProfit%\n\n['A)32.25%.', 'B)32', 'C)42.25%', 'D)42', 'E)50']", "role": "user", "uuid": "ea174588-f11e-4c28-aa38-feac9470b281" }, { "content": "Solution\n=15+15+(15*15 / 100)=30 + 225/100 =30+2.25=32.25%.\nAnswer A", "role": "assistant", "uuid": "ec87a7d5-e32d-4c3d-8088-da34326cce50" } ]

{ "coherence": 3.02, "complexity": 1.67, "correctness": 2.86, "helpfulness": 2.78, "instruction-following": 3.27, "safety": 4.81, "verbosity": 1.76, "verbosity-coeff": -0.1226 }

[ { "content": "The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is:\n\n['A)35 years', 'B)40 years', 'C)50 years', 'D)60 years', 'E)None of these']", "role": "user", "uuid": "d8b1dd54-acb1-41e7-a08a-bc498731f292" }, { "content": "Explanation:\nSum of the present ages of husband, wife and child = (27 x 3 + 3 x 3) years = 90 years.\nSum of the present ages of wife and child = (20 x 2 + 5 x 2) years = 50 years.\nHusband's present age = (90 - 50) years = 40 years.\nANSWER IS B", "role": "assistant", "uuid": "19111ea9-41be-4e4f-85aa-3c2bf1ff0cdc" } ]

{ "coherence": 2.76, "complexity": 1.76, "correctness": 2.25, "helpfulness": 2.61, "instruction-following": 3.62, "safety": 4.17, "verbosity": 1.32, "verbosity-coeff": -0.1273 }

[ { "content": "If U is a negative integer and K is a positive integer, which of the following could be the standard deviation of a set {-7, -5, -3, U, 0, 1, 3, K, 7}?\nI. -1.5\nII. -2\nIII. 0\n\n['A) I only', 'B) II only', 'C) III only', 'D) I and III only', 'E) None']", "role": "user", "uuid": "3a08e06a-9379-41af-818d-fbec026a8b5c" }, { "content": "If U is a negative integer and K is a positive integer, The answer should be (E) as S.D cannot be negative. It is only 0 if all numbers in the set are equal, which is not the case either.E", "role": "assistant", "uuid": "9965d2e7-25a4-4658-b116-1f83e19a2f98" } ]

{ "coherence": 2.55, "complexity": 1.68, "correctness": 1.8, "helpfulness": 1.78, "instruction-following": 1.81, "safety": 5.67, "verbosity": 0.96, "verbosity-coeff": -0.2159 }

[ { "content": "In how many ways to select 3 girls and 2 boys from a class? A class contains 5 boys and 5 girls.\n\n['A)10', 'B)30', 'C)22', 'D)20', 'E)25']", "role": "user", "uuid": "0e81c209-6642-4b22-8dcb-076005522fc2" }, { "content": "The way is 5C3+5C2\n5C3=5!/2!*3!=5*4*3!/3!*2*1=10\n5C2=5!/2!*3!=5*4*3!/3!*2*1=10\n=10+10=20 ways to select 3 girls and 2 boys from a class\nAnswer is option D", "role": "assistant", "uuid": "f4c6c37a-5423-4d4e-9b69-a832ce224f03" } ]

{ "coherence": 2.92, "complexity": 1.96, "correctness": 2.51, "helpfulness": 2.57, "instruction-following": 2.62, "safety": 4.77, "verbosity": 1.43, "verbosity-coeff": -0.1272 }

[ { "content": "If (x^2 + 1)y=6, which of the following is not a possible value for y?\n\n['A)3/2', 'B)2', 'C)1/3', 'D)2/13', 'E)13/2']", "role": "user", "uuid": "94c9f84c-b0fd-4a63-ad9c-28cf2f7c5513" }, { "content": "Its simple\nequation is (x^2 +1)y = 6 ===> x^2 = (6/y) - 1 . As , in LHS, it is x^2 the value has to be positive or zero in RHS.\nHence, (6/y) - 1>= 0 ===> y =< 6. Now only option E has greater value of 'y' than 6.\nThus, correct ans is E", "role": "assistant", "uuid": "4f7d247d-ec36-470f-8d7f-7064c596e023" } ]

{ "coherence": 2.66, "complexity": 1.73, "correctness": 2.18, "helpfulness": 2.16, "instruction-following": 2.47, "safety": 5.52, "verbosity": 1.33, "verbosity-coeff": -0.2045 }

[ { "content": "Find the cost of fencing around a circular field of diameter 70 m at the rate of Rs.1 a meter?\n\n['A)288', 'B)132', 'C)220', 'D)592', 'E)261']", "role": "user", "uuid": "7c5aa46e-ca6b-4ab6-9ce4-d93d120d9d12" }, { "content": "2 * 22/7 * 35 = 220\n220* 1 = Rs.220\nAnswer: C", "role": "assistant", "uuid": "adfabfaf-a348-4547-bf1d-f774a6884318" } ]

{ "coherence": 2.62, "complexity": 0.8, "correctness": 2.39, "helpfulness": 2.72, "instruction-following": 3.43, "safety": 5.09, "verbosity": 0.36, "verbosity-coeff": -0.1077 }

[ { "content": "Alex has $246,713 dollars in his savings account. What is the least amount of money (in whole number of dollars) that he must remove from his account if he wants to split this money evenly among his 6 children?\n\n['A)$1', 'B)$2', 'C)$3', 'D)$4', 'E)$5']", "role": "user", "uuid": "72c8048a-f67c-49f3-a4fd-3a77b945cef7" }, { "content": "In order to divide the sum into 6 parts, the amount must be divisible by 6.\nDivisibility rule of 6: A number is divisible by 6 if it is divisible by both 2 and 3\nDivisibility rule of 3: A number is divisible by 3 if the sum of the digits is divisible by 3\nWe need to make this number even in order for it to be divisible by 2.\nSum of digits 246,713 = 23 and 21 is divisible by 3. Subtracting 2 does not yields an even number.\nSum of digits 246,713 = 23 and 18 is divisible by 3. Subtracting 5 yields an even number.\nHence, we need to subtract 5 from this number for it to be divisible by 6.\nCorrect Option: E", "role": "assistant", "uuid": "7884e3c4-e2fc-4f47-abb3-176e3fd5038f" } ]

{ "coherence": 2.31, "complexity": 0.75, "correctness": 1.65, "helpfulness": 1.57, "instruction-following": 1.84, "safety": 3.97, "verbosity": 0.96, "verbosity-coeff": -0.2008 }

[ { "content": "Three boys are ages 4, 6 and 7 respectively. Three girls are ages 5, 8 and 9, respectively. If two of the boys and two of the girls are randomly selected and the sum of the selected children's ages is r, what is the difference between the probability that r is even and the probability that r is odd?\n\n['A) 1/9', 'B) 1/6', 'C) 2/9', 'D) 1/4', 'E) 1/2']", "role": "user", "uuid": "922abfbc-6147-4a43-87ef-8ee784b7b27a" }, { "content": "Age of Boys r:4, 6, 7\nSum of ages taken 2 at a time: 10,13,11\nAges of Girls:5, 8, 9\nSum of ages taken 2 at a time: 13,17,14\n9 Combinations of sum between sets(10,12,11)(13,17,14)\n=23,27,24- 16,30,17- 24,28,25\nProb(Even)= 5/9\nProb(Odd) =4/9\nAnswer=5/9 - 4/9 = 1/9", "role": "assistant", "uuid": "02f10a1d-79d2-48ab-af9c-9de3091afe21" } ]

{ "coherence": 2.74, "complexity": 1.95, "correctness": 2.23, "helpfulness": 2.14, "instruction-following": 2.04, "safety": 3.76, "verbosity": 1.2, "verbosity-coeff": -0.1734 }

[ { "content": "The sum of the present ages of two persons A and B is 60. If the age of A is twice that of B, find the sum of their ages 7 years hence?\n\n['A)58', 'B)74', 'C)62', 'D)70', 'E)74']", "role": "user", "uuid": "3412b873-8baf-433f-a892-0b03c21f0ff2" }, { "content": "Explanation:\nA + B = 60, A = 2B\n2B + B = 60 => B = 20 then A = 40.\n7 years, their ages will be 47 and 27.\nSum of their ages = 47 + 27 = 74.\nB)", "role": "assistant", "uuid": "47760e63-da5a-40bb-9904-bec7d13d0b9f" } ]

{ "coherence": 3.11, "complexity": 1.17, "correctness": 2.37, "helpfulness": 2.8, "instruction-following": 2.94, "safety": 6.41, "verbosity": 0.94, "verbosity-coeff": -0.1433 }

[ { "content": "A train 125 m long passes a man, running at 3 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?\n\n['A)65 km/hr', 'B)17 km/hr', 'C)76 km/hr', 'D)50 km/hr', 'E)48 km/hr']", "role": "user", "uuid": "ed109602-5056-4c7b-b0c8-93189cea3245" }, { "content": "Speed of the train relative to man = 125/10 = 25/2 m/sec.\n= 25/2 * 18/5 = 45 km/hr\nLet the speed of the train be x km/hr. Then, relative speed = (x - 3) km/hr.\nx - 3 = 45 => x = 48 km/hr.\nAnswer: E", "role": "assistant", "uuid": "17036645-36e2-4b43-aad1-c77ca8efeec9" } ]

{ "coherence": 2.88, "complexity": 1.49, "correctness": 2.35, "helpfulness": 2.37, "instruction-following": 4.05, "safety": 5.28, "verbosity": 0.67, "verbosity-coeff": -0.1186 }

[ { "content": "The average marks of a class of 30 students is 40 and that of another class of 50 students is 60. Find the average marks of all the students?\n\n['A)52.6', 'B)52.4', 'C)52.1', 'D)52.5', 'E)52.9']", "role": "user", "uuid": "c803d2b0-aad0-46b2-8f90-e71e5915012f" }, { "content": "Sum of the marks for the class of 30 students = 30 * 40 = 1200\nSum of the marks for the class of 50 students = 50 * 60 = 3000\nSum of the marks for the class of 80 students =\n1200 + 3000 = 4200\nAverage marks of all the students = 4200/80 = 52.5.Answer: D", "role": "assistant", "uuid": "4f3624a4-87cf-4170-98fc-c730f3dc2ac1" } ]

{ "coherence": 3.13, "complexity": 1.27, "correctness": 3.04, "helpfulness": 3.11, "instruction-following": 4.11, "safety": 4.73, "verbosity": 1.05, "verbosity-coeff": -0.1158 }

[ { "content": "Kelly and Jody packed boxes with books. If Jody packed 80% of the total number of boxes, what was the ratio of the number of boxes Kelly packed to the number that Jody packed?\n\n['A)1 to 6', 'B)1 to 4', 'C)2 to 5', 'D)3 to 5', 'E)2 to 3']", "role": "user", "uuid": "04c7f454-f235-44dd-8fc1-bbc02411c246" }, { "content": "Explanation:\nIf Jody packed 80% of the boxes then Kelly packed 20%. The ratio of the number of boxes Kelly packed to the number Jody packed is thus 20%/80%=1/4\nAnswer: Option B", "role": "assistant", "uuid": "145362ed-afff-4018-a46b-ad245d34067d" } ]

{ "coherence": 3.05, "complexity": 1.54, "correctness": 2.96, "helpfulness": 2.98, "instruction-following": 3.39, "safety": 6.38, "verbosity": 1.18, "verbosity-coeff": -0.1888 }

[ { "content": "At 30 minutes past 6 o'clock, what is the angle between the two hands?\n\n['A)15', 'B)30', 'C)45', 'D)60', 'E)75']", "role": "user", "uuid": "83a69ff5-c0cf-4d0e-bc1a-8c39d739b0c4" }, { "content": "The hour hand moves 360 degrees in 12 hours.\nThe hour hand moves 30 degrees in 1 hour and 15 degrees in 30 minutes.\nThe minute hand moves 360 degrees in 60 minutes and 180 degrees in 30 minutes.\nAt 30 minutes past 6, the hour hand has moved 195 degrees.\nAt 30 minutes past 6, the hour hand has moved 180 degrees.\nThe angle between the two hands is 15 degrees.\nThe answer is A.", "role": "assistant", "uuid": "59878abf-10ae-433b-a6fa-5c2c30cae9a5" } ]

{ "coherence": 3, "complexity": 1.34, "correctness": 2.33, "helpfulness": 2.41, "instruction-following": 2.33, "safety": 5.2, "verbosity": 1.61, "verbosity-coeff": -0.2275 }

[ { "content": "How many positive integers W less than 10,000 are such that the product of their digits is 210?\n\n['A)24', 'B)30', 'C)48', 'D)54', 'E)72']", "role": "user", "uuid": "e3b02613-dbf1-4bc6-b7cb-3c3bea538f01" }, { "content": "210 is the answer when 2, 3, 5 and 7 are multiplied. 210 can also be arrive using 5,6 and 7 and 1, 5, 6 and 7.\nSo sum of arrangements of 2357, 567 and 1567. This translates to 4! +3! + 4!, this equals to 24 + 6 + 24 = 54, D is the answer.", "role": "assistant", "uuid": "9c5c594d-316c-45a5-b4ea-5d55b6cbce19" } ]

{ "coherence": 2.72, "complexity": 1.41, "correctness": 1.9, "helpfulness": 2.16, "instruction-following": 2.1, "safety": 4.81, "verbosity": 0.81, "verbosity-coeff": -0.2578 }

[ { "content": "The “z-number” of a number x is defined as the ones digit of 2^x. Antony rolls a die with 6 sides labeled with the integers from 1 to 6, each of which has an equal probability of landing face-up. He then takes 3^z, where z is the z-number of the result of his die roll, and plots 3^z on a number line as the point A. Finally, he repeats this entire process, this time plotting the result as the point B. What is the probability that the distance between A and B is greater than the value of B?\n\n['A) 3/8', 'B) 13/36', 'C) 17/36', 'D) 19/36', 'E) 23/36']", "role": "user", "uuid": "e1380a1f-a810-46aa-a544-22f53637b912" }, { "content": "If you calculate 3^z for 1st roll, all 6 results will be 9, 81, 6561, 729, 9, 81. This result is the same for 2nd roll. 9, 81, 6561, 729, 9, 81.\nAbout distance: If the first result is 9 and the second is also 9, the distance is 9-9=0 which is smaller than 9. If the first result is 9 and the second is 81, the distance is 81-9=72 which is also smaller than B which has the value of 81. If the first result is 81 and the second is 9, the distance will be greater than B. Distance 81-9=72>9.\nOn the first roll, the probability of getting result 9 is 2/6. In this case no other alternative values for second roll which would make the distance greater than B. So probability is 0. So next estimations are:\nprobability of getting 81 on the first roll (2/6) * probability of getting 9 on the second roll (2/6) = 1/9\nprobability of getting 729 on the first roll (1/6) * probability of getting 9, 81 on the second roll (4/6) = 1/9\nprobability of getting 6561 on the first roll (1/6) * probability of getting 9, 81, 729 on the first roll (5/6) = 5/36\nAll together: 1/9 + 1/9 + 5/36 = 13/36=B", "role": "assistant", "uuid": "bfb77e11-11cd-4087-ac04-9de12b4f58e4" } ]

{ "coherence": 2.49, "complexity": 1.72, "correctness": 1.79, "helpfulness": 1.85, "instruction-following": 1.66, "safety": 4.05, "verbosity": 1.32, "verbosity-coeff": -0.1657 }

[ { "content": "For what k value(s) is the following equation satisfied: 2k-9-k = 4k+6-3k\n\n['A)a. -5', 'B)b. 0 only', 'C)c. 5/2 only', 'D)d. No value', 'E)e. Any value']", "role": "user", "uuid": "b7ea6600-6d89-4ead-9def-0f0278c70110" }, { "content": "9k-9-8k = 4k+4-3k\nk - 9 = k + 4\n-9 = 4, which is false.\nSo, no k satisfies given equation.\nAnswer: D.", "role": "assistant", "uuid": "244804c0-e51d-4963-922f-83a5ce7d401e" } ]

{ "coherence": 2.27, "complexity": 1.31, "correctness": 1.22, "helpfulness": 1.21, "instruction-following": 2.02, "safety": 5.4, "verbosity": 0.75, "verbosity-coeff": -0.1702 }

[ { "content": "A certain car increased its average speed by 5 miles per hour in each successive 5-minute interval after the first interval. If in the first 5-minute interval its average speed was 38 miles per hour, how many miles did the car travel in the third 5-minute interval?\n\n['A)1.0', 'B)1.5', 'C)2.0', 'D)2.5', 'E)4.0']", "role": "user", "uuid": "9650b0dd-a7b0-4208-ab03-6f073aa236a1" }, { "content": "In the third time interval the average speed of the car was 38+5+5=30 miles per hour;\nIn 5 minutes (1/12 hour) at that speed car would travel 48*1/12=4 miles.\nAnswer: E.", "role": "assistant", "uuid": "06c4e0f5-3aa3-410b-896b-76ee4f3c088c" } ]

{ "coherence": 2.7, "complexity": 0.57, "correctness": 1.78, "helpfulness": 1.75, "instruction-following": 1.73, "safety": 4.73, "verbosity": 0.05, "verbosity-coeff": -0.2229 }

[ { "content": "How many numbers from 29 to 79 are exactly divisible by 11?\n\n['A)5', 'B)7', 'C)9', 'D)11', 'E)12']", "role": "user", "uuid": "ae3c53ef-1ce8-4ef2-b021-27186c50faf7" }, { "content": "Option 'A'\n29/11 = 2 and 79/11 = 7 ==> 7 - 2 = 5 Numbers", "role": "assistant", "uuid": "75d840ba-14be-4f27-b6d8-3b03ec9b7f7e" } ]

{ "coherence": 2.55, "complexity": 1.25, "correctness": 2.1, "helpfulness": 2.27, "instruction-following": 2.43, "safety": 4.5, "verbosity": 0.79, "verbosity-coeff": -0.1125 }

[ { "content": "A cube is painted red on all faces. It is then cut into 27 equal smaller cubes. How many J cubes are painted on only 2 faces?\n\n['A)12', 'B)8', 'C)6', 'D)10', 'E)16']", "role": "user", "uuid": "b2ef28c4-8044-4808-a171-750d65e397fc" }, { "content": "1) Draw a simple cube\n2) Draw 9 squares on each face of the cube (so that it looks like a Rubik's Cube) - this is what the cube will look like when it's cut into 27 equal smaller cubes.\n3) Remember that the OUTSIDE of the cube is the part that's painted....\nThe mini-cubes with 2 painted sides are ALL on the edge of the cube, in themiddleof the edge. There are 4 in front, 4 in back and 4 more on thestripthat runs around the left/top/right/bottom of the cube. J=4 + 4 + 4 = 12. Answer A", "role": "assistant", "uuid": "d83cd9b1-2b39-4c56-b6e6-3ccadea71c10" } ]

{ "coherence": 2.94, "complexity": 1.64, "correctness": 2.37, "helpfulness": 2.35, "instruction-following": 2.51, "safety": 5.05, "verbosity": 1.5, "verbosity-coeff": -0.1748 }

[ { "content": "Exactly 36% of the numbers in set Q are even multiples of 3. If 40% of the even integers in set Q are not multiples of 3, what percent of the numbers in set Q are not even integers?\n\n['A) 76%', 'B) 60%', 'C) 50%', 'D) 40%', 'E) 24%']", "role": "user", "uuid": "b0b9a490-344a-4d1b-adfe-45fb3caf18fd" }, { "content": "Everything is correct except the red part with a typo: it should be N=0.6Q --> even numbers are 60% of Q --> 40% of Q are not even integers.\nAnswer: D.", "role": "assistant", "uuid": "5331653d-8ca8-4f57-8e1d-319e3f8b1951" } ]

{ "coherence": 2.61, "complexity": 1.29, "correctness": 1.92, "helpfulness": 1.61, "instruction-following": 1.79, "safety": 6.18, "verbosity": 0.68, "verbosity-coeff": -0.1844 }

[ { "content": "A baker filled with a measuring cup with 1/3 cup water. He poured 1/2 of the water into the batter, and then spilled 1/8 of the water on the floor. How much water will the baker needed to add what is left in the cup to have 50% more than what he started with?\n\n['A)1/8 cup', 'B)3/8 cup', 'C)11/24 cup', 'D)1/2 cup', 'E)7/8 cup']", "role": "user", "uuid": "8bc0e866-a444-4a43-833a-6cae053c36f7" }, { "content": "1/3 is the original water in cup .half in batter.So left is 1/6 out which 1/8 is spilled out.So again left with 1/24.\nso 50% more than what he started was = 1/3+1/2*(1/3)=1/2\nAmount of water needed to add = 1/2 - 1/24=11/24\nC", "role": "assistant", "uuid": "f203dc59-b2a2-46a4-af2f-4c978f0d4eee" } ]

{ "coherence": 2.64, "complexity": 1.94, "correctness": 1.9, "helpfulness": 1.79, "instruction-following": 2.04, "safety": 5.12, "verbosity": 1.28, "verbosity-coeff": -0.1286 }

[ { "content": "A can do a piece of work 30 days. B can do work in 45 days. In how many days they will complete the work together?\n\n['A)15 days', 'B)16 days', 'C)19 days', 'D)17 days', 'E)18 days']", "role": "user", "uuid": "7ffdaf54-935f-4b4f-83eb-5ce8c8dbdbbb" }, { "content": "LCM = 90, Ratio= 30:45=2:3\nNo of days= 90/(2 + 3) = 90/5 = 18 days\nANSWER:E", "role": "assistant", "uuid": "9472099b-3f4d-484c-815f-ce74b4fa3a5d" } ]

{ "coherence": 2.55, "complexity": 0.96, "correctness": 1.89, "helpfulness": 1.92, "instruction-following": 3.11, "safety": 5.36, "verbosity": 0.66, "verbosity-coeff": -0.1168 }

[ { "content": "How many digits are there to the right of the decimal point in the product of .32546 and 75.21 ?\n\n['A)7', 'B)6', 'C)8', 'D)2', 'E)9']", "role": "user", "uuid": "a6a7d514-7984-4879-8a8b-6f3d1592c37e" }, { "content": "Product of is .32546 and 75.21 is 24.4778466.\nTherefore number of digits to right of decimal point is 7\nAnswer is A.", "role": "assistant", "uuid": "d2e746ab-4a5b-4564-8adc-9ea2d3cc463e" } ]

{ "coherence": 2.78, "complexity": 0.75, "correctness": 2.02, "helpfulness": 2.14, "instruction-following": 2.43, "safety": 4.73, "verbosity": 0.81, "verbosity-coeff": -0.1525 }

[ { "content": "The average of 10 numbers is 23. If each number is increased by 4, what will the new average be?\n\n['A)17', 'B)27', 'C)19', 'D)16', 'E)87']", "role": "user", "uuid": "a99a680d-d10a-4acc-84c7-a69e6d94a85e" }, { "content": "Sum of the 10 numbers = 230\nIf each number is increased by 4, the total increase =\n4 * 10 = 40\nThe new sum = 230 + 40 = 270 The new average = 270/10 = 27.\nAnswer:B", "role": "assistant", "uuid": "5e382253-ac39-4e3a-b429-e30f6e9a4239" } ]

{ "coherence": 2.88, "complexity": 1.26, "correctness": 2.68, "helpfulness": 2.94, "instruction-following": 3.31, "safety": 5.59, "verbosity": 1.56, "verbosity-coeff": -0.1322 }

[ { "content": "The ratio of alcohol and water in three mixtures of alcohol and water is 3:2, 4:1, and 7:3. If equal quantities of the mixture are drawn and mixed, the concentration of alcohol in the resulting mixture will be?\n\n['A)65%', 'B)70%', 'C)75%', 'D)80%', 'E)90%']", "role": "user", "uuid": "31b3cb62-35aa-487d-83d3-36f6c8e73255" }, { "content": "The ratios are given such that the sum of alcohol and water can be brought up to 10 for each mixture. (Since equal quantities are to be added)\nFor 3:2 lets take 6 parts alcohol and 4 parts water\nFor 4:1 lets take 8 parts alcohol and 2 parts water\nFor last since the sum is already 10, 7 parts alcohol and 3 parts water.\nMixing these three will give 6+8+7 =21 units alcohol and 4+2+3=9 units water\nor, 21 units alcohol in 30 units of mixture\n21/30 *100 = 70%\nAnswer : B", "role": "assistant", "uuid": "b32a756b-4dde-4c3f-a8b2-9e7c672bddcf" } ]

{ "coherence": 2.96, "complexity": 1.67, "correctness": 2.35, "helpfulness": 2.39, "instruction-following": 3.05, "safety": 5.32, "verbosity": 1.61, "verbosity-coeff": -0.1188 }

[ { "content": "In a certain city each of 15 Girl Scout troops is represented by a colored flag. Each flag consists of either a single color or a pair of two different colors. If each troop has a different flag, what is the minimum number of colors needed for the flags. (Assume that the order of colors in a pair on a flag does not matter.)\n\n['A)3', 'B)4', 'C)6', 'D)5', 'E)7']", "role": "user", "uuid": "ec8d46c7-5c81-4add-92d6-a129c87c6938" }, { "content": "D.5:\nif we have 5 colors we can choose pairs in 5C2 ways = 10 and single color flags are 5. Therefore total number of flags = 15.\nANS D.", "role": "assistant", "uuid": "f79f178b-2604-4413-a3be-09f079c2b2b4" } ]

{ "coherence": 2.78, "complexity": 1.36, "correctness": 1.83, "helpfulness": 1.95, "instruction-following": 2.16, "safety": 5.67, "verbosity": 1.19, "verbosity-coeff": -0.2352 }

[ { "content": "In the following sequence of alphabets, if the second half is reversed, which letter would be the fifth to the right of the letter which is twelveth from the left ?\nA B C D E F G H I J K L M N O P Q R S T U V W X Y Z\n\n['A)J', 'B)W', 'C)T', 'D)G', 'E)K']", "role": "user", "uuid": "38b0b4b0-b3aa-47e2-a247-bfa2637d3cb7" }, { "content": "Explanation:\nCase 1 : A B C D E F G H I J K L M N O P Q R S T U V W X Y Z\nAfter reversal of the second half of the sequence of alphabet, we get,\nCase 2 : A B C D E F G H I J K L M Z Y X W V U T S R Q P O N\nThe twelveth letter from the left end of the above sequence of alphabet Case 2 is L. The letter which is 5th to the right of L is W.\nANSWER: B", "role": "assistant", "uuid": "3f90ddaf-5d6e-4a6f-b625-5ea5ac33ee6e" } ]

{ "coherence": 2.7, "complexity": 1.74, "correctness": 2.18, "helpfulness": 2.35, "instruction-following": 2.74, "safety": 4.3, "verbosity": 1.79, "verbosity-coeff": -0.1005 }

[ { "content": "Find the ones digit of 73^320\n\n['A)3', 'B)5', 'C)6', 'D)7', 'E)9']", "role": "user", "uuid": "7e01c4fb-6192-4cbc-be6c-6339ecb376a0" }, { "content": "Cyclicity of 3 is 3,9,7,1after 4 multiplication again the cycle repeats.\nSo divide 320 by 4 and we get 87 as quotient and 2 as remainder. So cycle will run for 87 times and then 2 times more. So pick up the 2nd item from the cycle.\nHence Answer D.", "role": "assistant", "uuid": "9298a0cc-f317-40af-99b1-d8199a5385e5" } ]

{ "coherence": 2.57, "complexity": 1.98, "correctness": 1.85, "helpfulness": 1.63, "instruction-following": 2.04, "safety": 4.93, "verbosity": 1.01, "verbosity-coeff": -0.1972 }

[ { "content": "Rahim bought 65 books for Rs.1150 from one shop and 50 books for Rs.920 from another. What is the average price he paid per book ?\n\n['A)28', 'B)18', 'C)27', 'D)29', 'E)21']", "role": "user", "uuid": "6c785c7b-faff-4695-833e-fad2ec79bc3e" }, { "content": "Average price per book\n= (1150 + 920) / (65 + 50)\n= 2070 / 115\n= Rs.18\nAnswer:B", "role": "assistant", "uuid": "27fdc4c5-897b-4921-84ff-bfd151cfbf06" } ]

{ "coherence": 3.13, "complexity": 0.83, "correctness": 2.57, "helpfulness": 2.9, "instruction-following": 4.11, "safety": 5.55, "verbosity": 1.15, "verbosity-coeff": -0.1183 }

[ { "content": "Three seventh of a number is 12 more than 40% of that number. What will be the 30% of that number?\n\n['A)A)148', 'B)B)210', 'C)C)63', 'D)D)248', 'E)E)258']", "role": "user", "uuid": "437910ce-06fd-4219-93a6-398419bed986" }, { "content": "3/7 x – 40/100 x = 12\nx = 35 * 12\n35 * 12 * 30/100 = 126/2 = 63\nANSWER:C", "role": "assistant", "uuid": "b267d892-eb29-4089-9f14-ab64b264a81c" } ]

{ "coherence": 2.61, "complexity": 1.39, "correctness": 2.08, "helpfulness": 2.37, "instruction-following": 3, "safety": 6.84, "verbosity": 0.84, "verbosity-coeff": -0.1327 }

[ { "content": "Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a man in the slower train in 25 seconds. Find the length of the faster train?\n\n['A)270', 'B)250', 'C)187', 'D)257', 'E)271']", "role": "user", "uuid": "cb554dda-2b09-4fba-b31b-3a16c4821639" }, { "content": "Relative speed = (72 - 36) * 5/18 = 2 * 5 = 10 mps.\nDistance covered in 25 sec = 25 * 10 = 250 m.\nThe length of the faster train = 250 m.\nAnswer: B", "role": "assistant", "uuid": "750d9ebf-f242-4a2c-b0b8-a74a20ca18fb" } ]

{ "coherence": 2.98, "complexity": 1.34, "correctness": 2.66, "helpfulness": 3.02, "instruction-following": 4.17, "safety": 4.73, "verbosity": 0.76, "verbosity-coeff": -0.1186 }

[ { "content": "Two equally sized jugs full of water are each emptied into two separate unequally sized empty jugs, X and Y. Now, jug X is 1/6 full, while jug Y is 2/3 full. If water is poured from jug X into jug Y until jug Y is filled, what fraction of jug X then contains water?\n\n['A)0', 'B)1/12', 'C)2/15', 'D)1/10', 'E)2/10']", "role": "user", "uuid": "9f961ac5-60dd-49e7-9838-c28a987dfd25" }, { "content": "Suppose the water in each jug is L liters\nCX x (1/6) = L\nCX = 6L liters\nCX is capacity of X\nCY x (2/3) = L\nCY = 3L/2 liters\nCY is capacity of Y\nNow, Y is 3L/2 - L empty = L/2 empty\nSo, we can put only L/2 water in jug Y from Jug X\nJug X's remaining water = L - L/2 = L/2\nFraction of X which contains water = water / CX\n= (L/2)/ 6L\n= 1/12\nAnswer will be B", "role": "assistant", "uuid": "3fdfe3de-7001-4bd4-824e-877c295ff877" } ]

{ "coherence": 2.76, "complexity": 1.48, "correctness": 2.35, "helpfulness": 2.45, "instruction-following": 2.45, "safety": 4.89, "verbosity": 1.05, "verbosity-coeff": -0.1837 }

[ { "content": "Each of three investments has a 20% of becoming worthless within a year of purchase, independently of what happens to the other two investments. If Simone invests an equal sum M in each of these three investments on January 1, the approximate chance that by the end of the year, she loses no more than 1/3 of her original investment is\n\n['A)90%', 'B)80%', 'C)70%', 'D)60%', 'E)40%']", "role": "user", "uuid": "56fa19a1-2a23-43bf-a3f9-b7c4716dbd89" }, { "content": "The problem asks for the approximate chance that no more than 1/3 of the original investment is lost. We can apply the “1 – x” technique: what’s the chance that more than 1/3 of the original investment is lost? There are two outcomes we have to separately measure:\n(a) All 3 investments become worthless.\n(b) 2 of the 3 investments become worthless, while 1 doesn’t.\nOutcome (a): The probability is (0.2)(0.2)(0.2) = 0.008, or a little less than 1%.\nOutcome (b): Call the investments X, Y, and Z. The probability that X retains value, while Y and Z become worthless, is (0.8)(0.2)(0.2) = 0.032. Now, we have to do the same thing for the specific scenarios in which Y retains value (while X and Z don’t) and in which Z retains value (while X and Y don’t). Each of those scenarios results in the same math: 0.032. Thus, we can simply multiply 0.032 by 3 to get 0.096, or a little less than 10%.\nThe sum of these two probabilities is 0.008 + 0.096 = 0.104, or a little more than 10%. Finally, subtracting from 100% and rounding, we find that the probability we were looking for is approximately 90%.\nThe correct answer is A.\nThis problem illustrates the power of diversification in financial investments. All else being equal, it’s less risky to hold a third of your money in three uncorrelated (independent) but otherwise equivalent investments than to put all your eggs in one of the baskets. That said, be wary of historical correlations! Housing price changes in different US cities were not so correlated—and then they became highly correlated during the recent housing crisis (they all fell together), fatally undermining spreadsheet models that assumed that these price changes were independent.", "role": "assistant", "uuid": "6ff4da15-8d52-4fc6-a28f-3c476a1b5483" } ]

{ "coherence": 3.23, "complexity": 2.06, "correctness": 2.8, "helpfulness": 2.7, "instruction-following": 3.02, "safety": 4.89, "verbosity": 2.06, "verbosity-coeff": -0.1482 }

[ { "content": "(1^2 + 2^2 + 3^2 + ... + 10^2) = ?\n\n['A)385', 'B)395', 'C)375', 'D)55', 'E)58']", "role": "user", "uuid": "f04c7e41-c8bd-488d-ac2f-bb7e5f1a985e" }, { "content": "Explanation :\n1^2+2^2+3^2+⋯+n^2=∑n^2=n(n+1)(2n+1)/6\n1^2+2^2+3^2+⋯+10^2=n(n+1)(2n+1)/6=(10(10+1)[(2×10)+1])/6=(10×11×21)/6=(10×11×7)/2=385\nAnswer is A", "role": "assistant", "uuid": "42660034-3566-4ac5-8413-79755b7eaac8" } ]

{ "coherence": 2.96, "complexity": 2, "correctness": 2.68, "helpfulness": 2.72, "instruction-following": 3.11, "safety": 5.32, "verbosity": 1.44, "verbosity-coeff": -0.1149 }

[ { "content": "The average age 11 members of a committee are the same as it was 5 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number?\n\n['A)20 years', 'B)21 years', 'C)18 years', 'D)55 years', 'E)30 years']", "role": "user", "uuid": "dd70da11-8e7e-49d3-ad49-39fd88e4c072" }, { "content": "11 * 5 = 55 years\nAnswer:D", "role": "assistant", "uuid": "3c5ab09a-5f12-4aba-a699-2a54c521e5b7" } ]

{ "coherence": 2.84, "complexity": 0.61, "correctness": 2.23, "helpfulness": 2.23, "instruction-following": 2.31, "safety": 5.09, "verbosity": 0.66, "verbosity-coeff": -0.1806 }

[ { "content": "In 1970 there were 8,902 women stockbrokers in the United States. By 1978 the number had increased to 19,947. Approximately what was the percent increase?\n\n['A)45%', 'B)125%', 'C)145%', 'D)150%', 'E)225%']", "role": "user", "uuid": "c0968f36-187d-4220-8f5f-785a188a125e" }, { "content": "We can use approximation to get the answer quickly.\nLike,\n19,947 is approx 20000\n8902 is approx 8900\nSo, Total increase = 20000 - 8900 = 11100\nHence, % increase = 11100 / 8900 = approx. 11/9 = 1.22 = approx. 1.25\nSo, Choice is B.", "role": "assistant", "uuid": "47cb739f-ecbe-42ed-a967-93afea36ff39" } ]

{ "coherence": 2.55, "complexity": 0.99, "correctness": 1.5, "helpfulness": 1.48, "instruction-following": 1.59, "safety": 4.81, "verbosity": 0.89, "verbosity-coeff": -0.1833 }

[ { "content": "At a certain restaurant, the average (arithmetic mean) number of customers served for the past x days was 65. If the restaurant serves 120 customers today, raising the average to 90 customers per day, what is the value of x?\n\n['A)1', 'B)5', 'C)9', 'D)15', 'E)30']", "role": "user", "uuid": "6e74080a-afd4-49e8-904d-57ee0db3acca" }, { "content": "WITHOUTusing the formula, we can see that today the restaurant served 30 customers above the average. The total amount ABOVE the average must equal total amount BELOW the average. This additional 30 customers must offset the “deficit” below the average of 90 created on the x days the restaurant served only 60 customers per day.\n30/30 = 1 day.Choice (A).\nWITHthe formula, we can set up the following:\n90 = (60x + 120)/(x + 1)\n90x + 90 = 60x + 120\n30x = 30\nx = 1Answer Choice (A)", "role": "assistant", "uuid": "36545772-cafa-4797-8228-884eedbcadb2" } ]

{ "coherence": 2.82, "complexity": 1.45, "correctness": 2.76, "helpfulness": 2.68, "instruction-following": 3.19, "safety": 4.77, "verbosity": 1.49, "verbosity-coeff": -0.21 }

[ { "content": "How many multiples of 3 are there between 10 and 100, exclusive ?\n\n['A)30', 'B)29', 'C)28', 'D)31', 'E)33']", "role": "user", "uuid": "1b1dc354-7e35-4d10-8865-d3defe669129" }, { "content": "3 * 4 = 12\n3 * 33 = 99\nTotal multiples = (33 - 4) + 1 = 30\nExclude 10 and 100 = 30\nAnswer is A", "role": "assistant", "uuid": "1dd8ccfe-45a5-4240-8590-b6c0a95a0553" } ]

{ "coherence": 2.41, "complexity": 1.33, "correctness": 1.69, "helpfulness": 1.73, "instruction-following": 2.29, "safety": 6.06, "verbosity": 1.11, "verbosity-coeff": -0.206 }

[ { "content": "A bus 15 m long is running with a speed of 40 km/hr. In what time will it pass a man who is skateboarding at 8 km/hr in the direction opposite to that in which the car is going?\n\n['A)1.125', 'B)1.5', 'C)1.75', 'D)1.25', 'E)1']", "role": "user", "uuid": "72f9cb70-6395-49f9-9640-55f25ab9cceb" }, { "content": "Speed of bus relative to man = 40 + 8 = 48 km/hr.\n= 48 * 5/18 = 40/3 m/sec.\nTime taken to pass the man = 5 * 3/40\n= 1.125 sec.\nAnswer: A", "role": "assistant", "uuid": "04265cf4-2360-4297-be74-aecf0f7eea99" } ]

{ "coherence": 2.72, "complexity": 1.41, "correctness": 2.02, "helpfulness": 2.23, "instruction-following": 3.31, "safety": 5.63, "verbosity": 1.16, "verbosity-coeff": -0.1155 }

[ { "content": "During the first two weeks of June, the total rainfall in Springdale was 40 inches. If the rainfall during the second week was 1.5 times the rainfall during the first week, what was the rainfall in inches during the second week of June?\n\n['A)15', 'B)18', 'C)21', 'D)24', 'E)27']", "role": "user", "uuid": "02ec3e1f-3e16-4373-babc-1d4ce34fbf67" }, { "content": "Let x be the rainfall in the first week. Then 1.5x was the rainfall in the second week.\n2.5x = 40\nx = 16\nThe rainfall during the second week was 1.5 * 16 = 24 inches\nThe answer is D.", "role": "assistant", "uuid": "607563dc-d768-4652-b80c-4f94ee9774d6" } ]

{ "coherence": 3.54, "complexity": 1.38, "correctness": 3.02, "helpfulness": 3.35, "instruction-following": 3.43, "safety": 4.48, "verbosity": 0.8, "verbosity-coeff": -0.2192 }

[ { "content": "A man complete a journey in 10 hrs. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km?\n\n['A)334', 'B)224', 'C)667', 'D)2678', 'E)112']", "role": "user", "uuid": "1511fa50-2741-4520-a0d2-f1c074bdcd91" }, { "content": "Let the total distance be x km.\nThen, [(1/2 x) / 21 + (1/2 x) / 24] = 10\n15x = 168 * 20 => x = 224 km\nAnswer: B", "role": "assistant", "uuid": "4f56fac3-4808-4b3c-ab77-10d23d2c96d2" } ]

{ "coherence": 3.15, "complexity": 1.16, "correctness": 2.39, "helpfulness": 2.62, "instruction-following": 3.58, "safety": 6.18, "verbosity": 0.28, "verbosity-coeff": -0.109 }

[ { "content": "A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?\n\n['A)177 m', 'B)166 m', 'C)776 m', 'D)150 m', 'E)176 m']", "role": "user", "uuid": "513eb319-fc2c-48c7-b3fd-3fa867d6bfb4" }, { "content": "Speed=(60 * 5/18) m/sec\n= (50/3) m/sec Length of the train\n= (Speed x Time)\n= (50/3 * 9) m = 150 m.\nAnswer:D", "role": "assistant", "uuid": "8c4df829-c9db-45ca-8306-ba1f9291ef8a" } ]

{ "coherence": 2.66, "complexity": 0.95, "correctness": 1.94, "helpfulness": 2.18, "instruction-following": 3.56, "safety": 5.28, "verbosity": 0.9, "verbosity-coeff": -0.1116 }

[ { "content": "150 liters of a mixture of milk and water contains in the ratio 3:2. How much water should now be added so that the ratio of milk and water becomes 3:4?\n\n['A)90 liters', 'B)20 liters', 'C)50 liters', 'D)20 liters', 'E)70 liters']", "role": "user", "uuid": "c9087e73-e8bc-4c0e-90f1-fdc4aaaf6a78" }, { "content": "Milk = 3/5 * 150 = 90 liters\nWater = 50 liters\n90 : (50+P) = 3:4\n150 + 3P = 360 => P = 70\n50 liters of water are to be added for the ratio become 3:4.\nANSWER:C", "role": "assistant", "uuid": "7c90c0a9-1b2a-4905-b8e6-0a677598533e" } ]

{ "coherence": 2.7, "complexity": 1.64, "correctness": 2.06, "helpfulness": 2.21, "instruction-following": 3.23, "safety": 5.36, "verbosity": 1.42, "verbosity-coeff": -0.116 }

[ { "content": "79 laboratories raise the bacterium, the laboratory have 48 culture dishes on average, which has about 25,070 bacteria each. How many bacteria are there approximately?\n\n['A)10^7', 'B)10^8', 'C)10^9', 'D)10^10', 'E)10^11']", "role": "user", "uuid": "8d05e8cf-4d23-4ed7-86f4-beda17a9b411" }, { "content": "79 laboratories raise the bacterium, the laboratory have 48 culture dishes on average, which has about 25,070 bacteria each. How many bacteria are there approximately?\nA. 10^7\nB. 10^8\nC. 10^9\nD. 10^10\nE. 10^11\n-> Due to approximately, 79=80, 48=50, 25,070=25,000 are derived, which makes (79)(48)(25,075)=(80)(50)(25,000)=10^8. The answer is B.", "role": "assistant", "uuid": "a63c2fc3-2c54-47fb-8074-8effde639536" } ]

{ "coherence": 2.84, "complexity": 0.92, "correctness": 2.27, "helpfulness": 2.51, "instruction-following": 3.04, "safety": 5.55, "verbosity": 1.04, "verbosity-coeff": -0.1071 }

[ { "content": "A girl purchased “m” number of pens of type “A” at the unit price of “Rs. x” each, “n” number of pens of type “B” at the unit price of “Rs. y” each and “p” number of pens of type “C” at the unit price of “Rs. z” each. Which of the following represents the average price of all the pens taken together?\n\n['A)(mx + ny + pz) / (m + n + p)', 'B)(mA + nB + pC) / (m + n + p)', 'C)(mA + nB + pC) / (A + B + C)', 'D)(mx + ny + pz) / (A +B + C)', 'E)None of these']", "role": "user", "uuid": "12b27b30-442c-464a-ad74-1005a47f5af1" }, { "content": "Explanation:\n(mx + ny + pz) / (m + n + p)\nRequired Average = Total Price / Total number = (mx + ny + pz) / (m + n + p)\nANSWER: A", "role": "assistant", "uuid": "636bbd48-2bbc-4069-b8c9-10b662e5796d" } ]

{ "coherence": 2.92, "complexity": 1.83, "correctness": 2.8, "helpfulness": 3.19, "instruction-following": 3.48, "safety": 3.5, "verbosity": 1.12, "verbosity-coeff": -0.1188 }

[ { "content": "A can do a piece of work in 6 days and B can do it in 6 days how long will they both work together to complete the work?\n\n['A)6/11', 'B)1/2', 'C)3/4', 'D)9/11', 'E)10/11']", "role": "user", "uuid": "511ed91c-fbbd-4692-8a94-9e59bbf31fea" }, { "content": "Explanation:\nA’s one day work = 1/5\nB’s one day work = 1/6\n(A+B)’s one day work = 1/6 + 1/6 = 2/3= => time = 3/2 = 1 1/2 days\nAnswer: Option B", "role": "assistant", "uuid": "347fce4a-6624-4c99-9593-1c945c9b69f6" } ]

{ "coherence": 1.97, "complexity": 1.04, "correctness": 1.3, "helpfulness": 1.54, "instruction-following": 1.48, "safety": 5.59, "verbosity": 0.74, "verbosity-coeff": -0.1199 }

[ { "content": "The price of 2 sarees and 4 shirts is Rs. 1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ?\n\n['A)4800', 'B)none of these', 'C)3600', 'D)1200', 'E)2400']", "role": "user", "uuid": "c3e54187-3952-4039-a06a-22b9c0a7b00c" }, { "content": "Let the price of a saree and a shirt be Rs. x and Rs. y respectively.\nThen, 2x + 4y = 1600 .... (i)\nand x + 6y = 1600 .... (ii)\nDivide equation (i) by 2, we get the below equation.\n=> x + 2y = 800. --- (iii)\nNow subtract (iii) from (ii)\nx + 6y = 1600 (-)\nx + 2y = 800\n----------------\n4y = 800\n----------------\nTherefore, y = 200.\nNow apply value of y in (iii)\n=> x + 2 x 200 = 800\n=> x + 400 = 800\nTherefore x = 400\nSolving (i) and (ii) we get x = 400, y = 200.\nCost of 12 shirts = Rs. (12 x 200) = Rs. 2400.\nAnswer is E.", "role": "assistant", "uuid": "21635ef6-cb4e-4ccd-bfcd-ac7be9e674b6" } ]

{ "coherence": 3, "complexity": 1.45, "correctness": 2.64, "helpfulness": 2.98, "instruction-following": 3.72, "safety": 4.62, "verbosity": 1.27, "verbosity-coeff": -0.1167 }

[ { "content": "Rahim bought 52 books for Rs.1200 from one shop and 32 books for Rs.480 from another. What is the average price he paid per book ?\n\n['A)s.17', 'B)s.18', 'C)s.12', 'D)s.20', 'E)s.10']", "role": "user", "uuid": "81aeab7d-55fd-4892-b118-bad01041a8e4" }, { "content": "Average price per book\n= (1200+ 480) / (52 + 32) = 1680/ 84\n= Rs.20\nAnswer:D", "role": "assistant", "uuid": "dbd4e996-9a71-498a-94c7-7bdbe2ec2038" } ]

{ "coherence": 2.8, "complexity": 1.09, "correctness": 2.39, "helpfulness": 2.61, "instruction-following": 3.64, "safety": 5.09, "verbosity": 1.01, "verbosity-coeff": -0.1115 }

[ { "content": "For which of the following values of n is (600+n)/n NOT an integer?\n\n['A) 1', 'B) 2', 'C) 3', 'D) 4', 'E) 9']", "role": "user", "uuid": "6d19a581-9da0-40f3-a75d-ce8b24a86243" }, { "content": "Solution:\nThis problem is easiest solved by plugging in each answer choice.\nA) (600 + 1)/1 = 601/1 = 601\nAnswer choice A yields an integer.\nB) (600 + 2)/2 = 602/2 = 301\nAnswer choice B yields an integer.\nC) (600 + 3)/3 = 603/3 = 201\nAnswer choice C yields an integer.\nD) (600 + 4)/4 = 604/4 = 126\nAnswer choice D yields an integer.\nE) (600 + 9)/5 = 609/9 = 65, remainder 4\nAnswer choice E DOES NOT yield an integer.\nThus, the correct answer is answer choice E.", "role": "assistant", "uuid": "535c8fb7-54b1-4368-9717-8ee7f7ecc947" } ]

{ "coherence": 2.98, "complexity": 2.35, "correctness": 1.91, "helpfulness": 1.88, "instruction-following": 1.81, "safety": 4.77, "verbosity": 1.71, "verbosity-coeff": -0.2388 }

[ { "content": "The arithmetic mean and standard deviation of a certain normal distribution are 14.5 and 1.7, respectively. What value is exactly 2 standard deviations less than the mean?\n\n['A)10.5', 'B)11', 'C)11.1', 'D)12', 'E)12.5']", "role": "user", "uuid": "c0630017-e8ff-47c5-a8b9-0cecd66f008d" }, { "content": "Mean = 14.5\nTwo standard deviations is 1.7 + 1.7 = 3.4\nThere could be two calues for this.\nMean + two standard deviations = 17.9\nMean - Two standard deviations = 11.1\nAnswer choice has 11.1 and so C is the answer.", "role": "assistant", "uuid": "5c5d3b1b-2d6b-495e-b966-4f11618d4c36" } ]

{ "coherence": 2.94, "complexity": 1.23, "correctness": 2.35, "helpfulness": 2.51, "instruction-following": 2.33, "safety": 5.24, "verbosity": 0.93, "verbosity-coeff": -0.2093 }

[ { "content": "What is the ratio Q of the surface area of a cube to the surface area of a rectangular solid identical to the cube in all ways except that its length has been doubled?\n\n['A)1/4', 'B)3/8', 'C)1/2', 'D)3/5', 'E)2']", "role": "user", "uuid": "a2da19f1-d292-4ae5-907f-98d2d40b6c3e" }, { "content": "Let X be the side of the cube. Therefore X^2*6= surface area.\nthe rectangle is the same other than length is 2X. The width and height are the same as the cube. 2*W*H+2*W*L+2*H*L= 2X^2+4X^2+4X^2= 10X^2.\n6X^2/10X^2 = 3/5.= Q\nAnswer = D", "role": "assistant", "uuid": "3c86c091-e7b1-4cfc-a383-747e9df333a5" } ]

{ "coherence": 2.61, "complexity": 1.81, "correctness": 1.98, "helpfulness": 2.04, "instruction-following": 2.68, "safety": 5.75, "verbosity": 0.78, "verbosity-coeff": -0.2018 }

[ { "content": "The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?\n\n['A)140', 'B)156', 'C)175', 'D)214', 'E)216']", "role": "user", "uuid": "78c986bc-0409-4ccf-a029-daabf977e515" }, { "content": "Given that the area of the square = 1225 sq.units\n=> Side of square = √1225 = 35 units\nThe radius of the circle = side of the square = 35 units Length of the rectangle = 2/5 * 35 = 14 units\nGiven that breadth = 10 units\nArea of the rectangle = lb = 14 * 10 = 140 sq.units\nANSWER:A", "role": "assistant", "uuid": "52611154-34ee-4ab6-94dd-c36d91d20fff" } ]

{ "coherence": 3.35, "complexity": 1.51, "correctness": 3.11, "helpfulness": 3.41, "instruction-following": 4.09, "safety": 5.24, "verbosity": 1.24, "verbosity-coeff": -0.1214 }

[ { "content": "A letter lock consists of three rings each marked with six different letters. The number of distinct unsuccessful attempts to open the lock is at the most -.\n\n['A)216', 'B)243', 'C)215', 'D)729', 'E)728']", "role": "user", "uuid": "414593e7-ea0f-4971-9f7d-91a4e69b1eff" }, { "content": "Since each ring consists of six different letters, the total number of attempts possible with the three rings is = 6 * 6 * 6 = 216. Of these attempts, one of them is a successful attempt.\nMaximum number of unsuccessful attempts = 216 - 1 = 215.\nANSWER:C", "role": "assistant", "uuid": "edd7944a-7d63-438c-8339-b7d71cce6b32" } ]

{ "coherence": 2.92, "complexity": 1.71, "correctness": 2.78, "helpfulness": 3.05, "instruction-following": 3.78, "safety": 4.77, "verbosity": 1.72, "verbosity-coeff": -0.1002 }

[ { "content": "My cat keeps to himself most of the time. I only heard him meow, hiss, and purr on one day\nout of the last 23 days. But I did hear him make at least one of these sounds each day. I heard\nhim hiss on 6 days, purr on 12 days, and meow on 15 days. On 2 days, I heard him meow and\nhiss but not purr, and on 2 days, I heard him purr and hiss but not meow. On how many days\ndid I hear him meow and purr but not hiss?\n\n['A)1', 'B)2', 'C)3', 'D)4', 'E)5']", "role": "user", "uuid": "9ed81540-0594-4d2f-8fca-a191aefbaacc" }, { "content": "Let M denote the days on which the cat meowed, H the days on which he hissed,\nand P the days on which he purred. Given the data, the following Venn diagram represents\nthe situation, where the expressions inside the circles are the cardinalities of disjoint sections:\nWe are looking for x. The labeled sections of the Venn diagram are disjoint sets, so they\nshould add to 23. That is,\n23 = 1 + 1 + 2 + 2 + x + (9 􀀀 x) + (12 􀀀 x) = 27 􀀀 x:\nTherefore,x = 4.\nor\nThe inclusion-exclusion principle gives\n23 = jM [ H [ Pj = jMj + jHj + jPj 􀀀 jM \\ Hj 􀀀 jH \\ Pj 􀀀 jM \\ Pj + jM \\ H \\ Pj\n= 15 + 6 + 12 􀀀 (2 + 1) 􀀀 (2 + 1) 􀀀 (x + 1) + 1:\nSo x = 4.\ncorrect answer D", "role": "assistant", "uuid": "3be62c21-22ff-4e83-9964-19f595bb2860" } ]

{ "coherence": 2.78, "complexity": 1.78, "correctness": 2.04, "helpfulness": 1.81, "instruction-following": 2.27, "safety": 4.97, "verbosity": 1.71, "verbosity-coeff": -0.117 }

[ { "content": "four concentric circles r given .the radius of 1st circle is x.next is 2x,then 3x and 4x. given that area b/w 2nd and 1st is A and 4th and 3rd circles being B.find ratio of A to B\n\n['A)2:7', 'B)1:7', 'C)3:5', 'D)3:7', 'E)3:4']", "role": "user", "uuid": "aea085f3-5e2d-4eba-abe8-67916effcf0e" }, { "content": "area of first circle = pi*(x)^2 = pi*x^2\narea of second circle = pi*(2x)^2 = 4*pi*x^2\narea of third circle = pi*(3x)^2 = 9*pi*x^2\narea of fourth circle = pi*(4x)^2 = 16*pi*x^2\narea b/w 1st and 2nd circles = 3*pi*x^2\narea b/w 3rd and 4th circles = 7*pi*x^2\nso ratio = 3:7\nANSWER:D", "role": "assistant", "uuid": "900df7c4-ec95-4078-93f1-e72f1c09002a" } ]

{ "coherence": 2.61, "complexity": 1.63, "correctness": 2.47, "helpfulness": 2.55, "instruction-following": 3.17, "safety": 5.28, "verbosity": 1.23, "verbosity-coeff": -0.103 }

[ { "content": "A man bought 40 shares of Rs. 60 at 8 discount, the rate of dividend being 1212%The rate of interest obtained is\n\n['A)13.64%', 'B)15.5%', 'C)14%', 'D)14.42%', 'E)14.95%']", "role": "user", "uuid": "4dba3a7e-fd8d-4d39-a425-54075ac65a76" }, { "content": "Explanation :\nFace Value of a share = Rs.60\nHe bought each share at Rs.60 - Rs.8 = Rs.52\nNumber of shares = 40\nDividend = 12 1/2%=25/2%\nDividend per share = 60×25/2×100=Rs.7.5\nTotal dividend = (40 × 7.5)\nie, He got a dividend of (40 × 7.5) for an investment of Rs.(40 × 52)\nInterest obtained = 40×7.5×100/40×52=14.42%\nAnswer : Option D", "role": "assistant", "uuid": "7f53f159-756b-48c3-a9d0-c8165176aa68" } ]

{ "coherence": 2.53, "complexity": 2, "correctness": 2.12, "helpfulness": 2.25, "instruction-following": 3.19, "safety": 5.32, "verbosity": 1.21, "verbosity-coeff": -0.1135 }

[ { "content": "If Jake loses 20 pounds, he will weigh twice as much as his sister. Together they now weigh 224 pounds. What is Jake’s present weight, in pounds?\n\n['A)131', 'B)135', 'C)156', 'D)177', 'E)188']", "role": "user", "uuid": "8a25bdc8-26d7-4a76-b346-4e851c4aaff3" }, { "content": "Lets say J is the weight of Jack and S is the wt of his sister.\nIf he loses 20 pounds, he s twice as heavy as his sister.\nJ-20=2*S\nAlso, together they weight 224 pounds\nJ+S=224\nsolvong the 2 equation ,we get J=156 pounds !\nC", "role": "assistant", "uuid": "21ebf3e3-f8a6-4370-8a24-d9cce3831349" } ]

{ "coherence": 3.05, "complexity": 1.06, "correctness": 2.16, "helpfulness": 2.29, "instruction-following": 2.33, "safety": 5.01, "verbosity": 0.43, "verbosity-coeff": -0.1548 }

[ { "content": "By weight, liquid X makes up 0.8 percent of solution A and 1.8 percent of solution B. If 250 grams of solution A are mixed with 700 grams of solution B, then liquid X accounts for what percent of the weight of the resulting solution?\n\n['A)1.46%', 'B)1.93%', 'C)10%', 'D)15%', 'E)19%']", "role": "user", "uuid": "c1969228-ebad-4964-86ac-d5941a551f2e" }, { "content": "I think there is a typo in question.\nIt should have been \"By weight Liquid 'X ' makes up..... \"\nWeight of Liquid X = 0.8 % of Weight of A + 1.8% of Weight of B\nWhen 250gms of A and 700gms of B is mixed :\nWeight of Liquid X = (0.8 * 250)/100 + (1.8* 700)/100 = 14.6gms\n% of Liquid X in resultant mixture = (14.6/1000) *100 = 1.46%\nA", "role": "assistant", "uuid": "b22bb7ee-8cd0-4f46-b16e-020db6de356e" } ]

{ "coherence": 2.57, "complexity": 1.66, "correctness": 1.68, "helpfulness": 1.68, "instruction-following": 1.88, "safety": 3.68, "verbosity": 1.2, "verbosity-coeff": -0.1883 }

[ { "content": "54 is to be divided into two parts such that the sum of 10 times the first and 22 times the second is 780. The bigger part is\n\n['A)24', 'B)30', 'C)32', 'D)34', 'E)36']", "role": "user", "uuid": "9e248b6d-59b6-48fc-85d3-30a116081861" }, { "content": "Solution\nLet the two parts be (54 - x) and x.\nThen, 10(54-x)+22x=780\n= 12x = 240\n‹=›x = 20.\nTherefore Bigger part = (54-x) = 34.\nAnswer D", "role": "assistant", "uuid": "04118fb4-734c-4622-8a14-33c262e766f6" } ]

{ "coherence": 2.72, "complexity": 1.79, "correctness": 2.43, "helpfulness": 2.61, "instruction-following": 2.92, "safety": 5.36, "verbosity": 0.99, "verbosity-coeff": -0.136 }

[ { "content": "The rate of a certain chemical reaction is directly proportional to the square of the concentration of chemical A present and inversely proportional to the concentration of chemical B present. If the concentration of chemical B is increased by 50%, which of the following is closest to the percent change in the concentration of chemical A required to keep the reaction rate unchanged?\n\n['A)100% decrease', 'B)50% decrease', 'C)40% decrease', 'D)40% increase', 'E)50% increase']", "role": "user", "uuid": "4bec6675-8bd0-49e5-82c5-ac14cb3e83fb" }, { "content": "The rate of reaction is invesrsly proportional to the concentration of chemical B present. It used to have B=1 . Now that B is increased by 50%. So the new equation would be 2B=(1/2). In order for the rate of reaction to still be 1, we need to change the concentration of A to yield a 2. It used to be A^2=1, now the new equation should be (sqrt(2)*A)^2=2. The change in the concentration of A can be calculated as (sqrt(2) -1)/1 or approximately 40% increase. Answer C.", "role": "assistant", "uuid": "fcb5e5cd-d156-4b86-8dcf-23eeb3cb88d9" } ]

{ "coherence": 2.55, "complexity": 2.08, "correctness": 1.94, "helpfulness": 1.84, "instruction-following": 2.29, "safety": 5.09, "verbosity": 1.81, "verbosity-coeff": -0.2122 }

[ { "content": "Of the following quadratic equations, which is the one whose roots are 2 and – 15 ?\n\n['A)x2 - 2x + 15 = 0', 'B)x2 + 15x - 2 = 0', 'C)x2 + 13x - 30 = 0', 'D)x2 - 30 = 0', 'E)None of these']", "role": "user", "uuid": "c0f2a41a-310f-4519-ba3d-5a422ecf99e9" }, { "content": "Sol.\n(c) Sum of roots = 2 – 15 = – 13\nProduct of roots = 2 × (– 15) = – 30\nRequired equation\n= x2 - x(sum of roots) + product of roots = 0\n=> x2 + 13x - 30 = 0\nAnswer C", "role": "assistant", "uuid": "4f384b35-6da7-4639-ae68-c8a86ffe656d" } ]

{ "coherence": 2.7, "complexity": 2.1, "correctness": 2.61, "helpfulness": 2.8, "instruction-following": 3.62, "safety": 3.56, "verbosity": 1.3, "verbosity-coeff": -0.1122 }

[ { "content": "A person travelled from his house to office at 30km/hr and office to house at 15km/hr. Then find the average speed?\n\n['A)15km/hr', 'B)20km/hr', 'C)32km/hr', 'D)24km/hr', 'E)25km/hr']", "role": "user", "uuid": "e1e2fe7e-1885-403a-92f3-e7e9df7410d9" }, { "content": "Average speed = (2*30*15)/(30+15)\n= 20km/hr\nAnswer is B", "role": "assistant", "uuid": "bf5bcfee-9c41-4291-a96f-4f6e40ae1f84" } ]

{ "coherence": 3.11, "complexity": 1.33, "correctness": 2.21, "helpfulness": 2.43, "instruction-following": 3.23, "safety": 5.52, "verbosity": 0.41, "verbosity-coeff": -0.1179 }

[ { "content": "a man owns 2/3 of the market research beauro business and sells 3/4 of his shares for Rs.75000. what is the value of business ?\n\n['A)170000', 'B)120000', 'C)130000', 'D)140000', 'E)150000']", "role": "user", "uuid": "159ff8f0-502d-4f5a-b929-56e4b62f4e01" }, { "content": "x*(3/4)=75000 this is cost of his owns value\non solving we get x=100000\nnow, y*(2/3)=100000 we get y=150000\nso 150000 is the cost of whole business.\nANSWER:E", "role": "assistant", "uuid": "dbc913c3-8240-4066-9855-1be178322c13" } ]

{ "coherence": 2.82, "complexity": 2.04, "correctness": 2.16, "helpfulness": 2.2, "instruction-following": 3.09, "safety": 4.93, "verbosity": 1.18, "verbosity-coeff": -0.1082 }

[ { "content": "When positive integer N is divided by positive integer J, the remainder is 12. If N/J = 134.02, what is value of J?\n\n['A)300', 'B)600', 'C)500', 'D)112', 'E)620']", "role": "user", "uuid": "b86bcfd1-1102-405c-aaf4-4da57471987a" }, { "content": "1) We know that\ndecimal part of decimal quotient ={remainder/divisor}\nSo 0.02, the decimal part of the decimal quotient, must equal the remainder, 12, divided by the divisor J.\n0.02 = 12/J\n0.02*J = 12\nJ = 12/0.02 = 1200/2 = 600/1 = 600\nSo J = 600, answer = B.", "role": "assistant", "uuid": "a1b6f4c8-0baa-4956-b39b-b85964a6f387" } ]

{ "coherence": 2.68, "complexity": 1.47, "correctness": 2.02, "helpfulness": 2.29, "instruction-following": 2.55, "safety": 5.09, "verbosity": 1.48, "verbosity-coeff": -0.1723 }

[ { "content": "The unit digit in the product 1256*6785*4587*9785 is?\n\n['A)0', 'B)1', 'C)2', 'D)3', 'E)4']", "role": "user", "uuid": "40f212d8-3910-4f34-85c0-2e469ed812da" }, { "content": "Unit digit in the given product = unit digit in 6*5*7*5 = 0\nAnswer is A", "role": "assistant", "uuid": "9ab7d48d-8dda-4a16-a007-f3687fad1612" } ]

{ "coherence": 3.19, "complexity": 1.73, "correctness": 2.96, "helpfulness": 3.04, "instruction-following": 3.17, "safety": 5.71, "verbosity": 0.81, "verbosity-coeff": -0.1119 }

[ { "content": "A dealer offers a cash discount of 20% and still makes a profit of 20%, when he further allows 16 articles to a dozen to a particularly sticky bargainer. How much percent above the cost price were his wares listed?\n\n['A)100%', 'B)80%', 'C)75%', 'D)66(2/3)%', 'E)NOne']", "role": "user", "uuid": "3a6301b8-cb00-48eb-997c-9dc62ee2dc17" }, { "content": "Solution: Let the CP of the article be Rs. x, since he earns a profit of 20%, hence SP= X + 20% of X = 1.2x.\nIt is given that he incurs loss by selling 16 articles at the cost of 12 articles [loss = (16-12)/16 = 25%]\nHis selling price = SP - 25% of SP = SP*0.75;\nHence, SP*0.75 = 1.2X.\nOr, SP = (1.2*x/0.75) = 1.6X.\nThis SP is arrived after giving a discount of 20% on MP.\nLet MP = Y.\nY - 20% of Y = SP\n0.80Y = 1.6X.\nY = 2X.\nIt means that the article has been marked 100% above the cost price. Or Marked Price was twice of cost price.\nAnswer: Option A", "role": "assistant", "uuid": "3eedf7ba-5a7e-4546-a361-127155fca674" } ]

{ "coherence": 2.82, "complexity": 2.8, "correctness": 2.66, "helpfulness": 2.76, "instruction-following": 2.74, "safety": 4.25, "verbosity": 2.08, "verbosity-coeff": -0.1224 }

[ { "content": "Mr. X, a mathematician, defines a number as 'connected with 6 if it is divisible by 6 or if the sum of its digits is 6, or if 6 is one of the digits of the number. Other numbers are all 'not connected with 6'. As per this definition, the number of integers from 1 to 60 (both inclusive) which are not connected with 6 is\n\n['A)18', 'B)22', 'C)42', 'D)43', 'E)45']", "role": "user", "uuid": "e94c4feb-c03e-4dee-9f50-052f3f96de52" }, { "content": "Explanation:\nNumbers from 1 to 60, which are divisible by 6 are : 6,12,18, 24, 30, 36,42, 48, 54, 60.\nThere are 10 such numbers.\nNumbers from 1 to 60, the sum of whose digits is 6 are : 6, 15, 24, 33, 42, 51, 60.\nThere are 7 such numbers of which 4 are common to the above ones. So, there are 3such uncommon numbers.\nNumbers from 1 to 60, which have 6 as one of the digits are 6, 16, 26, 36, 46, 56, 60.\nClearly, there are 4 such uncommon numbers.\nSo, numbers 'not connected with 6' = 60 - (10 + 3 + 4) = 43.\nAnswer: D", "role": "assistant", "uuid": "cbebbfa2-6267-44d4-9cc8-007147c0237f" } ]

{ "coherence": 2.74, "complexity": 1.63, "correctness": 2.51, "helpfulness": 2.61, "instruction-following": 3.45, "safety": 6.57, "verbosity": 1.83, "verbosity-coeff": -0.1152 }

[ { "content": "One man selling a lottery there are 10 prizes and 25 no prizes. if a lottery is drawn randomly, What is the probability of getting a prize?\n\n['A)1/5', 'B)2/7', 'C)2/9', 'D)3/11', 'E)4/11']", "role": "user", "uuid": "f8f1d37e-bfb7-4b81-9e63-c554ae87a146" }, { "content": "P (getting a prize) =\t10\t=\t10\t=\t2/7\n(10 + 25)\t35\nB", "role": "assistant", "uuid": "d33bbc24-cc28-40f0-b8a2-a9674b10b9e6" } ]

{ "coherence": 2.66, "complexity": 0.67, "correctness": 2, "helpfulness": 2.23, "instruction-following": 3.52, "safety": 5.09, "verbosity": 0.87, "verbosity-coeff": -0.1155 }

[ { "content": "Two cogged wheels of which one has 32 cogs and other 54 cogs, work into each other. If the latter turns 80 times in three quarters of a minute, how often does the other turn in 8 seconds?\n\n['A)22', 'B)24', 'C)99', 'D)27', 'E)17']", "role": "user", "uuid": "f004a14e-9cf7-4c15-ba1c-f7c7079d5555" }, { "content": "Explanation:\nLess Cogs more turns and less time less turns\nNumber of turns required=80 × × = 24 times\nAnswer: B) 24", "role": "assistant", "uuid": "ef898c3e-e026-44cc-adcf-fafe5375695e" } ]

{ "coherence": 2.96, "complexity": 0.64, "correctness": 2.29, "helpfulness": 2.51, "instruction-following": 2.45, "safety": 4.93, "verbosity": 0.5, "verbosity-coeff": -0.1152 }

[ { "content": "If 2^z is a factor of 24!, which of the following could be the value of z?\nI. 22\nII. 23\nIII. 24\n\n['A)I \\u200bonly', 'B)II only', 'C)I\\u200b and II', 'D)I, II, and III', 'E)None']", "role": "user", "uuid": "31f8b866-9649-4210-b617-9d65eaf7bc39" }, { "content": "24! contains all numbers from 1 to 24. To find the factor with the highest power of 2, we count the number of multiples of 2, 4, 8 and 16.\nMultiples of 2 = 12\nMultiples of 4 = 6\nMultiples of 8 = 3\nMultiples of 16 = 1\nTotal count = 22\nThe answer is A.", "role": "assistant", "uuid": "d26d2591-8957-4e7b-ab31-6fe240827519" } ]

{ "coherence": 2.55, "complexity": 2.21, "correctness": 1.82, "helpfulness": 1.78, "instruction-following": 2.27, "safety": 6.61, "verbosity": 1.39, "verbosity-coeff": -0.1632 }

[ { "content": "A man decided to cover a distance of 80km in 8 hrs. He can walk at a speed of 6 km/hr and cycle at 8 km/hr successively. How long will he walk and how long will he cycle ?\n\n['A)26.6km,53.3km', 'B)27.6km,53.3km', 'C)26.6km,54.3km', 'D)26.6km,55.3km', 'E)28.6km,53.3km']", "role": "user", "uuid": "c53dce7b-a3a3-4617-87c3-2f5ffdeca733" }, { "content": "as speed in 80km/8hrs=10 km/hr\nas ques solve through mixture and alligation method\n6 km/hr and 8km/hr\n10km/hr\n10-8 10-6\n2km/hr 4km/hr\nso the ratio is 1:2\nahd we have to find the distance through walk and through cycle\n1/3*80=26.6km\n2/3*80=53.3km\nANSWER:A", "role": "assistant", "uuid": "8b6ff796-ae00-4d70-92b8-0641447fc8e8" } ]

{ "coherence": 2.57, "complexity": 1.31, "correctness": 1.91, "helpfulness": 1.83, "instruction-following": 2.43, "safety": 5.98, "verbosity": 1.19, "verbosity-coeff": -0.1237 }

[ { "content": "A bag contains eight white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color?\n\n['A)5/8', 'B)16/33', 'C)25/63', 'D)15/33', 'E)5/1']", "role": "user", "uuid": "e3fd79c6-dc09-4324-8ad7-07c1ee1d2ecb" }, { "content": "Two balls can be picked from twelve balls in 12C₂ ways.\nWe select one white ball and one red ball from five white balls and four red balls. This can be done ⁵ ways.\nThe required probability = (8 * 4) = 32/66 = 16/33\nAnswer: B", "role": "assistant", "uuid": "bee1620d-54d8-4759-a7eb-02d439cf92e1" } ]

{ "coherence": 2.64, "complexity": 1.72, "correctness": 2.25, "helpfulness": 2.41, "instruction-following": 2.9, "safety": 5.2, "verbosity": 1.79, "verbosity-coeff": -0.1831 }

[ { "content": "what is the smallest integer that is multiple of 3,5,7\n\n['A)A)105', 'B)B)35', 'C)C)200', 'D)D)280', 'E)E)140']", "role": "user", "uuid": "f133bbd6-e2be-48d4-a435-f23b2762fa64" }, { "content": "It is the lcm of 3, 5 and 7 which is 105.\nThe answer is A.", "role": "assistant", "uuid": "a4dfbbd9-d0f8-4586-bbe0-ce885d056d9e" } ]

{ "coherence": 3.21, "complexity": 1.5, "correctness": 3.19, "helpfulness": 3.25, "instruction-following": 3.37, "safety": 5.44, "verbosity": 1.1, "verbosity-coeff": -0.1244 }

[ { "content": "A, B and C, each working alone can complete a job in 6, 8 and 12 days respectively. If all three of them work together to complete a job and earn $ 2340, what will be A's share of the earnings?\n\n['A)$1100', 'B)$520', 'C)$1040', 'D)$1170', 'E)$630']", "role": "user", "uuid": "c3a8c203-84dd-46e2-9042-7e8c8ba7a322" }, { "content": "Explanatory Answer\nA, B and C will share the amount of $2340 in the ratio of the amounts of work done by them.\nAs A takes 6 days to complete the job, if A works alone, A will be able to complete 1/6 th of the work in a day.\nSimilarly, B will complete 1/8th and C will complete 1/12th of the work.\nSo, the ratio of the work done by A : B : C when they work together will be equal to 1/6 : 1/8 : 1/12\nMultiplying the numerator of all 3 fractions by 24, the LCM of 6, 8 and 12 will not change the relative values of the three values.\nWe get 24/6 : 24/8 : 24/12 = 4 : 3 : 2.\ni.e., the ratio in which A : B : C will share $2340 will be 4 : 3 : 2.\nHence, A's share will be 4*2340/9 = 1040\ncorrect choice is (C)", "role": "assistant", "uuid": "65403e6b-f46c-4cfc-b45b-9f8e9ef4a1aa" } ]

{ "coherence": 3.19, "complexity": 1.02, "correctness": 3.15, "helpfulness": 3.39, "instruction-following": 3.39, "safety": 3.66, "verbosity": 1.19, "verbosity-coeff": -0.1186 }