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[ { "content": "If 3 persons can do 3 times of a particular work in 3 days, then, 7 persons can do 7 times of that work in\n\n['A)3 days', 'B)4 days', 'C)5 days', 'D)6 days', 'E)7 days']", "role": "user", "uuid": "4b11e396-dd84-4bab-8cc4-c2563775801a" }, { "content": "Answer: Option 'A'\nThat is, 1 person can do one time of the work in 3 days.\nTherefore, 7 persons can do 7 times work in the same 3 days itself.", "role": "assistant", "uuid": "c628b567-4612-4d4c-9c7a-774c2b4216b2" } ]

{ "coherence": 3.19, "complexity": 1.76, "correctness": 2.84, "helpfulness": 2.9, "instruction-following": 3.11, "safety": 5.05, "verbosity": 1.12, "verbosity-coeff": -0.1217 }

[ { "content": "How many diagonals does a polygon with 13 sides have, if one of its vertices does not connect to any diagonal?\n\n['A)65', 'B)62', 'C)58', 'D)54', 'E)60']", "role": "user", "uuid": "894cd09e-2818-4868-84a7-d99b1cb1537c" }, { "content": "If I calculate it using the formulae, #diagonals = n (n-3)/2Each vertex sends of n-3 diagonals\nn= 13-1 then 12*(12-3)/2 = 54\nCorrect Option:D", "role": "assistant", "uuid": "7e9435ba-1b0d-40ea-86f9-0a5d0774046b" } ]

{ "coherence": 2.92, "complexity": 1.59, "correctness": 2.27, "helpfulness": 2.39, "instruction-following": 2.84, "safety": 6.14, "verbosity": 1.16, "verbosity-coeff": -0.1915 }

[ { "content": "7 people average age is 30. youngest person age is 7. find average of the people when youngest was born.\n\n['A)23', 'B)24', 'C)25', 'D)26', 'E)27']", "role": "user", "uuid": "96445a68-e8ce-4842-ba9e-af4f25156f13" }, { "content": "average age of people =30\nso have total age =210\nbefore 7 years we have to deduct each person age by seven years 210-49=161\nso average age would be 161/7=23\nANSWER:A", "role": "assistant", "uuid": "bda188b0-56c5-4a99-82e7-8abf871fea43" } ]

{ "coherence": 2.98, "complexity": 1.55, "correctness": 2.96, "helpfulness": 2.88, "instruction-following": 3.48, "safety": 4.29, "verbosity": 1.53, "verbosity-coeff": -0.1219 }

[ { "content": "If (x^2 + x - 8)/2 ≤ x + 1, then x could be represented by which of the following?\n\n['A)− 4 ≤ x ≤ − 3', 'B)− 4 ≤ x ≤ 3', 'C)− 3 ≤ x ≤ 4', 'D)− 3 ≤ x ≤ 3', 'E)3 ≤ x ≤ 4']", "role": "user", "uuid": "d9804fde-5d70-42d9-bf9b-d606edd1f5a4" }, { "content": "IMO C is correct answer\nsolving through eqautions\nx^2 +x-8<= 2x+2\n(x+3)(x-4)<=0", "role": "assistant", "uuid": "3e678841-191e-4e03-ab78-907d24234941" } ]

{ "coherence": 2.51, "complexity": 1.4, "correctness": 1.69, "helpfulness": 1.56, "instruction-following": 1.64, "safety": 4.5, "verbosity": 0.77, "verbosity-coeff": -0.1457 }

[ { "content": "Kamal is 60 years old and Karthi is 80 years old. How many years ago was the ratio of their ages 4 : 6?\n\n['A)20 yrs', 'B)30 yrs', 'C)25 yrs', 'D)40 yrs', 'E)15 yrs']", "role": "user", "uuid": "5fb59e36-6914-4616-982d-e7471aaddece" }, { "content": "(60-x)/(80-x) = 4/6\n6(60-x)=4(80-x)\nx = 20\nANSWER A", "role": "assistant", "uuid": "0b5d3847-1db6-4eb0-9eb7-44cc90922bc5" } ]

{ "coherence": 2.62, "complexity": 1.55, "correctness": 2.43, "helpfulness": 2.37, "instruction-following": 3.05, "safety": 5.01, "verbosity": 1.3, "verbosity-coeff": -0.1229 }

[ { "content": "How many seconds will a 800 meter long train moving with a speed of 63 km/hr take to cross a man walking with a speed of 3 km/hr in the direction of the train ?\n\n['A)48', 'B)36', 'C)26', 'D)11', 'E)18']", "role": "user", "uuid": "e341f40b-87e9-44e5-b238-e2f28f911b5d" }, { "content": "Explanation:\nHere distance d = 800 mts\nspeed s = 63 - 3 = 60 kmph = 60 x 5/18 m/s\ntime t = = 48 sec.\nAnswer: A", "role": "assistant", "uuid": "0de47592-e8a4-4323-a981-87b17b88bd22" } ]

{ "coherence": 2.76, "complexity": 1.63, "correctness": 2.39, "helpfulness": 2.55, "instruction-following": 3.29, "safety": 6.3, "verbosity": 0.78, "verbosity-coeff": -0.119 }

[ { "content": "Fathers age is 5 times his son's age. 4 years back the father was 9 times older than son.Find the fathers' present age.\n\n['A)41', 'B)40', 'C)39', 'D)45', 'E)30']", "role": "user", "uuid": "0d6c1870-1b63-410f-a318-956571937ce6" }, { "content": "fathers age =x sons age =y\nx=5y;x-4=9(y-4)\n5y-4=9y-36\ny=8 so x=40\nANSWER:B", "role": "assistant", "uuid": "b17b803c-2c13-4133-8146-973f7dffd827" } ]

{ "coherence": 2.96, "complexity": 1.86, "correctness": 2.57, "helpfulness": 2.7, "instruction-following": 3.37, "safety": 5.4, "verbosity": 1.17, "verbosity-coeff": -0.1259 }

[ { "content": "what is next number in sequence\n212 427 303 336 394 ?\n\n['A)123', 'B)345', 'C)560', 'D)567', 'E)245']", "role": "user", "uuid": "d50c8d76-31d7-4c80-bff9-f9f37823b0aa" }, { "content": "E\n245\nspace them properly as 21 24 27 30 33 36 39 42 45 ?", "role": "assistant", "uuid": "09e6b47b-7248-4f95-8877-15e24f0fdb2b" } ]

{ "coherence": 2, "complexity": 0.88, "correctness": 1.16, "helpfulness": 1.38, "instruction-following": 0.97, "safety": 2.27, "verbosity": 0.81, "verbosity-coeff": -0.0858 }

[ { "content": "Set A contains all the even numbers between 42 and 90 inclusive. Set B contains all the even numbers between 62 and 110 inclusive. What is the difference between the sum of elements of set B and the sum of the elements of set A?\n\n['A)300', 'B)350', 'C)400', 'D)450', 'E)500']", "role": "user", "uuid": "07d01dd7-9db8-4e95-a925-145936032b81" }, { "content": "Each term in set B is 20 more than the corresponding term in set A.\nThe difference of the sums = 25 * 20 = 500.\nThe answer is E.", "role": "assistant", "uuid": "a32f28ae-42d4-44a1-8c37-d3730de6b7f0" } ]

{ "coherence": 2.64, "complexity": 1.86, "correctness": 2, "helpfulness": 2.2, "instruction-following": 2.68, "safety": 4.85, "verbosity": 1.25, "verbosity-coeff": -0.1095 }

[ { "content": "A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?\n\n['A)210m', 'B)240m', 'C)963m', 'D)874m', 'E)578m']", "role": "user", "uuid": "5a549ce2-b6b1-44f7-9efa-c0922ee218b7" }, { "content": "Explanation:\nSpeed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x = 240 m.\nAnswer: B)240m", "role": "assistant", "uuid": "23aac20b-dff1-4ccd-833f-c705c993e1f6" } ]

{ "coherence": 3.23, "complexity": 1.52, "correctness": 2.98, "helpfulness": 3.37, "instruction-following": 4.4, "safety": 4.27, "verbosity": 1, "verbosity-coeff": -0.1178 }

[ { "content": "The average age of a husband and a wife is 23 years when they were married THREE years ago but now the average age of the husband, wife and child is 20 years(the child was born during the interval). What is the present age of the child?\n\n['A)6', 'B)5', 'C)8', 'D)4', 'E)2']", "role": "user", "uuid": "02fc934c-87b3-456b-a024-7b68ced6e6e7" }, { "content": "26 * 2 = 52\n20 * 3 = 60\n-----------\n8 years.Answer: C", "role": "assistant", "uuid": "9951741c-ae76-47b7-805d-b67ddfe01747" } ]

{ "coherence": 2.53, "complexity": 0.91, "correctness": 1.72, "helpfulness": 1.8, "instruction-following": 2.04, "safety": 5.44, "verbosity": 0.37, "verbosity-coeff": -0.1591 }

[ { "content": "Rs 50000 is divided into two parts One part is given to a person with 10% interest and another part is given to a person with 20 % interest. At the end of first year he gets profit 8000 Find money given by 10%?\n\n['A)20000', 'B)40000', 'C)50000', 'D)60000', 'E)70000']", "role": "user", "uuid": "c001e650-9959-495c-9d65-57a40065938c" }, { "content": "let first parrt is x and second part is y then x+y=50000----------eq1\ntotal profit=profit on x +profit on y\n8000=(x*10*1)/100 + (y*20*1)/100\n80000=x+2y-----------------------------------eq2\n80000=50000+y\nso y=30000 then x =50000-30000=20000\nfirst part =20000\nANSWER:A", "role": "assistant", "uuid": "415b38be-02ee-44f6-94e5-805058dcf19c" } ]

{ "coherence": 2.86, "complexity": 1.8, "correctness": 2.49, "helpfulness": 2.49, "instruction-following": 2.82, "safety": 5.09, "verbosity": 1.35, "verbosity-coeff": -0.1169 }

[ { "content": "Sushil got thrice as many marks in English as in Science. His total marks in English, Science and Maths are 162. If the ratio of his marks in English and Maths is 3:5, find his marks in Science?\n\n['A)18', 'B)87', 'C)57', 'D)17', 'E)16']", "role": "user", "uuid": "dd51d967-020c-4d3a-a623-e9cbaf706c33" }, { "content": "S:E = 1:3\nE:M = 3:5\n------------\nS:E:M = 3:9:15\n3/27 * 162 = 18\nAnswer: A", "role": "assistant", "uuid": "076e72ad-3f46-4f31-af13-44e8ee7e6178" } ]

{ "coherence": 2.76, "complexity": 0.82, "correctness": 1.92, "helpfulness": 2.21, "instruction-following": 3, "safety": 4.7, "verbosity": 0.54, "verbosity-coeff": -0.1199 }

[ { "content": "Valentine day 14 Feb. 2005 was celebrated by Anand and shilpa on Monday. They were very happy. What day of the week would come on 14 Feb. 2010?\n\n['A)monday', 'B)tuesday', 'C)sunday', 'D)wednesday', 'E)thursday']", "role": "user", "uuid": "c2fd66c5-b761-4679-9376-8c89eb662c1d" }, { "content": "feb 14 2005 - monday\nfeb 14 2006 - tuesday\nfeb 14 2007 - wednesday\nfeb 14 2008 - thursday\nfeb 14 2009 - saturday [since 2008 is leap year , 2 days ll go forward]\nfeb 14 2010 - sunday\nANSWER:C", "role": "assistant", "uuid": "9548d28f-8744-4872-8f57-ef4beb624fb8" } ]

{ "coherence": 2.86, "complexity": 1.04, "correctness": 2.29, "helpfulness": 2.53, "instruction-following": 3.21, "safety": 5.71, "verbosity": 1.41, "verbosity-coeff": -0.123 }

[ { "content": "In a certain town, there are nine times as many people who were born in the town’s state as there are people who were born in another state or country. The ratio of those residents born in the town’s state to the town’s total population is\n\n['A)1 to 4', 'B)1 to 3', 'C)1 to 2', 'D)3 to 4', 'E)9 to 10']", "role": "user", "uuid": "a7240d83-af59-49e2-a95d-e3de3966e48e" }, { "content": "Town state: 9 times the whole town or country\nthen ratio will be 9 (times)/10 total(times)\nSo the answer is 9/10.\nE", "role": "assistant", "uuid": "ee978057-157d-421c-9786-b9396789058a" } ]

{ "coherence": 2.86, "complexity": 1.55, "correctness": 2.27, "helpfulness": 2.31, "instruction-following": 1.89, "safety": 4.62, "verbosity": 0.61, "verbosity-coeff": -0.1811 }

[ { "content": "Suraj has a certain average of runs for 12 innings. In the 13th innings he scores 96 runs thereby increasing his average by 5 runs. What is his average after the 13th innings?\n\n['A)48', 'B)64', 'C)36', 'D)72', 'E)27']", "role": "user", "uuid": "001bae38-8479-4d9c-8220-77f3a1a25ead" }, { "content": "To improve his average by 5 runs per innings he has to contribute 12 x 5 = 60 runs for the previous 12 innings.\nThus, the average after the 13th innings\n= 96 - 60 = 36.\nANSWER:C", "role": "assistant", "uuid": "40bf56f2-5d42-4f35-b6e3-a5bede0efb14" } ]

{ "coherence": 2.45, "complexity": 1.78, "correctness": 1.88, "helpfulness": 2.06, "instruction-following": 2.66, "safety": 5.09, "verbosity": 1.23, "verbosity-coeff": -0.1211 }

[ { "content": "The average age of students in section A of 100 students is 20 years and the average age of students in section B of 150 students is 30 years. Find the average age of students in both sections taken together?\n\n['A)26 years', 'B)30years', 'C)15years', 'D)25years', 'E)20years']", "role": "user", "uuid": "7ad24bdb-1eef-480e-8c51-ecd874fa9bd6" }, { "content": "The required average = (100*20+150*30)/100+150 = 26 years\nAnswer is A", "role": "assistant", "uuid": "2e502585-ba81-4ccd-b1a0-deea752ce3c6" } ]

{ "coherence": 2.84, "complexity": 1.39, "correctness": 2.2, "helpfulness": 2.25, "instruction-following": 3.29, "safety": 5.75, "verbosity": 1, "verbosity-coeff": -0.1266 }

[ { "content": "A, B and C started a business with a total investment of Rs. 90000. A invests Rs. 6000 more than B and B invests Rs. 3000 less than C. If the total profit at the end of a year is Rs. 8640, Find C's share.\n\n['A)Rs. 3240', 'B)Rs. 2520', 'C)Rs. 2880', 'D)Rs. 3360', 'E)None of these']", "role": "user", "uuid": "869f78f2-983a-4bb7-90c2-862f763f4585" }, { "content": "Explanation:\nLet C's investment = Rs. x\nB's investment = Rs. (x - 3000)\nA's investment = Rs. (x - 3000 + 6000) = Rs. (x + 3000)\nNow, (A + B + C)'s investment = Rs. 90000\n=> x + (x - 3000) + (x + 3000) = 90000\n=> 3x = 90000\n=> x = 30000\nHence, A's investment = Rs. 33000\nB's investment = Rs. 27000\nC's investment = Rs. 30000\nRatio of the capitals of A, B and C\n= 33000 : 27000 : 30000\n= 11 : 9 : 10\nA's share = Rs. [(10/30) × 8640] = Rs. 2880\nAnswer: Option C", "role": "assistant", "uuid": "88395593-2268-478f-a59b-5730586442d4" } ]

{ "coherence": 2.98, "complexity": 1.85, "correctness": 2.47, "helpfulness": 2.9, "instruction-following": 3.35, "safety": 3.76, "verbosity": 1.44, "verbosity-coeff": -0.1066 }

[ { "content": "There are 8 men and 10 women and you need to form a committee of 5 men and 6 women. In how many ways can the committee be formed?\n\n['A)11660', 'B)11700', 'C)11760', 'D)11800', 'E)11850']", "role": "user", "uuid": "0f3305f0-fbd1-4840-bd54-dd5169409e7a" }, { "content": "Explanation:\nWe need to select 5 men from 8 men and 6 women from 10 women\nNumber of ways to do this\n= 8C5 × 10C6\n= 8C3 × 10C4 [∵ nCr = nC(n-r)]\n=\n(\n8\n×\n7\n×\n6\n3\n×\n2\n×\n1\n)\n(\n10\n×\n9\n×\n8\n×\n7\n4\n×\n3\n×\n2\n×\n1\n)\n=\n56\n×\n210\n=11760\nOption C", "role": "assistant", "uuid": "6426bfdd-9772-4118-afda-12e70a0e00dd" } ]

{ "coherence": 2.64, "complexity": 1.65, "correctness": 2.25, "helpfulness": 2.55, "instruction-following": 3.56, "safety": 5.52, "verbosity": 1.11, "verbosity-coeff": -0.1849 }

[ { "content": "Set A consists of the integers from 1 to 12, inclusive, while set B consists of the integers from 5 to 15, inclusive. How many distinct integers do belong to the both sets at the same time?\n\n['A)8', 'B)10', 'C)12', 'D)15', 'E)9']", "role": "user", "uuid": "f6f14c71-dbe6-4736-a2f5-70a18dd8419e" }, { "content": "A = {1,2,3,4, 5,6, 7, 8, 9, 10, 11, 12}\nB = {5,6, 7, 8, 9, 10, 11, 12, 13, 14, 15}\nCommon elements = {5,6, 7, 8, 9, 10, 11, 12} = 8 elements\nAnswer: Option A.", "role": "assistant", "uuid": "7010f20b-2d54-4ea7-ac3a-90d37f889793" } ]

{ "coherence": 2.76, "complexity": 1.04, "correctness": 2.21, "helpfulness": 2.37, "instruction-following": 2.8, "safety": 5.59, "verbosity": 1.16, "verbosity-coeff": -0.2399 }

[ { "content": "A restaurant buys fruit in cans containing 3 1/2 cups of fruit each. If the restaurant uses 1/2 cup of the fruit in each serving of its fruit compote, what is the least number of cans needed to prepare 60 servings of the compote ?\n\n['A)7', 'B)8', 'C)9', 'D)10', 'E)12']", "role": "user", "uuid": "ba623247-4aa2-46e4-bcf1-7d09f0f51491" }, { "content": "7/2 cups = 1 can\n1/2 cup of each serving. so 7 serving per 1 can.\nLeast number is 7*9=63 =60 approx\nAnswer -9\nANSWER:C", "role": "assistant", "uuid": "2f9c5044-f8fd-49dc-8426-6ca9f2705492" } ]

{ "coherence": 2.29, "complexity": 0.85, "correctness": 1.38, "helpfulness": 1.58, "instruction-following": 2.16, "safety": 6.14, "verbosity": 0.83, "verbosity-coeff": -0.1901 }

[ { "content": "A bat is bought for Rs.800 and sold at a gain of 20% find its selling price\n\n['A)Rs.920/-', 'B)Rs.950/-', 'C)Rs.860/-', 'D)Rs.960/-', 'E)None of these']", "role": "user", "uuid": "0be5138b-d2c9-42a6-b16c-bd2d6aa1217b" }, { "content": "Explanation:\n100 % ------> 800 (100 * 8 = 800)\n120 % ------> 960 (120 * 8 = 960)\nSelling price = Rs. 960/-\nAnswer: Option D", "role": "assistant", "uuid": "99c5ab6e-15fb-405e-8215-1fca1773b3f2" } ]

{ "coherence": 2.57, "complexity": 1.95, "correctness": 2.25, "helpfulness": 2.55, "instruction-following": 2.86, "safety": 5.01, "verbosity": 1.56, "verbosity-coeff": -0.1103 }

[ { "content": "If f(x) = 5x − √x and g(x) = x^2, what is f(g(6))?\n\n['A)-4', 'B)8', 'C)16', 'D)32', 'E)174']", "role": "user", "uuid": "227c5e0e-801b-4ff4-9fb8-e7f59e1677b6" }, { "content": "g(x) = x²\ng(6) = 6² = 36\nSo, f(g(6)) = f(36)\nf(x) = 5x − √x\nSo, f(36) = 5(36) − √36\n= 180 - 6\n= 174\n= E", "role": "assistant", "uuid": "d52d0687-5955-4282-9321-0f1584ccefeb" } ]

{ "coherence": 3.02, "complexity": 1.59, "correctness": 2.33, "helpfulness": 2.43, "instruction-following": 3.33, "safety": 5.01, "verbosity": 0.54, "verbosity-coeff": -0.1702 }

[ { "content": "The value of x + x(xx) when x = 2 is:\n\n['A)10', 'B)18', 'C)16', 'D)64', 'E)36']", "role": "user", "uuid": "731bd34a-0b52-435e-8fce-2280954f3c65" }, { "content": "x + x(xx)\nPut the value of x = 2 in the above expression we get,\n2 + 2(22)\n= 2 + 2(2 × 2)\n= 2 + 2(4)\n= 2 + 8\n= 10CORRECT ANSWER : A", "role": "assistant", "uuid": "6cfe9081-17fd-4c8a-9330-7b757ca2c686" } ]

{ "coherence": 2.96, "complexity": 1.87, "correctness": 2.88, "helpfulness": 3.05, "instruction-following": 3.7, "safety": 4.85, "verbosity": 1.5, "verbosity-coeff": -0.1055 }

[ { "content": "A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 72 km/hr. What is the length of the platform?\n\n['A)229', 'B)240', 'C)288', 'D)277', 'E)320']", "role": "user", "uuid": "3a6d1a58-1ed2-48e2-800e-9035400e271e" }, { "content": "Speed = 72 * 5/18 = 20 m/sec.\nLength of the train = 20 * 20 = 400 m.\nLet the length of the platform be x m . Then,\n(x + 400)/36 = 20 => x = 320 m.\nAnswer: E", "role": "assistant", "uuid": "591dc26b-446e-4ef3-b533-22d42f80e913" } ]

{ "coherence": 2.82, "complexity": 1.89, "correctness": 2.23, "helpfulness": 2.33, "instruction-following": 3.68, "safety": 5.4, "verbosity": 1.29, "verbosity-coeff": -0.1193 }

[ { "content": "If g and y are integers, then gy(g + y) is\n\n['A)Always positive', 'B)Always negative', 'C)Positive when g is positive', 'D)Negative when g is negative', 'E)It cannot be determined by the information given']", "role": "user", "uuid": "b499231e-561d-49fd-a0c8-da233bcdf4a8" }, { "content": "Given g and y are integers, then gy(g + y)\nLet's take even as 2 / -2 and odd as 3 / -3..we get the following.. and IMO option D is correct answer..\nI presume its Option E if am not missing anything.\ng=-3 and y=1\ngy(g + y) is positive = 6", "role": "assistant", "uuid": "ad3c041d-676d-434f-b6b9-f699ebc90e1e" } ]

{ "coherence": 2.66, "complexity": 2.14, "correctness": 1.93, "helpfulness": 1.79, "instruction-following": 1.33, "safety": 3.64, "verbosity": 1.58, "verbosity-coeff": -0.1613 }

[ { "content": "A certain basketball team that has played 2/3 of its games has a record of 13 wins and 7 losses. What is the greatest number of the remaining games that the team can lose and still win at least 3/4 of all of its games?\n\n['A) 0', 'B) 1', 'C) 2', 'D) 4', 'E) 3']", "role": "user", "uuid": "520ad54e-bc29-4c4c-92d8-1ac2fccd1021" }, { "content": "13 wins, 7 losses - total 20 games played.\nThe team has played 2/3rd of all games so total number of games = 30\n3/4th of 30 is 22.5 so the team must win 23 games and can afford to lose at most 7 total games. It has already lost 7 games so it can lose another 0 at most.\nAnswer (A)", "role": "assistant", "uuid": "5a2c713b-4e26-45b1-b05b-b7228d7e4488" } ]

{ "coherence": 2.9, "complexity": 0.94, "correctness": 2.62, "helpfulness": 2.64, "instruction-following": 2.55, "safety": 4.48, "verbosity": 0.83, "verbosity-coeff": -0.2326 }

[ { "content": "The price of 2 sarees and 4 shirts is $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)3800', 'B)3300', 'C)2400', 'D)4200', 'E)1400']", "role": "user", "uuid": "eaad939d-f46f-4205-a850-0de7977f4d44" }, { "content": "C\n$2400\nLet the price of a saree and a shirt be $x and $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 = $(12 x 200) = $2400.", "role": "assistant", "uuid": "8e737258-49da-4923-9391-70da055e6223" } ]

{ "coherence": 3.33, "complexity": 1.72, "correctness": 3.07, "helpfulness": 3.52, "instruction-following": 3.43, "safety": 4.4, "verbosity": 1.21, "verbosity-coeff": -0.1229 }

[ { "content": "A sum of money becomes triple itself in 5 years at simple interest. How many years will it become six times at the same rate?\n\n['A)12 1/2 years', 'B)2 1/2 years', 'C)12 1/5 years', 'D)12 6/2 years', 'E)13 1/2 years']", "role": "user", "uuid": "d8e052df-fb92-4f67-8cfc-31c6dbe8af8e" }, { "content": "100 ---- 200 ---- 5\n200 ---- 5\n100 ---- 2 1/2\n------------------\n600 ---- 12 1/2 years\nAnswer: A", "role": "assistant", "uuid": "8c7fd558-1902-4718-a4c3-7ac438ab4f25" } ]

{ "coherence": 2.74, "complexity": 0.85, "correctness": 2.04, "helpfulness": 2.18, "instruction-following": 2.49, "safety": 5.28, "verbosity": 0.12, "verbosity-coeff": -0.1309 }

[ { "content": "If the sum of 8 consecutive integers is x, which of the must be true?\nI. x is even\nII. x is odd\nIII. x is a multiple of 8\n\n['A)I only', 'B)II only', 'C)III only', 'D)I and III', 'E)II and III']", "role": "user", "uuid": "f7bc7276-91d9-4b26-86a2-805c27cc0003" }, { "content": "sum of 6 consecutive integers\n= (n) + (n+1) + (n+2) + (n+3) + (n+4) + (n+5)+(n+6)+(n+7)\n= 8n + 28\n= even + even = even\n= 4(2n+7) = divisible by 4\nHence, x is even and divisible by 4.\nAnswer: D", "role": "assistant", "uuid": "b9c923cf-e2e4-4e50-a495-4af55f8906f9" } ]

{ "coherence": 2.61, "complexity": 2.31, "correctness": 1.6, "helpfulness": 1.8, "instruction-following": 2.06, "safety": 5.48, "verbosity": 1.49, "verbosity-coeff": -0.2223 }

[ { "content": "a is x % of b, b is x% more than a. Find x.\n\n['A)50%', 'B)62%', 'C)75%', 'D)37%', 'E)39%']", "role": "user", "uuid": "4be295e3-7c29-437d-af39-fbb1396b9e78" }, { "content": "DETAILED SOLUTION\na = bx\nb = a (1 + x), substituting this in the previous equation, we get\nx (x + 1) = 1\nx2 + x - 1 = 0\nor x is approximately 0.62 or 62%.\nCorrect Answer: (B).", "role": "assistant", "uuid": "de7ca53a-8269-4db9-a7f5-1692b4c78503" } ]

{ "coherence": 3, "complexity": 2.16, "correctness": 2.2, "helpfulness": 2.18, "instruction-following": 2.64, "safety": 4.97, "verbosity": 1.24, "verbosity-coeff": -0.1019 }

[ { "content": "Which letter will come exactly between the tenth letter from your left and the seventh letter from your right. Without changing any order in the original from the alphabet?\n\n['A)o', 'B)p', 'C)e', 'D)r', 'E)s']", "role": "user", "uuid": "0686decc-3843-477c-8bef-1bb3d9e9dac9" }, { "content": "10th letter from your left is J\n7th letter from your right is T\nThe mid letter between J and T is O.\nANSWER A", "role": "assistant", "uuid": "eeb75280-e6bc-4537-bc17-7a6bb2ba10b2" } ]

{ "coherence": 2.68, "complexity": 1.78, "correctness": 2.18, "helpfulness": 2.61, "instruction-following": 2.1, "safety": 3.99, "verbosity": 1.72, "verbosity-coeff": -0.0898 }

[ { "content": "If n is an integer and 5^n > 40,000,000,000, what is the least possible value of n?\n\n['A)16', 'B)8', 'C)9', 'D)10', 'E)11']", "role": "user", "uuid": "a076c31e-d6a3-424e-92f9-956f3035d217" }, { "content": "When you seperate the 40000000000 into factors of 5 and 2 you get - > 10^10 x 2^2 = 5^10 x 2^12\n2 to the ^ 8 = 4096 so its4096 x 5^10\nthat means 5^10 x 5^x must be greater\n5^x > 4096\n5^1=5\n5^2=25\n5^3= 125\n5^6= 15625 - > so x must be at least 6\n5^(10+6)= 5^16\nA", "role": "assistant", "uuid": "f3940a51-d6f9-4296-b10d-6125fae5325d" } ]

{ "coherence": 2.57, "complexity": 1.57, "correctness": 2, "helpfulness": 1.93, "instruction-following": 1.64, "safety": 4.5, "verbosity": 1.14, "verbosity-coeff": -0.2252 }

[ { "content": "Danny is sitting on a rectangular box. The area of the front face of the box is half the area of the top face, and the area of the top face is 1.5 times the area of the side face. If the volume of the box is 5184, what is the area of the side face of the box?\n\n['A)123', 'B)167', 'C)178', 'D)199', 'E)288']", "role": "user", "uuid": "2a4bc063-e371-440d-880a-e96ddbd3c156" }, { "content": "Lets suppose length= l, breadth= b, depth= d\nFront face area= l*w = 1/2 w*d (l=1/2 d or d=2l)\ntop face area= w*d\nside face area= w*d = 1.5 d*l (w=1.5l)\nVolume = l*w*d= 5184\nl*1.5l*2l= 5184\nl=12\nSide face area= l*d= l*2l= 12*2*12=288\nE is the answer", "role": "assistant", "uuid": "7e286ad1-a263-48d7-aca1-e58b76edfe97" } ]

{ "coherence": 2.84, "complexity": 1.63, "correctness": 1.56, "helpfulness": 1.8, "instruction-following": 1.97, "safety": 5.36, "verbosity": 0.79, "verbosity-coeff": -0.2124 }

[ { "content": "In how many different number of ways 3 boys and 2 girls can sit on a bench?\n\n['A)700', 'B)710', 'C)120', 'D)720', 'E)740']", "role": "user", "uuid": "7f4e7a5e-607e-4e3b-bd28-439f4d837191" }, { "content": "npn = n!\n5p5 = 5 × 4 × 3 × 2 × 1 = 120\nC", "role": "assistant", "uuid": "958de678-b641-4246-947c-f098972b299e" } ]

{ "coherence": 1.67, "complexity": 1.09, "correctness": 1.03, "helpfulness": 0.95, "instruction-following": 1.81, "safety": 4.4, "verbosity": 0.88, "verbosity-coeff": -0.1236 }

[ { "content": "A profit of Rs. 800 is divided between X and Y in the ratio of 1/2:1/3 . What is the difference between their profit shares ?\n\n['A)s. 260', 'B)s. 160', 'C)s. 360', 'D)s. 50', 'E)s. 90']", "role": "user", "uuid": "ff957b5d-558a-40e8-93b2-4f07a542fce1" }, { "content": "A profit of Rs. 800 is divided between X and Y in the ratio of 1/2 : 1/3 or 3:2.\nso profits are 480 and 320.\ndifference in profit share = 480-320=160\nANSWER:B", "role": "assistant", "uuid": "b8034bb9-71f1-4718-84a8-35e8aee5e4ee" } ]

{ "coherence": 2.8, "complexity": 1.43, "correctness": 2.62, "helpfulness": 2.64, "instruction-following": 3.58, "safety": 4.93, "verbosity": 1.31, "verbosity-coeff": -0.1166 }

[ { "content": "A deer is standing 60 meters in from the west end of a tunnel. The deer sees a train approaching from the west at a constant speed ten times the speed the deer can run. The deer reacts by running toward the train and clears the exit when the train is 33 meters from the tunnel. If the deer ran in the opposite direction it would barely escape out the eastern entrance just as the train came out of the eastern entrance. How long is the tunnel in meters?\n\n['A)127', 'B)132', 'C)137', 'D)142', 'E)147']", "role": "user", "uuid": "33889cc0-45c7-4154-8489-e97d17b5b90a" }, { "content": "Let x be the length of the tunnel.\nWhen the deer runs 60 meters west , the train goes 600 meters to a point 33 meters from the west entrance of the tunnel.\nWhen the deer runs east, the deer runs x-60 meters while the train goes x + 600 + 33 meters.\nx + 600 + 33 = 10(x-60)\n9x = 1233\nx = 137 meters\nThe answer is C.", "role": "assistant", "uuid": "62d4fef8-e90c-47ff-9584-d73b6ed5471f" } ]

{ "coherence": 3.11, "complexity": 1.55, "correctness": 2.49, "helpfulness": 2.51, "instruction-following": 3.25, "safety": 5.28, "verbosity": 0.77, "verbosity-coeff": -0.17 }

[ { "content": "The population of a bacteria colony doubles every day. If it was started 3 days ago with 3 bacteria and each bacteria lives for 12 days, how large is the colony today?\n\n['A)512', 'B)1024', 'C)768', 'D)2048', 'E)4096']", "role": "user", "uuid": "67efde8f-6049-44de-84c6-0bb485d7e3e6" }, { "content": "9 days ago- 2\n8 days ago- 4\n7 days ago- 8\n6 days ago- 16\n5 days ago- 32\n4 days ago- 64\n3 days ago- 128\n2 days ago- 256\nYesterday- 512\nToday- 1024\nAnswer:B", "role": "assistant", "uuid": "46aa876c-da7c-4d35-88ec-3f4bf18eeeab" } ]

{ "coherence": 2.88, "complexity": 1.26, "correctness": 2.29, "helpfulness": 2.47, "instruction-following": 3.07, "safety": 6.22, "verbosity": 1.03, "verbosity-coeff": -0.1234 }

[ { "content": "Two numbers are respectively 20% and 50% more than a third number. The percentage that is first of the second is?\n\n['A)45%', 'B)80%', 'C)78%', 'D)94%', 'E)68%']", "role": "user", "uuid": "73b01ac7-3f69-437a-bf4a-7d87e9d390ed" }, { "content": "I II III\n120 150 100\n150----------120\n100-----------? => 80%\nAnswer:B", "role": "assistant", "uuid": "c9c0b794-6da3-427d-87fb-4a2ce44a9535" } ]

{ "coherence": 2.78, "complexity": 1.2, "correctness": 1.82, "helpfulness": 1.74, "instruction-following": 1.93, "safety": 6.84, "verbosity": 0.28, "verbosity-coeff": -0.1225 }

[ { "content": "A city had 400 migrants in the year 2000. Since then, The number of migrants in a countrythe city has doubled every 3 years. If there were 400 migrants in the country in the year 2000, What was the increase in the population of migrants during the period from 2009 to 2012?\n\n['A)1400', 'B)2300', 'C)3000', 'D)3200', 'E)3800']", "role": "user", "uuid": "d68a9928-6009-424c-b82f-41edb3827966" }, { "content": "The population will increase in the following order:\n2000: 400\n2003: 800\n2006: 1600\n2009: 3200\n2012: 6400\nDifference between 2009 and 2012 = 3200\nOption D", "role": "assistant", "uuid": "8f25e8d0-e52b-4d8e-892a-fcb21575dcca" } ]

{ "coherence": 2.74, "complexity": 1.23, "correctness": 2.25, "helpfulness": 2.47, "instruction-following": 2.41, "safety": 5.79, "verbosity": 0.96, "verbosity-coeff": -0.1199 }

[ { "content": "For all positive integers f, f◎ equals the distinct pairs of positive integer factors. For example, 16◎ =3, since there are three positive integer factor pairs in 16: 1 x 16, 2 x 8, and 4 x 4.\nWhat is the greatest possible value for f◎ if f is less than 100?\n\n['A)6', 'B)7', 'C)8', 'D)9', 'E)10']", "role": "user", "uuid": "c49f8bb4-dc3a-43b9-85ac-6b126782818f" }, { "content": "I took numbers in reverse order from 99 and got 6 distinct pairs in 96.\nI thought it may be because 96=(2^5*3) has (5+1)*(1+1)=12(perhaps maximum) factors.\n1*96,2*48*4*24,8*12,16*6,32*3\nHowever, I was not sure while answering this. Please let us know if there is a better way.\nAns: \"A\"", "role": "assistant", "uuid": "5c86ba29-c749-43e8-8b07-0168fd04e12b" } ]

{ "coherence": 2.27, "complexity": 1.15, "correctness": 1.56, "helpfulness": 1.45, "instruction-following": 1.52, "safety": 4.66, "verbosity": 0.94, "verbosity-coeff": -0.1537 }

[ { "content": "A dog takes 4 leaps for every 5 leaps of a hare but 3 leaps of a dog are equal to 4 leaps of the hare. Compare their speeds?\n\n['A)4:5', 'B)16:15', 'C)9:13', 'D)5:15', 'E)9:17']", "role": "user", "uuid": "2f97bb72-65a4-40df-8449-73256309118d" }, { "content": "Let the distance covered in 1 leap of the dog be x and that covered in 1 leap of the hare be y\nThen 3x = 4y\nx = 4/3 y\n4x = 16/3 y\nRatio of speeds of dog and hare = Ratio of distances covered by them in the same time\n= 4x:5y = 16/3 y : 5 = 16:15\nAnswer is B", "role": "assistant", "uuid": "171f310a-935b-48fc-86f8-db2ef5137803" } ]

{ "coherence": 2.82, "complexity": 2.12, "correctness": 2.47, "helpfulness": 2.49, "instruction-following": 3.39, "safety": 5.05, "verbosity": 1.43, "verbosity-coeff": -0.1224 }

[ { "content": "A man's speed with the current is 30km/hr and the speed of the current is 5 km/hr. The man's speed against the current is\n\n['A)10 km/hr', 'B)20 km/hr', 'C)25 km/hr', 'D)30 km/hr', 'E)35 km/hr']", "role": "user", "uuid": "f9882de3-5ac7-494d-86b0-962d797bca81" }, { "content": "Explanation:\nSpeed of man with the current = 30 km/hr\nSpeed of current = 5\nSince, Speed of current + speed of man = 30\n5 + speed of man = 30\nSpeed of man = 25 km/hr\nman's speed against the current is = speed of man - speed of current = 25 - 5 = 20 km/hr\nAnswer: Option B", "role": "assistant", "uuid": "6b4131a7-9572-4c26-a74f-e0efe305fb41" } ]

{ "coherence": 3.31, "complexity": 1.34, "correctness": 2.78, "helpfulness": 2.96, "instruction-following": 2.92, "safety": 4.66, "verbosity": 0.78, "verbosity-coeff": -0.1164 }

[ { "content": "The sector of a circle has radius of 21 cm and central angle 135o. Find its perimeter?\n\n['A)91.5 cm', 'B)91.8 cm', 'C)99.5 cm', 'D)91.6 cm', 'E)91.3 cm']", "role": "user", "uuid": "47aaa9de-b666-4c98-94b6-1f1f5c803181" }, { "content": "Perimeter of the sector\n= length of the arc + 2(radius)\n= (135/360 * 2 * 22/7 * 21) + 2(21)\n= 49.5 + 42\n= 91.5 cm\nAnswer: A", "role": "assistant", "uuid": "953f9edb-5809-4bab-a40a-de401a4b70a6" } ]

{ "coherence": 3.07, "complexity": 1.32, "correctness": 2.47, "helpfulness": 2.62, "instruction-following": 4.29, "safety": 5.36, "verbosity": 1.23, "verbosity-coeff": -0.1228 }

[ { "content": "A tyre has two punctures. The first puncture alone would have made the tyre flat in 10 minutes and the second alone would have done it in 6 minutes. If air leaks out at a constant rate, how long does it take both the punctures together to make it flat ?\n\n['A)3 1/5min', 'B)3 2/5min', 'C)3 3/5min', 'D)3 3/4min', 'E)3 min']", "role": "user", "uuid": "4d126a1b-d1ea-4fef-8c17-33eec6c69b95" }, { "content": "Explanation:\nDo not be confused, Take this question same as that of work done question's. Like work done by 1st puncture in 1 minute and by second in 1 minute.\nLets Solve it:\n1 minute work done by both the punctures =\n(1/10+1/6)=(8/30) = (4/15)\nSo both punctures will make the type flat in\n(15/4)mins=3 3/4mins\nOption D", "role": "assistant", "uuid": "b85aab4f-47fd-4a8e-960c-be0b54039fed" } ]

{ "coherence": 2.57, "complexity": 1.74, "correctness": 1.99, "helpfulness": 2.16, "instruction-following": 2.88, "safety": 6.02, "verbosity": 1.24, "verbosity-coeff": -0.1176 }

[ { "content": "In a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 100?\n\n['A)22', 'B)28', 'C)025', 'D)20', 'E)11']", "role": "user", "uuid": "8aa332ae-b6cc-478c-91df-de3baa7a77ac" }, { "content": "A scores 60 while B score 40 and C scores 30.\nThe number of points that C scores when B scores 100 = (100 * 30)/40 = 25 * 3 = 75.\nIn a game of 100 points, B gives (100 - 75) = 25 points to C.\nAnswer: C", "role": "assistant", "uuid": "22d0736c-f02b-44c0-a9c3-7ecf091c82da" } ]

{ "coherence": 2.82, "complexity": 1.56, "correctness": 2.37, "helpfulness": 2.41, "instruction-following": 2.68, "safety": 4.34, "verbosity": 1.3, "verbosity-coeff": -0.1286 }

[ { "content": "The first flight out of Phoenix airport had a late departure. If the next three flights departed on-time, how many subsequent flights need to depart from Phoenix on-time, for the airport's on-time departure rate to be higher than 40%?\n\n['A)4', 'B)6', 'C)5', 'D)2', 'E)8']", "role": "user", "uuid": "c706aad1-9bcf-4b22-b70a-649876755c8e" }, { "content": "We need on-time departure rate to be higher than 4/10, so it should be at least 5/11, which means that 5 out of 11 flights must depart on time. Since for now 3 out of 4 flights departed on time then 5-3=2 subsequent flights need to depart on-time.\nAnswer: D", "role": "assistant", "uuid": "a96b0db6-ab15-44d4-b2bf-1f1d2a46dfe2" } ]

{ "coherence": 3.04, "complexity": 0.73, "correctness": 2.94, "helpfulness": 3.04, "instruction-following": 3.74, "safety": 5.44, "verbosity": 0.87, "verbosity-coeff": -0.1388 }

[ { "content": "X and Y started a business by investing Rs.36000 and Rs.42000 respectively after 4 months Z joined in the business with an investment of Rs.48000, then find share of Z in the profit of Rs.13750 ?\n\n['A)3200', 'B)4000', 'C)3250', 'D)3825', 'E)3985']", "role": "user", "uuid": "c6b3f2c5-9f09-442e-872c-4bb50c72a452" }, { "content": "Ratio of investment, as investments is for different time.\nInvestment x Number of units of time.\nRatio of investments X : Y : Z = 36000 : 42000 : 48000 => 6 : 7 : 8.\nX = 6 x 12 Months = 72, Y = 7 x 12 = 84, Z = 8 X 8 = 64 => 18 : 21 : 16.\nRatio of investments => X : Y : Z = 18 : 21 : 16.\nInvestment Ratio = Profit sharing Ratio.\nZ = 13750 × 16/55 = Rs.4000.\nShare of Z in the profit is Rs.4000.\nOption B", "role": "assistant", "uuid": "2978298a-dee0-4572-92f5-c2d7945240f2" } ]

{ "coherence": 2.74, "complexity": 1.47, "correctness": 2.1, "helpfulness": 2.31, "instruction-following": 2.78, "safety": 4.09, "verbosity": 1.37, "verbosity-coeff": -0.0867 }

[ { "content": "A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 8 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?\n\n['A)42', 'B)70', 'C)140', 'D)196', 'E)315']", "role": "user", "uuid": "d1597e60-7a03-4335-84e8-093a76410f12" }, { "content": "Ans: 196\n7C1 * 8C2\nAnswer D)", "role": "assistant", "uuid": "a240c9c9-585e-4860-9b0e-19fe3339c61b" } ]

{ "coherence": 2.62, "complexity": 0.57, "correctness": 1.99, "helpfulness": 2.12, "instruction-following": 2.25, "safety": 5.52, "verbosity": 0.43, "verbosity-coeff": -0.2464 }

[ { "content": "Find the odd man out.\n6, 9, 15, 21, 24, 28, 30\n\n['A)28', 'B)27', 'C)26', 'D)98', 'E)12']", "role": "user", "uuid": "e041eb0a-9bee-4320-8a17-3197223e3d01" }, { "content": "Explanation:\nEach of the numbers except 28, is a multiple of 3.\nAnswer: A) 28", "role": "assistant", "uuid": "8c7299cd-f609-44f9-a735-e6fcd44eaf8a" } ]

{ "coherence": 3.35, "complexity": 1.07, "correctness": 3.13, "helpfulness": 3.29, "instruction-following": 3.05, "safety": 3.39, "verbosity": 0.96, "verbosity-coeff": -0.0771 }

[ { "content": "In a certificate by mistake a candidate gave his height as 25% more than actual height. In the interview panel, he clarified that his height was 5feet 5 nches. Find the % correction made by the candidate from his stated height to his actual height?\n\n['A)10', 'B)20', 'C)40', 'D)50', 'E)60']", "role": "user", "uuid": "664592f7-84cc-47d3-b0c5-53741d89539a" }, { "content": "His height was = 5 feet 5 inch = 5 + 60 = 65 inch. Required % correction =65*(1.25-1)* 100 = 20\nB", "role": "assistant", "uuid": "3cd14781-9452-4fee-9dfc-28d1df7bf288" } ]

{ "coherence": 2.53, "complexity": 1.29, "correctness": 1.42, "helpfulness": 1.47, "instruction-following": 2.29, "safety": 4.97, "verbosity": 0.96, "verbosity-coeff": -0.1175 }

[ { "content": "How many of the factors of 168 are divisible by 2?\n\n['A)4', 'B)8', 'C)10', 'D)12', 'E)16']", "role": "user", "uuid": "63ac586b-acca-41ca-9d6f-d32413d38259" }, { "content": "168 = 2^3*3*7\nThe total number of factors is (1+3)(1+1)(1+1) = 16\nThe odd factors are 1, 3, 7, and 21.\nThe number of even factors is 16-4 = 12\nThe answer is D.", "role": "assistant", "uuid": "beef9b5b-74a8-4532-8cd6-5ee61edab001" } ]

{ "coherence": 3.17, "complexity": 1.56, "correctness": 2.45, "helpfulness": 2.45, "instruction-following": 2.8, "safety": 5.95, "verbosity": 1.17, "verbosity-coeff": -0.2027 }

[ { "content": "In a group of 90 students, 36 are taking History, and 32 are taking Statistics. If 57 students are taking History or Statistics or both, then how many students are taking History but not Statistics?\n\n['A)9', 'B)19', 'C)25', 'D)27', 'E)31']", "role": "user", "uuid": "eaf76df4-df0f-491a-b0b5-768f4b4c1c3a" }, { "content": "Number of students taking history =H=36\nNumber of students taking statistics =S= 32\nTotal number of students =T= 90\nNumber of students taking History or Statistics or both =B= 57\nNumber of students taking neither history nor statistics =N= 90-57=33\nLetXbe the number of students taking both history and statistics.\nThen\nT = H + S + N - X\nor 90 = 36 + 32 +33 - X\nor X = 11\nNow,\nNumber of students taking only history will be\nH-X\nor 36-11 = 25\nAnswer:- C", "role": "assistant", "uuid": "dae23e31-f365-4beb-a564-182ae3cede52" } ]

{ "coherence": 2.68, "complexity": 1.37, "correctness": 2, "helpfulness": 1.92, "instruction-following": 3.62, "safety": 5.98, "verbosity": 1.47, "verbosity-coeff": -0.1884 }

[ { "content": "A train running at the speed of 50 km/hr crosses a post in 4 seconds. What is the length of the train?\n\n['A)90', 'B)120', 'C)60', 'D)95', 'E)75']", "role": "user", "uuid": "b7d9ec7e-00f2-40bf-b492-f1d944218c4e" }, { "content": "Speed=(54x5/18)=15 m/sec.\nLength of the train=(Speed x Time).\nLength of the train=15x4m=60m.\nAnswer: C", "role": "assistant", "uuid": "3b77bdb3-be8f-4f31-8126-e76d8a440ede" } ]

{ "coherence": 2.57, "complexity": 1.5, "correctness": 2.1, "helpfulness": 2.33, "instruction-following": 3.23, "safety": 5.59, "verbosity": 1.02, "verbosity-coeff": -0.1139 }

[ { "content": "If a, b, and c are consecutive positive integers and a < b < c, which of the following must be true?\nI. c - a = 2\nII. abc is an even integer.\nIII. (a + b + c)/3 is an decimal.\n\n['A) I only', 'B) II only', 'C) I and II only', 'D) II and III only', 'E) I, II, and III']", "role": "user", "uuid": "30be8e85-1aa7-4886-ba5f-6cd864209be1" }, { "content": "Since a, b, and c are consecutive positive integers and a < b < c, then c = a + 2, from which it follows that c - a = 2. So, I is true.\nNext, out of 3 consecutive integers at least 1 must be even, thus abc=even. II is true.\nFinally, since b = a + 1, and c = a + 2, then (a + b + c)/3 = (a + a + 1 + a + 2)/3 = a + 1 = integer. III is false.\nAnswer: C", "role": "assistant", "uuid": "020a79ae-cb5a-41cc-aa9a-4e01a121f1b5" } ]

{ "coherence": 2.88, "complexity": 2.64, "correctness": 2.23, "helpfulness": 2.23, "instruction-following": 2.98, "safety": 6.14, "verbosity": 1.62, "verbosity-coeff": -0.2257 }

[ { "content": "If six persons sit in a row, then the probability that three particular persons are always together is ?\n\n['A)1/5', 'B)2/8', 'C)1/6', 'D)1/7', 'E)1/2']", "role": "user", "uuid": "01d4704a-284f-41b6-a9ab-74839f84295a" }, { "content": "Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability\n= 3!4!/6!\n= 1/5\nAnswer: C", "role": "assistant", "uuid": "c74f75ef-2a13-480d-8678-4bb8fd0869a4" } ]

{ "coherence": 2.7, "complexity": 2.29, "correctness": 2.16, "helpfulness": 2.41, "instruction-following": 3.05, "safety": 5.44, "verbosity": 1.79, "verbosity-coeff": -0.0989 }

[ { "content": "After the typist writes 12 letters and addresses 12 envelopes, she inserts the letters randomly into the envelopes (1 letter per envelope). What is the probability that exactly 1 letter is inserted in an improper envelope?\n\n['A)1/12', 'B)0', 'C)12/212', 'D)11/12', 'E)11/13']", "role": "user", "uuid": "569f359b-8fd2-44d4-81aa-5a6b419bf104" }, { "content": "0\nIf one letter is in wrong envelope, the letter corresponding to that letter will also be in wrong envelope.\nANSWER:B", "role": "assistant", "uuid": "bb19e7dc-0890-4f52-b106-253166adccae" } ]

{ "coherence": 2.84, "complexity": 1.28, "correctness": 2.2, "helpfulness": 2.2, "instruction-following": 2.06, "safety": 5.32, "verbosity": 1.48, "verbosity-coeff": -0.2188 }

[ { "content": "The speed of a boat in upstream is 100 kmph and the speed of the boat downstream is 112 kmph. Find the speed of the boat in still water and the speed of the stream?\n\n['A)70, 10 kmph', 'B)106, 6 kmph', 'C)50, 60 kmph', 'D)45, 55 kmph', 'E)45, 65 kmph']", "role": "user", "uuid": "e12f942c-46d1-4e57-85bd-3d25b9d26cc5" }, { "content": "Speed of the boat in still water = (100+112)/2 = 106 kmph. Speed of the stream = (100-112)/2 = 6 kmph\nANSWER:B", "role": "assistant", "uuid": "31e554f3-6f5d-4b1d-8987-6cc935b8b6a5" } ]

{ "coherence": 2.96, "complexity": 0.64, "correctness": 2.25, "helpfulness": 2.49, "instruction-following": 3.05, "safety": 4.7, "verbosity": 0.18, "verbosity-coeff": -0.1183 }

[ { "content": "A baseball card decreased in value 30% in its first year and 10% in its second year. What was the total percent decrease of the card's value over the two years?\n\n['A)28%', 'B)30%', 'C)32%', 'D)36%', 'E)37%']", "role": "user", "uuid": "d5b2e1f1-98e4-4100-815f-36fd4fad3741" }, { "content": "Let the initial value of baseball card = 100\nAfter first year , value of baseball card = (1- 30/100)* 100 = 70\nAfter second year , value of baseball card =(1 - 10/100)* 70 = 63\ntotal percent decrease of the card's value over the two years = (100-63/100 *100%\n=37%\nAnswer E", "role": "assistant", "uuid": "b9f122f3-37df-462d-9dc6-54061af5612f" } ]

{ "coherence": 2.55, "complexity": 1.38, "correctness": 2.47, "helpfulness": 2.43, "instruction-following": 3.37, "safety": 5.12, "verbosity": 1.44, "verbosity-coeff": -0.1764 }

[ { "content": "A person started from point A to point B and returned back to A with a speed of 60 kmh. If the distance between A and B is 120km, calculate the time he travelled\n\n['A)4 hours', 'B)2 hours', 'C)3 hours', 'D)6 hours', 'E)5 hours']", "role": "user", "uuid": "c3ad9dfe-bb43-4521-8079-331e3c1ab601" }, { "content": "Time = Distance/Speed\nTotal distance = (from A->B and from B->A) = 120+120=240 km\nSpeed = 60 kmh\n240/60 = 4\nAnswer: A", "role": "assistant", "uuid": "d1bd34f6-560d-4d68-bb8f-b13586cbe96c" } ]

{ "coherence": 2.86, "complexity": 1.5, "correctness": 2.72, "helpfulness": 3.02, "instruction-following": 3.54, "safety": 4.73, "verbosity": 1.4, "verbosity-coeff": -0.0974 }

[ { "content": "In 100 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race A beats B by:\n\n['A)10', 'B)12', 'C)30', 'D)40', 'E)20']", "role": "user", "uuid": "74ab4ac3-8f05-43a8-93c2-ac684c264c12" }, { "content": "Dist = (100/45*9) = 20 m\nANSWER E", "role": "assistant", "uuid": "6a8022b1-b9e4-4e78-bcc5-84610a48f3b9" } ]

{ "coherence": 2.14, "complexity": 1.12, "correctness": 1.76, "helpfulness": 1.72, "instruction-following": 2.43, "safety": 4.73, "verbosity": 0.97, "verbosity-coeff": -0.118 }

[ { "content": "By selling 50 meters of dress. I gain the selling price of 15 meters. Find the gain percent?\n\n['A)52 6/9%', 'B)45 8/7%', 'C)42 6/7%', 'D)12 8/3%', 'E)56 6/7%']", "role": "user", "uuid": "c7c1c3fc-c7b7-4405-bae3-2e0703d276c0" }, { "content": "C\nSP = CP + g\n50 SP = 50 CP + 15 SP\n35 SP = 50 CP\n35 --- 15 CP gain\n100 --- ? => 42 6/7%", "role": "assistant", "uuid": "6229fae3-b84f-429e-8f8d-42bf227e1a81" } ]

{ "coherence": 2.88, "complexity": 1.66, "correctness": 2.23, "helpfulness": 2.37, "instruction-following": 2.68, "safety": 4.48, "verbosity": 1.01, "verbosity-coeff": -0.1168 }

[ { "content": "How many points (x, y) lie on the line segment between (32, 12 2/3) and (7, 17 2/3) such that x and y are both integers?\n\n['A)one', 'B)4', 'C)5', 'D)8', 'E)9']", "role": "user", "uuid": "62d1e85f-764a-4987-9f9a-4e137001c7b2" }, { "content": "slope = (17 2/3 - 12 2/3) / (7 - 32) = -1/5\ny = mx + b => 12 2/3 = -22/3 + b => b = 19\ny = -x/5 + 19\nOnly integer values work, and the only multiples of 5 between 7 and 32 for x values are 10, 15, 20, 25 and 30, thus 5 points.\nC", "role": "assistant", "uuid": "73ca33e8-595a-438a-b013-892aaf9c96f7" } ]

{ "coherence": 3.27, "complexity": 1.83, "correctness": 2.59, "helpfulness": 2.62, "instruction-following": 3.27, "safety": 4.5, "verbosity": 0.99, "verbosity-coeff": -0.2335 }

[ { "content": "The average price of an antique car increases over the years. If from 1990 to 1996, the price of the car increased by 13% and from 1996 to 2001 it increased by 20%, what is the price of the car in 2001 if the price in 1990 was $11,500?\n\n['A)$15,594.', 'B)$15,322.', 'C)$14,786.', 'D)$14,543.', 'E)$12,988.']", "role": "user", "uuid": "92300c2d-d842-4cd7-9665-5a1a817335b2" }, { "content": "Whenever you have a question in which a value is increased by x% and then increased by y% then the overall effective increase = (x + y + xy/100 ) %\nThe effective increase = 13 + 20 + (13×20/100) = 35.6%\nThis is a little more 33% or 1/3 the original value.\nTHE QUICKEST WAY TO SOLVE THIS QUESTION IS TO USE APPROXIMATION.\n11500 + 1/ 3 (12000) = 15500\nTherefore option A is the answer.\nI selected 12000 because it's value is a little more 11500 and it's easier to divide by 3 ( ie to calculate 1/3 or 33%).", "role": "assistant", "uuid": "f6a2ef3b-f889-45d0-a162-2ac222ffc4ac" } ]

{ "coherence": 2.59, "complexity": 1.36, "correctness": 1.98, "helpfulness": 1.87, "instruction-following": 1.92, "safety": 4.85, "verbosity": 1.03, "verbosity-coeff": -0.1943 }

[ { "content": "A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in:\n\n['A)4 days', 'B)6 days', 'C)8 days', 'D)12 days', 'E)15 days']", "role": "user", "uuid": "c644b0b4-035a-406d-a469-4d64840dae78" }, { "content": "Explanation:\nSuppose A, B and C take x,\tx/2\tand\tx/3\tdays respectively to finish the work.\nThen, 1/X\t+\t2/X\t+\t3/X =\t1/2\n6/X\t=\t1/2\nx = 12.\nSo, B takes (12/2) = 6 days to finish the work.\nANSWER IS B", "role": "assistant", "uuid": "a17383f5-dd11-47bc-b6cf-56d82ee20895" } ]

{ "coherence": 2.88, "complexity": 1.68, "correctness": 2.68, "helpfulness": 2.86, "instruction-following": 3.68, "safety": 5.12, "verbosity": 1.08, "verbosity-coeff": -0.1268 }

[ { "content": "A fruit seller had some apples. He sells 40% apples and still he has 420. Originally he had how many apples?\n\n['A)400', 'B)500', 'C)700', 'D)450', 'E)650']", "role": "user", "uuid": "f607b1b0-3a51-438b-9db9-3a8cfe042e9c" }, { "content": "Suppose originally he had x apples\nthen (100-40)% of x = 420\n60x/100 = 420\nx= 700\nAnswer is C", "role": "assistant", "uuid": "94b1ed67-13d1-4d87-8234-2ae9d1dca7f2" } ]

{ "coherence": 3.17, "complexity": 1.62, "correctness": 2.94, "helpfulness": 2.92, "instruction-following": 3.41, "safety": 4.5, "verbosity": 0.96, "verbosity-coeff": -0.1065 }

[ { "content": "What will be 60 percent of a number whose 200 percent is 90 ?\n\n['A)144', 'B)72', 'C)27', 'D)None of these', 'E)Cannot be determined']", "role": "user", "uuid": "0e6c13ea-1314-4cd6-886c-f36f867666de" }, { "content": "Answer\n∵ 200% of N = 90\n⇒ N = (90 x 100) / 200 = 45\n∴ 60% of N = (60 x 45) / 100 = 27\nCorrect Option: C", "role": "assistant", "uuid": "7a50432e-9437-49e2-8d38-6a73e5d7f777" } ]

{ "coherence": 2.78, "complexity": 1.23, "correctness": 2.51, "helpfulness": 2.55, "instruction-following": 3.86, "safety": 5.4, "verbosity": 0.5, "verbosity-coeff": -0.1183 }

[ { "content": "In a lottery draw there are 4 jars containing 5 choices with only one choice as the lucky draw. A candidate wins the lottery draw if he/she picks up all the lucky draws from all the jars. What is the total number of ways in which a candidate will not win the lucky draw?\n\n['A)19', 'B)85', 'C)120', 'D)624', 'E)1024']", "role": "user", "uuid": "8b61b4f2-a3de-46bc-91dd-0d170bff37fa" }, { "content": "A candidate can pick up draws in 5*5*5*5=5^4 number of ways (each jar has 5 draws and we have total of 4 jars). Now, out of these cases there will be only one case when the candidate picked all the four lucky draws. Therefore the total number of ways in which a candidate will NOT win the lottery is 5^4-1=624.\nAnswer: D.", "role": "assistant", "uuid": "aca85884-867d-4b27-8a6e-b95be1bcf22a" } ]

{ "coherence": 3.11, "complexity": 1.57, "correctness": 3.02, "helpfulness": 3.04, "instruction-following": 3.88, "safety": 5.28, "verbosity": 1.54, "verbosity-coeff": -0.1072 }

[ { "content": "The true discount on a bill of Rs.1080 is Rs.180.The banker's discount is\n\n['A)210', 'B)212', 'C)214', 'D)216', 'E)None of these']", "role": "user", "uuid": "6bf368bc-6ec0-4b31-813f-a38b11e0e6f5" }, { "content": "Solution\nP.W\t= Rs.(1080 - 180)\n= Rs. 900\nS.I on Rs. 1080\t=Rs.(180/900 x 1080)\n= Rs. 216.\nAnswer D", "role": "assistant", "uuid": "9e273224-bf5f-4c3a-9b72-af49157d714b" } ]

{ "coherence": 2.86, "complexity": 1.56, "correctness": 2.74, "helpfulness": 2.9, "instruction-following": 3.52, "safety": 5.55, "verbosity": 1.46, "verbosity-coeff": -0.1141 }

[ { "content": "The radius of a circular wheel is 1.75 m, how many revolutions will it make in traveling 1 km?\n\n['A)100', 'B)277', 'C)288', 'D)267', 'E)281']", "role": "user", "uuid": "c6d4f4ad-cece-4888-8ea9-ea7500e4feb6" }, { "content": "2 * 22/7 * 1.75 * x = 11000\nx = 1000\nAnswer: A", "role": "assistant", "uuid": "0b095809-ea52-4919-9ef6-a824e3059264" } ]

{ "coherence": 2.7, "complexity": 0.86, "correctness": 2.12, "helpfulness": 2.18, "instruction-following": 3.21, "safety": 5.28, "verbosity": 0.87, "verbosity-coeff": -0.1122 }

[ { "content": "If y exceeds x by 25%, then x is less than y by?\n\n['A)28%', 'B)21%', 'C)20%', 'D)30%', 'E)29%']", "role": "user", "uuid": "ca24f474-c72e-4a07-bf82-7709208eddf0" }, { "content": "X=100\ty=125\n125--------25\n100--------? => 20%\nAnswer:C", "role": "assistant", "uuid": "4f5caad3-9e66-43fc-8aa5-26b97797667f" } ]

{ "coherence": 3.13, "complexity": 1.36, "correctness": 2.41, "helpfulness": 2.23, "instruction-following": 2.61, "safety": 4.97, "verbosity": 0.36, "verbosity-coeff": -0.1139 }

[ { "content": "What is the probability that a three digit number is divisible by 7?\n\n['A)1/7', 'B)127/900', 'C)32/225', 'D)129/900', 'E)1/8']", "role": "user", "uuid": "dd1bc110-e03d-491c-aee5-7ffcf99bdbc2" }, { "content": "Total 3 digit integers which are divisible by 7 :\n(994-105)/7+1 = 128\nThe total number of 3 digit integers = (999-100)+1 = 900\nThe required probability : 128/900 = 32/225\nanswer:C.", "role": "assistant", "uuid": "44045b19-6b59-458e-b053-db1bfd3dc36a" } ]

{ "coherence": 2.7, "complexity": 1.51, "correctness": 2.06, "helpfulness": 2.29, "instruction-following": 3.04, "safety": 6.06, "verbosity": 1.16, "verbosity-coeff": -0.2115 }

[ { "content": "How many diagonals does a polygon with 23 sides have, if one of its vertices does not connect to any diagonal?\n\n['A)201', 'B)159', 'C)179', 'D)189', 'E)209']", "role": "user", "uuid": "5f3a7a26-0cff-4032-ab1f-679b1fa1c100" }, { "content": "If I calculate it using the formulae, #diagonals = n (n-3)/2Each vertex sends of n-3 diagonals\nn= 23-1 then 22*(22-3)/2 = 209\nCorrect Option:E", "role": "assistant", "uuid": "9308f5e9-6136-47f7-b57d-0757d182ecad" } ]

{ "coherence": 2.9, "complexity": 1.51, "correctness": 2.21, "helpfulness": 2.29, "instruction-following": 2.98, "safety": 5.75, "verbosity": 0.87, "verbosity-coeff": -0.2043 }

[ { "content": "Three cubes of edges 6 cms, 8 cms and 10 cms are meted without loss of metal into a single cube. The edge of the new cube will be:\n\n['A)8 cms', 'B)12 cms', 'C)14 cms', 'D)16 cms', 'E)None']", "role": "user", "uuid": "84d6155b-e444-44cb-9843-99986934c29a" }, { "content": "Volume of new cube = Volume of cube 1 + cube 2 + cube 3 = 63 + 83 + 103, = 216 + 512 + 1000\na3 = 1728,\na = (1728)1/3 = 12\nAnswer: B", "role": "assistant", "uuid": "9272ddf1-63f4-4bc4-af01-ad436fb552c1" } ]

{ "coherence": 2.55, "complexity": 1.64, "correctness": 2.02, "helpfulness": 2.29, "instruction-following": 3.56, "safety": 5.91, "verbosity": 1.27, "verbosity-coeff": -0.1127 }

[ { "content": "A vending machine randomly dispenses four different types of fruit candy. There are twice as many apple candies as orange candies, twice as many strawberry candies as grape candies, and twice as many apple candies as strawberry candies. If each candy cost $0.2, and there are exactly 90 candies, what is the minimum amount of money required to guarantee that you would buy at least three of each type of candy?\n\n['A)$16.60', 'B)$20.75', 'C)$22.50', 'D)$42.75', 'E)$45.00']", "role": "user", "uuid": "a4561c2d-e254-41c9-b03b-fffa3172b100" }, { "content": "Let number of Apple , Orange , strawberry and grape candies be A, O ,S and G respectively .\nA= 2O\nS= 2G\nA= 2S\nA= 4G\nA+O+S+G = 90\n=>A + A/2 + A/2 +A/4 = 90\n=> 9A/4 = 90\n=> A = 40\nO = 20\nS = 20\nG = 10\nCost of each candy = .2 $\nMininum amount of money required to guarantee that you would buy at least three of each type of candy\nWe can buy 40 Apple candies , 20 orange candies , 20 strawberry candies and 3 grape candies to ensure atleast 3 of each type of candies .\nTotal = 83 candies\nAmount required = 83 * .2 = 16.60 $\nAnswer A", "role": "assistant", "uuid": "42d529db-c5b5-4589-a8d7-d4d3223fcc46" } ]

{ "coherence": 3.05, "complexity": 1.36, "correctness": 2.57, "helpfulness": 2.53, "instruction-following": 2.72, "safety": 3.23, "verbosity": 1.3, "verbosity-coeff": -0.1748 }

[ { "content": "The area of a rectangle plot is 460 square metres. If the length is 15% more than the breadth, what is the breadth of the plot?\n\n['A)10m', 'B)20m', 'C)50m', 'D)40m', 'E)30m']", "role": "user", "uuid": "cde6082b-ce20-43df-9b9c-0439cfae043c" }, { "content": "lb = 460 m power2...(Equation 1)\nLet the breadth = b\nThen length, l = b × (100+15)/100 = 115b/100 ...(Equation 2)\nFrom Equation 1 and Equation 2,\n115b/100 × b = 460\nb2 = 46000/115 = 400\n⇒ b = √400 = 20 m\nAnswer is B.", "role": "assistant", "uuid": "36127348-a219-4fd5-892d-2c6629f32590" } ]

{ "coherence": 3.04, "complexity": 1.95, "correctness": 2.27, "helpfulness": 2.37, "instruction-following": 3.19, "safety": 4.44, "verbosity": 0.73, "verbosity-coeff": -0.1127 }

[ { "content": "If a population of women in a town is 60% of men . What is the population of men as a % of population of women ?\n\n['A)A)200%', 'B)B)100%', 'C)C)50%', 'D)D)65%', 'E)E)166%']", "role": "user", "uuid": "9e229697-3c23-42ac-8514-04c76c466ee1" }, { "content": "We're told that the number of Women in a town is equal to 60% of the number of Men in that town.\nIF....\nMen = 10\nWomen = 6\nWe're asked for the number of Men, as a percentage of the number of Women.\nM/W = 10/6 = 5/3 = 166%\nAnswer is E", "role": "assistant", "uuid": "b99257d2-f13c-4798-b6c7-9c17112e6326" } ]

{ "coherence": 3.15, "complexity": 1.84, "correctness": 2.29, "helpfulness": 2.25, "instruction-following": 2.55, "safety": 6.06, "verbosity": 0.79, "verbosity-coeff": -0.1127 }

[ { "content": "A glass was filled with 10 ounces of water, and 0.01 ounce of the water evaporated each day during a 20-day period. What percent of the original amount of water evaporated during this period?\n\n['A)0.002%', 'B)0.02%', 'C)0.2%', 'D)2%', 'E)20%']", "role": "user", "uuid": "2a839486-c711-495a-8ad8-d895b99f70bf" }, { "content": "In 20 days 20*0.01=0.2 ounces of water evaporated, which is 0.2/10∗100=2 of the original amount of water.\nAnswer: D.", "role": "assistant", "uuid": "9fe79296-bd5b-46ce-8959-95989319b829" } ]

{ "coherence": 2.98, "complexity": 1.49, "correctness": 2.8, "helpfulness": 2.49, "instruction-following": 3.15, "safety": 5.16, "verbosity": 0.68, "verbosity-coeff": -0.1921 }

[ { "content": "On a windy day, out of every 3 sand dunes formed, only 1 remains. Out of 5 blown-out\nsand-dunes, 1 has treasure and only 4 out of 5 sand dunes formed have lucky coupons. Find\nthe probability that the blown-out sand dune will contain both the things.\n\n['A)2/25', 'B)4/75', 'C)8/75', 'D)3/5', 'E)4/5']", "role": "user", "uuid": "0cffbe92-b585-4b8c-8ea4-689f51c984cd" }, { "content": "Probability of sand dune blown out = 2/3\nProbability that it has treasure = 1/5\nProbability that it has lucky coupon = 4/5\ntotal probability = 2/3 * 1/5 * 4/5 = 8/75\nANSWER:C", "role": "assistant", "uuid": "81942752-a214-4405-a968-4b43d7558746" } ]

{ "coherence": 3.04, "complexity": 1.58, "correctness": 2.88, "helpfulness": 3, "instruction-following": 3.88, "safety": 4.46, "verbosity": 1.19, "verbosity-coeff": -0.1235 }

[ { "content": "What is the positive difference between the sum of the squares of the first 6 positive integers and the sum of the prime numbers between the first square and fourth square?\n\n['A)11', 'B)12', 'C)13', 'D)14', 'E)50']", "role": "user", "uuid": "5cc926b0-2451-48a3-a95e-14392b689d3e" }, { "content": "Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.\nthe sum of the squares of the first 4 positive integers = 1^2 + 2^2 + 3^2 +4^2+5^2+6^2 = 91\nthe sum of the prime numbers between the first square(=1) and fourth square(=16) = 2+3+5+7+11+13=41.\nSo the difference between 41 and 91 is 50.\nSo the answer is (E).", "role": "assistant", "uuid": "73ce3d57-731a-4136-a06b-cce7a13b7946" } ]

{ "coherence": 2.61, "complexity": 2.16, "correctness": 2.21, "helpfulness": 1.99, "instruction-following": 1.94, "safety": 6.06, "verbosity": 1.59, "verbosity-coeff": -0.2531 }

[ { "content": "What is the average (arithmetic mean) of all the multiples of ten from 10 to 250 inclusive?\n\n['A)90', 'B)95', 'C)100', 'D)130', 'E)170']", "role": "user", "uuid": "58e693ff-682e-4bb5-b839-febd49ab5b92" }, { "content": "The multiples of ten from 10 to 250 inclusive would be an evenly spaced set with 25 terms - 10, 20, 30,.......250\nSo average = (First term + Last Term)/2 = (10 + 250)/2 = 260/2 = 130\nHence, the correct answer is D.", "role": "assistant", "uuid": "f873a1f0-4b60-49b6-aa31-3b0ba04eecd4" } ]

{ "coherence": 3.07, "complexity": 1.7, "correctness": 2.51, "helpfulness": 2.64, "instruction-following": 2.86, "safety": 5.87, "verbosity": 1.27, "verbosity-coeff": -0.221 }

[ { "content": "The present ages of three persons are in proportions 4:7:9. Eight years ago, the sum of their ages was 56. Find their present ages.\n\n['A)16, 18, 36', 'B)16, 28, 36', 'C)8, 20, 28', 'D)20, 35, 45', 'E)None of these']", "role": "user", "uuid": "64ec123c-b7b4-4d35-aad6-b1c1c37ff567" }, { "content": "Answer: Option B\nLet their present ages be 4x, 7x and 9x years respectively.\nThen, (4x - 8) + (7x - 8) + (9x - 8) = 56\n20x = 80 => x = 4\nTheir present ages are 16, 28 and 36 years respectively.", "role": "assistant", "uuid": "0563a2f0-33a2-42e0-85d0-a304e7f69fb9" } ]

{ "coherence": 3.41, "complexity": 1.78, "correctness": 3.09, "helpfulness": 3.25, "instruction-following": 3.91, "safety": 4.11, "verbosity": 0.61, "verbosity-coeff": -0.1225 }

[ { "content": "A and B enter into partnership with capital as 7:9. At the end of 8 months, A withdraws. If they receive the profits in the ratio of 8:9 find how long B's capital was used?\n\n['A)2 months', 'B)7 months', 'C)8 months', 'D)10 months', 'E)12 months']", "role": "user", "uuid": "94a90c57-0c01-45f3-802f-c2e6cd7420a1" }, { "content": "Explanation:\n7 * 8 : 9 * x = 8:9 => x= 7 months\nANSWER:B", "role": "assistant", "uuid": "9791328c-ad9c-44f1-8364-98ff8d9088a5" } ]

{ "coherence": 2.82, "complexity": 1.39, "correctness": 2.39, "helpfulness": 2.76, "instruction-following": 3.62, "safety": 5.2, "verbosity": 0.65, "verbosity-coeff": -0.1273 }

[ { "content": "What is the sum of the different positive prime factors of 1092?\n\n['A)5', 'B)12', 'C)20', 'D)25', 'E)27']", "role": "user", "uuid": "185207e1-ac57-4a32-8b3e-00d28f8c8245" }, { "content": "First, we make a prime factorization by dividing 1096 by 2 then 3, etc.\n1096=2^2*3*7*13\n2*2+3+7+13=27\nAnswer (E)", "role": "assistant", "uuid": "dd85b071-be7e-4cd3-9bb5-46d8887bb9ec" } ]

{ "coherence": 2.72, "complexity": 1.32, "correctness": 1.67, "helpfulness": 1.57, "instruction-following": 1.91, "safety": 4.89, "verbosity": 0.77, "verbosity-coeff": -0.2474 }

[ { "content": "The citizens of planet nigiet are 5 fingered and have thus developed their decimal system in base 8. A certain street in nigiet contains 1000 (in base 5) buildings numbered 1 to 1000. How many 3s are used in numbering these buildings? Express result in terms of base 10.\n\n['A)54', 'B)64', 'C)75', 'D)85', 'E)100']", "role": "user", "uuid": "9fa84173-2da0-45f1-adf7-86297437c0c2" }, { "content": "no of 3s b/w 1-99 is 20,100-199 is 20 and so on. so leavn d range b/w 300-399 total no of 3s is(9*20=)180. no of 3s b/w 300-399 is(20+100=)120.\ntotal no of 3s b/w 1-1000=120+180=300\nin base 10 300=3*5^2=75.\nANSWER:C", "role": "assistant", "uuid": "5e52da97-10ac-493b-ad16-a518acfa52b2" } ]

{ "coherence": 2.16, "complexity": 2.1, "correctness": 1.53, "helpfulness": 1.57, "instruction-following": 2.33, "safety": 5.36, "verbosity": 1.28, "verbosity-coeff": -0.1248 }

[ { "content": "At what rate percent per annum will the simple interest on a sum of money be 2/5 of the amount in 10 years?\n\n['A)4 %', 'B)5 %', 'C)6 %', 'D)7 %', 'E)8 %']", "role": "user", "uuid": "f6491b08-1dad-4681-8acf-39174f96fc7d" }, { "content": "Sol.\nLet sum = x. Then, S.I. = 2x/5, Time = 10 years.\n∴ Rate = [100 * 2x / x*5*10]% = 4%.\nAnswer A", "role": "assistant", "uuid": "584fc947-e17c-4ce0-b246-12515e7fbc16" } ]

{ "coherence": 3.11, "complexity": 2.06, "correctness": 3.19, "helpfulness": 3, "instruction-following": 3.86, "safety": 5.12, "verbosity": 1.38, "verbosity-coeff": -0.1543 }

[ { "content": "During 2005, a company produced an average of 2,500 products per month. How many products will the company need to produce from 2006 through 2008 in order to increase its monthly average for the period from 2005 through 2008 by 300% over its 2005 average?\n\n['A)450,000', 'B)475,000', 'C)500,000', 'D)525,000', 'E)550,000']", "role": "user", "uuid": "c9109795-1faa-42bf-a904-2b809f19d4b2" }, { "content": "Company produced 12*2500 = 30,000 products in 2005. If company produces X products from 2006 to 2008, then total amount of product produced in 4 years (2005 through 2008) is X+30,000. The gives the average of (X+30,000)/4.\nThis average needs to be 200% higher than that in 2005. In math terms, 30,000+300%(30,000) = 120,000. So:\n(X+30,000)/4 = 120,000\nX+30,000 = 480,000\nX = 450,000\nThe answer is A.", "role": "assistant", "uuid": "502d552e-1ea0-4ed6-a319-ddcdd4bf28bd" } ]

{ "coherence": 3.13, "complexity": 1.72, "correctness": 2.47, "helpfulness": 2.76, "instruction-following": 2.55, "safety": 3.91, "verbosity": 1.23, "verbosity-coeff": -0.1869 }

[ { "content": "Evaluate permutation\n5P5\n\n['A)120', 'B)110', 'C)98', 'D)24', 'E)None of these']", "role": "user", "uuid": "be733443-3e5d-493b-9864-f094fe5aa47b" }, { "content": "Explanation:\nnPn=n!\n5P5=5∗4∗3∗2∗1=120\nOption A", "role": "assistant", "uuid": "c9031fc0-8f6f-4fbd-86f3-0e531c471475" } ]

{ "coherence": 3.11, "complexity": 2.23, "correctness": 3.37, "helpfulness": 3.19, "instruction-following": 3.43, "safety": 3.46, "verbosity": 1.35, "verbosity-coeff": -0.1012 }

[ { "content": "3 Years ago, the average age of a family of 5 members was 21 years. A baby having been born, the average age of the family is the same today. The present age of the baby is\n\n['A)1 year.', 'B)1.5 Years.', 'C)2 Years.', 'D)3 Years.', 'E)6 Years.']", "role": "user", "uuid": "a7fc60b1-3f39-40e8-bece-64787710c99c" }, { "content": "We're told that 3 YEARS AGO, the average age of a family of 5 members was 21 years.\nThis means that the SUM of their ages was (5)(21) = 105 years.\nA baby was born (meaning that there are now 6 family members). We're told that the PRESENT average age of the family members is the SAME.\nThis means that the sum of the ages is (6)(17) = 102 years.\nWe're asked for the PRESENT age of the baby.\nSince each of the original 5 family members has aged 3 years since the initial average was calculated, the sum of their PRESENT ages is...\n105 + (5)(3) = 120.\n126-120 =6\nE", "role": "assistant", "uuid": "82f40d56-bcab-4f4d-a311-eb2ce2adac9d" } ]

{ "coherence": 2.29, "complexity": 1.34, "correctness": 1.52, "helpfulness": 1.66, "instruction-following": 2.1, "safety": 5.28, "verbosity": 0.7, "verbosity-coeff": -0.168 }

[ { "content": "The average age of seven persons sitting in a row facing east is 28 years. If the average age of the first three persons is 21 years and the average age of the last three persons is 34 years, then find the age of the person sitting in the middle of the row?\n\n['A)22', 'B)31', 'C)17', 'D)12', 'E)91']", "role": "user", "uuid": "bd4d0aef-9dc8-4412-9b44-7bff8cfa62fe" }, { "content": "Total age seven persons = (28 * 7)years\nTotal age of the first three persons and the last three persons are (21 * 3) years and (34 * 3) years respectively.\nAge of the person sitting in the middle of the row = 28 * 7 - 21 * 3 - 34 * 3 = 196 - 63 - 102 = 31 years.\nAnswer: B", "role": "assistant", "uuid": "3de7a944-148c-4aac-aec3-3a7b8eda83ea" } ]

{ "coherence": 2.9, "complexity": 0.91, "correctness": 2.16, "helpfulness": 2.64, "instruction-following": 3.02, "safety": 5.52, "verbosity": 0.65, "verbosity-coeff": -0.1471 }

[ { "content": ". Data sufficiency question:\nWhat will be the percentage profit of selling one liter milk.?\n1) 16 liter of milk is sold at cost price after adding 20% water to it.\n2) the cost price of one liter milk is Rs.16.\n\n['A)23', 'B)29', 'C)27', 'D)1291', 'E)11']", "role": "user", "uuid": "a79ac3f6-b791-4645-bc15-43134b38a4e6" }, { "content": "Explanation:\nLet us assume one liter costs Rs.1. So C.P = Rs.16\nWhen 20% water is added, then total volume = 20 liters. So SP = 20. Profit can be calculated.\nStatement 1 is sufficient.\nStatement 2 is not required.\nAnswer:B", "role": "assistant", "uuid": "7b128df2-d5ed-4c55-8abb-2bca77e9e132" } ]

{ "coherence": 2.76, "complexity": 1.11, "correctness": 1.83, "helpfulness": 2.18, "instruction-following": 2, "safety": 5.4, "verbosity": 0.82, "verbosity-coeff": -0.1105 }

[ { "content": "A speaks truth in 75% and B in 80% cases. In what percentage of cases are they likely to contradict each other when narrating the same incident?\n\n['A)35', 'B)30', 'C)25', 'D)20', 'E)None of these']", "role": "user", "uuid": "c2c4f821-0398-4658-bbfc-ed64de70c1cb" }, { "content": "Let the truth spoken by A and B be pl and p2\nrespectively, i.e., pl = 3⁄4 and p2 = 4⁄5\nThey will contradict each other only when one speaks truth and the other is lying.\ni.e., 3⁄4 × 1⁄5 + 4⁄5 × 1⁄4 = 3⁄20 + 4⁄20 = 7⁄20 = 35⁄100 i.e, 35%\nAnswer A", "role": "assistant", "uuid": "a275e3d9-37d2-43b4-a952-e49bb11e29ed" } ]

{ "coherence": 2.76, "complexity": 2.33, "correctness": 2.84, "helpfulness": 2.72, "instruction-following": 3.62, "safety": 3.82, "verbosity": 1.7, "verbosity-coeff": -0.1256 }

[ { "content": "three mobsters have arrived at the theater for the premiere of the film “Goodbuddies.” One of the mobsters, Frankie, is an informer, and he's afraid that another member of his crew, Joey, is on to him. Frankie, wanting to keep Joey in his sights, insists upon standing behind Joey in line at the concession stand, though not necessarily right behind him. How many ways can the six arrange themselves in line such that Frankie’s requirement is satisfied?\n\n['A)6', 'B)24', 'C)120', 'D)360', 'E)3']", "role": "user", "uuid": "3b0dfbb1-065e-4f1d-b4b1-37267dc5b519" }, { "content": "Arrangement of 3=3!. In half of the cases Frankie will be behind Joey and in half of the cases Joey will be behind Frankie (as probability doesn't favor any of them). So, the needed arrangement is 3!/2=3.\nAnswer: E", "role": "assistant", "uuid": "694cef82-0ad8-4d9b-81f2-01a8a98725af" } ]

{ "coherence": 2.68, "complexity": 1.27, "correctness": 2.2, "helpfulness": 2.06, "instruction-following": 2.06, "safety": 4.42, "verbosity": 0.98, "verbosity-coeff": -0.1832 }

[ { "content": "How many of the following numbers are divisible by 132 ?\n264, 396, 462, 792, 968, 2178, 5184, 6336\n\n['A)3', 'B)4', 'C)5', 'D)6', 'E)7']", "role": "user", "uuid": "5c090bca-baed-4a78-8cdb-bac920398748" }, { "content": "B\n4\nBy using your calculator you can calculate that the following numbers are divisible by 132 : 264, 396, 792 and 6336.\nRequired number of number = 4.", "role": "assistant", "uuid": "e25b616e-8c54-43de-95f1-dbec41445c01" } ]

{ "coherence": 2.72, "complexity": 1.01, "correctness": 2.33, "helpfulness": 2.27, "instruction-following": 2.82, "safety": 5.09, "verbosity": 0.87, "verbosity-coeff": -0.1163 }

[ { "content": "Tough and Tricky questions: Word Problems.\nA salesman's income consists of commission and base salary. His weekly income totals over the past 7 weeks have been $406, $413, $420, $436, $395, $410, $360. What must his average (arithmetic mean) income over the next two weeks be to increase his average weekly income to $500 over the 9-week period?\n\n['A)$570', 'B)$790', 'C)$630', 'D)$830', 'E)$715']", "role": "user", "uuid": "1ba57d7c-04b6-47dc-ac83-b397ecd7d59b" }, { "content": "OFFICIAL SOLUTION:\n(D) First, we need to add up the wages over the past 7 weeks: $406 + $413 + $420 + $436 + $395 + $410 + $360 = $2840.\nTo average $500 over 9 weeks, the salesman would need to earn: $500 × 9 = $4500.\nSubtract $2840 from $4500 to determine how much he would need to earn, in total, over the next 2 weeks to average $500 for the 9 weeks: $4500 – $2840 = $1660.\nDividing $1660 by 2 will give us the amount he needs to earn on average over the next 2 weeks: $1660/2 = $830.\nThe correct answer is choice (D).", "role": "assistant", "uuid": "be5d76b2-178f-4354-ba9b-4b51cbd530c9" } ]

{ "coherence": 3.04, "complexity": 0.96, "correctness": 2.39, "helpfulness": 2.62, "instruction-following": 2.9, "safety": 4.32, "verbosity": 1.45, "verbosity-coeff": -0.1188 }

[ { "content": "The difference of the squares of two consecutive even integers is divisible by which of the following numbers?\n\n['A)4', 'B)3', 'C)7', 'D)6', 'E)9']", "role": "user", "uuid": "79c53378-d667-460c-a65b-bfb49ec68273" }, { "content": "Let the consecutive even integers are n and (n + 2)\ndifference of the squares = (n + 2)^2 - n^2 = (n^2 + 4n + 4) - n^2 = 4n + 4 = 4(n + 1)\nwhich is divisible by 4\nAnswer is A", "role": "assistant", "uuid": "b1677566-7a3a-4fef-a53d-e624763900c2" } ]

{ "coherence": 3.27, "complexity": 2.49, "correctness": 3.31, "helpfulness": 3.39, "instruction-following": 3.76, "safety": 4.93, "verbosity": 1.78, "verbosity-coeff": -0.241 }

[ { "content": "The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and breadth is increased by 5 cm, the area of the rectangle is increased by 75 sq. cm. Find the length of the rectangle.\n\n['A)5', 'B)10', 'C)15', 'D)20', 'E)None of them']", "role": "user", "uuid": "2a137e38-6db7-4083-94ae-d92fcf844d95" }, { "content": "Let breadth = x. Then, length = 2x. Then,\n(2x - 5) (x + 5) - 2x * x = 75 <=> 5x - 25 = 75 <=> x = 20.\nTherefore, Length of the rectangle = 20 cm.\nAnswer is D", "role": "assistant", "uuid": "56effc84-37cd-4f8a-8819-7d95852b3595" } ]

{ "coherence": 2.98, "complexity": 1.54, "correctness": 1.98, "helpfulness": 2.27, "instruction-following": 3.19, "safety": 5.16, "verbosity": 0.71, "verbosity-coeff": -0.1227 }

[ { "content": "A man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?\n\n['A)45', 'B)60', 'C)75', 'D)90', 'E)95']", "role": "user", "uuid": "3ccbbc67-9f01-45ac-a93a-56b9fca0aaf5" }, { "content": "Let number of notes of each denomination be x.\nThen x + 5x + 10x = 480\n16x = 480\nx = 30.\nHence, total number of notes = 3x = 90.\nAnswer: Option D", "role": "assistant", "uuid": "3fcbbb9f-1aa8-4791-9b87-fe368059219a" } ]

{ "coherence": 3.15, "complexity": 1.39, "correctness": 2.76, "helpfulness": 3.02, "instruction-following": 3.8, "safety": 5.12, "verbosity": 0.73, "verbosity-coeff": -0.129 }

[ { "content": "The food in a camp lasts for 10 men for 50 days. If 10 more men join, how many days will the food last?\n\n['A)22 days', 'B)25 days', 'C)50 days', 'D)16 days', 'E)17 days']", "role": "user", "uuid": "22f0d9c5-bd4d-4488-8132-895339930cf4" }, { "content": "one man can consume the same food in 10*50 = 500 days.\n10 more men join, the total number of men = 20\nThe number of days the food will last = 500/20 = 25 days.\nAnswer:B", "role": "assistant", "uuid": "ead1a059-a764-4eb8-9e36-91feeb7df7bd" } ]

{ "coherence": 3.39, "complexity": 1.38, "correctness": 3.05, "helpfulness": 3.09, "instruction-following": 3.56, "safety": 5.71, "verbosity": 1.54, "verbosity-coeff": -0.1352 }

[ { "content": "Peter has $642,986 in his savings account. What is the least amount of money (in whole number of dollars) that he must add to his account if he wants to split this money evenly among his nine children?\n\n['A)$642,986', 'B)$642,987', 'C)$642,988', 'D)$642,989', 'E)$642,990']", "role": "user", "uuid": "2ca405b7-7fd1-4c9b-be2e-e88ca77fb32c" }, { "content": "To find the least amount the man should add to his saving account to split the money evenly among his 9 children, he needs to make the total divisible by 9\nSimply add the individual digits of the total = 6+4+2+9+8+6= 35\nIf you add 1 , the number is divisible by 9 (35+ 1)\nCorrect Option : B", "role": "assistant", "uuid": "7020244b-a951-4a1e-86bf-67052ca6aaf4" } ]

{ "coherence": 2.45, "complexity": 1.07, "correctness": 2.33, "helpfulness": 2.31, "instruction-following": 1.92, "safety": 4.62, "verbosity": 1.17, "verbosity-coeff": -0.2233 }