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[ { "content": "One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in:\n\n['A)144 min', 'B)145 min', 'C)150 min', 'D)200 min', 'E)250 min']", "role": "user", "uuid": "15f79f1b-6ce1-4cc0-84e9-b69d8310b9a1" }, { "content": "slower pipe alone fill the tank = x\nfaster pipe will fill in x/3 min\n1/x+3/x=1/36\nx=144 min\nANSWER A", "role": "assistant", "uuid": "8bc1da01-0d48-46be-9ba5-a4b9762650d4" } ]

{ "coherence": 2.59, "complexity": 1.44, "correctness": 2.53, "helpfulness": 2.47, "instruction-following": 3.25, "safety": 4.5, "verbosity": 0.99, "verbosity-coeff": -0.1155 }

[ { "content": "In 1998 the profits of company N were 10 percent of revenues. In 1999, the revenues of company N fell by 30 percent, but profits were 16 percent of revenues. The profits in 1999 were what percent of the profits in 1998?\n\n['A)80%', 'B)105%', 'C)120%', 'D)112%', 'E)138%']", "role": "user", "uuid": "b0a54f2a-43d1-4c0d-9eb2-ae496c922a09" }, { "content": "0,112R = x/100*0.1R\nAnswer D", "role": "assistant", "uuid": "89b606ec-5992-4d82-a7f9-55f10b92d157" } ]

{ "coherence": 1.93, "complexity": 1.14, "correctness": 1.11, "helpfulness": 0.97, "instruction-following": 0.89, "safety": 5.95, "verbosity": 0.24, "verbosity-coeff": -0.2188 }

[ { "content": "Two trains running in the same direction with a speed of 60kph and 50kph having lengths of 200m each. How long it will take the trains to completely pass each other(in seconds)?\n\n['A)13.09', 'B)32.17', 'C)54.9', 'D)112.98', 'E)143.88']", "role": "user", "uuid": "45f8f0cf-bad4-45c9-a86c-9700b8cf24a7" }, { "content": "Relative speed of trains with respect to each other=60-50=10kph=2.78m/s\nDistance need to be covered=200+200=400\nTime taken to pass each other=400/2.78=143.88s\nAnswer: E", "role": "assistant", "uuid": "ed5c9f76-7ad1-4904-ad1d-6524b69667d3" } ]

{ "coherence": 2.53, "complexity": 1.5, "correctness": 1.76, "helpfulness": 1.78, "instruction-following": 3.39, "safety": 4.97, "verbosity": 0.84, "verbosity-coeff": -0.1178 }

[ { "content": "A train 210 m long, running with a speed of 63 km/hr will pass a tree in?\n\n['A)15 sec', 'B)16 sec', 'C)18 sec', 'D)12 sec', 'E)25 sec']", "role": "user", "uuid": "cdea2e82-ff3b-4fc1-a731-382c7b6484ae" }, { "content": "Speed = 63 * 5/18 = 35/2 m/sec\nTime taken = 210 * 2/35 = 12 sec\nANSWER: D", "role": "assistant", "uuid": "7e88b741-9983-4643-a65b-12678f86b45c" } ]

{ "coherence": 2.9, "complexity": 1.48, "correctness": 2.98, "helpfulness": 3.05, "instruction-following": 4.3, "safety": 5.36, "verbosity": 1.48, "verbosity-coeff": -0.1114 }

[ { "content": "The reduction in the speed of an engine is directly proportional to the square of the number of bogies attached to it. The speed of the train is 100 km/hr when there are 4 bogies and 55 km/hr when there are 5 bogies. What is the maximum number of bogies that can be attached to the train so that, even with those many numbers of bogies, it can just move?\n\n['A)3', 'B)4', 'C)5', 'D)6', 'E)7']", "role": "user", "uuid": "3adc0f29-c62a-4eb5-bcf1-a860367e77a8" }, { "content": "We know that S=Smax−K×(bogies)2\nWhen there are 4 bogies speed of the train is 100km/hr 100=Smax−K×(4)2 ⇒100=Smax−K×16.......(1)\nWhen there are 5 bogies speed of the train is 55km/hr\n55=Smax−K×(5)2⇒ 55 = Smax−K×25 ........(2)\n(2) - (1) gives 9K=45⇒K=5\nBy substituting K = 5 in either (1) or (2) we can find the maximum speed of the train = 180 km/hr\nAssume, for N number of bogies the train does not move.\n⇒0=180−5(N)2⇒N=6\nIf the engine is attached to 6 bogies, it does not move. If we want the train to move we need to attach maximum of 5 bogies\nAnswer C", "role": "assistant", "uuid": "c61f4868-5f16-4aef-8787-f836f850fddf" } ]

{ "coherence": 2.53, "complexity": 1.78, "correctness": 2.18, "helpfulness": 2.2, "instruction-following": 3.48, "safety": 5.36, "verbosity": 1.65, "verbosity-coeff": -0.1594 }

[ { "content": "A firm has 4 senior partners and 6 junior partners. How many different groups F of 3 partners can be formed in which at least one member of the group is a senior partner. (2 groups are considered different if at least one group member is different)\n\n['A)48', 'B)100', 'C)120', 'D)288', 'E)600']", "role": "user", "uuid": "b85c4b87-755b-4cb9-a153-6116e152657c" }, { "content": "What seems to work as well, though its tougher to come up with this solution:\n(10*9*8) * 2/3 + (10*9*4)*1/3 = 600. Divided by all possible permutations (=3!) yields 100.\nExplanation: For the first spot you have 10 possible canditates, for the 2nd 9. For the 3rd spot you need to differentiate if a senior partner has been picked for one of the first 2 spots or not. If yes, then you can pick one of the 8 remaining guys, so 10*9*8. If no senior partner has been picked yet, you need 10*9*4.\nNow you need to weight the 2 cases with the corresponding probabilities: probability of no senior partner being picked in the first 2 draws = 6/10*5/9=1/3, so you weight 10*9*4 with 1/3. For the complementary case (senior partner was picked in the first 2 draws) you just take the complementary prob (1-1/3)= 2/3 and weight 10*9*8 with it.\nNow you just need to divide the answer (600) by the number of different positions (=3!) and get F=600/6=100.B", "role": "assistant", "uuid": "b998b779-b511-4f98-a2ad-d0b6df74aadc" } ]

{ "coherence": 2.64, "complexity": 1.94, "correctness": 2.29, "helpfulness": 2.33, "instruction-following": 2.68, "safety": 5.28, "verbosity": 1.45, "verbosity-coeff": -0.1758 }

[ { "content": "The average age 10 members of a committee are the same as it was 2 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number?\n\n['A)14 years', 'B)17 years', 'C)20 years', 'D)12 years', 'E)11 years']", "role": "user", "uuid": "3accdaff-6041-4672-9611-b1cd0b835fc6" }, { "content": "10 * 2\n= 20\nAnswer:C", "role": "assistant", "uuid": "bf2a4c8b-fcb1-42a0-85b6-11bdc6398e76" } ]

{ "coherence": 2.57, "complexity": 0.87, "correctness": 1.73, "helpfulness": 1.75, "instruction-following": 1.99, "safety": 5.09, "verbosity": 0.62, "verbosity-coeff": -0.1776 }

[ { "content": "The average of 9 numbers is 104. Average of the first 5 of them is 99 and that of the last 5 is 100. Find the 5th number?\n\n['A)46', 'B)59', 'C)63', 'D)75', 'E)88']", "role": "user", "uuid": "1d419148-82b4-40f1-8324-85e2942e0b56" }, { "content": "Sum of all the 9 numbers = 9 * 104 = 936\rSum of the first 5 of them = 5 * 99 = 495\rSum of the last 5 of them = 5 * 100 = 500\rSo, the 5th number = 495 + 500 - 936\r= 59.\rAnswer: B", "role": "assistant", "uuid": "35aacabc-9302-4170-8f30-1bdaf9adbf12" } ]

{ "coherence": 2.84, "complexity": 1.17, "correctness": 2.02, "helpfulness": 2.29, "instruction-following": 3.13, "safety": 5.52, "verbosity": 0.76, "verbosity-coeff": -0.1212 }

[ { "content": "0.35 represents what percent of 0.007?\n\n['A)0.05%', 'B)0.5%', 'C)5%', 'D)500%', 'E)5000%']", "role": "user", "uuid": "1de7e31b-8b33-4c2c-b3fc-7801a6621934" }, { "content": "One more method\n0.35 represents what percent of 0.007?\nAdjusting the decimal\n350 represents what percent of 7?\nDivide by 7\n50 represents what percent of 1?\nAnswer = 50*100 = 5000%\nANSWER:E", "role": "assistant", "uuid": "aaea9562-6869-4c99-806c-ca420e705485" } ]

{ "coherence": 2.72, "complexity": 1.95, "correctness": 2.41, "helpfulness": 2.06, "instruction-following": 3.13, "safety": 4.54, "verbosity": 1.59, "verbosity-coeff": -0.1624 }

[ { "content": "What is the product of all positive factors of 12?\n\n['A)39', 'B)324', 'C)1728', 'D)3042', 'E)5832']", "role": "user", "uuid": "2da9d7bd-d325-438c-b1cc-e19a177ae486" }, { "content": "Positive factors of 12 are 1, 2, 3, 4, 6, 12.\nSo product is: 12*6*4*3*2*1 = 1728\nAnswer: C", "role": "assistant", "uuid": "d60f3bf6-86e2-4cb2-914b-ab1c5e45dfc4" } ]

{ "coherence": 3.13, "complexity": 1.54, "correctness": 2.55, "helpfulness": 2.76, "instruction-following": 3.41, "safety": 5.12, "verbosity": 0.59, "verbosity-coeff": -0.2324 }

[ { "content": "A train running at the speed of 60 km/hr crosses a pole in 15 seconds. What is the length of the train?\n\n['A)187 m', 'B)250 m', 'C)876 m', 'D)150 m', 'E)267 m']", "role": "user", "uuid": "6c305039-bfc3-4625-8815-5dc8f1a20fd7" }, { "content": "Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train\n= (Speed x Time)\n= (50/3 * 15) m\n= 250 m.\nAnswer: B", "role": "assistant", "uuid": "476e2e9f-e4b6-43fe-b759-5eb50e632699" } ]

{ "coherence": 2.76, "complexity": 1.17, "correctness": 2.29, "helpfulness": 2.49, "instruction-following": 3.97, "safety": 4.93, "verbosity": 0.64, "verbosity-coeff": -0.1104 }

[ { "content": "At a speed of 40 miles per hour, a certain car uses 1 gallon of gasoline every 40 miles. If the car starts with a full 12 gallon tank of gasoline and travels for 5 hours at 40 miles per hour, the amount of gasoline used would be what fraction of a full tank?\n\n['A)3/25', 'B)5/12', 'C)7/12', 'D)2/3', 'E)25/36']", "role": "user", "uuid": "5f2d3e25-164d-4ab8-bdff-40109f8d2a26" }, { "content": "Gas used = (5 hours)*(40 miles/hour)*(1 gallon/40 miles) = 5 gallons\nPortion used = (5) / 12 = 5/12\nAns B", "role": "assistant", "uuid": "fe7c6219-d735-4a33-a1f7-ca2b4f0c5267" } ]

{ "coherence": 3.04, "complexity": 1.12, "correctness": 2.66, "helpfulness": 2.72, "instruction-following": 3.25, "safety": 5.71, "verbosity": 0.87, "verbosity-coeff": -0.1972 }

[ { "content": "20/25 = 4/5 . which method did you use to determine whether this proportion is true or false?\n\n['A)true', 'B)neutral', 'C)false', 'D)not sure', 'E)none']", "role": "user", "uuid": "20128538-6f2e-4b74-ae35-e0dcfe69fff1" }, { "content": "20/25= 4/5 cross multiplication: 20 * 5= 100, 4 * 25 =100,\nwe see that 100 are not equal to 100. so there is proportion. corrcet answer: (A)", "role": "assistant", "uuid": "9a0c3696-6d98-4ad2-a87d-583da818f7a6" } ]

{ "coherence": 2.43, "complexity": 1.8, "correctness": 1.6, "helpfulness": 1.54, "instruction-following": 2.2, "safety": 3.72, "verbosity": 1.46, "verbosity-coeff": -0.0918 }

[ { "content": "A and B can do a piece of work in 3 days, B and C in 4 days, C and A in 6 days. How long will C take to do it?\n\n['A)33 days', 'B)27 days', 'C)24 days', 'D)18 days', 'E)17 days']", "role": "user", "uuid": "4ff355bf-46a3-4724-86e4-3bc71e14da43" }, { "content": "2c = 1/4 + 1/6 – 1/3 = 1/12\nc = 1/24 => 24 days\nAnswer: C", "role": "assistant", "uuid": "2c39b219-b474-4c61-a8d2-30bbea7aaf98" } ]

{ "coherence": 2.66, "complexity": 1.07, "correctness": 2.12, "helpfulness": 2.29, "instruction-following": 3.17, "safety": 6.1, "verbosity": 0.19, "verbosity-coeff": -0.11 }

[ { "content": "Express a speed of 60 kmph in meters per second?\n\n['A)10 mps', 'B)16.67 mps', 'C)97.67 mps', 'D)17.67 mps', 'E)18 mps']", "role": "user", "uuid": "6d932818-cc9c-4c04-bc67-c9c644df95dd" }, { "content": "60 * 5/18\n= 16.67 mps\nAnswer: B", "role": "assistant", "uuid": "7289031a-2eb1-439e-82c0-700d30ae3302" } ]

{ "coherence": 2.86, "complexity": 1.21, "correctness": 2.61, "helpfulness": 2.84, "instruction-following": 3.88, "safety": 4.73, "verbosity": 0.56, "verbosity-coeff": -0.1054 }

[ { "content": "If (a-3)(b-2) =0, which of the following must be true ?\nI. a=3 and b=2\nII. if a is not = 3, then b=2\nIII. if a=3, then b is not=2\n\n['A)I only', 'B)II only', 'C)III only', 'D)I and II', 'E)II and III']", "role": "user", "uuid": "90d8cdf9-8413-4328-a236-7467eb2314eb" }, { "content": "(a-3)(b-2)=0\nSo either a=3 or b=2 or both. It is 'or' not 'and', so it could be any of the three possibilities. Thus I and III are not necessarily true.\nThe answer is B.", "role": "assistant", "uuid": "790c425a-75f3-4b67-af0f-8ff9040f0598" } ]

{ "coherence": 2.94, "complexity": 1.97, "correctness": 2.16, "helpfulness": 2.2, "instruction-following": 2.47, "safety": 5.59, "verbosity": 1.12, "verbosity-coeff": -0.2046 }

[ { "content": "A photography dealer ordered 60 Model X cameras to be sold for $250 each, which represents a 10 percent markup over the dealer’s initial cost for each camera. Of the cameras ordered, 6 were never sold and were returned to the manufacturer for a refund of 50 percent of the dealer's initial cost. What was the dealer's approximate profit or loss as a percent of the dealer’s initial cost for the 60 cameras?\n\n['A)7% loss', 'B)13% loss', 'C)5% profit', 'D)13% profit', 'E)15% profit']", "role": "user", "uuid": "a5e39be0-14b6-48eb-923b-3f0be843524d" }, { "content": "Total cost 60*($250/1.1)=54.54*250;\n# of cameras sold is 60-5=55 total revenue is 55*250;\n# of cameras returned is 6 total refund 6*(250/1.1)*0.5;\nSo, total income 55*250+ 6*(250/1.1)*0.5\nThe dealer's approximate profit is (55*250+ 6*(250/1.1)*0.5-54.54*250)/(54.54*250)*100=5%\nAnswer: C.", "role": "assistant", "uuid": "c01c8673-eabc-4f42-889b-137501cfa0c5" } ]

{ "coherence": 2.59, "complexity": 1.59, "correctness": 1.74, "helpfulness": 1.73, "instruction-following": 1.88, "safety": 3.89, "verbosity": 0.97, "verbosity-coeff": -0.211 }

[ { "content": "Of the 420 members at a health club, 260 use the weight room and 300 use the pool. If at least 60 of the members do not use either, then the number of members using both the weight room and the pool must be between:\n\n['A)200 to 260', 'B)160 to 260', 'C)220 to 260', 'D)220 to 300', 'E)40 to 100']", "role": "user", "uuid": "b60faa7a-5a98-414c-8be5-011197368e99" }, { "content": "W=260\nP=300\nALL=420\nN(NEITHER)=AT LEAST 60\nBOTH=?\nW+P-BOTH+N=ALL\n260+300-BOTH+60=420\nBOTH=200\nnow pay attention to the fact, that both at most can be 260, since W=260\nso, the answer is A", "role": "assistant", "uuid": "d7e5577b-4a91-4bc2-94e0-f33beb64ccae" } ]

{ "coherence": 2.8, "complexity": 1.37, "correctness": 2.29, "helpfulness": 2.37, "instruction-following": 2.66, "safety": 5.01, "verbosity": 1.22, "verbosity-coeff": -0.14 }

[ { "content": "what is the remainder when 9614241 is divided by 99\n\n['A)50', 'B)65', 'C)45', 'D)54', 'E)60']", "role": "user", "uuid": "e5a43535-78ea-48d5-807d-0f113333c6c8" }, { "content": "9614241 / 99\n9614241 / 9*11\n1068249 / 11 => rem = 6\nwe have cancelled it by 9\nreqd remainder = 9*6 = 54\nANSWER:D", "role": "assistant", "uuid": "849e2f61-1db8-43f8-a101-e5f594d80a64" } ]

{ "coherence": 2.59, "complexity": 1.62, "correctness": 1.99, "helpfulness": 1.99, "instruction-following": 2.53, "safety": 4.73, "verbosity": 1.21, "verbosity-coeff": -0.13 }

[ { "content": "A certain truck uses 18 gallons of diesel fuel in traveling 230 miles. In order for the truck to travel the same distance using 10 gallons of diesel fuel, by how many miles per gallon must the truck’s fuel mileage be increased?\n\n['A)8', 'B)9', 'C)12', 'D)15', 'E)27']", "role": "user", "uuid": "476e8d6f-bf91-40a6-a8cd-47638fc762d8" }, { "content": "There are two sets 18G1 gallons and 10G2 gallons details given.\n18 gallons covering 230 miles\nThen 1 G1 is used to cover 15 miles.\nNow for 10 G2 covering 230 miles.\nthen 1 G2 is used to cover 23 miles.\nThere must 23 - 15 = 8 miles per gallon increment is needed for 10 gallons to improve the mileage to cover 230 miles.\nIMO A is correct answer.", "role": "assistant", "uuid": "76d4d162-0156-4569-b82d-164c483c8ac7" } ]

{ "coherence": 2.9, "complexity": 1.28, "correctness": 2.06, "helpfulness": 2.25, "instruction-following": 1.96, "safety": 4.7, "verbosity": 0.71, "verbosity-coeff": -0.2131 }

[ { "content": "The length of rectangle is thrice its breadth and its perimeter is 40 m, find the area of the rectangle?\n\n['A)432', 'B)212', 'C)75', 'D)992', 'E)212']", "role": "user", "uuid": "7129a7d2-5739-475c-910f-47fe4f93792a" }, { "content": "2(3x + x) = 40\nl = 15 b = 5\nlb = 15 * 5 = 75\nAnswer:C", "role": "assistant", "uuid": "c26cdbc3-8f0f-4d1c-b294-d447b8ecd9de" } ]

{ "coherence": 2.66, "complexity": 0.9, "correctness": 2.18, "helpfulness": 2.25, "instruction-following": 3.27, "safety": 5.63, "verbosity": 0.3, "verbosity-coeff": -0.0947 }

[ { "content": "Two right circular cylinders of equal volumes have their heights in the ratio 1:2. Find the ratio of their radii.\n\n['A)√2:6', 'B)√2:1', 'C)√2:1', 'D)√2:2', 'E)√2:4']", "role": "user", "uuid": "3f75c4f1-37d4-4e70-89cf-d400fc6974cd" }, { "content": "Let their heights be h and 2h and radii be r and R respectively then.\nπr2h=πR2(2h)=>r2R2=2hh=21=>rR=2–√1=>r:R=√2:1\nAnswer:C", "role": "assistant", "uuid": "98624a1e-96f7-431d-9369-d8d58d2de7a2" } ]

{ "coherence": 2.31, "complexity": 1.94, "correctness": 1.72, "helpfulness": 1.65, "instruction-following": 3, "safety": 5.4, "verbosity": 0.93, "verbosity-coeff": -0.1511 }

[ { "content": "If you divide 7^115 by 5, which remainder do you get?\n\n['A)0', 'B)1', 'C)2', 'D)3', 'E)4']", "role": "user", "uuid": "b69c12ff-0d34-4aab-84de-ef7a33a46864" }, { "content": "The units digit of 7^1 is 7.\nThe units digit of 7^2 is 9.\nThe units digit of 7^3 is 3.\nThe units digit of 7^4 is 1.\nThe units digit of 7^5 is 7.\netc...\nThe units digit of 7^n repeats in blocks of 4: {7, 9, 3, 1}\nThe remainder of 115/4 is 3.\nSo the units digit of 7^115 is 3.\nThe remainder of 7^115 / 5 is 3.\nThe answer is D.", "role": "assistant", "uuid": "7ddb1e40-3277-4a7e-b052-a0558298fbdb" } ]

{ "coherence": 3.46, "complexity": 1.99, "correctness": 3.04, "helpfulness": 2.88, "instruction-following": 3.43, "safety": 5.59, "verbosity": 1.53, "verbosity-coeff": -0.1162 }

[ { "content": "For any number Z, Z* is defined as the greatest positive even integer less than or equal to y. What is the value of 6.30 – 6.30*?\n\n['A)1.5', 'B)0.5', 'C)6.25', 'D)0.25', 'E)0.3']", "role": "user", "uuid": "ef7f26ae-67f5-4660-aa3d-0b6f50e605d5" }, { "content": "Since Z* is defined as the greatest positive even integer less than or equal to Z, then 6.30* =6 (the greatest positive even integer less than or equal to 6.30 is 6).\nHence, 6.30 – 6.30* = 6.30 - 6 = 0.30\nAnswer: E.", "role": "assistant", "uuid": "9db6b7bd-9a7c-4a24-8f98-2bab05af6b96" } ]

{ "coherence": 3.33, "complexity": 1.33, "correctness": 2.84, "helpfulness": 3.07, "instruction-following": 3.15, "safety": 4.46, "verbosity": 1.2, "verbosity-coeff": -0.115 }

[ { "content": "If it is assumed that 70 percent of those who receive a questionnaire by mail will respond and 300 responses are needed, what is the minimum number of questionnaires that should be mailed?\n\n['A)400', 'B)428.5', 'C)480', 'D)500', 'E)600']", "role": "user", "uuid": "a007709c-d941-43e1-b915-9373163fffcb" }, { "content": "Minimum no of mail to be sent for getting 300 responses at 70%\n= 300/0.7 = 428.5\nOption B", "role": "assistant", "uuid": "93692794-180d-48d6-ba87-9289cbffc046" } ]

{ "coherence": 2.82, "complexity": 0.79, "correctness": 1.94, "helpfulness": 2.23, "instruction-following": 2.98, "safety": 4.81, "verbosity": 0.88, "verbosity-coeff": -0.1628 }

[ { "content": "Marla is hanging a banner diagonally across a rectangular room. The length of the room is 2 feet shorter than its width. If the total area of the room is 120 square feet, what is the length of the banner (in feet)?\n\n['A)Between 13 and 14', 'B)Between 14 and 15', 'C)Between 15 and 16', 'D)Between 16 and 17', 'E)Between 17 and 18']", "role": "user", "uuid": "ec0d587e-6d18-4fcd-9eb4-b0793ce1a399" }, { "content": "To solve this, we first need to set up an equation for the area of the room. If x is the width, then we have\nx(x - 2) = 120. By putting the equation in standard form, we get x^2-2x-120=0. By using the quadratic formula, we get roots of -10 and 12. We know that x is the width, and x-2 is the length, so by using the roots, we get 12 as the width (x), and 10 as the length (x-2).\nOnce we have this, we can use the Pythagorean Theorem to solve for the diagonal. Plugging in the length and width, we will get d^2=12^2+10^2\n=144+100\n=244\nThe square root of 244 is less than 16, since 16^2 = 256. Going down a number, we can compute 15^2 = 225 < 224. Therefore, the length of the diagonal must be between 15 and 16.\nThe correct answer is C.", "role": "assistant", "uuid": "24eebb16-2826-4b86-a787-345a4c82968c" } ]

{ "coherence": 2.92, "complexity": 1.91, "correctness": 2.2, "helpfulness": 2.31, "instruction-following": 3.21, "safety": 4.89, "verbosity": 1.67, "verbosity-coeff": -0.2098 }

[ { "content": "If (5)(x^2) has three different prime factors, at most how many different prime factors does x have?\n\n['A)1', 'B)2', 'C)3', 'D)4', 'E)5']", "role": "user", "uuid": "eb472dc2-bdf1-4f53-8202-4ba145a61115" }, { "content": "x can have at most 3 prime factors, namely the prime factor 5 plus two others.\nIf x had more than this number of prime factors, then (5)(x^2) would have more than 3 prime factors.\nThe answer is C.", "role": "assistant", "uuid": "4e8131e0-4164-4cc0-8b49-3c01f1c06311" } ]

{ "coherence": 3.17, "complexity": 1.74, "correctness": 2.33, "helpfulness": 2.29, "instruction-following": 2.62, "safety": 5.59, "verbosity": 1.32, "verbosity-coeff": -0.2207 }

[ { "content": "Today Chris ate 15 jellybeans. Bella ate 2/3 of the jellybeans Chris did, Frances ate 5 more jellybeans than Bella did , and Sandhya ate 20% more than Frances. How many jellybeans did Sandhya eat?\n\n['A)18', 'B)20', 'C)13', 'D)25', 'E)15']", "role": "user", "uuid": "e395501b-b19a-4b80-8853-04e83e3521af" }, { "content": "A\n13\nChris ate 15 jellybeans\nBella ate 2/3 of the jellybeans Chris did.\nBella= 2/3 x 15\n=10\nFrances ate 5 more jellybeans than Bella.\nFrances= 10+5 jellybeans.\n=15\nSandhya ate 20% more jellybeans than Frances.\nSandhya = 15 + 15 × 20%\n= 15 + 15 × 0.20\n= 15 + 3\n= 18\nSandhya ate 18 jellybeans.\nThe correct answer is A.", "role": "assistant", "uuid": "09aac68e-6a92-41af-8a56-76c4d1aacd18" } ]

{ "coherence": 3.09, "complexity": 1.37, "correctness": 2.33, "helpfulness": 2.57, "instruction-following": 3.04, "safety": 5.4, "verbosity": 1.4, "verbosity-coeff": -0.1245 }

[ { "content": "The difference of 2 digit no. & the number obtained by interchanging the digits is 36. What is the difference the sum and the number if the ratio between the digits of the number is 1:2 ?\n\n['A)6', 'B)8', 'C)9', 'D)10', 'E)14']", "role": "user", "uuid": "2dd4d8d8-9cbc-40fa-b794-f7fa1ffd6335" }, { "content": "Let the number be xy.\nGiven xy – yx = 36.\nThis means the number is greater is than the number got on reversing the digits.\nThis shows that the ten’s digit x > unit digit y.\nAlso given ratio between digits is 1 : 2 => x = 2y\n(10x + y) – (10y +x) = 36 => x – y = 4 => 2y – y =4.\nHence, (x + y) – (x – y) = 3y – y = 2y = 8\nB", "role": "assistant", "uuid": "128e0368-9077-4a7b-b0a4-d6f7e512ea80" } ]

{ "coherence": 2.18, "complexity": 1.95, "correctness": 1.63, "helpfulness": 1.71, "instruction-following": 2.29, "safety": 6.14, "verbosity": 0.85, "verbosity-coeff": -0.1434 }

[ { "content": "3 men and 7 women can complete a work in 10 days . But 4 men and 6 women need 8 days to complete the same work . In how many days will 10 women complete the same work?\n\n['A)40', 'B)45', 'C)50', 'D)35', 'E)30']", "role": "user", "uuid": "f18d908f-1360-4bb8-83b8-3639be02e3c2" }, { "content": "Work done by 4 men and 6 women in 1 day = 1/8\nWork done by 3 men and 7 women in 1 day = 1/10\nLet 1 man does m work in 1 day and 1 woman does w work in 1 day. The above equations can be written as\n4m + 6w = 1/8 ---(1)\n3m + 7w = 1/10 ---(2)\nSolving equation (1) and (2) , we get m=11/400 and w=1/400\nAmount of work 10 women can do in a day = 10 × (1/400) = 1/40\nIe, 10 women can complete the work in 40 days\nAnswer is A.", "role": "assistant", "uuid": "796ed340-3170-44dd-952f-86bd0591e47c" } ]

{ "coherence": 3.02, "complexity": 1.87, "correctness": 2.68, "helpfulness": 2.7, "instruction-following": 3.7, "safety": 5.48, "verbosity": 1.36, "verbosity-coeff": -0.1237 }

[ { "content": "The average mark of the students of a class in a particular exam is 80. If 5 students whose average mark in that exam is 50 are excluded, the average mark of the remaining will be 90. Find the number of students who wrote the exam.\n\n['A)20', 'B)27', 'C)25', 'D)99', 'E)21']", "role": "user", "uuid": "b269509e-b968-4ee7-aa73-38d5f4302de9" }, { "content": "Let the number of students who wrote the exam be x.\nTotal marks of students = 80 x.\nTotal marks of (x - 5) students = 90(x - 5)\n80x - (5 * 50) = 90(x - 5)\n200 = 10x => x = 20.Answer: A", "role": "assistant", "uuid": "ccb43d30-82d8-441c-8ff9-005aafd3cd5b" } ]

{ "coherence": 2.88, "complexity": 1.53, "correctness": 1.88, "helpfulness": 2.2, "instruction-following": 2.7, "safety": 4.85, "verbosity": 1.24, "verbosity-coeff": -0.1477 }

[ { "content": "If three distinct positive divisors of 128 are randomly selected, what is the probability that their sum will be less than 64?\n\n['A)1/3', 'B)3/7', 'C)5/14', 'D)9/28', 'E)21/56']", "role": "user", "uuid": "b8810659-1d41-47a7-8665-442d496b2f78" }, { "content": "The positive divisors are 1, 2, 4, 8, 16, 32, 64, 128.\nIf any of the first six are chosen, the sum will be less than 64.\nP(sum is less than 64) = 6/8 * 5/7 * 4/6 = 20/56 = 5/14\nThe answer is C.", "role": "assistant", "uuid": "329f0151-da9f-4ef9-9d7d-b38dfa0017a8" } ]

{ "coherence": 3.11, "complexity": 1.46, "correctness": 2.59, "helpfulness": 2.7, "instruction-following": 3.11, "safety": 5.12, "verbosity": 1.13, "verbosity-coeff": -0.2647 }

[ { "content": "There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is?\n\n['A)60', 'B)70', 'C)80', 'D)90', 'E)100']", "role": "user", "uuid": "a96065b4-6edf-4ec0-ab97-112fdffa6240" }, { "content": "Let the number of students in rooms A and B be x and y respectively.\nThen, x - 10 = y + 10 x - y = 20 .... (i)\nand x + 20 = 2(y - 20) x - 2y = -60 .... (ii)\nSolving (i) and (ii) we get: x = 100 , y = 80.\nThe required answer A = 100.\nE)", "role": "assistant", "uuid": "c42aa706-9d1d-4459-af57-8cab72b9c3c4" } ]

{ "coherence": 3.27, "complexity": 1.54, "correctness": 2.37, "helpfulness": 2.43, "instruction-following": 3.27, "safety": 5.2, "verbosity": 0.81, "verbosity-coeff": -0.1129 }

[ { "content": "Find the odd man out\n1, 2, 5, 14, 41, 124\n\n['A)2', 'B)14', 'C)124', 'D)41', 'E)21']", "role": "user", "uuid": "273980f1-254d-406b-b2d5-e70194369e69" }, { "content": "1*3-1 =2\n2*3-1 = 5\n5*3-1 = 14\n14*3-1 = 41\n41*3 -1 = 122\nANSWER:C", "role": "assistant", "uuid": "cc67269e-623f-43f3-95f0-ae785b13c6b2" } ]

{ "coherence": 2.33, "complexity": 1.39, "correctness": 2.12, "helpfulness": 2.14, "instruction-following": 2.62, "safety": 4.34, "verbosity": 1.22, "verbosity-coeff": -0.0778 }

[ { "content": "Annie will be half as old as Larry in 3 years. Annie will also be one-third as old as Jerome in 5 years. If Jerome is 10 years older than Larry, how old is Annie?\n\n['A)3', 'B)8', 'C)19', 'D)26', 'E)34']", "role": "user", "uuid": "deac9beb-0485-4c3b-b65a-a79c5a3126b9" }, { "content": "J = L+10\n(1) 2(A+3) = L+3\n(2) 3(A+5) = J+5 = L+15\nLet's subtract equation (1) from equation (2)\nA+9 = 12\nA = 3\nThe answer is A.", "role": "assistant", "uuid": "d39fa7a8-2635-4bad-84e1-78221bf39589" } ]

{ "coherence": 3.04, "complexity": 1.57, "correctness": 2.1, "helpfulness": 2.51, "instruction-following": 3.04, "safety": 6.65, "verbosity": 0.47, "verbosity-coeff": -0.1456 }

[ { "content": "In a stack of cards, 8 cards are blue and the rest are red. If 2 cards are to be chosen at random from the stack without replacement, the probability that the cards chosen will both be blue is 1/2. What is the number of cards in the stack?\n\n['A)10', 'B)11', 'C)12', 'D)15', 'E)18']", "role": "user", "uuid": "ef16849d-5959-4641-b714-fae62acc7af6" }, { "content": "This question can be solved by TESTing THE ANSWERS.\nWe're told that we have 9 blue cards and an unknown number of red cards. We're also told that if 2 cards are to be chosen at random from the stack WITHOUT replacement, then the probability that the cards chosen will BOTH be BLUE is 1/2. We're asked for the TOTAL number of cards.\nNormally, when TESTing THE ANSWERS, we should start with either B or D. Answer B looks easier, so let's start there.\nAnswer B: 11 total cards\nWith 11 total cards, and 8 blue cards, the probability of pulling two blue cards is...\n(8/11)(7/10) = 56/110~0.509\nSince 1/2 = 0.5, this is clearly the answer.\nB", "role": "assistant", "uuid": "9cd8076f-1599-4c88-83b5-c6692f175938" } ]

{ "coherence": 2.76, "complexity": 1.37, "correctness": 2, "helpfulness": 1.98, "instruction-following": 2.2, "safety": 3.8, "verbosity": 1, "verbosity-coeff": -0.2274 }

[ { "content": "The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %?\n\n['A)18%', 'B)12%', 'C)22%', 'D)24%', 'E)21']", "role": "user", "uuid": "d6bd3f44-be20-45b9-a726-ea03718c8b6e" }, { "content": "1500 ---- 270\n100 ---- ? => 18%\nAnswer:A", "role": "assistant", "uuid": "bfb91577-3e92-4f0b-8958-c6e1c8c93c71" } ]

{ "coherence": 2.82, "complexity": 0.86, "correctness": 2.82, "helpfulness": 2.68, "instruction-following": 3.82, "safety": 5.01, "verbosity": 0.81, "verbosity-coeff": -0.112 }

[ { "content": "If a particular is never chosen, in how many ways can a cricketbe chosen out of 15 players?\n\n['A)250', 'B)320', 'C)364', 'D)390', 'E)430']", "role": "user", "uuid": "f01d7edb-ff77-47ed-9504-d9f33b342712" }, { "content": "A particular players is never chosen, it means that 11 players are selected out of 14 players.\n=> Required number of ways = 14C11\n= 14!/11!x3! = 364\nC", "role": "assistant", "uuid": "b8e8663e-5e9e-492b-8d4e-cae943fbcf2a" } ]

{ "coherence": 3.25, "complexity": 1.89, "correctness": 3.23, "helpfulness": 3.19, "instruction-following": 3.6, "safety": 5.44, "verbosity": 1.83, "verbosity-coeff": -0.1086 }

[ { "content": "If Jake loses 8 pounds, he will weigh twice as much as his sister Kendra. Together they now weigh 290 pounds. What is Jake’s present weight, in pounds?\n\n['A)180', 'B)184', 'C)188', 'D)192', 'E)196']", "role": "user", "uuid": "b311e46b-8c7a-4c2e-b7b4-c63136d852ba" }, { "content": "J + K = 290 and so K = 290 - J\nJ - 8 = 2K\nJ - 8 = 2(290-J)\n3J = 588\nJ = 196\nThe answer is E.", "role": "assistant", "uuid": "08420ff2-770b-481a-b5fa-b847ce840cff" } ]

{ "coherence": 3.27, "complexity": 1.14, "correctness": 2.16, "helpfulness": 2.61, "instruction-following": 2.53, "safety": 5.05, "verbosity": 0.08, "verbosity-coeff": -0.165 }

[ { "content": "X = 101102103104105106107......146147148149150 (From numbers 101-150). Find out the remainder when this number is divided by 9.\n\n['A)2', 'B)4', 'C)5', 'D)6', 'E)7']", "role": "user", "uuid": "f4223e80-12e4-4018-b382-4cd853f89bd6" }, { "content": "Sol:\nThe divisibility rule for 9 is sum of the digits is to be divisible by 9. So\nWe calculate separately, sum of the digits in hundreds place, tenths place, and units place.\nSum of the digits in hundreds place: 1 x 50 = 50\nSum of the digits in tenths place : 0 x 9 + 1 x 10 + 2 x 10 + 3 x 10 + 4 x 10 + 5 x 1 = 105\nSum of the digits in units place : (1 + 2 + 3 + ...+ 9) x 5 = 225\nSo total = 380\nSo remainder = 380 / 9 = 2\nAnswer:A", "role": "assistant", "uuid": "608a3ede-cc96-494d-a7b8-c2f6af96a81f" } ]

{ "coherence": 2.72, "complexity": 1.98, "correctness": 1.9, "helpfulness": 1.98, "instruction-following": 2.21, "safety": 3.89, "verbosity": 1.56, "verbosity-coeff": -0.1113 }

[ { "content": "In a games hour 4 different types of players came to the ground? cricket 15, hokey 12, football 13, softball 15. How many players are present in the ground?\n\n['A)70', 'B)52', 'C)55', 'D)49', 'E)50']", "role": "user", "uuid": "e1bf27d8-d2bc-4745-9a67-e457a41b55cd" }, { "content": "total number of players= 15+12+13+15= 55\nAnswer is C", "role": "assistant", "uuid": "34847c7b-ff34-4f4e-ad74-afd490835cd3" } ]

{ "coherence": 3.09, "complexity": 1.13, "correctness": 3.02, "helpfulness": 3.04, "instruction-following": 3.5, "safety": 6.14, "verbosity": 1.25, "verbosity-coeff": -0.0658 }

[ { "content": "How many odd, positive divisors does 500 have?\n\n['A)6', 'B)5', 'C)12', 'D)15', 'E)24']", "role": "user", "uuid": "a99428d3-5046-489e-994e-2a508998b115" }, { "content": "Make a prime factorization of a number: 540=2^2*3^3*5 --> get rid of powers of 2 as they give even factors --> you'll have 3^3*5 which has (3+1)(1+1)=5 factors.\nAnother example: 60=2^2*3*5 it has (2+1)(1+1)(1+1)=12 factors out of which (1+1)(1+1)=4 are odd: 1, 3, 5 and 15 the same # of odd factors as 60/2^2=15 has.\nAnswer: B.", "role": "assistant", "uuid": "0e44faf7-a7bb-46d7-ae01-f5adb21391b5" } ]

{ "coherence": 2.62, "complexity": 1.18, "correctness": 1.94, "helpfulness": 1.69, "instruction-following": 2.1, "safety": 5.48, "verbosity": 1.19, "verbosity-coeff": -0.2451 }

[ { "content": "The sum of three consecutive integers is 102. Find the lowest of the three?\n\n['A)15', 'B)33', 'C)56', 'D)96', 'E)88']", "role": "user", "uuid": "563a5b06-5f67-4041-b49f-22865b0e70a1" }, { "content": "Explanation:\nThree consecutive numbers can be taken as (P - 1), P, (P + 1).\nSo, (P - 1) + P + (P + 1) = 102\n3P = 102 => P = 34.\nThe lowest of the three = (P - 1) = 34 - 1 = 33.\nAnswer B", "role": "assistant", "uuid": "246a9cc5-0815-4aed-a91e-e24c5e9c9c89" } ]

{ "coherence": 2.98, "complexity": 1.54, "correctness": 2.86, "helpfulness": 3, "instruction-following": 3.78, "safety": 4.48, "verbosity": 1.28, "verbosity-coeff": -0.1534 }

[ { "content": "A train is 310 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length?\n\n['A)36 seconds', 'B)18 seconds', 'C)40 seconds', 'D)19 seconds', 'E)45 seconds']", "role": "user", "uuid": "37e414a0-e7cc-436e-8a46-37e24f5358ac" }, { "content": "Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec\nTotal distance = 310+140 = 500 meter\nTime = Distance/speed\n= 450 * (2/25)\n= 36 seconds\nAnswer: A", "role": "assistant", "uuid": "c19d7bd4-7e74-4e3d-95ad-4342a3915e06" } ]

{ "coherence": 2.64, "complexity": 1.57, "correctness": 2.29, "helpfulness": 2.43, "instruction-following": 3.72, "safety": 5.05, "verbosity": 1.34, "verbosity-coeff": -0.1117 }

[ { "content": "Out of n consecutive natural numbers, four numbers are selected such that the differences of all the possible pairs are distinct. What is the least value of n for which this is possible?\n\n['A)6', 'B)7', 'C)8', 'D)9', 'E)10']", "role": "user", "uuid": "a180262a-30dd-413e-901a-f7d87eb6f237" }, { "content": "Explanation :\nLet the 4 numbers be X1, X2, X3, X4 where X1<X2<X3<X4. Let X1 + a1 = X2, X2 + a2 = X3, X3 + a3 = X4. The difference of X1 and each of the other three, of X2 and each of the greater two, of X3 and X4 are tabulated.\nX1\tX2\tX3\nX2\ta1\nX3\ta1+a2\ta2\nX4\ta1+a2+a3\ta2+a3\ta3\nWe require that n be minimized and these 6 expressions have distinct values. Let X1 = 1\nNow, n = 1+a1+a2+a3. Now a1, a2, a3 can be chosen as the least possible values i.e. 1,2 and 3. However the order of chosing should be such that the six expressions (differences) should all be distinct.\nBy little trial and error (a1, a2, a3) can be (1, 3, 2) or (2, 3, 1) in which case n = 7 and the four numbers can be (1, 2, 5, 7) or (1, 3, 6, 7) respectively.\nHence the minimum value of n is 7.\nAnswer : B", "role": "assistant", "uuid": "a143e890-afc5-4e15-abb2-3f6daf3a65b6" } ]

{ "coherence": 2.72, "complexity": 2.04, "correctness": 2.33, "helpfulness": 2.45, "instruction-following": 3.5, "safety": 6.8, "verbosity": 1.43, "verbosity-coeff": -0.2468 }

[ { "content": "The number 189 is equal to the sum of the cubes of two integers. What is the product of those integers?\n\n['A)8', 'B)15', 'C)20', 'D)27', 'E)39']", "role": "user", "uuid": "604a79d4-b8b5-4e0d-a992-edbf70ebdcc4" }, { "content": "4^3+ 5^3= 189 the number is 4*5= 20\nC", "role": "assistant", "uuid": "ba273c87-f4e7-4e1c-9364-1eccceef0cb7" } ]

{ "coherence": 2.78, "complexity": 1.58, "correctness": 2.21, "helpfulness": 1.95, "instruction-following": 2.74, "safety": 4.66, "verbosity": 0.66, "verbosity-coeff": -0.2461 }

[ { "content": "fill in ht blank:\r(a) the point with coordinates (0,0) is called ____ of a rectangular coordinate system,\r(b) to find the y-intercept of a line, we let ___ equal ___ and solve for ___; to find x- intercept , we let ____ equal 0 and solve for___\n\n['A)(a) the point with coordinates (0,0) is called axis of a rectangular coordinate system, (b) to find the y-intercept of a line, we let x equal 0 and solve for y ; to find x- intercept , we let y equal 0 and solve for y', 'B)(a) the point with coordinates (0,0) is called end of a rectangular coordinate system, (b) to find the y-intercept of a line, we let x equal 0 and solve for x ; to find x- intercept , we let y equal 0 and solve for y', 'C)(a) the point with coordinates (0,0) is called origin of a rectangular coordinate system, (b) to find the y-intercept of a line, we let y equal z and solve for x ; to find x- intercept , we let x equal 0 and solve for z', 'D)(a) the point with coordinates (0,0) is called origin of a rectangular coordinate system, (b) to find the y-intercept of a line, we let x equal 0 and solve for y ; to find x- intercept , we let y equal 0 and solve for x', 'E)none of the above']", "role": "user", "uuid": "b043880c-c614-4818-8b5e-9688deb92ee9" }, { "content": "(a) the point with coordinates (0,0) is called origin of a rectangular coordinate system, (b) to find the y-intercept of a line, we let x equal 0 and solve for y ; to find x- intercept , we let y equal 0 and solve for x\rcorrect answer (D)", "role": "assistant", "uuid": "865ea4c4-2bbf-401b-bc73-ae70ae12aa33" } ]

{ "coherence": 3, "complexity": 1.37, "correctness": 2.47, "helpfulness": 2.62, "instruction-following": 3.21, "safety": 3.8, "verbosity": 1.24, "verbosity-coeff": -0.0979 }

[ { "content": "Anand and Deepak started a business investing Rs. 1000 and Rs. 5000 respectively. Out of a total profit of Rs. 2000, Deepak's share is:\n\n['A)3776', 'B)1284.2', 'C)8400', 'D)1666.6', 'E)1671.8']", "role": "user", "uuid": "0d72219d-e160-49e7-b9e5-94eff87f0d22" }, { "content": "Ratio of their shares = 1000: 5000= 1:5\nDeepak's share = 2000 * 5/6 = Rs. 1666.6.\nAnswer: D", "role": "assistant", "uuid": "847087e4-01fb-40e3-8b9a-10873f2ca17d" } ]

{ "coherence": 3.07, "complexity": 1.07, "correctness": 2.62, "helpfulness": 2.86, "instruction-following": 3.93, "safety": 4.54, "verbosity": 0.62, "verbosity-coeff": -0.1042 }

[ { "content": "A train covers the first 16 km at a speed of 20 km per hour another 20 km at 40 km per hour and the last 10 km at 15 km per hour. Find the average speed for the entire journey.\n\n['A)24 km', 'B)26 km', 'C)21 km', 'D)23(23/59) km', 'E)None']", "role": "user", "uuid": "9c5b7cff-47ca-47db-8216-dc320c812fbd" }, { "content": "Solution: Average speed = total distance covered/ total time\nTotal distance = (16+40+10) = 46 km\nTime taken = (16/20)+ (20/40)+ (10/15) = 59/30\nAverage speed = 46*30/59 = 23(23/59) km/hr.\nAnswer: Option D", "role": "assistant", "uuid": "dc1b6109-8e27-47cc-b289-e6ed644b4ed5" } ]

{ "coherence": 2.98, "complexity": 1.57, "correctness": 2.25, "helpfulness": 2.37, "instruction-following": 3.27, "safety": 5.71, "verbosity": 1.15, "verbosity-coeff": -0.1488 }

[ { "content": "What is the sum of all 3 digit positive integers that can be formed using the digits 1, 4, and 7, if the digits are allowed to repeat within a number?\n\n['A)10,655', 'B)11,988', 'C)12,433', 'D)13,766', 'E)14,322']", "role": "user", "uuid": "4a941688-e5e4-4b73-8fb8-c796cb2bb087" }, { "content": "The number of these 3-digit numbers is 3*3*3 = 27\nEach digit 1, 4, and 7 will appear in the ones, tens, and hundreds place 9 times each.\nThe sum equals 9(111) + 9(444) + 9(777) = 11,988\nThe answer is B.", "role": "assistant", "uuid": "8e8d5636-13b2-4c6e-b601-3b871587dabb" } ]

{ "coherence": 2.78, "complexity": 1.6, "correctness": 2.08, "helpfulness": 2.31, "instruction-following": 2.98, "safety": 4.62, "verbosity": 0.73, "verbosity-coeff": -0.2399 }

[ { "content": "What is the greatest prime factor of 8^11 - 2^30?\n\n['A)2', 'B)3', 'C)5', 'D)7', 'E)11']", "role": "user", "uuid": "b1e306af-6778-4e6f-b03a-9dd9235f8c43" }, { "content": "8^11 - 2^30\n=(2^3)^11 - 2^30\n= 2^33 - 2^30\n= 2^30 (2^3 -1)\n= 2^30 * (8-1)\n= 2^30 * 7\nThe greatest prime factor is 7.\nThe answer is D.", "role": "assistant", "uuid": "65ef433f-384f-4ca8-9856-a786b2bf8709" } ]

{ "coherence": 3.31, "complexity": 2.06, "correctness": 2.59, "helpfulness": 2.7, "instruction-following": 2.9, "safety": 5.12, "verbosity": 1.39, "verbosity-coeff": -0.2471 }

[ { "content": "A reduction of 20% in the price of salt enables a lady to obtain 5 kgs more for Rs.100, find the original price per kg?\n\n['A)6', 'B)1', 'C)5', 'D)4', 'E)7']", "role": "user", "uuid": "d7c7b503-bb88-4802-9101-57f0af7d7a2a" }, { "content": "100*(20/100) = 20 --- 5\n? --- 1 => Rs.4\n100 --- 80\n? ---4 => Rs.5\nAnswer: C", "role": "assistant", "uuid": "917f5b3e-4bba-424e-abcf-891e557305f2" } ]

{ "coherence": 2.62, "complexity": 1.79, "correctness": 1.72, "helpfulness": 1.92, "instruction-following": 2.64, "safety": 5.2, "verbosity": 0.96, "verbosity-coeff": -0.1221 }

[ { "content": "A five-digit number divisible by 3 is to be formed using numerical 0, 1, 2, 3, 4 and 5 without repetition. The total number Q of ways this can be done is:\n\n['A)122', 'B)210', 'C)216', 'D)217', 'E)225']", "role": "user", "uuid": "c3b089ce-7a51-4597-bbf1-1339a75c47f3" }, { "content": "We should determine which 5 digits from given 6, would form the 5 digit number divisible by 3.\nWe have six digits: 0, 1, 2, 3, 4, 5. Their sum=15.\nFor a number to be divisible by 3 the sum of the digits must be divisible by 3. As the sum of the six given numbers is 15 (divisible by 3) only 5 digits good to form our 5 digit number would be 15-0={1, 2, 3, 4, 5} and 15-3={0, 1, 2, 4, 5}. Meaning that no other 5 from given six will total the number divisible by 3.\nSecond step:\nWe have two set of numbers:\n1, 2, 3, 4, 5 and 0, 1, 2, 4, 5. How many 5 digit numbers can be formed using these two sets:\n1, 2, 3, 4, 5 --> 5! as any combination of these digits would give us 5 digit number divisible by 3. 5!=120.\n0, 1, 2, 4, 5 --> here we can not use 0 as the first digit, otherwise number won't be any more 5 digit and become 4 digit. So, desired # would be total combinations 5!, minus combinations with 0 as the first digit (combination of 4) 4! --> 5!-4!=4!(5-1)=4!*4=96\n120+96=216=Q\nAnswer: C.", "role": "assistant", "uuid": "e6dafcc5-2067-4703-b3a9-9ed0f9256c34" } ]

{ "coherence": 2.51, "complexity": 2.02, "correctness": 2.51, "helpfulness": 2.55, "instruction-following": 2.78, "safety": 5.16, "verbosity": 1.97, "verbosity-coeff": -0.1584 }

[ { "content": "Three partners A, B, C in a business invested money such that 4(A’s capital) = 2(B’s capital) = 12(C’s capital) then, The ratio of their capitals is\n\n['A)63 : 45 : 34', 'B)63 : 54 : 34', 'C)36 : 54 : 28', 'D)3 : 6 : 1', 'E)None of these']", "role": "user", "uuid": "d1373e16-d1ff-49a8-ba6a-a3153b6cc43b" }, { "content": "Explanation:\nLet 4(A’s capital) = 2(B’s capital) = 12(C’s capital) = Rs.x\nThen, A’s capital = Rs x/4, B’s capital = Rs. x/2 and C’s capital = Rs. x/12\nA : B : C = x/4 : x/2 : x/12\n3 : 6 : 1\nAnswer: Option D", "role": "assistant", "uuid": "fa25ddbb-7b35-4b11-b597-ec52777d88c8" } ]

{ "coherence": 2.2, "complexity": 1.31, "correctness": 1.68, "helpfulness": 1.98, "instruction-following": 1.74, "safety": 5.16, "verbosity": 0.96, "verbosity-coeff": -0.1292 }

[ { "content": "Calculate the circumference of a circular field whose radius is 6 centimeters.\n\n['A)2 π cm', 'B)1 π cm', 'C)15 π cm', 'D)12 π cm', 'E)19 π cm']", "role": "user", "uuid": "ffff096b-5078-4f37-891e-bd360834aa82" }, { "content": "Circumference C is given by\nC = 2πr = 2π*6 = 12 π cm\nAnswer: D", "role": "assistant", "uuid": "9a955d23-548c-4bfb-82f7-4b25a71adcb8" } ]

{ "coherence": 2.94, "complexity": 0.96, "correctness": 2.55, "helpfulness": 2.57, "instruction-following": 3.74, "safety": 4.58, "verbosity": 0.36, "verbosity-coeff": -0.094 }

[ { "content": "If |z|/w = 3,which of the following must be true?\n\n['A)z = -3w', 'B)z = 3w', 'C)z^2 = 9w^2', 'D)z^2 = 9w^3', 'E)z^3 = 27w^3']", "role": "user", "uuid": "5eafcd1b-964f-49f9-8804-0f01cb979e57" }, { "content": "|z|/w = 3.\n|z| = 3w.\nThen z = 3w or -3w and so z^2 = 9w^2.\nThe answer is C.", "role": "assistant", "uuid": "a2885025-5957-41dc-8245-8018fcc3cb9c" } ]

{ "coherence": 3.27, "complexity": 2.02, "correctness": 2.98, "helpfulness": 3.04, "instruction-following": 3.05, "safety": 4.93, "verbosity": 1.06, "verbosity-coeff": -0.2287 }

[ { "content": "In a 400 member association consisting of men and women, exactly 20% of men and exactly 25 % women are homeowners. What is the least number of members who are homeowners?\n\n['A)81', 'B)147', 'C)145', 'D)143', 'E)141']", "role": "user", "uuid": "8a46b895-6b88-425f-b8bf-7b8c3cedc0ce" }, { "content": "Solution simple\nOut of 400 20% are male i.e 80 and 25% are female i.e 100 , so total homeowner is 180.\nNow min number homeowner is 80 and max is 180 so question ask us to find least and 81 has least value among all option.\nSo ans is 81.\nAnswer : A", "role": "assistant", "uuid": "27e06101-2d4c-4a65-b787-568f3c8cda1c" } ]

{ "coherence": 2.66, "complexity": 0.84, "correctness": 1.88, "helpfulness": 1.95, "instruction-following": 2.39, "safety": 7.16, "verbosity": 1.18, "verbosity-coeff": -0.1958 }

[ { "content": "A dog takes 10 leaps for every 2 leaps of a hare. If one leap of the dog is equal to 2 leaps of the hare, the ratio of the speed of the dog to that of the hare is :\n\n['A)5:1', 'B)10:1', 'C)15:1', 'D)20:1', 'E)25:1']", "role": "user", "uuid": "c4ecc65a-ad74-468e-b5ee-e51673ca5aec" }, { "content": "Explanation:\nDog : Hare = (10*2) leaps of hare : 2 leaps of hare = 20 : 2.\nAnswer: B) 10:1", "role": "assistant", "uuid": "2e026fb8-e36e-43c7-86c9-06acd1ce32f3" } ]

{ "coherence": 3.48, "complexity": 1.46, "correctness": 3.25, "helpfulness": 3.29, "instruction-following": 3.7, "safety": 3.8, "verbosity": 0.64, "verbosity-coeff": -0.1189 }

[ { "content": "Ratio between Rahul and Deepak is 4:3, After 6 Years Rahul age will be 30 years. What is Deepak present age?\n\n['A)18', 'B)15', 'C)77', 'D)266', 'E)182']", "role": "user", "uuid": "17714cbf-0b1f-4111-b313-1b493e89c8af" }, { "content": "Present age is 4x and 3x,\n=> 4x + 6 = 30 => x = 6\nSo Deepak age is = 3(6) = 18\nAnswer: A", "role": "assistant", "uuid": "4c37c3f0-d16b-4b1a-8c64-7afc1cccd124" } ]

{ "coherence": 3, "complexity": 1.15, "correctness": 2.78, "helpfulness": 2.9, "instruction-following": 3.46, "safety": 5.55, "verbosity": 0.6, "verbosity-coeff": -0.1255 }

[ { "content": "For every integer n ≥ 3, the function h(n) is defined as the product of all the odd integers from 1 to n, inclusive. What is the value of h(102) – h(101)?\n\n['A)102', 'B)0', 'C)101', 'D)98', 'E)100']", "role": "user", "uuid": "bc53081f-111c-492c-81eb-b4985bbdf151" }, { "content": "h(101) = 1*3*5*7*9*...*99*101\nh(102) = 1*3*5*7*9*...*99*101\nThey are going to be the same. Hence their difference will be 0\nhence:B", "role": "assistant", "uuid": "4fb30481-f3c8-45f8-a8bf-f69755f39a74" } ]

{ "coherence": 2.62, "complexity": 1.77, "correctness": 2.04, "helpfulness": 2.21, "instruction-following": 2.1, "safety": 4.44, "verbosity": 1.41, "verbosity-coeff": -0.2337 }

[ { "content": "20 marbles were pulled out of a bag of only white marbles, painted black, and then put back in. Then, another 20 marbles were pulled out, of which 1 was black, after which they were all returned to the bag. If the percentage of black marbles pulled out the second time represents their percentage in the bag, how many marbles in total Q does the bag currently hold?\n\n['A)40', 'B)200', 'C)380', 'D)400', 'E)3200']", "role": "user", "uuid": "93845c4c-aa1d-469d-999e-12737bc639cc" }, { "content": "We know that there are 20 black marbles in the bag and this number represent 1/20 th of the number of all marbles in the bag, thus there are total Q of 20*20=400 marbles.\nAnswer: D.", "role": "assistant", "uuid": "7b3b18cc-33ae-4845-8238-33d9200b8617" } ]

{ "coherence": 3.07, "complexity": 1.65, "correctness": 2.64, "helpfulness": 2.66, "instruction-following": 2.61, "safety": 4.54, "verbosity": 1.15, "verbosity-coeff": -0.1534 }

[ { "content": "The faces of pyramid are to be painted by 4 different colors. In how many ways can be this be done?\n\n['A)A.720', 'B)B.256', 'C)C.24', 'D)D.12', 'E)E.36']", "role": "user", "uuid": "0af1e61e-1dd5-427c-90ae-7c0bc874172a" }, { "content": "If I have to paint 4 sides with 4 different colour...\nFirst face can have 4c1 options,\n2nd would have 3c1, and subsequent ones would have 2c1 and 1 options respectively.\nTotal options = 4c1 x 3c1 x 2c1 x 1 = 24 distinct ways\nCorrect answer - C", "role": "assistant", "uuid": "248f8a77-dd96-4bf8-b94a-4bdc23abe0cf" } ]

{ "coherence": 2.59, "complexity": 2.2, "correctness": 2.33, "helpfulness": 2.41, "instruction-following": 3, "safety": 4.58, "verbosity": 1.55, "verbosity-coeff": -0.1808 }

[ { "content": "Divide $1000 among A,B in the ratio 1:3. How many $ that A get?\n\n['A)$50', 'B)$500', 'C)$150', 'D)$250', 'E)$600']", "role": "user", "uuid": "c6d010a6-6249-4c56-8a11-cb04bcf636e5" }, { "content": "Sum of ratio terms = 1+3 = 4\nA = 1000*1/4 = $250\nAnswer is D", "role": "assistant", "uuid": "1b1be8c0-2138-456b-a0e5-c06865bc05bc" } ]

{ "coherence": 2.92, "complexity": 0.55, "correctness": 3.13, "helpfulness": 3.33, "instruction-following": 3.56, "safety": 4.01, "verbosity": 1.14, "verbosity-coeff": -0.1349 }

[ { "content": "A wholesaler marks his wares 60% more than the real price and allows 25% discount. His profit is:\n\n['A)15%', 'B)20%', 'C)25%', 'D)30%', 'E)None of these']", "role": "user", "uuid": "7f3fe643-8c97-4718-ac65-52c5a7ac862b" }, { "content": "Let the CP = 100 Rs.\nMark Price = 160\nDiscount = 25%\nSelling price 75/100 × 160\nHence profit = 20%\nAnswer: B.", "role": "assistant", "uuid": "5d52c20f-637c-492a-a67a-a6d8c66ce9ab" } ]

{ "coherence": 2.84, "complexity": 1.82, "correctness": 2.39, "helpfulness": 2.49, "instruction-following": 2.84, "safety": 5.36, "verbosity": 1.25, "verbosity-coeff": -0.1167 }

[ { "content": "20 is subtracted from 80% of a number, the result is 60. Find the number?\n\n['A)150', 'B)997', 'C)100', 'D)288', 'E)271']", "role": "user", "uuid": "f5f4f2d1-e145-47a8-9d1d-226ff63d599f" }, { "content": "(80/100) * X – 20 = 60\n8X = 800\nX = 100\nAnswer:C", "role": "assistant", "uuid": "868c0fda-d4e0-411f-b465-183fd8a8e537" } ]

{ "coherence": 3.02, "complexity": 1.33, "correctness": 2.61, "helpfulness": 2.7, "instruction-following": 3.6, "safety": 4.89, "verbosity": 0.59, "verbosity-coeff": -0.1102 }

[ { "content": "If k is a non-negative integer and 15^k is a divisor of 759,325 then 3^k - k^3 =\n\n['A)0', 'B)1', 'C)37', 'D)118', 'E)513']", "role": "user", "uuid": "b1b44ee8-8356-4da7-85d9-dcbdadc9d0bc" }, { "content": "At first we should understand whether 759325 divisible by 15.\n15 is equal to 3 * 5 so 759325 should be divisible on these integers\n759325 is divisible by 5 because of last digit 5\nbut not divisible by 3 because sum of its digits doesn't divisible by 3: 7 + 5 + 9 + 3 + 2 + 5 = 31 and 31 doesn't divisible by 3\nso 759325 can be divisible by 15^k only if k = 0 and 15^k = 1\nso 3^k - k^3 = 1 - 0 = 1\nAnswer is B", "role": "assistant", "uuid": "f61fa77b-a894-47fd-8349-7af0f7ceb44f" } ]

{ "coherence": 2.53, "complexity": 1.78, "correctness": 1.95, "helpfulness": 1.86, "instruction-following": 1.46, "safety": 4.05, "verbosity": 1, "verbosity-coeff": -0.2154 }

[ { "content": "A trader sells 85 meters of cloth for Rs. 8925 at the profit of Rs. 15 per metre of cloth. What is the cost price of one metre of cloth?\n\n['A)Rs.92', 'B)Rs.70', 'C)Rs.90', 'D)Rs.28', 'E)Rs.20']", "role": "user", "uuid": "63103638-aed0-4822-816a-26d1ce32490e" }, { "content": "SP of 1m of cloth = 8925/85 = Rs. 105\nCP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth\n= Rs. 105 - Rs. 15\n= Rs.90.\nAnswer:C", "role": "assistant", "uuid": "f30aed09-70b3-4c52-9591-c68b1fd45367" } ]

{ "coherence": 3.11, "complexity": 1.36, "correctness": 2.21, "helpfulness": 2.59, "instruction-following": 3.21, "safety": 5.44, "verbosity": 1.71, "verbosity-coeff": -0.1399 }

[ { "content": "In a graduating class of 232 students, 144 took geometry and 119 took biology. What is the difference between the greatest possible number and the smallest possible number of students that could have taken both geometry and biology?\n\n['A)144', 'B)119', 'C)113', 'D)88', 'E)31']", "role": "user", "uuid": "fd948d1c-bb05-45d7-af4f-5a3a620e2f9d" }, { "content": "Greatest Possible Number taken both should be 144 (As it is maximum for One)\nSmallest Possible Number taken both should be given by\nTotal - Neither = A + B - Both\nBoth = A+B+Neither - Total (Neither must be 0 to minimize the both)\nSo 144 + 119 + 0 - 232 = 31\nGreatest - Smallest is 144-31 = 113\nSo answer must be C. 113", "role": "assistant", "uuid": "2840b229-4e83-49a8-887c-d62463ea759e" } ]

{ "coherence": 2.66, "complexity": 1.5, "correctness": 1.98, "helpfulness": 2.23, "instruction-following": 2.2, "safety": 4.89, "verbosity": 1.22, "verbosity-coeff": -0.2539 }

[ { "content": "How many Q ways are there of placing 6 marbles in 4 bowls, if any number of them can be placed in each bowl?\n\n['A)6C4', 'B)6P4', 'C)4^6', 'D)6^4', 'E)6!']", "role": "user", "uuid": "c4b54b98-7be7-4fee-83b2-0b5c8bfec671" }, { "content": "Each marble has 4 options, so there are total of Q= 4*4*4*4*4*4=4^6 ways.\nAnswer: C.\nThe total number of ways of dividing n identical items among r persons, each one of whom, can receive 0,1,2 or more items is (n+r -1)C(r-1).", "role": "assistant", "uuid": "cc455cdb-200c-4d2c-82a2-46fece0782c0" } ]

{ "coherence": 3.33, "complexity": 1.72, "correctness": 2.59, "helpfulness": 2.8, "instruction-following": 2.62, "safety": 3.78, "verbosity": 1.14, "verbosity-coeff": -0.1329 }

[ { "content": "A salesman’s terms were changed from a flat commission of 5% on all his sales to a fixed salary of Rs.1000 plus 2.5% commission on all sales exceeding Rs. 4,000. If his remuneration as per new scheme was Rs. 600 more than that by the previous schema, his sales were worth?\n\n['A)12028', 'B)12000', 'C)12019', 'D)12197', 'E)12012']", "role": "user", "uuid": "18d5df1c-f455-4610-8479-33b943d7be2f" }, { "content": "[1000 + (X-4000) * (2.5/100)] - X * (5/100)\n= 600\nX = 12000\nAnswer: B", "role": "assistant", "uuid": "ce8ee15c-aa4c-4cc0-b4ff-cfee1ecc0368" } ]

{ "coherence": 2.76, "complexity": 1.49, "correctness": 2.1, "helpfulness": 2.43, "instruction-following": 3.05, "safety": 5.59, "verbosity": 0.64, "verbosity-coeff": -0.1256 }

[ { "content": "If air is called green , green is called blue, blue is called sky, sky is called yellow, yellow is called water and water is called pink, then what is the color of clear sky ?\n\n['A)Blue', 'B)Sky', 'C)Water', 'D)Yellow', 'E)Black']", "role": "user", "uuid": "74eae85f-007b-48f4-a4d8-69ec2d0a4e5a" }, { "content": "Explanation:\nThe colour of clear sky is 'blue' and as given, 'blue' is called 'sky'.\nSo, the colour of clear sky is 'sky'.\nAnswer: B", "role": "assistant", "uuid": "5b66b1a6-2984-4a14-bf2f-0e292bda60e7" } ]

{ "coherence": 3.11, "complexity": 1.18, "correctness": 2.51, "helpfulness": 2.64, "instruction-following": 2.96, "safety": 5.48, "verbosity": 1.12, "verbosity-coeff": -0.1043 }

[ { "content": "On the independence day, bananas were be equally distributed among the children in a school so that each child would get two bananas. On the particular day 160 children were absent and as a result each child got two extra bananas. Find the actual number of children in the school?\n\n['A)600', 'B)320', 'C)500', 'D)520', 'E)720']", "role": "user", "uuid": "fae30c2c-3ac1-4e81-aa8c-754cd9e4bd81" }, { "content": "Let the number of children in the school be x. Since each child gets 2 bananas, total number of bananas = 2x.\n2x/(x - 160) = 2 + 2(extra)\n=> 2x - 320 = x => x = 320.\nANSWER:B", "role": "assistant", "uuid": "3da1ad26-28e2-4945-96e4-2f66b5c439ca" } ]

{ "coherence": 2.8, "complexity": 1.73, "correctness": 2.08, "helpfulness": 2.41, "instruction-following": 2.86, "safety": 5.52, "verbosity": 1.31, "verbosity-coeff": -0.1154 }

[ { "content": "Using all the letters of the word \"WEDNESDAY\", how many different words can be formed?\n\n['A)A)7', 'B)B)9!', 'C)C)8', 'D)D)7!', 'E)E)3']", "role": "user", "uuid": "7e67ab1f-e7ce-4df0-bd38-49a6aeb0f845" }, { "content": "Explanation:\nTotal number of letters = 9\nUsing these letters the number of 9 letters words formed is 8!.\nAnswer: Option B", "role": "assistant", "uuid": "d21ae651-7da5-40c3-8dbd-ab044e458571" } ]

{ "coherence": 1.98, "complexity": 0.8, "correctness": 1.3, "helpfulness": 1.66, "instruction-following": 1.16, "safety": 4.11, "verbosity": 1.1, "verbosity-coeff": -0.0967 }

[ { "content": "If x is the sum of six consecutive integers, then x is divisible by which of the following: I. 6 II. 5\nIII. 7\n\n['A)I only', 'B)II only', 'C)III only', 'D)I,III only', 'E)II,III only']", "role": "user", "uuid": "181e690a-9e8a-4199-a343-357c027902d9" }, { "content": "We're told that X is the SUM of 6 CONSECUTIVE INTEGERS. We're asked what X is divisible by....\nLet's TEST VALUES....\nIF we use the 6 consecutive integers: 5, 6, 7,8,9 and 10, then the sum = 45.\n45 is divisible by 5\n45 is NOT divisible by 6\n45 is NOT divisible by 7\nThere's only one answer that 'fits' with these facts. Answer : B", "role": "assistant", "uuid": "27696f1d-380d-4a76-ada0-369f5c018733" } ]

{ "coherence": 2.18, "complexity": 1.72, "correctness": 1.19, "helpfulness": 1.38, "instruction-following": 1.03, "safety": 5.48, "verbosity": 0.96, "verbosity-coeff": -0.2154 }

[ { "content": "Look at this series: 15, 15, 27, 27, 39, 39, 51, 51, 63, 63, ? ... What number should fill the blank?\n\n['A)51', 'B)39', 'C)75', 'D)15', 'E)None']", "role": "user", "uuid": "f39706e4-295f-40f3-8cce-67dc2f33a5d4" }, { "content": "Explanation: In this simple addition with repetition series, each number in the series repeats itself, and then increases by 12 to arrive at the next number.\nAnswer: Option C", "role": "assistant", "uuid": "1d11c490-b560-4993-ba22-7b67ced48761" } ]

{ "coherence": 2.59, "complexity": 1.57, "correctness": 2.31, "helpfulness": 2.31, "instruction-following": 2.43, "safety": 4.23, "verbosity": 1.28, "verbosity-coeff": -0.1008 }

[ { "content": "10% of a 50% alcohol solution is replaced with water. From the resulting solution, again 10% is replaced with water. This step is repeated once more. What is the concentration of alcohol in the final solution obtained?\n\n['A)3%', 'B)20%', 'C)25%', 'D)36%', 'E)40%']", "role": "user", "uuid": "1d3471a3-a615-4ae2-bb19-a3ac96a7bb34" }, { "content": "Since the numbers in the answers are pretty far apart. I just simplified and rounded.\nAlcohol = 50%\nTotal - 10% * 3 = 70%\n.5 * .7 = .35 (so that means 70% of 50% of the total is 35%)\nAnswer: D) 36", "role": "assistant", "uuid": "f38d6f1c-e603-4a6a-ad22-00814dbfdbb9" } ]

{ "coherence": 2.51, "complexity": 2.04, "correctness": 1.44, "helpfulness": 1.33, "instruction-following": 1.47, "safety": 4.66, "verbosity": 1.29, "verbosity-coeff": -0.1578 }

[ { "content": "There are a cities. What is the number of airlines that connected 2 different cities (airline from city A to city B is different with airline from city B to city A)?\n\n['A)n(n-1)', 'B)n(n+1)', 'C)a(a-1)', 'D)n(n+1)/2', 'E)n2']", "role": "user", "uuid": "1bb4927a-f2cf-46f6-ae85-2fa6a87baaf8" }, { "content": "First of all, the possible number of airlines is a. Then, the possible number of airlines departing from one city to another becomes (a-1). Hence, the answer is a(a-1), which makes C", "role": "assistant", "uuid": "ad14ca12-0e48-4347-ade1-cc6050880727" } ]

{ "coherence": 2.88, "complexity": 1.76, "correctness": 1.62, "helpfulness": 1.89, "instruction-following": 2.14, "safety": 4.42, "verbosity": 0.85, "verbosity-coeff": -0.0988 }

[ { "content": "If the number is divided by 3, it reduced by 42. The number is\n\n['A)A)51', 'B)B)63', 'C)C)45', 'D)D)40', 'E)E)36']", "role": "user", "uuid": "973a760d-96a0-46f4-932f-1be3fc591e09" }, { "content": "Explanation:\nLet the number be x. Then,\nx - (x/3) = 42 => 2x/3 = 42\n=> x = 63\nAnswer: Option B", "role": "assistant", "uuid": "c657b96c-f5b4-4c90-be57-6f611bd8b868" } ]

{ "coherence": 2.96, "complexity": 2.04, "correctness": 2.88, "helpfulness": 3.04, "instruction-following": 3.27, "safety": 3.29, "verbosity": 1.31, "verbosity-coeff": -0.1013 }

[ { "content": "Working at their respective constant rates, Paul, Abdul and Adam alone can finish a certain work in 3, 4, and 5 hours respectively. If all three work together to finish the work, what fraction W of the work will be done by Adam?\n\n['A) 1/4', 'B) 12/47', 'C) 1/3', 'D) 5/12', 'E) 20/47']", "role": "user", "uuid": "dc9ff355-8289-4f96-9027-d27ee6e69453" }, { "content": "Let the total work be 60 units. Pual does 60/3 =20 units of work per hr. abdul does 15 units per hr and adam does 12 units per hr. If all work together they do (20 + 15 + 12) units per hr = 47 units per hr. So the time taken to finish the work = 60/47 hrs.\nadam will do 60/47 * 12 units of work in 60/47 hr . fraction of work adam does =work done by adam / total work\nW>( 60/47 *12)/60 =12/47\nAnswer B", "role": "assistant", "uuid": "dcb6ff6d-6def-4f6f-8c7c-ea6a00087004" } ]

{ "coherence": 2.66, "complexity": 0.94, "correctness": 2.27, "helpfulness": 2.43, "instruction-following": 2.98, "safety": 5.63, "verbosity": 1.3, "verbosity-coeff": -0.1742 }

[ { "content": "The cost price of an article is 64% of the marked price. Calculate the gain percent after allowing a discount of 12%.\n\n['A)37.5 %', 'B)38.5 %', 'C)42 %', 'D)27.5 %', 'E)none']", "role": "user", "uuid": "eaac2453-a138-42ef-8fd3-77debc6305fe" }, { "content": "Sol.\nLet marked price = Rs. 100. Then, C.P. = Rs. 64. S.P = Rs. 88.\n∴ Gain % = [24/64 * 100]% = 37.5%.\nAnswer A", "role": "assistant", "uuid": "5b058265-1511-472f-866c-758ec969a924" } ]

{ "coherence": 3.04, "complexity": 1.71, "correctness": 3.13, "helpfulness": 2.98, "instruction-following": 4.05, "safety": 4.93, "verbosity": 1.8, "verbosity-coeff": -0.1143 }

[ { "content": "Victor gets 92 % marks in examinations. If these are 460 marks, find the maximum marks.\n\n['A)334', 'B)500', 'C)376', 'D)288', 'E)271']", "role": "user", "uuid": "2add3e76-1c69-4894-8fd6-dd1118d7f081" }, { "content": "Let the maximum marks be m\nThen 92 % of m = 460\n⇒ 92/100 × m = 460\n⇒ m = (460 × 100)/92\n⇒ m = 46000/92\n⇒ m = 500\nTherefore, maximum marks in the examinations are 500.\nAnswer:B", "role": "assistant", "uuid": "bd64cf2a-1f1b-4230-8eb9-53be585f9a23" } ]

{ "coherence": 3.29, "complexity": 1.58, "correctness": 3.27, "helpfulness": 3.48, "instruction-following": 4.48, "safety": 4.07, "verbosity": 2.12, "verbosity-coeff": -0.1028 }

[ { "content": "A began business with Rs.27000 and was joined afterwards by B with Rs.54000. When did B join if the profits at the end of the year were divided in the ratio of 2:1?\n\n['A)9', 'B)6', 'C)7', 'D)8', 'E)2']", "role": "user", "uuid": "5e8290f7-82f8-4624-9747-c000502142af" }, { "content": "27*12 : 54*x = 2: 1\nx = 3\n12 -3 = 9\nAnswer: A", "role": "assistant", "uuid": "193ffc0a-f1be-452c-bd95-3876fe7bf4ed" } ]

{ "coherence": 2.35, "complexity": 1.03, "correctness": 1.94, "helpfulness": 2.2, "instruction-following": 2.29, "safety": 5.95, "verbosity": 0.55, "verbosity-coeff": -0.1166 }

[ { "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 integer.\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": "9a656b2b-16b0-40c6-91e1-1b0803dd7375" }, { "content": "Since a, b, and c are consecutive positive integers and a < b < c, then a = c + 2, from which it follows that c - a = -2. So, I is false.\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 true as well.\nAnswer: D.", "role": "assistant", "uuid": "a5f80bab-b67a-48ed-9430-caf3b7fcdb5c" } ]

{ "coherence": 2.76, "complexity": 2.08, "correctness": 2.08, "helpfulness": 2.16, "instruction-following": 2.39, "safety": 6.14, "verbosity": 1.14, "verbosity-coeff": -0.2369 }

[ { "content": "The value of x + x(xx) when x = 2\n\n['A) 10', 'B) 16', 'C) 18', 'D) 36', 'E) 64']", "role": "user", "uuid": "bfd83a91-7f51-4b14-9f2c-454321f8d462" }, { "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= 10 The answer is (A)", "role": "assistant", "uuid": "b9094a6f-1212-4b72-a351-342f0f9847a4" } ]

{ "coherence": 2.96, "complexity": 1.38, "correctness": 2.7, "helpfulness": 2.96, "instruction-following": 3.5, "safety": 4.13, "verbosity": 0.92, "verbosity-coeff": -0.1085 }

[ { "content": "A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price?\n\n['A)299', 'B)375', 'C)27878', 'D)288', 'E)212']", "role": "user", "uuid": "fb8420da-b1e3-43b4-a08e-659b9143c62b" }, { "content": "CP1 = 100 SP1 = 120\nCP2 = 80 SP2 = 80 * (125/100) = 100\n20 ----- 100\n75 ----- ? => 375.Answer: B", "role": "assistant", "uuid": "776a844a-9d23-457d-b602-c8a95f31f480" } ]

{ "coherence": 2.7, "complexity": 1.09, "correctness": 1.86, "helpfulness": 2.1, "instruction-following": 2.78, "safety": 5.32, "verbosity": 0.35, "verbosity-coeff": -0.129 }

[ { "content": "How many three-digit integers between 311 and 401, exclusive, are divisible by 3 when the tens digit and the hundered digit are switched?\n\n['A)30', 'B)19', 'C)22', 'D)3', 'E)90']", "role": "user", "uuid": "061f5404-02a3-4088-bbe2-57396d911fcf" }, { "content": "Answer is 30\nNo of digits between 311 and 401 (exclusive) = 401-311-1 = 89\nNo Intergers divisble by 3 =~ 89/3 ~ 30\nDivsiblivity rule for 3 is Sum of all digits must be divisble by 3. It doesn't matter if hundred digit and tens digits are switched.\ne.g 372 is divisble by 3 (becae 3+7+2= 12 (divisble by 3))\nswitch digits 732 also divisble by 3 (becae 7+3+2= 12 (divisble by 3))\nDivsiblivity rule for 3 is Sum of all digits must be divisble by 3. It doesn't matter if hundred digit and tens digits are switched.\nYou have right. So it is enough to proceed like usual to find the numbers in a given range that are divisible by 3. So 399-312/3 +1 =30.\nAnswer : A", "role": "assistant", "uuid": "501c0cbe-7502-4437-b83e-a7e2c605fc43" } ]

{ "coherence": 2.37, "complexity": 1.85, "correctness": 1.98, "helpfulness": 2.08, "instruction-following": 2.31, "safety": 5.4, "verbosity": 1.74, "verbosity-coeff": -0.2483 }

[ { "content": "What is the ratio W of the surface area of a cube to the surface area of a rectangular solid identical to the cube in all ways except that its length has been doubled?\n\n['A)1/4', 'B)3/8', 'C)1/2', 'D)3/5', 'E)2']", "role": "user", "uuid": "e9a78f01-1a89-42a8-a4e9-b817adb759fc" }, { "content": "Let X be the side of the cube. Therefore X^2*6= surface area.\nthe rectangle is the same other than length is 2X. The width and height are the same as the cube. 2*W*H+2*W*L+2*H*L= 2X^2+4X^2+4X^2= 10X^2.\n6X^2/10X^2 = 3/5 = W.\nAnswer = D", "role": "assistant", "uuid": "58c6eac9-f080-49ca-b5ea-64a89cbd0875" } ]

{ "coherence": 2.7, "complexity": 1.79, "correctness": 2.02, "helpfulness": 2.06, "instruction-following": 2.59, "safety": 5.24, "verbosity": 0.85, "verbosity-coeff": -0.1963 }

[ { "content": "How many four letter words are formed using the letters of the word ENTERTAINMENT?\n\n['A)1716', 'B)1616', 'C)1816', 'D)1516', 'E)1761']", "role": "user", "uuid": "3cff693d-947f-4ff1-ae46-e6b1af67f521" }, { "content": "The number of letters in the given word is thirteen.\nThe number of four letter words that can be formed using these thirteen letters is 13P4\n= 13 * 12 * 11 = 1716.\nAnswer: A", "role": "assistant", "uuid": "623c80bb-a3a1-4427-80c4-7a488b9c3dd1" } ]

{ "coherence": 2.55, "complexity": 0.97, "correctness": 1.73, "helpfulness": 2.02, "instruction-following": 2.35, "safety": 4.48, "verbosity": 1.28, "verbosity-coeff": -0.1157 }

[ { "content": "The 19th of September 1987 was a Saturday. If 1988 was a leap-year, what day of the week was the 23rd of September 1990?\n\n['A)Sunday', 'B)Monday', 'C)Wednesday', 'D)Thursday', 'E)Friday']", "role": "user", "uuid": "b34fd437-c30d-44f0-8d7c-be5354f6c5dc" }, { "content": "19th September\n1987: Saturday\n1988: Monday (due to leap year)\n1989: Tuesday\n1990: Wednesday\nHence 23rd September was a Sunday.\nThe answer is A.", "role": "assistant", "uuid": "44bf79fa-6ef9-4e8b-977b-2859f7160f5f" } ]

{ "coherence": 3.07, "complexity": 1.48, "correctness": 1.82, "helpfulness": 2.06, "instruction-following": 2.2, "safety": 5.2, "verbosity": 1.42, "verbosity-coeff": -0.1162 }

[ { "content": "A bag contains 9 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is\n\n['A)8/17', 'B)2/5', 'C)3/5', 'D)11/15', 'E)7/15']", "role": "user", "uuid": "b7fec0bf-168e-4ca8-acdc-580aec5e30ae" }, { "content": "Drawing two balls of same color from nine green balls can be done in 9C₂ ways.\nSimilarly from eight white balls two can be drawn in ⁸C₂ ways.\nP = 9C₂/¹⁵C₂ + ⁸C₂/¹⁵C₂ = 8/17\nANSWER:A", "role": "assistant", "uuid": "cfa4395d-b5b7-4c05-af98-752f476e4e4b" } ]

{ "coherence": 2.98, "complexity": 1.66, "correctness": 2.61, "helpfulness": 2.74, "instruction-following": 3.6, "safety": 4.17, "verbosity": 1.49, "verbosity-coeff": -0.1614 }

[ { "content": "A can do a job in 15days and B in 30days. If they work on it together for 4 days, then the fraction of the work that is left is?\n\n['A)2/15', 'B)3/5', 'C)3/11', 'D)1/12', 'E)6/13']", "role": "user", "uuid": "33a9987e-8a96-41cc-a42b-a442d4496119" }, { "content": "A's 1 day work = 1/15\nB's 1day work = 1/30\nA+B 1day work = 1/15 + 1/30 = 3/30=1/10\nA+B 4days work = 1/10*4 = 2/5\nRemaining work = 1 - 2/5 = 3/5\nAnswer is B", "role": "assistant", "uuid": "ebe297d6-9327-4a40-ba5f-467a38f53d5e" } ]

{ "coherence": 2.68, "complexity": 1.12, "correctness": 2.1, "helpfulness": 2.2, "instruction-following": 2.98, "safety": 5.52, "verbosity": 0.65, "verbosity-coeff": -0.1292 }

[ { "content": "A house seller can deduct 5 percent from the total sales value. If he has sold 5 houses, and the price of two houses is between $150,000 and $250,000, one of them is $300,000 house, two houses are between $500,000 and 800,000, what is the range of his revenue?\n\n['A)750', 'B)800', 'C)850', 'D)860', 'E)880']", "role": "user", "uuid": "64a9228d-65f6-4ef8-bcd1-6bd508766617" }, { "content": "(1) 2(150)+300+2(500) = 1600\n1600*0.95=1520 (Revenue considering the minimum values with the discount)\n(2) 2(250)+300+2(800) = 2400 (Revenue considering the maximum values without the discount)\nSo, the the revenue range could be = 2400 - 1520 = 880\n(Answ E)", "role": "assistant", "uuid": "5df6c2fd-965c-431e-835d-32add7c0fd24" } ]

{ "coherence": 2.57, "complexity": 1.46, "correctness": 1.75, "helpfulness": 1.61, "instruction-following": 1.79, "safety": 3.45, "verbosity": 0.69, "verbosity-coeff": -0.1322 }

[ { "content": "A welder received an order to make a 1 million liter cube-shaped tank. If he has only 4x2 meter sheets of metal that can be cut, how many metal sheets will be required for this orderT? (1 cubic meter = 1,000 liters)\n\n['A)92', 'B)90', 'C)82', 'D)78', 'E)75']", "role": "user", "uuid": "4c416f2a-0b46-4a89-ba28-507f7db0c196" }, { "content": "I get 75. A cube with 1 million liters cube would be a cube with the dimensions of 100*100*100. 4*2 covers 8 sq liters so 100/8 = 12.5.\nT=12.5*6 = 75.E", "role": "assistant", "uuid": "cd724c50-3c0f-41e1-b752-184b4d723978" } ]

{ "coherence": 2.7, "complexity": 1.09, "correctness": 1.67, "helpfulness": 1.7, "instruction-following": 2.08, "safety": 5.55, "verbosity": 0.68, "verbosity-coeff": -0.1218 }

[ { "content": "If a sum of money doubles itself in 15 years at simple interest, the ratepercent per annum is\n\n['A)12', 'B)12.5', 'C)6.67', 'D)13.5', 'E)14']", "role": "user", "uuid": "b129ae95-ff0f-4d1e-8cdb-e1f897123061" }, { "content": "Explanation:\nLet sum = x then Simple Interest = x\nRate = (100 * x) / (x * 15) = 6.67\nOption C", "role": "assistant", "uuid": "93625738-629f-4855-9343-89e5d9609c73" } ]

{ "coherence": 2.78, "complexity": 1.77, "correctness": 1.96, "helpfulness": 2.25, "instruction-following": 2.66, "safety": 4.11, "verbosity": 0.83, "verbosity-coeff": -0.1032 }

[ { "content": "111 = O\n222 = E\n333 = T\n444 = S\nReading and analyzing the above, can you find out the following ?\n555 = ?\n\n['A)8', 'B)3', 'C)1', 'D)5', 'E)0']", "role": "user", "uuid": "cfa8112e-8d92-4888-8d16-11e8c20caae1" }, { "content": "E\n0\n1 * 1 * 1 = One\n2 * 2 * 2 = Eight\n3 * 3 * 3 = Twenty seven\n4 * 4 * 4 = Sixty Four\nFor all the above, you can see that the first letter of the sum is the code.\nThus 5 * 5 * 5 = One twenty five\nThus 555 = O.", "role": "assistant", "uuid": "da9e66a2-c786-4128-ba7e-d9637a089df0" } ]

{ "coherence": 2.29, "complexity": 1.88, "correctness": 1.77, "helpfulness": 1.99, "instruction-following": 1.63, "safety": 3.41, "verbosity": 1.5, "verbosity-coeff": -0.0852 }

[ { "content": "An electric motor makes 1,400 revolutions per minutes. How many degrees does it rotate in one second?\n\n['A)8.400 d/sec', 'B)28.000 d/sec', 'C)38.000 d/sec', 'D)26.000 d/sec', 'E)35.000 d/sec']", "role": "user", "uuid": "20ca028c-32e0-41e4-9cda-e23120967d31" }, { "content": "1400 revolutions / minute\n= 1400*360 degrees / 60 seconds\n= 8400 degrees / second\nA", "role": "assistant", "uuid": "a8fa5e10-ffcf-4e66-8eb4-14f02b0b9837" } ]

{ "coherence": 2.76, "complexity": 1.26, "correctness": 1.76, "helpfulness": 1.79, "instruction-following": 2.29, "safety": 3.72, "verbosity": 1.32, "verbosity-coeff": -0.103 }

[ { "content": "Express a speed of 54 kmph in meters per second?\n\n['A)10 mps', 'B)18 mps', 'C)15 mps', 'D)17 mps', 'E)12 mps']", "role": "user", "uuid": "14011141-2252-44c4-9d72-9550e6af7f9e" }, { "content": "54 * 5/18\n= 15 mps\nAnswer:C", "role": "assistant", "uuid": "ea614069-616c-4ef7-a17f-44bac0415409" } ]

{ "coherence": 2.8, "complexity": 0.9, "correctness": 2.47, "helpfulness": 2.68, "instruction-following": 3.86, "safety": 5.44, "verbosity": 0.65, "verbosity-coeff": -0.1073 }

[ { "content": "If P = 775 × 778 × 781, what is the remainder when P is divided by 14?\n\n['A)6', 'B)7', 'C)8', 'D)9', 'E)10']", "role": "user", "uuid": "6a3bc8a0-5c65-4a17-8c38-f831b9447ca9" }, { "content": "P 775/14 leaves a remainder 5\n778/14 leaves a remainder 8\n781/14 leaves a remainder 11\n5*8*11 =440\nSo the remainder will be the remainder of 440/14 which is 6\nAns A", "role": "assistant", "uuid": "78b5a2f0-36bf-4dd4-8219-33b7a6bf6a65" } ]

{ "coherence": 2.76, "complexity": 1.72, "correctness": 2.16, "helpfulness": 2.04, "instruction-following": 2.57, "safety": 5.67, "verbosity": 1, "verbosity-coeff": -0.2129 }

[ { "content": "Rectangle A has sides a and b, and rectangle B has sides c and d. If a/c=b/d=4/5, what is the ratio of rectangle A’s area to rectangle B’s area?\n\n['A)5/4', 'B)25/16', 'C)4/5', 'D)16/25', 'E)16/5']", "role": "user", "uuid": "b707dd06-5f5e-44b2-bc16-423caff6ded8" }, { "content": "The area of rectangle A is ab.\nc=5a/4 and d=5b/4.\nThe area of rectangle B is cd=25ab/16.\nThe ratio of rectangle A's area to rectangle B's area is ab / (25ab/16) = 16/25.\nThe answer is D.", "role": "assistant", "uuid": "ea7e20ab-f6cf-4710-ae6a-8e1a9a9029d1" } ]

{ "coherence": 3.23, "complexity": 1.99, "correctness": 2.76, "helpfulness": 2.7, "instruction-following": 3.05, "safety": 5.48, "verbosity": 1.08, "verbosity-coeff": -0.1912 }

[ { "content": "3 cooks have to make 80 burgers.They are known to make 20 pieces every minute working together.The 1st cook began workin alone and made 20 pieces having worked for sometime more than 3 mins.The remaining part of the work was done by second and 3rd cook working together.It took a total of 8 minutes to complete the 80 burgers.How many minutes would it take the 1st cook alone to cook 160 burgers?\n\n['A)16 minutes', 'B)24 mins', 'C)32 mins', 'D)40 mins', 'E)30 mins']", "role": "user", "uuid": "223f8920-f6d5-4c98-b6ff-d6c705ba372b" }, { "content": "Denote by A, B, C the rates of the three cooks in units of burgers/minute.\nA + B + C = 20.\nLet t be the time in minutes it took the first cook A to make the 20 burgers. So, A*t = 20, and we know that t > 3.\nWe need to find 8t, as 160 burgers will be made by A in 8 times more than making 20 burgers.\nWe already know that 8t > 8*3 = 24, so we can eliminate answers (A) and (B).\nIn addition, (B + C)(8 - t) = 60, or (20 - A)(8 - t) = 60.\nSince 20 - A < 20 and 8 - t < 5, looking for integer solutions, we find the only acceptable solution 20 - A = 15 and 8 - t = 4, so t = 4.\nI am assuming integer numbers for the solutions based on the answer choices.\nAnyway, testing the answer choices, only (C) is a solution.\nTherefore, A will make 160 burgers in 8*4 = 32 minutes.\nAnswer C", "role": "assistant", "uuid": "4dacba25-d191-4ece-a461-5992991f8fa8" } ]

{ "coherence": 2.88, "complexity": 1.96, "correctness": 2.76, "helpfulness": 2.53, "instruction-following": 3.21, "safety": 4.7, "verbosity": 1.75, "verbosity-coeff": -0.1097 }