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[ { "content": "At Annie's party, there were five times as many females as males. There were three times as many adults as children. Which of the following could NOT be the number of people at the party?\n\n['A)384', 'B)258', 'C)216', 'D)120', 'E)72']", "role": "user", "uuid": "b6990d29-6a9f-476e-a574-6afd73e4f5e3" }, { "content": "we have to work on the info and understand what that info takes us to...\n1) there were five times as many females as males At Annie's party..\nthis means F=5M.. so total number=6M..\n2) There were three times as many adults as children..\nA=3C...\nor total = 4C..\nso the total is 4C or 6M..\nsince C and M have to be positive integers, we can say for sure that Total is a multiple of 4 and 6..\nor Total is multiple of LCM of 4,6..\nLCM of 4,6= 12..\nlets see which number is not multiple of 12..\nA. 384...12*32\nB. 258... no\nC. 216....12*18\nD. 120....12*10\nE. 72......12*6..\nso B is our answer..", "role": "assistant", "uuid": "58dc580f-2ccb-4caf-adc0-269d7d02c0d2" } ]

{ "coherence": 2.57, "complexity": 1.73, "correctness": 2.2, "helpfulness": 2.33, "instruction-following": 2.82, "safety": 5.12, "verbosity": 1.39, "verbosity-coeff": -0.2114 }

[ { "content": "In a particular course, only two grades are given all semester: the midterm exam, which counts for 25% of the semester grade, and the final exam, which counts for the remainder. Lindsey's semester grade was 88%. If the highest possible score on either exam is 100%, what is the lowest possible score P that Lindsey could have received on her midterm exam?\n\n['A)52%', 'B)64%', 'C)72%', 'D)76%', 'E)80%']", "role": "user", "uuid": "e7e34f10-5121-4b0f-ac49-c53d06a8234e" }, { "content": "If the midterm counts for 25% of the total grade, then the final exam must count for the remaining 75%, meaning that in this weighted average problem the final is weighted 3 times as much as the midterm. Using the weighted average mapping strategy, then, and maximizing her final exam score so that you minimize her midterm score, you have:\n100-------------88----------------------------x\nAnd you know that the ratio is 3:1. Since the final exam score of 100 is weighted heavier, then the difference of 12 between 100 and 88 is the1part of the ratio, meaning that 3(12) is the 3 portion. That equals 36, so the midterm score (x) is 36 less than the weighted average of 88. 88 - 36 = 52, sothe correct answer is 52%.", "role": "assistant", "uuid": "9d96ece9-0f50-486b-a035-21164edba337" } ]

{ "coherence": 3, "complexity": 1.41, "correctness": 2.66, "helpfulness": 2.57, "instruction-following": 2.25, "safety": 4.66, "verbosity": 1.16, "verbosity-coeff": -0.226 }

[ { "content": "Given a bag with 2 red balls and 3 yellow balls, you randomly select one of them, in order. If the second ball you take is yellow, what is the probability that the first one was also yellow?\n\n['A)1/2', 'B)1/5', 'C)3/4', 'D)1/3', 'E)3/5']", "role": "user", "uuid": "be024dff-371c-47f3-aac1-a45edb5df04b" }, { "content": "This is a conditional probability question. Basically we are told that out of 2 balls picked one is yellow and are asked to find the probability of the other one also to be yellow.\nSo, possible options for this other ball would be: W, W, B, B (as one yellow is already picked)\nSo the probability for that ball to be yellow too is 2/4=1/2.\nOption A", "role": "assistant", "uuid": "02eaacd4-8194-4ee0-8541-20e733585a6e" } ]

{ "coherence": 3.23, "complexity": 1.33, "correctness": 2.64, "helpfulness": 2.61, "instruction-following": 2.06, "safety": 4.42, "verbosity": 1.46, "verbosity-coeff": -0.1992 }

[ { "content": "loga(ab)=x then logb(ab) is\n\n['A)x/x-1', 'B)x/x+1', 'C)x(x-1)', 'D)x(x+1)', 'E)x+1']", "role": "user", "uuid": "fb10625f-4134-4249-b8b7-82fedce3a945" }, { "content": "loga(ab)=x\nlog(ab)/log(a)=x\nlog(b)/log(a)=x-1\nlog(a)/log(b)=1/x-1\n1+log(a)/log(b) = 1+ 1/x-1\nlogb(ab) = x/x-1\nANSWER A", "role": "assistant", "uuid": "b6864346-74f8-48a5-8e02-2faab47dfc1c" } ]

{ "coherence": 2.88, "complexity": 2.78, "correctness": 3.13, "helpfulness": 2.92, "instruction-following": 2.96, "safety": 5.28, "verbosity": 1.52, "verbosity-coeff": -0.1085 }

[ { "content": "A and B r 2 men who enter into business and they invest Rs 1000, Rs 2000respectively. How will they divide the income of Rs 5000\n\n['A)3336,1667', 'B)3339,1667', 'C)3333,1666', 'D)3333,1668', 'E)3333,1669']", "role": "user", "uuid": "4c9c0300-6fb0-47dc-8c0e-a5e4b70556ff" }, { "content": "they invested in the ratio 1:2\na's share =1/3*5000=1666\nb's share=2/3*5000=3333\nANSWER:C", "role": "assistant", "uuid": "5a58a9ce-6bbe-4b22-b2be-9871edae59ec" } ]

{ "coherence": 2.8, "complexity": 1.44, "correctness": 2.64, "helpfulness": 2.66, "instruction-following": 3.48, "safety": 5.09, "verbosity": 0.84, "verbosity-coeff": -0.1203 }

[ { "content": "If population of certain city increases at the rate of 2%. If population in 1981 was 138915, then population in 1978 was?\n\n['A)12,0000', 'B)130000', 'C)261000', 'D)130903', 'E)12690']", "role": "user", "uuid": "d512ce51-4505-4414-b849-66024c13caf7" }, { "content": "Explanation:\nX * (102/100) * (102/100) * (102/100) = 138915\nX = 138915/1.061208\nX = 130902.70=130903\nAnswer: Option D", "role": "assistant", "uuid": "1b49465b-75d1-48da-bd26-8f0f9da8f483" } ]

{ "coherence": 2.68, "complexity": 1.15, "correctness": 1.79, "helpfulness": 2.2, "instruction-following": 2.9, "safety": 5.2, "verbosity": 0.72, "verbosity-coeff": -0.1106 }

[ { "content": "A bag contains 12 white and 18 black balls. 2balls are drawn in succession. What is the probability that first is white and second is black?\n\n['A)21/115', 'B)36/145', 'C)31/111', 'D)11/154', 'E)11/151']", "role": "user", "uuid": "3b5ebdb6-dc48-445c-93c4-dd8b89b9578b" }, { "content": "The probability that first ball is white:\n=12C130C1=12C130C1\n=1230=1230\n=25=25\nSince, the ball is not replaced; hence the number of balls left in bag is 29.\nHence, the probability the second ball is black:\n=18C129C1=18C129C1\n=1829=1829\nRequired probability,\n=(25)×(1829)=(25)×(1829)\n=36/145\nB", "role": "assistant", "uuid": "3e3f4038-745b-4b1a-b86b-21121af825b2" } ]

{ "coherence": 2.59, "complexity": 1.96, "correctness": 2.06, "helpfulness": 2.2, "instruction-following": 3.05, "safety": 5.55, "verbosity": 1.8, "verbosity-coeff": -0.1524 }

[ { "content": "Following an increase in prices, the price of a candy box was 10 pounds and the price of a can of soda was 6 pounds. If the price of a candy box was raised by 25%, and the price of a can of soda was raised by 50%. What was the price of a box of candy plus a can of soda before prices were raised?\n\n['A)11.', 'B)12', 'C)13', 'D)14', 'E)14.5']", "role": "user", "uuid": "ef797fdb-3066-4e96-aa8a-40b3aad89bfb" }, { "content": "Let the Candy and Soda before the increase be C and S respectively\nso Increased price of can = C(1+ 25/100) =10 -----------> C= 8\nIncrease price of soda : S(1+1/2) = 6 -----------> S=4\nHence total = 8+4 =12.. hence answer: B", "role": "assistant", "uuid": "6f93d721-1ded-40c5-929a-c943174874db" } ]

{ "coherence": 2.7, "complexity": 1.27, "correctness": 1.9, "helpfulness": 2.16, "instruction-following": 2.64, "safety": 5.95, "verbosity": 0.24, "verbosity-coeff": -0.1608 }

[ { "content": "I bought two books; for Rs.420. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss?\n\n['A)197', 'B)245', 'C)189', 'D)278', 'E)268']", "role": "user", "uuid": "9afbe79a-74f3-4470-b0ef-61d55c5da3f1" }, { "content": "x*(85/100)\n= (420 - x)119/100\nx = 245\nAnswer: B", "role": "assistant", "uuid": "ccb90218-fdc6-4ae1-87c0-8fa4afc8cec1" } ]

{ "coherence": 2.68, "complexity": 1.17, "correctness": 1.71, "helpfulness": 2.02, "instruction-following": 2.64, "safety": 5.63, "verbosity": 0.17, "verbosity-coeff": -0.1173 }

[ { "content": "What amount does Kiran get if he invests Rs.8000 at 10% p.a. compound interest for two years, compounding done annually?\n\n['A)Rs.9880', 'B)Rs.9670', 'C)Rs.9780', 'D)Rs.9682', 'E)Rs.9680']", "role": "user", "uuid": "c484c710-f674-4f13-b7dd-9bebfd0733b3" }, { "content": "A= P{1 + R/100}n\n=> 8000{1 + 10/100}2\n= Rs.9680\nAnswer:E", "role": "assistant", "uuid": "f7185b1f-4588-465c-a3e5-73a3e1e4195f" } ]

{ "coherence": 2.78, "complexity": 1.38, "correctness": 2, "helpfulness": 2.25, "instruction-following": 3.68, "safety": 5.01, "verbosity": 0.91, "verbosity-coeff": -0.1119 }

[ { "content": "Crazy Eddie has a key chain factory. Eddie managed to decrease the cost of manufacturing his key chains while keeping the same selling price, and thus increased the profit from the sale of each key chain from 20% of the selling price to 50% of the selling price. If the manufacturing cost is now $50, what was it before the decrease?\n\n['A)$20', 'B)$40', 'C)$50', 'D)$80', 'E)$100']", "role": "user", "uuid": "efb6b060-9651-4904-a770-8851a2184f95" }, { "content": "cost+profit=income (selling price)\nprofit now = 0.5x or x-50\n0.5x=x-50\n50=0.5x\nx=100$ is selling price\nso, profit before was 0.2*100=20$\ncost=100-20=80$\nANSWER:D", "role": "assistant", "uuid": "b4396a9d-db94-41f3-afc8-7de2f48c9767" } ]

{ "coherence": 2.72, "complexity": 1.33, "correctness": 2.37, "helpfulness": 2.33, "instruction-following": 2.25, "safety": 5.36, "verbosity": 1.06, "verbosity-coeff": -0.1899 }

[ { "content": "A set of numbers has the property that for any number x in the set, x+3 is also in the set. If -3 is in the set, which of the following must also be in the set\n1. -6\n2. 0\n3. 6\n\n['A)1 only', 'B)2 only', 'C)1 and 2 only', 'D)2 and 3 only', 'E)1,2 and 3']", "role": "user", "uuid": "8ed1b332-e2cc-4ad9-b091-c913611e6a74" }, { "content": "If X is in the set than X+ 3 is also in the set\nIf -3 in the set than\n-3+3= 0 is also in the set\nSince + 3 is Present, 3 + 3= 6 Is also present in the set .\nTherefore Answer: D", "role": "assistant", "uuid": "86c4d97e-7d12-4378-8eeb-df3921360e9f" } ]

{ "coherence": 2.51, "complexity": 1.7, "correctness": 2.04, "helpfulness": 2.16, "instruction-following": 2.57, "safety": 6.22, "verbosity": 0.9, "verbosity-coeff": -0.208 }

[ { "content": "A certain collage has total of 200 seniors each majoring in exactly one of six subjects. A minimum of 20 seniors major in each six subjects. If three quarter of the seniors major in one of four subjects, what is the greatest possible number of seniors majoring in one of the other two subjects?\n\n['A)100', 'B)80', 'C)25', 'D)60', 'E)50']", "role": "user", "uuid": "91a5d00e-0331-4f6a-8ec7-4dcd00bacb3e" }, { "content": "Answer C\n200 = 150 + 20 + x => x = 25\n= 3/4 * 200 in 4 subjects + 20 min for 5th subject + x = 200", "role": "assistant", "uuid": "d51f1192-b679-4d23-ada4-2654ba291cdd" } ]

{ "coherence": 2.41, "complexity": 0.91, "correctness": 1.82, "helpfulness": 2.04, "instruction-following": 1.68, "safety": 4.7, "verbosity": 1.33, "verbosity-coeff": -0.2322 }

[ { "content": "Mike took 5 mock tests before appearing for the GMAT. In each mock test he scored 10 points more than the previous mock test. If he scored 750 on the GMAT and his average score for the mocks and the GMAT was 726.67, what was the difference in the score of his last mock and his GMAT score?\n\n['A)8', 'B)30', 'C)40', 'D)50', 'E)60']", "role": "user", "uuid": "3a48114e-34f8-490f-986f-0319bf78d620" }, { "content": "One way to do this would be weighted average method..\n1) let the average of 5 mocks be x...\nso take it as a mix of5 quantitites of xand1 quantity of 750resulting in an average of 726.67...\nBy alligation/weighted average..\nthe difference in 750 and 726.67 is 5/6 of difference of 750 and x..\n750-726.67 = 5/6 * (750-x)\n750-x= 23.33*6/5=28...\nso x = 722..\nthe last of mock test will be 722+10+10=742...\nso ans = 750-742=8\nA", "role": "assistant", "uuid": "1adc7faa-5f40-4c14-a80b-3c714708005b" } ]

{ "coherence": 2.33, "complexity": 1.83, "correctness": 1.88, "helpfulness": 1.84, "instruction-following": 2.33, "safety": 5.32, "verbosity": 1.69, "verbosity-coeff": -0.1299 }

[ { "content": "The ratio of the area of a square mirror to its frame is 16 to 33. If the frame has a uniform width (s) around the mirror, which of the following could be the value, in inches, of s ?\nI. 2\nII. 3 1/2\nIII. 5\n\n['A)I only', 'B)III only', 'C)I and II only', 'D)I and III only', 'E)I, II, and III']", "role": "user", "uuid": "5a37ab42-21b7-407f-b4d0-eb2b798d639d" }, { "content": "Area of picture = 16x Area of frame = 33x\nArea of picture / (Area of picture + area of frame) = 16x / 49x = 4x/7x.\nThis results in s value to be a multiple of 1.5 = multiple of 3/2 and since s is not constrained to be only integer all the three choices are possible\nFor i) the multiple of s is 4/3\nFor ii) the multiple of s is 7/3\nFor iii) the multiple of s is 10/3\nThe key is s can be any real positive number... very tricky problem.. took me > 15 minutes.\nAnswer is E", "role": "assistant", "uuid": "6c90c192-1ab7-435e-9d79-7248be76aee5" } ]

{ "coherence": 2.29, "complexity": 1.77, "correctness": 1.59, "helpfulness": 1.39, "instruction-following": 2.16, "safety": 5.09, "verbosity": 1.53, "verbosity-coeff": -0.1843 }

[ { "content": "A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either blue or yellow?\n\n['A)3/98', 'B)2/28', 'C)2/21', 'D)2/29', 'E)2/24']", "role": "user", "uuid": "cce49694-757f-42a8-b3bc-847a91d21f45" }, { "content": "Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that both marbles are blue = ³C₂/¹⁵C₂ = (3 * 2)/(15 * 14) = 1/35\nProbability that both are yellow = ²C₂/¹⁵C₂ = (2 * 1)/(15 * 14) = 1/105\nProbability that one blue and other is yellow = (³C₁ * ²C₁)/¹⁵C₂ = (2 * 3 * 2)/(15 * 14) = 2/35\nRequired probability = 1/35 + 1/105 + 2/35\n= 3/35 + 1/105 = 1/35(3 + 1/3)\n= 10/(3 * 35) = 2/21\nAnswer:C", "role": "assistant", "uuid": "379f0f74-6b72-4cea-9407-2d85b3b303ec" } ]

{ "coherence": 2.78, "complexity": 1.51, "correctness": 2.27, "helpfulness": 2.45, "instruction-following": 3.48, "safety": 4.66, "verbosity": 1.5, "verbosity-coeff": -0.1698 }

[ { "content": "During a special promotion, a certain filling station is offering a 10 percent discount on gas purchased after the first 6 gallons. If Kim purchased 20 gallons of gas, and Isabella purchased 25 gallons of gas, then Isabella‟s total per-gallon discount is what percent of Kim‟s total per-gallon discount?\n\n['A)80%', 'B)100%', 'C)109%', 'D)120%', 'E)140%']", "role": "user", "uuid": "fb084ccc-6049-445e-84be-5a7780a42280" }, { "content": "Kim purchased 20 gallons of gas. She paid for 6 + 0.9*14 = 18.6 gallons, so the overall discount she got was 1.4/20 = 7%.\nIsabella purchased 25 gallons of gas. She paid for 6 + 0.9*19 = 23.1 gallons, so the overall discount she got was 1.9/25 = 7.6%.\n7.6 is 7.6/7*100 = 109% of 7.\nAnswer: C.", "role": "assistant", "uuid": "f69c46bf-bed4-42e0-9ec4-bd912076d83f" } ]

{ "coherence": 2.57, "complexity": 1.62, "correctness": 1.91, "helpfulness": 1.99, "instruction-following": 3.25, "safety": 4.89, "verbosity": 1.26, "verbosity-coeff": -0.1496 }

[ { "content": "Evaluate : 37 x 181+ 37 x 319\n\n['A)22500', 'B)15500', 'C)18500', 'D)25000', 'E)None of them']", "role": "user", "uuid": "0b3fcd71-0053-4a46-ad15-0706323281ea" }, { "content": "37 x 181 + 37 x 319 = 37 x (181 + 319) = 37 x 500 = 18500.\nAnswer is C.", "role": "assistant", "uuid": "289f6480-861d-4b8c-8e31-78a849603101" } ]

{ "coherence": 3.33, "complexity": 1.71, "correctness": 2.96, "helpfulness": 3.05, "instruction-following": 3.82, "safety": 4.3, "verbosity": 0.99, "verbosity-coeff": -0.1062 }

[ { "content": "In a certain state, gasoline stations compute the price per gallon p, in dollars, charged at the pump by adding a 2 percent sales tax to the dealer's price per gallon d, in dollars, and then adding a gasoline tax of $0.18 per gallon. Which of the following gives the dealer's price per gallon d in terms of the price per gallon p charged at the pump?\n\n['A)d = (p-0.02)/1.18', 'B)d = p/1.20', 'C)d = p/1.02 - 0.18', 'D)d= (p-0.18)/1.02', 'E)d = p-0.20']", "role": "user", "uuid": "47439ca5-7376-4a69-95a7-2a3dc721dfd2" }, { "content": "Let dealers price (d) be 1. so adding 2% to dealers price is d+ 2% of d. i.e. 1 + 2% of 1 which is1 + 0.02. then add 0.18 to the value.\nNow 1.02 + 0.18. this is now 1.20. you have the gasoline stations price (p) as 1.20 dollars.\nNow sub 1.20 in the options to know which option gave you d = 1. d must equal 1 because you earlier picked 1 as the value of d in the question.\nPS: always remember to start from E upwards.\nAnswer : D", "role": "assistant", "uuid": "fed6bb2d-6458-4c0f-8931-de9dbcf92b44" } ]

{ "coherence": 2.27, "complexity": 1.44, "correctness": 1.64, "helpfulness": 1.74, "instruction-following": 2.49, "safety": 4.93, "verbosity": 1.22, "verbosity-coeff": -0.1559 }

[ { "content": "Divide $672 among A,B in the ratio 5:3. How many $ that A get?\n\n['A)$120', 'B)$500', 'C)$420', 'D)$610', 'E)$315']", "role": "user", "uuid": "316264f5-5fda-4265-a760-4640d012745b" }, { "content": "Sum of ratio terms = 5+3 = 8\nA = 672*5/8 = $420\nAnswer is C", "role": "assistant", "uuid": "8c0c2d48-38a8-4b0f-a508-b556ceee522a" } ]

{ "coherence": 2.7, "complexity": 0.61, "correctness": 2.72, "helpfulness": 2.98, "instruction-following": 3.68, "safety": 4.48, "verbosity": 1.15, "verbosity-coeff": -0.1582 }

[ { "content": "The difference between a positive proper fraction and its reciprocal is 9 / 20. Then the fraction is :\n\n['A)4/0', 'B)4/1', 'C)4/5', 'D)4/2', 'E)4/3']", "role": "user", "uuid": "79d1c200-7a37-48e4-8dce-7c5a0a3c3422" }, { "content": "Explanation:\nLet the required fraction be x. Then, (1 / x )- x = 9/20\n1 - x^(2) / x = 9 / 20 => 20 - 20 * x^(2) = 9 * x.\n20 * x^(2) + 9 *x - 20 = 0.\n=> (4 * x + 5) (5 * x - 4) = 0.\n=> x = 4 / 5.\nAnswer: C) 4/5", "role": "assistant", "uuid": "ad2fdd54-dcb3-4161-92bf-f042b5e7b7a0" } ]

{ "coherence": 3.11, "complexity": 2.21, "correctness": 2.39, "helpfulness": 2.57, "instruction-following": 3.33, "safety": 4.73, "verbosity": 1.18, "verbosity-coeff": -0.1436 }

[ { "content": "The first term in a sequence is 1 and the second term is 21. From the third term on each term is the average (arithmetic mean) of all preceding terms. What is the 38th term in the sequence?\n\n['A)8', 'B)11', 'C)21', 'D)38', 'E)49']", "role": "user", "uuid": "46e016c6-9eac-4e7d-8837-2cda75025c94" }, { "content": "The third term is 11 since this is the average of 1 and 21.\nThen the next terms will all be 11 since the average stays at 11.\nThe answer is B.", "role": "assistant", "uuid": "9d4ed9b9-e189-4fa6-a741-ef838cb5f53f" } ]

{ "coherence": 3.02, "complexity": 1.27, "correctness": 2.43, "helpfulness": 2.66, "instruction-following": 2.76, "safety": 5.95, "verbosity": 0.85, "verbosity-coeff": -0.1873 }

[ { "content": "Agatha has $460 in 5-and 10-dollar bills only. If she has fewer 10-than 5-dollar bills, what is the least possible number of 5-dollar bills she could have?\n\n['A) 32', 'B) 30', 'C) 29', 'D) 28', 'E) 27']", "role": "user", "uuid": "eb2cfd50-5606-492e-8b05-a34790aeeb9d" }, { "content": "5n + 10m = 460\nn > m\nPick an easy number to work with.\nsuppose n=30.\nThen you have 150.\nYou need another 310 and that means you need m=31 which is greater than n.\nTherefore, n > 30.\nThe only answer choice where n> 30 is if n = 32.\nA is the answer.", "role": "assistant", "uuid": "3ca28ae1-e8a4-4e3c-b504-e25a09b06d12" } ]

{ "coherence": 2.66, "complexity": 0.84, "correctness": 1.56, "helpfulness": 1.81, "instruction-following": 1.78, "safety": 5.44, "verbosity": 0.35, "verbosity-coeff": -0.2209 }

[ { "content": "One out of every 4000 computer chips is defective. If 2 out of every 30 defective chips have defective processors and there are 30 defective processors in the first batch, how many computer chips are there in the first batch?\n\n['A)450', 'B)900', 'C)90,000', 'D)1800,000', 'E)900,000']", "role": "user", "uuid": "3b199f0b-cce7-4a00-aec8-140c2db99e87" }, { "content": "(D) Read the whole question to get the feel of what they are asking you to find. Then start with the smallest amount and work your way outwards. We are told that two out of every 30 defective chips have a defective processor. Let x be the total number of defective processors in the batch. Because we know 2 out of every 30 defective chips will have defective processors, and the total number of defective processors in the batch is 30, we can write out an equation: (2/30)x = 30. This can be simplified to (1/15)x = 30. Multiplying each side by 15, we arrive at x = 450. This tells us that there are 450 defective chips in the whole batch. Because we know that 1 out of every 1000 chips is defective, we can set up a proportion. If 1 out of every 4000 chips is defective, then 450 out of y chips would be defective, where y is the total number of chips in the batch. This can be set up as an equation as follows: 1/4000 = 450/y. Solve for y and you will get the total number of chips in the batch: 1800,000.\nThe answer is (D).", "role": "assistant", "uuid": "1daf3e35-9ec0-4d5d-9017-4bb138f044c3" } ]

{ "coherence": 2.7, "complexity": 1.39, "correctness": 2.37, "helpfulness": 2.45, "instruction-following": 2.45, "safety": 4.4, "verbosity": 1.7, "verbosity-coeff": -0.1239 }

[ { "content": "Two pipes A and B can separately fill a cistern in 24 minutes and 48 minutes respectively. There is a third pipe in the bottom of the cistern to empty it. If all the three pipes are simultaneously opened, then the cistern is full in 12 minutes. In how much time, the third pipe alone can empty the cistern?\n\n['A)90 min', 'B)48 min', 'C)54 min', 'D)120 min', 'E)130 min']", "role": "user", "uuid": "f73db716-298b-4316-9fd5-071ee4b31e8c" }, { "content": "1/12-(1/24+1/48)=-1/48\nthird pipe can empty in 48 minutes\nANSWER:B", "role": "assistant", "uuid": "b7c63aac-1a63-4210-bed2-59a8d66b5c03" } ]

{ "coherence": 2.51, "complexity": 1.02, "correctness": 2.23, "helpfulness": 2.35, "instruction-following": 3.21, "safety": 6.34, "verbosity": 0.92, "verbosity-coeff": -0.1347 }

[ { "content": "Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?\n\n['A)10', 'B)11', 'C)12', 'D)10.8', 'E)13']", "role": "user", "uuid": "c00d01c5-bc47-4e41-aa9e-22fcc16bb792" }, { "content": "Relative speed = 60 + 40 = 100 km/hr.\n= 100 * 5/18 = 250/9 m/sec.\nDistance covered in crossing each other = 140 + 160 = 300 m.\nRequired time = 300 * 9/250 = 54/5 = 10.8 sec.\nAnswer: Option D", "role": "assistant", "uuid": "6aa9bbf4-e744-4cd2-bcd6-20f1e5047f25" } ]

{ "coherence": 2.84, "complexity": 2.08, "correctness": 2.51, "helpfulness": 2.76, "instruction-following": 4.13, "safety": 5.05, "verbosity": 1.54, "verbosity-coeff": -0.1204 }

[ { "content": "Find the number of factors E of 180 that are in the form (4*k + 2), where k is a non-negative integer?\n\n['A)1', 'B)2', 'C)3', 'D)4', 'E)E=6']", "role": "user", "uuid": "dcf30cb2-bf49-4f27-86b3-cd1c7c387aef" }, { "content": "As for the question, the most straightforward way is to list out the factors (this is fine for this question as 180 is a relatively small number). Number of factors of 180 E(=2^2*3^2*5) = 18. So listing the factors gives us:\n1, 180\n2, 90\n3, 60\n4, 45\n5, 36\n6, 30\n9, 20\n10, 18\n12, 15\nAs the question asks us about the factors of the form 4k+2 ---> eliminate all ODD factors. You are now left with\n2,4,6,10,12,18,20,30,36,60,90,180\nFor the form 4k+2, the first few values are 2, 6, 10, 14, 18, 22, 26, 30 ... already giving you 5 factors (=2,6,10,18,30). You can stop here and mark 6 (6th one = 90) as the correct answer as 5 is not given.\nFor checking any particular factor whether they conform to the form 4k+2---> do the following\n4k+2 = 36 ---> 4k = 34 --> this will NOT give you an integer value for k ---> reject. Proceed with others until you find all the values asked.\nE is thus the correct answer.", "role": "assistant", "uuid": "4ce40251-3ac6-4192-8ffc-01573055ec15" } ]

{ "coherence": 2.84, "complexity": 1.95, "correctness": 1.88, "helpfulness": 1.85, "instruction-following": 2.61, "safety": 5.12, "verbosity": 1.42, "verbosity-coeff": -0.213 }

[ { "content": "The speed of a boat in still water is 60kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?\n\n['A)29', 'B)40', 'C)99', 'D)28', 'E)12']", "role": "user", "uuid": "3c786e51-1539-4b3f-94e9-3b1317a323b6" }, { "content": "Speed downstream = 60 + 20 = 80 kmph\nSpeed upstream = 60 - 20\n= 40 kmph\nAnswer: B", "role": "assistant", "uuid": "90820632-cffc-4bf6-aecf-545c617b203f" } ]

{ "coherence": 3.11, "complexity": 1.02, "correctness": 2.7, "helpfulness": 2.96, "instruction-following": 3.6, "safety": 5.4, "verbosity": 0.65, "verbosity-coeff": -0.0915 }

[ { "content": "Arun and Tarun can do a work in 10 days.After 4 days tarun went to his village.How many days are required to complete the remaining work by Arun alone.Arun can do the work alone in 60 days.\n\n['A)36 days.', 'B)17 days.', 'C)18 days.', 'D)19 days.', 'E)20 days.']", "role": "user", "uuid": "72f053bd-58f8-47fd-9ba5-bb60420721d6" }, { "content": "They together completed 4/10 work in 4 days.\nbalance 6/10 work will be completed by Arun alone in 60*6/10 = 36 days.\nANSWER:A", "role": "assistant", "uuid": "da329aeb-a3a3-45f8-999e-9e09f6b1b329" } ]

{ "coherence": 2.9, "complexity": 1.08, "correctness": 2.49, "helpfulness": 2.51, "instruction-following": 3.33, "safety": 5.36, "verbosity": 0.74, "verbosity-coeff": -0.1185 }

[ { "content": "John has 5 flavors of chocolate in him shop. How many options are there for Jones to pick a one-flavor, two-flavor, three-flavor, four-flavor or five-flavor order?\n\n['A)22', 'B)31', 'C)43', 'D)37', 'E)38']", "role": "user", "uuid": "1e7bd5e2-9d50-4a8a-829e-053de8ea8f08" }, { "content": "5C1 + 5C2+ 5C3+5C4+5C5 = 31.\nAnswer: B", "role": "assistant", "uuid": "53d5d441-6511-476c-8db8-aa3551632a07" } ]

{ "coherence": 3.02, "complexity": 1.29, "correctness": 2.64, "helpfulness": 2.8, "instruction-following": 3.19, "safety": 4.38, "verbosity": 0.57, "verbosity-coeff": -0.1415 }

[ { "content": "Every length in a 45°-45°-90° triangle increases by 20%. By what percent does the area of the triangle increase?\n\n['A)20%', 'B)25%', 'C)40%', 'D)44%', 'E)80%']", "role": "user", "uuid": "990f4aa7-af14-4023-80ea-86f5d6f20a2f" }, { "content": "The irony of this question is, of course, the specifics of the shape don’t matter at all. Yes, in general it is a good idea to be familiar with the 45°-45°-90° triangle —- if you’re not, see this post —– but none of that matters here.\nWe have a 20% increase, so that’s a multiplier of 1.2, which means k = 1.2. The multiplier for area would be k^2 = (1.2)^2 = 1.44, which is the multiplier for a 44% increase. That’s the percent increase in area. Answer = D", "role": "assistant", "uuid": "8f88eb15-acc7-49bd-92bc-0c47c392307b" } ]

{ "coherence": 3.02, "complexity": 2.21, "correctness": 2.57, "helpfulness": 2.12, "instruction-following": 2.86, "safety": 5.71, "verbosity": 2.08, "verbosity-coeff": -0.2287 }

[ { "content": "A person travels from P to Q at a speed of 40 km/hr and returns by increasing his speed by 50%.\nWhat is his average speed for both the trips ?\n\n['A)44 km/hour', 'B)46 km/hour', 'C)48 km/hour', 'D)50 km/hour', 'E)None of these']", "role": "user", "uuid": "7bb5edab-b464-449e-9593-4686d286b1a6" }, { "content": "Explanation:\nSpeed while going = 40 km/hr\nSpeed while returning = 150% of 40 = 60 km/hr\nAverage speed =\n2xyx+y=2\n∗\n40\n∗\n6040+60=4800100=48Km/hr\nAnswer: C", "role": "assistant", "uuid": "7e7f54dd-5ffd-4894-9a9c-11c909eff2e9" } ]

{ "coherence": 2.41, "complexity": 1.8, "correctness": 1.87, "helpfulness": 1.91, "instruction-following": 2.98, "safety": 6.14, "verbosity": 0.47, "verbosity-coeff": -0.1181 }

[ { "content": "If the ratio of the sum of the first 6 terms of a G.P. to the sum of the first 3 terms of the G.P. is 217, what is the common ratio of the G.P?\n\n['A)3', 'B)1/3', 'C)2', 'D)6', 'E)1/6']", "role": "user", "uuid": "27d084b0-adf2-4d3a-af2b-b53198adb97d" }, { "content": "217=(a1+a2+a3+a4+a5+a6)/(a1+a2+a3)\nFactorize the same terms\n217=1+(a4+a5+a6)/(a1+a2+a3)\nWrite every term with respect to r\na1=a1\na2=a1*r^1\na3=a1*r^2\n.........\n217=1+(a1(r^3+r^4+r^5))/(a1(1+r^1+r^2))\n216=(r^3 (1+r^1+r^2))/((1+r^1+r^2))\n216=r^3\nr=6\nD", "role": "assistant", "uuid": "cadb445b-e908-474c-9e4d-1d4d512aa3e8" } ]

{ "coherence": 2.76, "complexity": 2.55, "correctness": 2.02, "helpfulness": 2.04, "instruction-following": 2.82, "safety": 4.46, "verbosity": 1.82, "verbosity-coeff": -0.2119 }

[ { "content": "If the S.P of Rs. 63 results in a 10% discount on the list price, What S.P would result in a 20% discount on the list price?\n\n['A)s. 55', 'B)s. 56', 'C)s. 57', 'D)s. 58', 'E)s. 59']", "role": "user", "uuid": "cb0d5b58-0ed0-4814-9077-958d291a39f4" }, { "content": "Let the list price be Rs. X,\n90/100*x = 63, x = 63*100/90 = 70\nRequired S.P = 80% of Rs. 70\n= 80*70/100\n=56\nANSWER:B", "role": "assistant", "uuid": "adb54166-d889-4fa3-88a1-03387cab4da1" } ]

{ "coherence": 2.82, "complexity": 1.52, "correctness": 2.43, "helpfulness": 2.72, "instruction-following": 3.91, "safety": 4.5, "verbosity": 1.23, "verbosity-coeff": -0.109 }

[ { "content": "What is the radius of the incircle of the triangle whose sides measure 5, 12 and 13 units?\n\n['A)2 units', 'B)12 units', 'C)6.5 units', 'D)6 units', 'E)7.5 units']", "role": "user", "uuid": "66ebdfcf-f75c-4140-86f2-8da2885008c7" }, { "content": "Explanatory Answer\nIn a right angled triangle, the radius of the incircle = s - h, where 's' is the semi perimeter of the triangle and 'r' is the radius of the inscribed circle.\nThe semi perimeter of the triangle = a + b + c /2=5+12+13 /2 = 15\nTherefore, r = 15 - 13 = 2 units.\nChoice A", "role": "assistant", "uuid": "1cd9ac24-409d-4b28-be00-1a78a53b1789" } ]

{ "coherence": 2.62, "complexity": 1.38, "correctness": 1.75, "helpfulness": 2.06, "instruction-following": 2.1, "safety": 5.87, "verbosity": 1.16, "verbosity-coeff": -0.2233 }

[ { "content": "In the Land of Oz only one or two-letter words are used. The local language has 65 different letters. The parliament decided to forbid the use of the seventh letter. How many words have the people of Oz lost because of the prohibition?\n\n['A)65', 'B)66', 'C)67', 'D)131', 'E)130']", "role": "user", "uuid": "8c8186b6-6ef4-4cc8-b646-8ed2ce209725" }, { "content": "The answer to the question is indeed E. The problem with above solutions is that they do not consider words like AA, BB, ...\nThe number of 1 letter words (X) that can be made from 65 letters is 65;\nThe number of 2 letter words (XX) that can be made from 65 letters is 65*65, since each X can take 65 values.\nTotal: 65+65*65.\nSimilarly:\nThe number of 1 letter words (X) that can be made from 64 letters is 64;\nThe number of 2 letter words (XX) that can be made from 64 letters is 64*64, since each X can take 64 values.\nTotal: 64+64*64.\nThe difference is (65+65*65)-(64+64*64)=130.\nAnswer: E.", "role": "assistant", "uuid": "437025c3-e276-497e-b0af-2cf9f33a5637" } ]

{ "coherence": 2.88, "complexity": 2.04, "correctness": 2.1, "helpfulness": 2.35, "instruction-following": 2.74, "safety": 4.62, "verbosity": 2.08, "verbosity-coeff": -0.1256 }

[ { "content": "In a class 30 students play cricket, 40 students play football and 20 play none of the two games.\nIf there are 80 students exactly in the class, how many play exactly ONE of the two games?\n\n['A)40', 'B)50', 'C)80', 'D)85', 'E)90']", "role": "user", "uuid": "4500fd4c-c298-42e3-a4f3-6309f40fae49" }, { "content": "n(C) = 30, n(F) = 40 and n(C' or F') = 20\n=> n(C or F) = 80 - 20 = 60\nalso, n(C or F) = n(C) + n(F) - n(C and F)\n=> 60 = 30 + 40 - n(C and F)\ni.e. n(C and F) = 10\nso, 30 - 10 = 20 students play just football and 40 - 10 = 30 students play just cricket\n=> 20 + 30 = 50 students play exactly ONE game\nB)", "role": "assistant", "uuid": "9799a8d8-f466-414b-be57-ffcda0fcb8f0" } ]

{ "coherence": 2.68, "complexity": 1.9, "correctness": 2.12, "helpfulness": 2.35, "instruction-following": 3.13, "safety": 6.96, "verbosity": 1.16, "verbosity-coeff": -0.1269 }

[ { "content": "A man takes 3 hours 45 minutes to row a boat 15 km downstream of a river and 2 hours 30 minutes\nto cover a distance of 5 km upstream. Find the speed of the current.\n\n['A)1 km/hr', 'B)2 km/hr', 'C)3 km/hr', 'D)4 km/hr', 'E)None of these']", "role": "user", "uuid": "d69351cd-8e68-40ae-8026-de6439975cc1" }, { "content": "Explanation:\nFirst of all, we know that\nspeed of current = 1/2(speed downstream - speed upstream) [important]\nSo we need to calculate speed downstream and speed upstream first.\nSpeed = Distance / Time [important]\nSpeed upstream =(15334)km/hr=15×415=4km/hrSpeed Downstream = (5212)km/hr=5×25=2km/hrSo\nspeed of current = 12(4−2)=1km/hr\nAnswer: A", "role": "assistant", "uuid": "1243d112-7f5d-4a27-ad81-ef06088e295e" } ]

{ "coherence": 2.51, "complexity": 1.35, "correctness": 1.86, "helpfulness": 1.89, "instruction-following": 2.41, "safety": 4.73, "verbosity": 0.51, "verbosity-coeff": -0.1247 }

[ { "content": "In 150 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race A beats B by:\n\n['A)20 m', 'B)25 m', 'C)22.5 m', 'D)9 m', 'E)30 m']", "role": "user", "uuid": "a98ca903-8d2e-4a5e-a010-db625b2d101a" }, { "content": "Distance covered by B in 9 sec. =\t150/45 x 9\tm = 30 m.\nA beats B by 30 metres.\nAnswer: Option E", "role": "assistant", "uuid": "766c8072-37ee-4798-9f93-e1bc39a241fc" } ]

{ "coherence": 2.68, "complexity": 1.05, "correctness": 1.91, "helpfulness": 2.18, "instruction-following": 2.33, "safety": 4.25, "verbosity": 0.96, "verbosity-coeff": -0.1337 }

[ { "content": "For integers x and y, if (x+2)(y+3) is even then 4xy must be divisible by:\n\n['A)4', 'B)8', 'C)9', 'D)10', 'E)12']", "role": "user", "uuid": "f4841273-ed50-4206-bb40-0c9536fb30dd" }, { "content": "Just looking at the question, (x+2)(y+3) could be even*even, odd*even, or even*odd in order for the whole expression to be even.\nHowever, just looking at 4xy, since x*y will always be an integer, it will always be divisible by 4. 4 divided by 4 is 1, hence preserving x*y.\nAnswer: A. 4", "role": "assistant", "uuid": "89f34c16-c816-4864-8879-5291069f2640" } ]

{ "coherence": 3.04, "complexity": 2.41, "correctness": 2.59, "helpfulness": 2.51, "instruction-following": 2.31, "safety": 4.46, "verbosity": 1.53, "verbosity-coeff": -0.2013 }

[ { "content": "In the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30. In the sport formulation, the ratio of flavoring to corn syrup is three times as great as in the standard formulation, and the ratio of flavoring to water is half that of the standard formulation. If a large bottle of the sport formulation contains 7 ounces of corn syrup, how many ounces of water does it contain?\n\n['A)45', 'B)50', 'C)55', 'D)60', 'E)105']", "role": "user", "uuid": "6dc20905-bc60-4ace-a9bd-419a704058c1" }, { "content": "F:C:W\n1:12:30\nSport version:\nF:C\n3:12\nF:W\n1:60\nOR 3:180\nSo C:F:W = 12:3:180\nC/W = 12/180 = 3 ounces/x ounces\nx = 7*180/12 = 105 ounces of water\nE", "role": "assistant", "uuid": "7ae8bb9d-2679-4df5-803b-33e7cd999421" } ]

{ "coherence": 2.94, "complexity": 1.46, "correctness": 1.73, "helpfulness": 1.91, "instruction-following": 2.02, "safety": 4.89, "verbosity": 0.6, "verbosity-coeff": -0.1987 }

[ { "content": "How many terms are there in 2, 4, 8, 16,..., 512?\n\n['A)14', 'B)11', 'C)12', 'D)9', 'E)8']", "role": "user", "uuid": "5b4add17-f5ce-4e1f-9e18-877200313475" }, { "content": "2, 4, 8, 16, ..., 512 is a G.P with a =2\nand r =4/2 =2\nLet the number of terms be n. Then\n2 x 2 ^n-1 = 512\nor 2^n-1 = 256 = 2^8\nThus n - 1 =8\nn= 9\nANSWER:D", "role": "assistant", "uuid": "b818c4ed-c4fb-40be-9b7b-6f67d347ea07" } ]

{ "coherence": 2.47, "complexity": 1.54, "correctness": 2.1, "helpfulness": 2.04, "instruction-following": 3.31, "safety": 5.44, "verbosity": 1.31, "verbosity-coeff": -0.158 }

[ { "content": "The Pinedale bus line travels at an average speed of 60 km/h, and has stops every 5 minutes along its route. Yahya wants to go from his house to the Pinedale Mall, which is 10 stops away. How far away, in kilometers, is Pinedale Mall away from Yahya's house?\n\n['A)20 km', 'B)30 km', 'C)40 km', 'D)50 km', 'E)60 km']", "role": "user", "uuid": "077ca19b-3ac4-4f77-a983-dcc2dc563f8f" }, { "content": "Number of stops in an hour: 60/5 = 12\nDistance between stops: 60/12 = 5 km\nDistance between Yahya's house and Pinedale Mall: 5 x 10 = 50 km\nIMO, correct answer is \"D.\"", "role": "assistant", "uuid": "2bb9506b-604b-4c2b-b4bb-3fe08c79e0ff" } ]

{ "coherence": 3.27, "complexity": 1.25, "correctness": 2.68, "helpfulness": 2.76, "instruction-following": 3.82, "safety": 4.97, "verbosity": 1.07, "verbosity-coeff": -0.1245 }

[ { "content": "List K consists of 12 consecutive integers. If -3 is the least integer in list K, what is the range of the positive integers in list K?\n\n['A)5', 'B)6', 'C)7', 'D)11', 'E)12']", "role": "user", "uuid": "1ee14704-3aed-45b9-bf61-5bcfefe8fca0" }, { "content": "Answer = C =7\nIf least = -3, then largest = 8\nRange = 8 - 1 = 7", "role": "assistant", "uuid": "183d8043-5eaf-44f8-a489-4057a5147b20" } ]

{ "coherence": 3.04, "complexity": 1.21, "correctness": 2.23, "helpfulness": 2.43, "instruction-following": 2.47, "safety": 4.85, "verbosity": 0.63, "verbosity-coeff": -0.1998 }

[ { "content": "When Q is divided by W, the quotient is R and the remainder is r. Which of the following expressions is equal to r?\n\n['A)RW + Q', 'B)Q - RW', 'C)RW - Q', 'D)QW - R', 'E)Q/R']", "role": "user", "uuid": "c52d7a5c-7bd4-4251-a8f5-ad752c5a36bc" }, { "content": "Q/W = R + r/W\nQ -RW = r\nAmswer: B", "role": "assistant", "uuid": "cc840b2e-57bc-4099-a835-edf2d6fb56a9" } ]

{ "coherence": 2.53, "complexity": 1.82, "correctness": 2.2, "helpfulness": 2.47, "instruction-following": 2.59, "safety": 5.01, "verbosity": 1.16, "verbosity-coeff": -0.1395 }

[ { "content": "Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternately, the tank will be full is?\n\n['A)6 hrs', 'B)6 2/3 hrs', 'C)7 hrs', 'D)7 1/2 hrs', 'E)8 hrs']", "role": "user", "uuid": "ba65a464-5ee9-4e28-8cf4-c478ee4f9eff" }, { "content": "Explanation:\n(A + B)'s 1 hour work = (1/12 + 1/15) = 3/20\n(A + C)'s 1 hour work = (1/12 + 1/20) = 2/15\nPart filled in 2 hrs = (3/20 + 2/15) = 17/60\nPart filled in 6 hrs = 3 * 17/60 = 17/20\nRemaining part = 1 - 17/20 = 3/20\nNow, it is the turn of A and B and 3/20 part is filled by A and B in 1 hour.\nTotal time taken to fill the tank = (6 + 1) = 7 hrs.\nANSWER IS C", "role": "assistant", "uuid": "ff881716-86a9-43e2-b0e5-abfafb0f83a1" } ]

{ "coherence": 2.86, "complexity": 2.25, "correctness": 2.62, "helpfulness": 2.82, "instruction-following": 3.97, "safety": 5.32, "verbosity": 1.96, "verbosity-coeff": -0.1097 }

[ { "content": "At an examination in which full marks were 500. A got 10% less than B, B got 25% more than C and C got 20% less than D. If A got 360marks, what percentage of full marks was obtained by D?\n\n['A)90%', 'B)88%', 'C)80%', 'D)90%', 'E)84%']", "role": "user", "uuid": "7800ff95-7da3-4bf4-954a-f587923de4ce" }, { "content": "A B C D\n90 100 80 100\nA D\n90 ----- 100\n360 ------ ? = 400\n500 ------ 400\n100 ------- ? => 80%\nAnswer:C", "role": "assistant", "uuid": "5750f0ff-f886-42b3-9aed-2bfa3278230e" } ]

{ "coherence": 2.35, "complexity": 1.37, "correctness": 1.41, "helpfulness": 1.3, "instruction-following": 2.02, "safety": 6.26, "verbosity": 0.69, "verbosity-coeff": -0.1287 }

[ { "content": "20 machines can do a work in 10days. How many machines are needed to complete the work in 40days?\n\n['A)10', 'B)6', 'C)4', 'D)7', 'E)5']", "role": "user", "uuid": "a289116b-31a3-4f75-be12-0129c67748f0" }, { "content": "Required number of machines = 20*10/40 = 5\nAnswer is E", "role": "assistant", "uuid": "ef2c8956-c865-4098-a59f-21bfda893bae" } ]

{ "coherence": 2.88, "complexity": 1.05, "correctness": 2.96, "helpfulness": 2.94, "instruction-following": 3.5, "safety": 6.1, "verbosity": 0.59, "verbosity-coeff": -0.1163 }

[ { "content": "In a partnership between A, B and C. A's capital is Rs.5000. If his share of a profit of Rs.800 is Rs.200 and C's share is Rs.150, what is B's capital?\n\n['A)19878', 'B)12798', 'C)26908', 'D)11250', 'E)22073']", "role": "user", "uuid": "76a83a9a-50e4-4453-8b0d-3c2a0982ccf8" }, { "content": "200 + 150 = 350\n800 - 350 = 450\n200 ---- 5000\n450 ---- ? => 11250\nAnswer: D", "role": "assistant", "uuid": "2abc1726-4a96-47bd-a41e-7bbf70696919" } ]

{ "coherence": 3.27, "complexity": 0.54, "correctness": 2.64, "helpfulness": 2.98, "instruction-following": 3.82, "safety": 4.93, "verbosity": 0.42, "verbosity-coeff": -0.1216 }

[ { "content": "What is the place value of 7 in the numeral 51468?\n\n['A)100', 'B)10', 'C)1', 'D)1000', 'E)11']", "role": "user", "uuid": "ba022ee9-acff-45de-9d47-d13d3b752109" }, { "content": "place value of 1 = 1 * 1000 = 1000\nAnswer is D", "role": "assistant", "uuid": "e1bedeb8-644a-4ef8-9148-ef18b4811e1b" } ]

{ "coherence": 2.06, "complexity": 0.63, "correctness": 1.05, "helpfulness": 1.11, "instruction-following": 1.3, "safety": 4.62, "verbosity": 0.42, "verbosity-coeff": -0.0995 }

[ { "content": "46080, 3840, 384, 48, 8, 2, ?\n\n['A)1', 'B)1⁄64', 'C)1⁄8', 'D)None of these', 'E)1/32']", "role": "user", "uuid": "a08d6856-f9a2-4f3e-a901-86e38d379f0d" }, { "content": "Explanation :\n46080 ÷ 12 = 3840\n3840 ÷ 10 = 384\n384 ÷ 8 = 48\n48 ÷ 6 = 8\n8 ÷ 4 = 2\n2 ÷ 2 = 1\nAnswer : Option A", "role": "assistant", "uuid": "dff2b8b3-e007-4ce1-b157-4fc35720c18b" } ]

{ "coherence": 2.14, "complexity": 1.86, "correctness": 2.27, "helpfulness": 2.47, "instruction-following": 2.29, "safety": 4.5, "verbosity": 1.23, "verbosity-coeff": -0.1014 }

[ { "content": "What is the last number in a sequence of 5 consecutive integers, given that their sum is 335?\n\n['A)69', 'B)70', 'C)68', 'D)66', 'E)67']", "role": "user", "uuid": "960bdba0-9009-45bd-bac7-a5953b288f2e" }, { "content": "The median is: 335/5 = 67. Middle position.\nMiddle position is also: 5/2 = 2.5, rounded up: 3rd position\n3rd position is: 5-3 = 2 positions away from the last position\n67 + 2 = 69\nAnswer: A", "role": "assistant", "uuid": "1706cd29-8d21-4670-b53f-d7883cc630bd" } ]

{ "coherence": 2.62, "complexity": 1.55, "correctness": 2.23, "helpfulness": 2.23, "instruction-following": 2.16, "safety": 4.73, "verbosity": 1.3, "verbosity-coeff": -0.1584 }

[ { "content": "3 men or 6 women can do a piece of work in 20 days. In how many days will 12 men and 8 women do the same work?\n\n['A)15/7 days', 'B)15/4 days', 'C)17/4 days', 'D)15/6 days', 'E)12/4 days']", "role": "user", "uuid": "5075649f-e61c-45a2-bd3d-3475488c05f5" }, { "content": "3M = 6W ---- 20 days\n12M + 8W -----?\n24W + 8 W = 32W ---?\n6W ---- 20 32 -----?\n6 * 20 = 32 * x => x = 15/4 days Answer: B", "role": "assistant", "uuid": "0114ee12-6c48-43fa-9fd3-1fb0ad2d5d83" } ]

{ "coherence": 2.64, "complexity": 0.8, "correctness": 1.97, "helpfulness": 2.1, "instruction-following": 2.9, "safety": 5.71, "verbosity": 0.29, "verbosity-coeff": -0.128 }

[ { "content": "If the sides of a triangle are 39 cm, 36 cm and 15 cm, what is its area?\n\n['A)230 cm^2', 'B)240 cm^2', 'C)250 cm^2', 'D)260 cm^2', 'E)270 cm^2']", "role": "user", "uuid": "e35f95db-bb14-4609-a0fe-4144a371fef7" }, { "content": "The triangle with sides 39 cm, 36 cm and 15 cm is right angled, where the hypotenuse is 39 cm.\nArea of the triangle\n= 1/2 * 36 * 15\n= 270 cm^2\nAnswer: E", "role": "assistant", "uuid": "fdc215dc-3fbf-49d3-b5d4-a7e98a976f1e" } ]

{ "coherence": 3.09, "complexity": 0.84, "correctness": 2.25, "helpfulness": 2.59, "instruction-following": 3.02, "safety": 5.55, "verbosity": 0.82, "verbosity-coeff": -0.1294 }

[ { "content": "A car is purchased on hire-purchase. The cash price is $22 000 and the terms are a deposit of 10% of the price, then the balance to be paid off over 60 equal monthly installments. Interest is charged at 12% p.a. What is the monthly installment?\n\n['A)$503', 'B)$504', 'C)$515', 'D)$528', 'E)$537']", "role": "user", "uuid": "1fb96161-0c65-499b-954c-985835b20ab5" }, { "content": "Explanation:\nCash price = $22 000\nDeposit = 10% × $22 000 = $2200\nLoan amount = $22000 − $2200\nNumber of payments = 60\n= $19800\nI=p*r*t/100\nI=11880\nTotal amount = 19800 + 11880 = $31680\nRegular payment = total amount /number of payments = 528\nAnswer: D", "role": "assistant", "uuid": "51142902-2778-4321-abb1-0e1a600c7f2e" } ]

{ "coherence": 2.37, "complexity": 0.91, "correctness": 1.8, "helpfulness": 2.14, "instruction-following": 2.76, "safety": 4.66, "verbosity": 0.93, "verbosity-coeff": -0.1226 }

[ { "content": "How long will a car take to run round a circular field of radius 2/π metres. If car runs at the rate of 8km/hr ?\n\n['A)2.5 sec.', 'B)10 sec.', 'C)3 sec', 'D)2 sec', 'E)1.8 sec']", "role": "user", "uuid": "5d7dc0e1-7f22-4aef-bc93-928336b8e87f" }, { "content": "Speed = 8 km/hr = 8*5/18 = 20/9 m/sec\ndistance = 2πr=2π*2/π=4 m\ntime taken = 4*9/20 = 1.8 sec.\nAnswer E", "role": "assistant", "uuid": "8f9b3a84-2f8f-4885-8aee-54d3726e03a0" } ]

{ "coherence": 2.88, "complexity": 2.14, "correctness": 2.47, "helpfulness": 2.39, "instruction-following": 3.29, "safety": 5.24, "verbosity": 1.45, "verbosity-coeff": -0.118 }

[ { "content": "A pipe can empty 1/4th of a cistern in 12mins. In 8 mins, what part of the cistern will be empty?\n\n['A)2/3', 'B)3/7', 'C)4/9', 'D)1/6', 'E)4/7']", "role": "user", "uuid": "118086ec-26d4-484a-9025-65ab0695d3d1" }, { "content": "1/4 ---- 12\n? ----- 8 ==> 1/6\nD", "role": "assistant", "uuid": "88e0fa79-4dda-4859-8d7b-cd1529722d6e" } ]

{ "coherence": 2.49, "complexity": 1.03, "correctness": 1.77, "helpfulness": 1.98, "instruction-following": 2.49, "safety": 5.75, "verbosity": 0.39, "verbosity-coeff": -0.1048 }

[ { "content": "A and B undertake to do a piece of work for Rs. 1200. A alone can do it in 6 days while B alone can do it in 8 days. With the help of C, they finish it in 3 days. Find the share of A.\n\n['A)500', 'B)600', 'C)750', 'D)800', 'E)None of them']", "role": "user", "uuid": "af45655d-457c-488c-a565-478b371a73a0" }, { "content": "C's 1 day's work = 1/3-(1/6+1/8)=24\nA : B : C = Ratio of their 1 day's work = 1/6:1/8:1/24= 4 : 3 : 1.\nA’s share = Rs. (1200 *4/8) = Rs.600, B's share = Rs. (1200 *3/8) = Rs. 450\nC's share = Rs. [1200 - (300 + 225») = Rs. 150.\nAnswer is B", "role": "assistant", "uuid": "d88499d4-3259-464a-bab4-7e1eac971a91" } ]

{ "coherence": 2.49, "complexity": 0.92, "correctness": 1.63, "helpfulness": 1.95, "instruction-following": 2.61, "safety": 5.63, "verbosity": 1.47, "verbosity-coeff": -0.1167 }

[ { "content": "The price of rice falls by 40%. How much rice can be bought now with the money that was sufficient to buy 20 kg of rice previously?\n\n['A)5 kg', 'B)15 kg', 'C)25 kg', 'D)30 kg', 'E)None']", "role": "user", "uuid": "b3734224-5917-43a2-822b-fef8e012abe1" }, { "content": "Solution: Let Rs. 100 be spend on rice initially for 20 kg.\nAs the price falls by 40%, new price for 20 kg rice,\n= (100 -40% of 100) = 60\nNew price of rice = 60/20 = Rs. 3 per kg.\nRice can bought now at = 100/3 = 33.33 kg.\nAnswer: Option E", "role": "assistant", "uuid": "00db2993-60e7-4505-a03e-703e2926f804" } ]

{ "coherence": 2.64, "complexity": 1.64, "correctness": 1.57, "helpfulness": 1.88, "instruction-following": 1.52, "safety": 4.81, "verbosity": 1.24, "verbosity-coeff": -0.1214 }

[ { "content": "Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?\n\n['A)17 a.m', 'B)10 a.m', 'C)70 a.m', 'D)16 a.m', 'E)18 a.m']", "role": "user", "uuid": "e608f8db-0832-4f39-bb0f-01ea0628d84b" }, { "content": "Suppose they meet x hours after 7 a.m.\nDistance covered by A in x hours = 20x km.\nDistance covered by B in (x - 1) hours = 25(x - 1) km.\nTherefore 20x + 25(x - 1) = 110\n45x = 135\nx = 3.\nSo, they meet at 10 a.m.\nAnswer:B", "role": "assistant", "uuid": "09739cd0-60a3-40f0-9ce3-eb82c4ea3762" } ]

{ "coherence": 3.25, "complexity": 1.54, "correctness": 3.29, "helpfulness": 3.43, "instruction-following": 4.17, "safety": 4.58, "verbosity": 1.61, "verbosity-coeff": -0.1204 }

[ { "content": "Find the no.of ways of arranging the boy and 8 guests at a circular table so that the boy always sits in a particular seat?\n\n['A)5!', 'B)8!', 'C)9!', 'D)10!', 'E)12!']", "role": "user", "uuid": "1d05f51b-fff4-43a0-90ba-9b58410f88d1" }, { "content": "Ans.(B)\nSol. Total number of persons = 9 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 8 places in 8P8 = 8! Ways ... The number of required arrangements = 8! x 1= 8! = 8! ways", "role": "assistant", "uuid": "43cc4b10-e97e-4d91-9ed0-66c6fa5b0937" } ]

{ "coherence": 3.13, "complexity": 1.69, "correctness": 3.05, "helpfulness": 3.09, "instruction-following": 2.94, "safety": 4.7, "verbosity": 1.39, "verbosity-coeff": -0.1293 }

[ { "content": "An equity analyst needs to select 3 stocks for the upcoming year and rank these securities in terms of their investment potential. If the analyst has narrowed down the list of potential stocks to 7, in how many ways can she choose and rank her top 3 picks?\n\n['A)21', 'B)35', 'C)210', 'D)420', 'E)840']", "role": "user", "uuid": "7ca64afc-6d2d-4def-b171-b96e5014b532" }, { "content": "Number of ways of choosing 3 stocks = 7C3\nNumber of ways of ranking the chosen stocks = 3!\nHence total ways of choosing and ranking = 7C3 * 3! = 7!/4! = 7*6*5 = 210\nCorrect Option: C", "role": "assistant", "uuid": "b8da870d-d16c-438d-a00a-06aae3635764" } ]

{ "coherence": 3.19, "complexity": 2.08, "correctness": 2.8, "helpfulness": 3.27, "instruction-following": 3.78, "safety": 6.06, "verbosity": 1.2, "verbosity-coeff": -0.119 }

[ { "content": "Sides of a rectangular park are in the ratio 3: 2 and its area is 4704 sq m, the cost of fencing it at 50 ps per meter is?\n\n['A)287', 'B)1287', 'C)140', 'D)988', 'E)271']", "role": "user", "uuid": "5534edcb-f13a-4e28-800a-156db9ee5411" }, { "content": "3x * 2x = 4704 => x = 28\n2(84 + 56) = 280 m\n280 * 1/2 = Rs.140\nAnswer: C", "role": "assistant", "uuid": "34af7e8b-2200-40d1-9725-bd70a775ae92" } ]

{ "coherence": 2.84, "complexity": 1.19, "correctness": 2.35, "helpfulness": 2.62, "instruction-following": 3.62, "safety": 6.34, "verbosity": 0.67, "verbosity-coeff": -0.1153 }

[ { "content": "For a race a distance of 224 meters can be covered by P in 28 seconds and Q in 32 seconds. By what distance does P defeat Q eventually?\n\n['A)32m', 'B)38m', 'C)34m', 'D)31m', 'E)36m']", "role": "user", "uuid": "f14ee567-d21f-4507-8648-64fc4da6d5f9" }, { "content": "Explanation:\nThis is a simple speed time problem. Given conditions:\n=>Speed of P= 224/28 = 8m/s\n=>Speed of Q=224/32 = 7m/s\n=>Difference in time taken = 4 seconds\nTherefore, Distance covered by P in that time= 8m/s x 4 seconds = 32 metres\nANSWER: A", "role": "assistant", "uuid": "84706408-1309-4603-9a6b-e49eb74109cc" } ]

{ "coherence": 2.9, "complexity": 1.55, "correctness": 2.68, "helpfulness": 2.9, "instruction-following": 3.84, "safety": 4.38, "verbosity": 1.38, "verbosity-coeff": -0.1485 }

[ { "content": "A is twice as good a workman as B and they took 7 days together to do the work B alone can do it in.\n\n['A)71 days', 'B)55 days', 'C)21 days', 'D)77 days', 'E)44 days']", "role": "user", "uuid": "0b0cecf9-c0fb-47e3-bae4-cf4bf15e9ee7" }, { "content": "WC = 2:1\n2x + x = 1/7\nx = 1/21 => 21 days\nAnswer: C", "role": "assistant", "uuid": "6d5d4625-4528-4284-b9ce-6f66a5d21505" } ]

{ "coherence": 2.96, "complexity": 1.02, "correctness": 2.37, "helpfulness": 2.53, "instruction-following": 3.43, "safety": 5.28, "verbosity": 0.11, "verbosity-coeff": -0.1028 }

[ { "content": "In a simultaneous throw of a pair of dice, find the probability of getting a total more than 10\n\n['A)5/13', 'B)2/15', 'C)1 by 12', 'D)3/17', 'E)6/19']", "role": "user", "uuid": "794ac57c-f082-470c-a93b-885886d25e27" }, { "content": "Total number of cases = 6*6 = 36\nFavourable cases = [(5,6)(6,5),(6,6)] = 3\nSo Probability = 3/36 = 1/12\nAnswer is C", "role": "assistant", "uuid": "55860495-9861-49d1-a0fb-f3d4ccdc15c0" } ]

{ "coherence": 2.78, "complexity": 1.34, "correctness": 2.04, "helpfulness": 2.04, "instruction-following": 2.66, "safety": 5.55, "verbosity": 0.79, "verbosity-coeff": -0.1001 }

[ { "content": "Ross has 160 shirts, 3/4 of the shirts are green and 1/10 is without buttons. Therefore Ross has between ___ and ___ shirts with buttons that are not green.\n\n['A)24 ; 40.', 'B)23 ; 40.', 'C)22 ; 40.', 'D)21 ; 40.', 'E)20 ; 40.']", "role": "user", "uuid": "a79ead31-7b14-4277-afaa-f3a8ecc648b4" }, { "content": "Total shirts = 160\nGreen shirts = 3/4*160 = 120, Non green shirts = 40\nShirts without button = 1/10*160 = 16, shirts with button = 144\nRequired: Range of shirts with buttons that are not green.\nMaximum non green shirts with buttons = number of non green shirts = 40\nMinimum non green shirts with buttons (All without button shirts are non green) = Non green shirts - shirts without button = 40 - 16 = 24\nHence the range would be (24, 40)\nCorrect Option: A", "role": "assistant", "uuid": "6f2c973f-947c-4d31-924a-34eb43ad50f8" } ]

{ "coherence": 3.23, "complexity": 1.45, "correctness": 2.78, "helpfulness": 2.98, "instruction-following": 3.68, "safety": 5.75, "verbosity": 1.02, "verbosity-coeff": -0.1105 }

[ { "content": "A certain company retirement plan has arule of 70provision that allows an employee to retire when the employee's age plus years of employment with the company total at least 70. In what year could a female employee hired in 1990 on her 32nd birthday first be eligible to retire under this provision?\n\n['A)2003', 'B)2009', 'C)2005', 'D)2006', 'E)2007']", "role": "user", "uuid": "bf75f990-5523-4a70-893f-9eade55732ef" }, { "content": "She must gain at least 70 points, now she has 31 and every year gives her two more points: one for age and one for additional year of employment, so 32 + 2*(# of years) = 70 --> (# of years) = 19 --> 1990+19=2009.\nAnswer: B.", "role": "assistant", "uuid": "0ec71a3b-c7dd-4651-a5b7-4e1760bc346f" } ]

{ "coherence": 3, "complexity": 0.84, "correctness": 2.59, "helpfulness": 2.84, "instruction-following": 3.45, "safety": 6.49, "verbosity": 0.26, "verbosity-coeff": -0.1325 }

[ { "content": "What is the largest number of four digits which is divisible by 15, 25, 40 and 75 ?\n\n['A)9600', 'B)5200', 'C)362', 'D)958', 'E)258']", "role": "user", "uuid": "b5e6575d-8c4c-40d3-b54f-db5a730f4260" }, { "content": "Explanation:\nLargest number of four digits = 9999\nLCM of 15, 25, 40 and 75 = 600\n9999 ÷ 600 = 16, remainder = 399\nHence,Largest number of four digits which is divisible by 15, 25, 40 and 75\n= 9999 - 399 = 9600\nAnswer:A", "role": "assistant", "uuid": "7b70715a-8cbe-48be-b92b-3b6e15267ba9" } ]

{ "coherence": 2.92, "complexity": 1.96, "correctness": 2.35, "helpfulness": 2.7, "instruction-following": 3.45, "safety": 5.09, "verbosity": 1.4, "verbosity-coeff": -0.1873 }

[ { "content": "Two pipes A and B can separately fill a cistern in 10 and 15 minutes respectively. A person opens both the pipes together when the cistern should have been was full he finds the waste pipe open. He then closes the waste pipe and in another 4 minutes the cistern was full. In what time can the waste pipe empty the cistern when fill?\n\n['A)7', 'B)9', 'C)5', 'D)4', 'E)8']", "role": "user", "uuid": "40a9d482-655e-41ca-87ea-3bbc762c886f" }, { "content": "1/10 + 1/15 = 1/6 * 4 = 2/3\n1 - 2/3 = 1/3\n1/10 + 1/15 - 1/x = 1/3\nx = 8\nANSWER E", "role": "assistant", "uuid": "067fc481-27b6-4cf8-ac28-67f34dec76f2" } ]

{ "coherence": 2.02, "complexity": 1.69, "correctness": 1.84, "helpfulness": 1.85, "instruction-following": 2.55, "safety": 6.02, "verbosity": 1.07, "verbosity-coeff": -0.1178 }

[ { "content": "A fruit vendor purchased 20 dozens of bananas at Rs. 15 per dozen. But one-fourth of the bananas were rotten and had to be thrown away. He sold two-third of the remaining bananas at Rs. 22.50 per dozen. At what price per dozen should he sell the remaining bananas to make neither a profit nor a loss?\n\n['A)18', 'B)15', 'C)16', 'D)19', 'E)11']", "role": "user", "uuid": "a8b00758-923a-496d-8c0e-8602a49d61bf" }, { "content": "CP of 20 dozen of bananas = 15 * 20 = Rs. 300\nNumber of bananas which are rotten = 1/4 * 20 = 5 dozen.\nSP of two-third of remaining bananas = (2/3 * 15) * 22.5 = Rs. 225\nSP of remaining 5 dozens of bananas to make no profit and no loss =(300 - 225) = Rs. 75.\nSP of 1 dozen bananas = 75/5 = Rs. 15.Answer:B", "role": "assistant", "uuid": "9c9f3041-07a8-4a19-9690-7de2aa54a9f6" } ]

{ "coherence": 2.9, "complexity": 1.51, "correctness": 2.8, "helpfulness": 2.94, "instruction-following": 3.41, "safety": 4.97, "verbosity": 1.73, "verbosity-coeff": -0.1468 }

[ { "content": "A typist uses a sheet measuring 20cm by 30cm lengthwise. If a margin of 2 cm is left on each side and a 3 cm margin on top and bottom, then percent of the page used for typing is\n\n['A)40', 'B)60', 'C)64', 'D)72', 'E)None']", "role": "user", "uuid": "c528f2d7-1784-41e7-9271-a4967ea9642f" }, { "content": "Solution\nArea of the sheet\t= (20 x 30 ) cm²\n= 600 cm²\nArea used for typing\t= [(20 - 4) x (30 - 6)] cm²\n= 384 cm²\nRequired percentage\t= (384 / 600 x 100)%\n=64%.\nAnswer C", "role": "assistant", "uuid": "c949e9fa-a3f5-4f7f-8e85-6b4a31548cba" } ]

{ "coherence": 2.98, "complexity": 1.72, "correctness": 2.57, "helpfulness": 2.68, "instruction-following": 4.05, "safety": 4.46, "verbosity": 1.88, "verbosity-coeff": -0.1177 }

[ { "content": "The profit earned by selling an article for Rs. 832 is equal to the loss incurred when the same article is sold for Rs. 448. What should be the sale price for making 50% profit ?\n\n['A)Rs. 660', 'B)Rs. 560', 'C)Rs. 1060', 'D)Rs. 960', 'E)None of these']", "role": "user", "uuid": "c887baa4-b68f-4458-8b63-71d8bb692726" }, { "content": "Explanation:\nLet C.P. = Rs. C.\nThen, 832 - C = C - 448\n2C = 1280 => C = 640\nRequired S.P. = 150% of Rs. 640 = 150/100 x 640 = Rs. 960.\nANSWER IS D", "role": "assistant", "uuid": "6bc0cd12-3896-4425-8ec1-22732c299beb" } ]

{ "coherence": 2.94, "complexity": 2.2, "correctness": 2.68, "helpfulness": 2.92, "instruction-following": 3.93, "safety": 5.55, "verbosity": 1.75, "verbosity-coeff": -0.1249 }

[ { "content": "The length of a rectangle is increased by 35% and its breadth is decreased by 20%. What is the effect on its area?\n\n['A)10800', 'B)1299', 'C)1000', 'D)10000', 'E)2887']", "role": "user", "uuid": "96b69ee7-146f-4661-9295-89b00dd3580b" }, { "content": "100 * 100 = 10000\n135 * 80 = 10800\nAnswer: A", "role": "assistant", "uuid": "22e03cc7-656a-4b93-be9c-e9b71e48603b" } ]

{ "coherence": 2.82, "complexity": 1.02, "correctness": 2.18, "helpfulness": 2.35, "instruction-following": 2.92, "safety": 5.55, "verbosity": 0.92, "verbosity-coeff": -0.1222 }

[ { "content": "Ronald and Elan are working on an assignment. Ronald takes 6 hours to type 32 pages on a computer, while Elan takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?\n\n['A)3 hours', 'B)6 hours', 'C)4 hours', 'D)8 hours', 'E)10 hours']", "role": "user", "uuid": "e953cda0-1808-4a4a-b1a6-189e07a3d5ae" }, { "content": "Number of pages typed by Ronald in one hour = 32/6 = 16/3\nNumber of pages typed by Elan in one hour = 40/5 = 8\nNumber of pages typed by both in one hour = ((16/3) + 8) = 40/3\nTherefore, time taken by both to type 110 pages = 110 x 3/40 = 8 hours.\nANSWER:D", "role": "assistant", "uuid": "1b3cc2f0-c266-4d13-b385-c07cf76bf4ea" } ]

{ "coherence": 2.72, "complexity": 1.51, "correctness": 2.27, "helpfulness": 2.45, "instruction-following": 3.43, "safety": 5.59, "verbosity": 1.38, "verbosity-coeff": -0.1227 }

[ { "content": "The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum is:\n\n['A)20', 'B)30', 'C)40', 'D)None of these', 'E)Either (a) or (b)']", "role": "user", "uuid": "9832fd15-73fe-4080-9114-cdb17dcfb19a" }, { "content": "Let the numbers be a, b and c.\nThen, a2 + b2 + c2 = 138 and (ab + bc + ca) = 131.\n(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca) = 138 + 2 x 131 = 400.\n(a + b + c) = 400 = 20.\nANSWER : A", "role": "assistant", "uuid": "24ee99b9-5fb5-4d82-bea0-f17044f7545b" } ]

{ "coherence": 2.78, "complexity": 2.29, "correctness": 2.31, "helpfulness": 2.64, "instruction-following": 2.88, "safety": 4.81, "verbosity": 1.59, "verbosity-coeff": -0.16 }

[ { "content": "The operation is defined for all integers a and b by the equation ab = (a - 1)(b - 1). If y12 = 110, what is the value of y ?\n\n['A)11', 'B)12', 'C)13', 'D)15', 'E)18']", "role": "user", "uuid": "963e353b-1601-4aa6-a579-570ac503e71f" }, { "content": "ab = (a - 1)(b - 1)\ny12 = (y-1)(12-1) =110 --> y-1=10 --> y=11\nAnswer: A", "role": "assistant", "uuid": "1215d7b5-1f84-4ff3-8b25-c39d08f08f6b" } ]

{ "coherence": 3.39, "complexity": 1.6, "correctness": 2.76, "helpfulness": 2.98, "instruction-following": 3.15, "safety": 5.83, "verbosity": 0.53, "verbosity-coeff": -0.1925 }

[ { "content": "At what rate percent per annum will a sum of money double in 8 years.\n\n['A)12.5%', 'B)12.9%', 'C)18.5%', 'D)11.5%', 'E)12.3%']", "role": "user", "uuid": "8a3b922c-ff00-48e6-a356-3b86d9298f89" }, { "content": "Explanation:\nLet principal = P, Then, S.I.=P and Time=8 years\nRate = [(100 x P)/ (P x 8)]% = 12.5% per annum.\nAnswer: A) 12.5%", "role": "assistant", "uuid": "578f267f-bcb5-473c-b60a-4bb291073597" } ]

{ "coherence": 3.43, "complexity": 1.66, "correctness": 2.74, "helpfulness": 2.8, "instruction-following": 3.19, "safety": 4.42, "verbosity": 1.06, "verbosity-coeff": -0.1328 }

[ { "content": "On decreasing the price of a colour TV by 15%, its sale is increased by 30%. The effect on the revenue is?\n\n['A)20 % decrease', 'B)25.5 % increase', 'C)16% decrease', 'D)30 % increase', 'E)none of these']", "role": "user", "uuid": "f3c44c4d-ee71-458c-b9da-03671d0c49a6" }, { "content": "Net% change in revenue\n= ( x + y + xy/100) %\n= [-15 + 30 + ( -15 x 30)/100]% or 25.5%\nANSWER:B", "role": "assistant", "uuid": "ae57756a-d85f-4003-ad4d-e7fe3e1692dc" } ]

{ "coherence": 2.72, "complexity": 2, "correctness": 2.55, "helpfulness": 2.64, "instruction-following": 3.27, "safety": 6.06, "verbosity": 1.7, "verbosity-coeff": -0.126 }

[ { "content": "The average of first 14 even numbers is?\n\n['A)10', 'B)11', 'C)12', 'D)13', 'E)15']", "role": "user", "uuid": "2ebab7c4-3960-4cf7-967d-ed625ed2f488" }, { "content": "Sum of 14 even numbers = 14 * 15 = 210\nAverage =210/14= 15\nANSWER:E", "role": "assistant", "uuid": "2ee006ce-fa90-4fc4-afb8-0cc3dcf15ee7" } ]

{ "coherence": 2.78, "complexity": 1.57, "correctness": 2.18, "helpfulness": 2.41, "instruction-following": 2.59, "safety": 3.82, "verbosity": 1.01, "verbosity-coeff": -0.1035 }

[ { "content": "Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate get?\n\n['A)57%', 'B)63%', 'C)73%', 'D)90%', 'E)58%']", "role": "user", "uuid": "1c6f6fa1-a10e-4100-9451-d5bd0f49f998" }, { "content": "Total number of votes polled = (1136 + 7636 + 11628) = 20400.\nRequired percentage =(11628/20400\t)x 100% = 57%.\nAnswer:A", "role": "assistant", "uuid": "34576008-13df-4c60-b222-b8fa77c2f02a" } ]

{ "coherence": 3.33, "complexity": 1.28, "correctness": 2.55, "helpfulness": 2.66, "instruction-following": 3.54, "safety": 5.71, "verbosity": 1.29, "verbosity-coeff": -0.1143 }

[ { "content": "If a function f is defined by f(x)= 3/(x-1) for all non zero numbers x. If f(a) = 3 and f(ab) = 9 then b= ?\n\n['A)1/3', 'B)1/2', 'C)-1/2', 'D)-1/3', 'E)-2']", "role": "user", "uuid": "9a5b8316-65d7-49fd-bc55-6758c4107f00" }, { "content": "Given that f(x) = 3/(x-1) and f(a) = 3, then f(a) =3/(x-1)=3 ===> x-1=1 ==> x =2, then backsolve using the answer choices:\nf(ab) = f(2b) = 3/(2b-1)\nA) 1/3 ===> f(2*1/3) = f(2/3) = 3/((2*2/3)-1) = 9 WINS\nB) 1/2 ===> f((2*1/2) = f(1) = 3/1-1 = undefined\nC) -1/2 ===> f(2*-1/2) = f(-1) = 3/1+1 = 3/2\nD) -1/3 ===> f(2*-1/3) = f(-2/3) = 3/(2*-2/3 -1) = -9/7\nE) -2 ===> f(2*-2) = f(-4) = 3/(2*-4 -1) = -1/3\nAnswer: A", "role": "assistant", "uuid": "d6cf40d9-cb4d-4fe1-9571-09b5c6b760ad" } ]

{ "coherence": 3.04, "complexity": 2.31, "correctness": 2.33, "helpfulness": 2.27, "instruction-following": 3.35, "safety": 4.7, "verbosity": 1.47, "verbosity-coeff": -0.1103 }

[ { "content": "What number is obtained by adding the units digits of 734^100 and 347^83?\n\n['A)7', 'B)8', 'C)9', 'D)10', 'E)11']", "role": "user", "uuid": "5ea01cb2-23d2-4d4c-aeca-1c66ce917822" }, { "content": "The units digit of 734^100 is 6 because 4 raised to the power of an even integer ends in 6.\nThe units digit of 347^83 is 3 because powers of 7 end in 7, 9, 3, or 1 cyclically. Since 83 is in the form 4n+3, the units digit is 3.\nThen 6+3 = 9.\nThe answer is C.", "role": "assistant", "uuid": "71fbb3b0-321b-43a4-86ad-f85a81f673cc" } ]

{ "coherence": 3.46, "complexity": 2.53, "correctness": 2.59, "helpfulness": 2.72, "instruction-following": 3.23, "safety": 5.87, "verbosity": 1.79, "verbosity-coeff": -0.219 }

[ { "content": "Find the least value of 'a' so that 365a24 is divisible by 8.\n\n['A)9', 'B)8', 'C)0', 'D)2', 'E)1']", "role": "user", "uuid": "63da08d8-8025-4097-9511-e892a1f82f12" }, { "content": "Explanation:\nGiven, number is divisible by 8 only if 'a24' is divisible by 8.\n.: Least value of a is '0'.\nAnswer: Option C", "role": "assistant", "uuid": "e643893a-ab5c-4bc2-adab-19ffe08ec38a" } ]

{ "coherence": 2.59, "complexity": 1.58, "correctness": 2.16, "helpfulness": 2.18, "instruction-following": 2.51, "safety": 5.36, "verbosity": 1.13, "verbosity-coeff": -0.1876 }

[ { "content": "The average of 11numbers is 60. Out of 11numbers the average of first 6no. is 98, and last 6numbers is 65 then find 6th number?\n\n['A)A)318', 'B)B)65', 'C)C)58', 'D)D)62', 'E)E)48']", "role": "user", "uuid": "3ed13419-4646-4433-971d-a87587a31cd2" }, { "content": "6th number = sum of 1st 6no.s + sum of last 6no.s - sum of 11no.s\nanswer = 6*98+6*65-11*60 = 318\nAnswer is A", "role": "assistant", "uuid": "ce1e4805-d97b-4f46-8ceb-fcf022a9c064" } ]

{ "coherence": 2.68, "complexity": 1.5, "correctness": 1.95, "helpfulness": 2.06, "instruction-following": 2.86, "safety": 5.32, "verbosity": 1.07, "verbosity-coeff": -0.1116 }

[ { "content": "In a recent survey at a local deli, it was observed that 3 out of 5 customers bought a bagel and 5 out of 7 customers bought a coffee. Some customers bought both. If 3 customers are selected, what are the chances that at least 1 customer bought a coffee and a bagel?\n\n['A)27/343', 'B)3/7', 'C)27/125', 'D)279/343', 'E)9/125']", "role": "user", "uuid": "5543743a-79f3-4bb8-8948-94a36a44d7ba" }, { "content": "Let us take 7*5=35 as the total number of customers. So 7*3=21 customers bought a bagel and 5*5=25 customers bought a coffee.\nchances that at least 1 customer bought a coffee and a bagel = 1 - chances that no customer bought a coffee and a bagel\nchances that no customer bought a coffee and a bagel= 24/35*23/34*22/33=12*23*2/35*17*3=552/1785\nchances that at least 1 customer bought a coffee and a bagel= 1 - 552/1785 = 1233/1785 = 279/343\nAnswer D.", "role": "assistant", "uuid": "a3f73382-a07b-49a0-9c96-be546d6b78c2" } ]

{ "coherence": 2.96, "complexity": 1.54, "correctness": 2.23, "helpfulness": 2.33, "instruction-following": 2.62, "safety": 4.66, "verbosity": 1.59, "verbosity-coeff": -0.1672 }

[ { "content": "If (A+B) = 4, (B+C) = 7 and (C+D) = 5, what is the value of (A+D)?\n\n['A)16.', 'B)8.', 'C)7.', 'D)2.', 'E)-2.']", "role": "user", "uuid": "94278721-daa5-4f35-908c-d0b688d85809" }, { "content": "Given A+B = 4\nB+C = 7\nC+D = 5\n(A+B)-(B+C)+(C+D)=(A+D)\n=>4 - 7+5 = 2.\nOption D...", "role": "assistant", "uuid": "a7b79ace-ba98-475d-acab-bd6fd29f401a" } ]

{ "coherence": 2.72, "complexity": 0.99, "correctness": 2.02, "helpfulness": 2.1, "instruction-following": 2.57, "safety": 5.4, "verbosity": 0.55, "verbosity-coeff": -0.13 }

[ { "content": "Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 31 kmph. Of how many minutes does the train stop per hour?\n\n['A)18.6', 'B)27', 'C)12', 'D)121', 'E)28']", "role": "user", "uuid": "ab7448f3-34e6-4d7f-8cc4-2fa4df85ae73" }, { "content": "Explanation:\nT = 14/45 * 60 = 18.6\nAnswer: Option A", "role": "assistant", "uuid": "2e07f97b-c55c-416b-909a-d73d9d609beb" } ]

{ "coherence": 2.53, "complexity": 0.87, "correctness": 2.37, "helpfulness": 2.57, "instruction-following": 2.78, "safety": 5.83, "verbosity": 0.9, "verbosity-coeff": -0.1442 }

[ { "content": "Mr. Smith calculated the average of 10 three digit numbers. But due to a mistake he reversed the digits of a number and thus his average increased by 19.8 The difference between the unit digit and hundreds digit of that number is :\n\n['A)2', 'B)6', 'C)5', 'D)3', 'E)4']", "role": "user", "uuid": "b2cc59be-4f6a-415b-af02-61b0b5af6c46" }, { "content": "Since the average increased by 29.7 and there were a total of 10 numbers, it means the incorrect number was 198 greater than the correct number.\nSay, the correct number was abc (where a, b and c are the digits of the 3 digit number)\nThen the incorrect number was cba.\n100c + 10b + a - (100a + 10b + c) = 198\n99c - 99a = 99(c - a) = 198\n198 = 99*2 = 99(c - a)\nSo c - a = 2\nAnswer (A)", "role": "assistant", "uuid": "a1d27f25-9105-4f4b-a6f7-d16c433ae219" } ]

{ "coherence": 2.66, "complexity": 1.92, "correctness": 2.35, "helpfulness": 2.61, "instruction-following": 2.57, "safety": 4.89, "verbosity": 1.42, "verbosity-coeff": -0.1427 }

[ { "content": "(√27+√243)/√75=?\n\n['A)2√2', 'B)2√3', 'C)3√2', 'D)3√3', 'E)12/5']", "role": "user", "uuid": "3a9e10d9-d954-4d3f-96d6-7be03f33f9bb" }, { "content": "(√27+√243)/√75\n=(3√3+9√3)/5√3\n=12√3/5√3\n=12/5.\nHence, the correct answer is E", "role": "assistant", "uuid": "6ec2b9f8-6cac-460c-a0a9-02dcc4b71da4" } ]

{ "coherence": 2.98, "complexity": 2.12, "correctness": 2.08, "helpfulness": 2.1, "instruction-following": 3.07, "safety": 4.89, "verbosity": 1.17, "verbosity-coeff": -0.0944 }

[ { "content": "If p is a positive integer and 10p/96 is an integer, then the minimum number of unique prime factors p could have is B:\n\n['A)B=1', 'B)B=2', 'C)B=3', 'D)B=4', 'E)B=5']", "role": "user", "uuid": "4e1b78f9-ea6d-4b24-9174-db5dd3a4bd2d" }, { "content": "10p/96 should resolve to a integer => 5p/48 should resolve to an integer.\nHence p/48 should resolve to a integer.\n48 -- > 2^4 * 3.\nHence p should have atleast 2^4*3 for p/48 to resolve to a int.\nThe unique prime factors in 2^4 * 3 is 2, 3 and hence the answer is B(2).", "role": "assistant", "uuid": "4cb8ebaf-fed0-4ef9-ab9f-06992ec9bc20" } ]

{ "coherence": 2.53, "complexity": 2.2, "correctness": 1.96, "helpfulness": 1.92, "instruction-following": 1.75, "safety": 4.81, "verbosity": 1.38, "verbosity-coeff": -0.172 }

[ { "content": "Find the lowest common multiple of 24, 36 and 40.\n\n['A)120', 'B)240', 'C)360', 'D)480', 'E)530']", "role": "user", "uuid": "75cd2eae-66ff-4681-831a-2925f0d68190" }, { "content": "2 | 24 - 36 - 40\n--------------------\n2 | 12 - 18 - 20\n--------------------\n2 | 6 - 9 - 10\n-------------------\n3 | 3 - 9 - 5\n-------------------\n| 1 - 3 - 5\nL.C.M. = 2 x 2 x 2 x 3 x 3 x 5 = 360.\nAnswer: Option C", "role": "assistant", "uuid": "d9a9d781-d347-4865-a8fd-ea0df6678a86" } ]

{ "coherence": 3.05, "complexity": 1.48, "correctness": 2.74, "helpfulness": 2.98, "instruction-following": 3.02, "safety": 5.52, "verbosity": 1.22, "verbosity-coeff": -0.2069 }

[ { "content": "In a certain province in France there are 15 cities. If a single road segment connects only two cities, how many road segments are required in order to connect the cities so that each city is connected to all other cities with a single road segment?\n\n['A)30', 'B)105', 'C)330', 'D)14!', 'E)15!']", "role": "user", "uuid": "388fac40-8730-4b08-b508-c0e663454dcf" }, { "content": "1 city needs 14 roads to connect directly to the rest => 15 city needs 15*14 roads.\nOne road is counted twice => the number of road needed is 15*14/2 = 105\nAnswer B", "role": "assistant", "uuid": "9f4eb000-2c76-4a65-8a22-22c5565c9a19" } ]

{ "coherence": 2.94, "complexity": 1.38, "correctness": 2.39, "helpfulness": 2.45, "instruction-following": 2.66, "safety": 6.1, "verbosity": 1.48, "verbosity-coeff": -0.2332 }

[ { "content": "Fresh dates contain 90% water while dry dates contain 28% water . How many kg of dry dates can be obtained from 36kg of fresh dates ?\n\n['A)5Kg', 'B)10Kg', 'C)12 Kg', 'D)16Kg', 'E)26Kg']", "role": "user", "uuid": "a8e2ad10-7f99-4333-8f58-6b42c30f92f4" }, { "content": "36 kilograms of fresh dates contain 0.1*36=3.6 kilograms of non-water.\nDry dates obtained from these fresh dates will contain the same amount of non-water and we are told that this amount should be 72% of the dry dates, thus x*0.72=3.6 --> x=5 kilograms.\nAnswer: A.", "role": "assistant", "uuid": "565cd909-ddd5-4d74-a01f-3f7614787d27" } ]

{ "coherence": 3.31, "complexity": 1.29, "correctness": 2.49, "helpfulness": 2.59, "instruction-following": 3.11, "safety": 5.95, "verbosity": 0.74, "verbosity-coeff": -0.0992 }

[ { "content": "A car covers a distance of 624 km in 6 ½ hours. Find its speed?\n\n['A)104', 'B)277', 'C)298', 'D)269', 'E)213']", "role": "user", "uuid": "1b81c65f-e6d2-4996-bcc5-01c23e1ddaca" }, { "content": "624/6 = 104 kmph\nAnswer:A", "role": "assistant", "uuid": "68c8f216-8463-4abb-9dac-4ef5f868d4b1" } ]

{ "coherence": 2.82, "complexity": 0.45, "correctness": 2.45, "helpfulness": 2.55, "instruction-following": 3.11, "safety": 4.81, "verbosity": 0.5, "verbosity-coeff": -0.1083 }

[ { "content": "Having scored 99 runs in the 19th inning, a cricketer increases his average score by 4. What will be his average score after 19 innings?\n\n['A)28', 'B)27', 'C)26', 'D)22', 'E)24']", "role": "user", "uuid": "139b195d-1522-4ba8-94ae-9d3e1abe5beb" }, { "content": "Explanation :\nLet the average score of the first 18 innings be n\n18n + 99 = 19(n+4)=> n = 23\nSo, Average score after 19th innings = x+4 =27.\nAnswer : B", "role": "assistant", "uuid": "9c88bf03-406f-4012-ba73-570b56e8c8a8" } ]

{ "coherence": 2.62, "complexity": 1.57, "correctness": 2.2, "helpfulness": 2.51, "instruction-following": 2.84, "safety": 5.55, "verbosity": 1.22, "verbosity-coeff": -0.1186 }

[ { "content": "If the sides of a square are multiplied by sqrt(2), the area of the original square is how many times as large as the area of the resultant square?\n\n['A)2%', 'B)4%', 'C)50%', 'D)100%', 'E)200%']", "role": "user", "uuid": "af554815-1cd1-4bd1-8724-321b4ec86af1" }, { "content": "Let x be the original length of one side.\nThen the original area is x^2.\nThe new square has sides of length sqrt(2)*x, so the area is 2x^2.\nThe area of the original square is 1/2 = 50% times the area of the new square.\nThe answer is C.", "role": "assistant", "uuid": "7941cc28-8dcc-4194-a97d-dc2e1030f846" } ]

{ "coherence": 3.46, "complexity": 2.14, "correctness": 2.8, "helpfulness": 2.74, "instruction-following": 3.5, "safety": 5.83, "verbosity": 1.08, "verbosity-coeff": -0.1735 }

[ { "content": "The difference between the ages of two persons is 10 years. Fifteen years ago, the elder one was twice as old as the younger one. The present age of the elder person is\n\n['A)25 years', 'B)30 years', 'C)35 years', 'D)40 years', 'E)None']", "role": "user", "uuid": "feb14ac0-cb73-480b-aa7d-290d7ab6d222" }, { "content": "Sol.\nLet their ages of x years and (x + 10) years respectively.\nThen, (x + 10) - 15 = 2(x - 15)\n⇔ x - 5 = 2x - 30\n⇔ x = 25.\n∴ Present age of the elder person = (x + 10)\n= 35 years.\nAnswer C", "role": "assistant", "uuid": "13bf12ce-1027-4b3a-9e5d-3c4a9c0eb569" } ]

{ "coherence": 3, "complexity": 1.79, "correctness": 2.68, "helpfulness": 2.8, "instruction-following": 4.03, "safety": 3.88, "verbosity": 1.61, "verbosity-coeff": -0.1206 }

[ { "content": "Two vessels having volumes in the ratio 3:5 are filled with water and milk solutions. The ratio of milk and water in the two vessels are 5:1 and 6:4 respectively. If the contents of both the vessel are empties into a larger vessel, find the ratio of milk and water in the larger vessel.\n\n['A)12:5', 'B)11:5', 'C)13:5', 'D)14:5', 'E)9:5']", "role": "user", "uuid": "d811e36d-3cdd-425e-913e-44762c1466ca" }, { "content": "Vessel A = 300 gallons --> milk = 250, water = 50;\nVessel B = 500 gallons --> milk = 300, water = 200;\nVessel A + B = 800 gallons --> milk = 550, water 250\nThe ratio =550/250-->11:5\nAnswer: B", "role": "assistant", "uuid": "ee332f19-295f-4224-b417-7f3e5f87774b" } ]

{ "coherence": 2.84, "complexity": 1.31, "correctness": 2.2, "helpfulness": 2.51, "instruction-following": 2.76, "safety": 5.4, "verbosity": 0.85, "verbosity-coeff": -0.144 }

[ { "content": "If the average of 5 positive integers is 60 and the difference between the largest and the smallest of these 5 numbers is 10, what is the maximum value possible for the largest of these 5 integers?\n\n['A)50', 'B)52', 'C)49', 'D)68', 'E)74']", "role": "user", "uuid": "ea7deef8-598e-4255-85da-cec81b110eaa" }, { "content": "Sum of 5 Integer (a, b, c, d, e) = 5*60 = 300\ne - a = 10\ni.e. e = a+10\nFor e to be maximum remaining 4 MUST be as small as possible\nSince smallest of 5 numbers is a so to minimize other numbers we can take them equal to the smallest of 5 numbers\ni.e. a+a+a+a+(a+10) = 300\ni.e. 5a = 290\ni.e. a = 58\ni.e. Largest e = 58+10 = 68\nAnswer: option D", "role": "assistant", "uuid": "02fe62b0-e909-42c0-9eb2-7fcd27d70253" } ]

{ "coherence": 2.96, "complexity": 1.68, "correctness": 2.21, "helpfulness": 2.45, "instruction-following": 2.61, "safety": 6.41, "verbosity": 1.22, "verbosity-coeff": -0.2359 }