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[ { "content": "A certain musical scale has has 13 notes, each having a different frequency, measured in cycles per second. In the scale, the notes are ordered by increasing frequency, and the highest frequency is twice the lowest. For each of the 12 lower frequencies, the ratio of a frequency to the next higher frequency is a fixed constant. If the lowest frequency is 550 cycles per second, then the frequency of the 7th note in the scale is how many cycles per second?\n\n['A)550 * sqrt 2', 'B)550 * sqrt (2^7)', 'C)550 * sqrt (2^12)', 'D)550 * the twelfth root of (2^7)', 'E)550 * the seventh root of (2^12)']", "role": "user", "uuid": "737e8648-cc5c-4b85-939e-26dbf0cd7750" }, { "content": "Let the constant be k.\nF1 = 550\nF2 = 550k\nF3 = 550 k * k = 550 * k^2\nF13= 550 * k^12\nwe know F13 = 2 *F1 = 2 * 550 = 1100\n1100/550 = k^12\nk = twelfth root of 2\nfor F7...\nF7 = 550 * k^6 ( as we wrote for F2 and F3)\nF7 = 550 * (twelfth root of 2) ^ 6\nF7 = 550 * sqrt (2)\nThe answer is A.", "role": "assistant", "uuid": "d52dd672-072d-4ac0-8cbf-67bf258f4ee5" } ]

{ "coherence": 2.9, "complexity": 1.3, "correctness": 1.92, "helpfulness": 2.16, "instruction-following": 2.29, "safety": 5.59, "verbosity": 0.68, "verbosity-coeff": -0.1803 }

[ { "content": "Simple interest on a certain sum of money for 2 years at 12% per annum is half the compound interest on Rs. 6000 for 2 years at 15% per annum. The sum placed on simple interest is\n\n['A)Rs.6000', 'B)Rs.7935', 'C)Rs.8265.63', 'D)Rs.3967.5', 'E)None']", "role": "user", "uuid": "3459062c-5b8a-42f7-aebc-b549aa7cfdc4" }, { "content": "Solution\nC.I.\t=Rs[6000x(1+15/100)²-4000]\nRs.(4000x115/100x115/100-6000)\t= Rs.7935.\nSum\t=Rs. [3967.5x100 /4x12]\n= Rs.8265.63.\nAnswer C", "role": "assistant", "uuid": "02fbe6a9-9178-42f7-b042-f06c95e94fbc" } ]

{ "coherence": 2.18, "complexity": 1.69, "correctness": 1.36, "helpfulness": 1.66, "instruction-following": 2.47, "safety": 4.7, "verbosity": 1.11, "verbosity-coeff": -0.116 }

[ { "content": "The present worth of Rs. 242 due in 2 years at 10% per annum compound interest is:\n\n['A)Rs. 200', 'B)Rs. 250', 'C)Rs. 240', 'D)Rs. 220', 'E)Rs. 230']", "role": "user", "uuid": "17e49236-9a6a-43a8-9216-12a4f4dcf423" }, { "content": "Explanation:\nPresent worth of Rs. x due T years hence is given by\nPresent Worth (PW) = x/(1+R/100)T\nPresent Worth (PW) = 242/(1+10/100)2 = 242/(11/10)2 = Rs. 200\nAnswer: Option A", "role": "assistant", "uuid": "22191ba4-7fd3-4091-b038-5857096e9177" } ]

{ "coherence": 3.13, "complexity": 1.72, "correctness": 2.62, "helpfulness": 2.88, "instruction-following": 3.15, "safety": 4.85, "verbosity": 1.3, "verbosity-coeff": -0.1226 }

[ { "content": "Find the largest 3 digit number which is exactly divisible by 88?\n\n['A)765', 'B)907', 'C)944', 'D)954', 'E)968']", "role": "user", "uuid": "14b69cc5-2a5f-4dc2-9678-5c3d479ef378" }, { "content": "Largest 3 digit number is 999\nAfter doing 999 ÷ 88 we get remainder 31\nHence largest 3 digit number exactly divisible by 88 = 999 - 31 = 968\nE", "role": "assistant", "uuid": "565aa4c0-9d10-499b-8e6d-0437f7329dc7" } ]

{ "coherence": 2.78, "complexity": 1.9, "correctness": 1.82, "helpfulness": 2.06, "instruction-following": 2.47, "safety": 4.85, "verbosity": 0.95, "verbosity-coeff": -0.1914 }

[ { "content": "A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform?\n\n['A)389 m', 'B)350 m', 'C)289 m', 'D)299 m', 'E)219 m']", "role": "user", "uuid": "7b3ef432-a39e-4745-9891-62989a6aa5e3" }, { "content": "Speed = 300/18 = 50/3 m/sec.\nLet the length of the platform be x meters.\nThen, (x + 300)/39 = 50/3\n3x + 900 = 1950 => x = 350 m.\nAnswer:B", "role": "assistant", "uuid": "81544d30-8740-41c3-98ee-005e7aca4d44" } ]

{ "coherence": 2.8, "complexity": 1.61, "correctness": 2.23, "helpfulness": 2.55, "instruction-following": 3.99, "safety": 5.28, "verbosity": 1.6, "verbosity-coeff": -0.1438 }

[ { "content": "Two pumps are connected to an empty tank. Pump X fills the tank with water at a constant rate, while pump Y drains water out of the tank at a constant rate. The two pumps finish filling the tank in two times the duration it would take pump X alone to fill the tank. If pump Y alone can empty a whole tank in 30 minutes, then how many minutes does it take pump X alone to fill the tank?\n\n['A)15', 'B)16', 'C)18', 'D)20', 'E)24']", "role": "user", "uuid": "1974a595-c5ab-40e3-a1e7-1d1a3cbc7c00" }, { "content": "Let V be the volume of the tank.\nLet R be the rate per minute that pump X fills the tank.\nLet T be the time it takes pump X to fill the tank.\nThe rate at which pump Y empties the tank is V/30 per minute.\n(R - V/30)*2T=V=RT.\n(R-V/30)*2=R\nR=V/15.\nIt takes pump X 15 minutes to fill the tank.\nThe answer is A.", "role": "assistant", "uuid": "05f68ef0-f412-4771-8835-1595131f7e13" } ]

{ "coherence": 3.39, "complexity": 2, "correctness": 2.61, "helpfulness": 2.78, "instruction-following": 3.13, "safety": 4.89, "verbosity": 0.97, "verbosity-coeff": -0.1795 }

[ { "content": "If in a book a total of 3209 digits are used for numbering, then find out the total number of pages in the book.\n\n['A)1079', 'B)1000', 'C)1100', 'D)1075', 'E)None of these']", "role": "user", "uuid": "8abf507b-f0a2-4dc7-b3a3-6c7e9092de65" }, { "content": "Explanation:\nNumber of digits used in 1 digit numbers = 1*9 = 9\nNumber of digits used in 2 digit numbers = 2*90 = 180\nNumber of digits used in 3 digit numbers = 3*900 = 2700\nNumber of digits used in 1 digit numbers = 3209 – (9+180+2700) = 320\nHence, number of pages with 4 digit number = 320/4 = 80\nTotal number of pages = 1079\nANSWER: A", "role": "assistant", "uuid": "650aa56e-c7da-41f6-b824-ac22df2ea869" } ]

{ "coherence": 2.61, "complexity": 1.95, "correctness": 2.33, "helpfulness": 2.76, "instruction-following": 3.33, "safety": 4.73, "verbosity": 1.72, "verbosity-coeff": -0.125 }

[ { "content": "Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.25 km and 1.00 km respectively. The time taken by the slower train to cross the faster train in seconds is?\n\n['A)48', 'B)9', 'C)7', 'D)67', 'E)54']", "role": "user", "uuid": "8e501777-8edc-4a29-8789-5f49f46bace7" }, { "content": ":\nRelative speed = 60 + 90 = 150 km/hr.\n= 150 * 5/18 = 125/3 m/sec.\nDistance covered = 1.25 + 1.0 = 2.25 km = 2250 m.\nRequired time = 2250 * 3/125\n= 54 sec.\nAnswer: E", "role": "assistant", "uuid": "18ca2539-ebbc-458d-96e7-0079b38ac251" } ]

{ "coherence": 2.51, "complexity": 1.38, "correctness": 2.14, "helpfulness": 2.37, "instruction-following": 3.45, "safety": 5.63, "verbosity": 0.82, "verbosity-coeff": -0.1058 }

[ { "content": "Given two cylindrical containers--A and B. Cylinder A has a diameter of 12 meters and a height of 10 meters. Cylinder B has a radius of 2 meters and a height of 4 meters. If cylinder A is filled to capacity with water, how many cylinder B will be filled to capacity with the content of cylinder A?\n\n['A)23', 'B)22', 'C)21', 'D)25', 'E)24']", "role": "user", "uuid": "b775c06a-71bd-4a26-9b7b-862bff7d0e3c" }, { "content": "Calculate the volume of the larger cylinder and divide it by the volume of the smaller cylinder.\nvolume of cylinder =πr2h\nCylinder A volume=1130.97\nCylinder B volume=50.27\ntherefore the number of cylinders B that can be filled to capacity=1130.97/50.27=22.5\nAnswer is B only 22 Cylinders B can be filled to capacity.", "role": "assistant", "uuid": "37c294c8-b8e6-4277-86ef-e58d484e23c2" } ]

{ "coherence": 2.88, "complexity": 1.44, "correctness": 2.37, "helpfulness": 2.47, "instruction-following": 2.39, "safety": 4.89, "verbosity": 1.43, "verbosity-coeff": -0.1179 }

[ { "content": "In year Y imported machine tools accounted for 25 percent of total machine-tools sales in the United States, and Japanese imports accounted for 25 percent of the sales of imported machine tools. If the total sales of machine tools imported from Japan that year was x billion dollars, then the total sales of all machine tools in the United States was how many billion dollars?\n\n['A)9x/80', 'B)13x/20', 'C)80/9x', 'D)16x', 'E)80x/9']", "role": "user", "uuid": "a739b2c6-a670-406e-bbc6-54f7eba259af" }, { "content": "Sales of imported tools = 25% of the total sales = 0.25*{total} = {total}/4;\nSales of Japanese tools = 25% of the sales of imported tools = 0.25*{total}/4 = 1/4*{total}/4 = 1*{total}/16.\nSince the sales of of Japanese tools was x, then 1*{total}/16 = x --> {total} = 16x.\nAnswer: D.", "role": "assistant", "uuid": "fd762b3b-4d9e-433a-b826-8321b8939795" } ]

{ "coherence": 3.21, "complexity": 1.79, "correctness": 2.94, "helpfulness": 3.15, "instruction-following": 3.35, "safety": 4.73, "verbosity": 0.38, "verbosity-coeff": -0.1854 }

[ { "content": "In how many ways can 7 boys and 2 girls be arranged a ta table if 2 girls are never together?\n\n['A)30240', 'B)31240', 'C)32410', 'D)32540', 'E)36540']", "role": "user", "uuid": "11487ebe-fa03-401e-bd69-410467ac3834" }, { "content": "Total ways of arranging 9 person in a circle = 8! = 40320 ways\nIf we consider two women as one, then we have 7+1=8 persons. Arranging these eight persons in circle will take = 7! = 5040 ways\nAnd two women can arrange themselves in 2! ways\nTotal ways in which two women sit together in circle = 7!*2! = 10080 ways\nTotal ways in which two women doesn’t sit together in circle = 8! - 7!*2! = 40320 - 10080 = 30240 ways\nA", "role": "assistant", "uuid": "c27a7237-d660-417f-b348-a53fbc59483e" } ]

{ "coherence": 2.76, "complexity": 2.39, "correctness": 2.49, "helpfulness": 2.49, "instruction-following": 3.31, "safety": 5.12, "verbosity": 1.93, "verbosity-coeff": -0.1613 }

[ { "content": "Three investors, A, B, and C, divide the profits from a business enterprise in the ratio of 5 : 7 : 8, respectively. If investor A earned $ 4,500, how much money did investors B and C earn in total?\n\n['A)$4,000', 'B)$4,900', 'C)$5,600', 'D)$9,500', 'E)$13,500']", "role": "user", "uuid": "80686ff9-8812-461e-938e-559ee7fc1a0e" }, { "content": "Let profit for A = 5x\nprofit for B = 7x\nprofit for C = 8x\nInvestor A earned = 34500\n5x = 4500=>x=900\nTotal profit for B and C = 7x+ 8x = 15x\nTherefore , 15x = 15*900 = 13,500\nAnswer E", "role": "assistant", "uuid": "7ecf47ba-83b1-4f0a-a512-063ddc14a717" } ]

{ "coherence": 2.66, "complexity": 1.35, "correctness": 2.82, "helpfulness": 3, "instruction-following": 3.39, "safety": 3.91, "verbosity": 1.05, "verbosity-coeff": -0.1272 }

[ { "content": "There were two candidates in an election. Winner candidate received 60% of votes and won the election by 288 votes. Find the number of votes casted to the winning candidate?\n\n['A)776', 'B)864', 'C)299', 'D)257', 'E)125']", "role": "user", "uuid": "35ec7823-6b02-4e65-bec3-f363a99c488c" }, { "content": "W = 60% L = 40%\n60% - 40% = 20%\n20% -------- 288\n60% -------- ? => 864\nAnswer:B", "role": "assistant", "uuid": "ff1e3b7c-d6fd-46f3-9f82-390a530a9a56" } ]

{ "coherence": 3.11, "complexity": 1.49, "correctness": 2.84, "helpfulness": 3.23, "instruction-following": 3.68, "safety": 6.02, "verbosity": 1.23, "verbosity-coeff": -0.1117 }

[ { "content": "I am three times as old as my son. Five year later, I shall be two and half times as old as my son. How old am I and how old is my son ?\n\n['A)45 year and 15 year', 'B)40 year and 10 year', 'C)42 year and 12 year', 'D)41 year and 11 year', 'E)None of these']", "role": "user", "uuid": "578a03ac-3987-4aff-9c5c-ed20bfcd841e" }, { "content": "Let my age is x years and my son’s age is y years, Then,\nx = 3y\nFive years later, my age will be (x + 5) years and my son’s age will be\n(y + 5) years\nThus, (x + 5) = 5/2 (y + 5)\n=> 2x - 5 y - 15 =0\nputting x = 3y, we get\n6y - 5y - 15 = 0\n=> y = 15\nThus, x = 45\nHence, my present age is 45 years and my son’s present age is 15 years.\nANSWER:A", "role": "assistant", "uuid": "74d20776-c5b6-4b55-81c2-a267c27e40aa" } ]

{ "coherence": 2.82, "complexity": 2.2, "correctness": 2.41, "helpfulness": 2.39, "instruction-following": 3.78, "safety": 4.54, "verbosity": 1.75, "verbosity-coeff": -0.1013 }

[ { "content": "Two pipes A and B can fill a tank in 12 and 24 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?\n\n['A)5 minutes', 'B)10 minutes', 'C)9 minutes', 'D)7 minutes', 'E)8 minutes']", "role": "user", "uuid": "581a26fe-fed1-4ec1-9266-95ff1871f206" }, { "content": "Part filled by pipe A in 1 minute =1/12\nPart filled by pipe B in 1 minute =1/24\nPart filled by pipe A and pipe B in 1 minute=1/12+1/24=1/8\nboth the pipe together can fill the tank in 8 minutes\nAnswer is E", "role": "assistant", "uuid": "a4687bad-d63f-46fd-bb79-b41ac7f1af71" } ]

{ "coherence": 2.84, "complexity": 1.12, "correctness": 2.59, "helpfulness": 2.76, "instruction-following": 3.74, "safety": 5.79, "verbosity": 1.12, "verbosity-coeff": -0.1054 }

[ { "content": "Due to construction, the speed limit along an 9-mile section of highway is reduced from 55 miles per hour to 35 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?\n\n['A) 5.61', 'B) 8', 'C) 10', 'D) 15', 'E) 24']", "role": "user", "uuid": "068c8c6a-c110-4324-b83c-e1116cecd429" }, { "content": "Old time in minutes to cross 9 miles stretch = 9*60/55 = 9*12/11 = 9.81\nNew time in minutes to cross 9 miles stretch = 9*60/35 = 9*12/7 = 15.42\nTime difference = 5.61\nAns:A", "role": "assistant", "uuid": "939b9d39-8f08-40c6-bb42-c687973a4186" } ]

{ "coherence": 2.49, "complexity": 1.37, "correctness": 1.7, "helpfulness": 1.89, "instruction-following": 2.92, "safety": 4.93, "verbosity": 1.05, "verbosity-coeff": -0.1686 }

[ { "content": "If 12 men or 20 women can do a piece of work in 54 days, then in how many days can 9 men and 12 women together do the work?\n\n['A)30 days', 'B)40 days', 'C)50 days', 'D)70 days', 'E)80 days']", "role": "user", "uuid": "d675f5a4-8bc0-4cf6-8706-584e3bb73118" }, { "content": "B\n40 days\nGiven that 12m = 20w => 3m = 5w\n9 men + 12 women = 15 women + 12 women = 27 women\n20 women can do the work in 54 days. So, 27 women can do it in (20 * 54) /27 = 40 days.", "role": "assistant", "uuid": "24b979f9-f548-4456-8aca-a9d18c339da9" } ]

{ "coherence": 2.88, "complexity": 1.38, "correctness": 1.79, "helpfulness": 2.02, "instruction-following": 2.51, "safety": 5.24, "verbosity": 0.87, "verbosity-coeff": -0.1423 }

[ { "content": "Eight persons in an organization including A and B were to be divided in two groups of 4 members each. The total number of groups which not containing both A and B is what fraction of the total number of groups which can be formed?\n\n['A)1/4', 'B)1/70', 'C)3/14', 'D)1/10', 'E)11/14']", "role": "user", "uuid": "a65bc806-d16c-4b17-acd1-ab162bd39bde" }, { "content": "The fraction is nothing but the probability..\nNumber to choose 4 out of 8= 8C4..\nNumber to choose A and B and 2 from remaining 6=6C2..\nprob of A and B choosen=6C2/8C4= {6!/4!2!}/{8!/4!4!}..\n6!4!4!/8!4!2!=3/2*7=3/14\nAnswer = 1-3/14 = 11/14\nAnswer : E", "role": "assistant", "uuid": "04e77a8f-532d-4769-b2fd-af0ffac51f1a" } ]

{ "coherence": 2.35, "complexity": 1.38, "correctness": 1.91, "helpfulness": 1.91, "instruction-following": 2.86, "safety": 5.12, "verbosity": 1.27, "verbosity-coeff": -0.1826 }

[ { "content": "If p and q are positive integers, how many integers are larger than pq and smaller than p(q + 3)?\n\n['A)3', 'B)P + 2', 'C)p – 2', 'D)3p – 1', 'E)2p + 1']", "role": "user", "uuid": "bfdc1c40-ea09-4922-8408-f62324640df8" }, { "content": "The number of integers between x and y, where x>y is (x-y)-1. For example, the number of integers between 1 and 5 is (5-1)-1=3: 2, 3, and 4.\nThus, the number of integers between pq and p(q+3)=pq+3p is (pq+3p-pq)-1=3p-1.\nAnswer: D.", "role": "assistant", "uuid": "6af9b20a-4b87-4f1a-825e-1a1efb2ac0e3" } ]

{ "coherence": 2.84, "complexity": 2.12, "correctness": 2.27, "helpfulness": 2.35, "instruction-following": 2.84, "safety": 4.32, "verbosity": 1.16, "verbosity-coeff": -0.1763 }

[ { "content": "What is the least number of cut pieces of equal length that can be cut out of two lengths 10 meters 857 millimeters and 15 meters 87 millimeters.\n\n['A)184', 'B)266', 'C)255', 'D)887', 'E)111']", "role": "user", "uuid": "9281a3a4-d362-497c-a25f-1adbb9d7ff3a" }, { "content": "Here, you need to find the HCF. Because, to get least number of equal cut pieces you should cut as big as possible. So, HCF of 10857 and 15087 = 141. (This is the size of each cut piece). Then the number of cut pieces = (10857 + 15087) ÷ 141 = 184.\nAnswer:A", "role": "assistant", "uuid": "a12aaa62-1590-45e4-a914-6727acc46d58" } ]

{ "coherence": 3.04, "complexity": 1.26, "correctness": 2.51, "helpfulness": 2.66, "instruction-following": 3.07, "safety": 5.16, "verbosity": 0.96, "verbosity-coeff": -0.128 }

[ { "content": "A man drive his car to the office at 20miles/hr.\nAfter reaching office, he realize that its a new year holiday so he went back home at a speed of 30miles/hr.\nDiscounting the time spent in the stoppage what was his average speed of his journey ?\n\n['A)23miles/hr', 'B)24miles/hr', 'C)25miles/hr', 'D)26miles/hr', 'E)None']", "role": "user", "uuid": "8a026d5a-bd8b-4c79-9932-50bf2164593e" }, { "content": "Solution:\n24miles/hr (not 25miles/hr which might be guessed by many)\nD : distance traveled\nT1 : time of going to office\nT2 : time of returning back\nY : Average Speed\nD = 20 * T1\nT1 = D/20\nD = 30 * T2\nT2 = D/30\n2D = Y(T2 + T1)\n2D = Y(D/20 + D/30)\n2D = Y(3D/60 + 2D/60)\n2D = Y(5D/60)\nY = 120D/5D\n=> Y = 24\nAnswer B", "role": "assistant", "uuid": "72ec7ecf-df05-4a7d-9b34-e053062608df" } ]

{ "coherence": 2.72, "complexity": 1.95, "correctness": 2.39, "helpfulness": 2.41, "instruction-following": 3.05, "safety": 4.89, "verbosity": 1.62, "verbosity-coeff": -0.1223 }

[ { "content": "In a Quiz the points in each round for the first,second and third were 1000,50,20 . No other points were given. Sam participated in several rounds in the competition and the product of his score was 50000. In How many rounds did he participate?\n\n['A)Cannot be determined', 'B)43', 'C)3', 'D)6', 'E)10']", "role": "user", "uuid": "6f069907-5343-4cd3-b506-bed26ebf0a6e" }, { "content": "Correct answer is A because we are given that there won't be any points awarded for rounds other than 1st three position.\nThus, it may happen that he played 100 rounds out of only 7 rounds were there in which he was awarded some points.", "role": "assistant", "uuid": "0f1dcb9d-47e3-4342-b4e7-0e1a1394fb97" } ]

{ "coherence": 2.88, "complexity": 2.25, "correctness": 2.18, "helpfulness": 2.21, "instruction-following": 1.83, "safety": 3.91, "verbosity": 1.71, "verbosity-coeff": -0.122 }

[ { "content": "The area of a triangle is with base 8m and height 4m?\n\n['A)88 m2', 'B)10 m2', 'C)16 m2', 'D)77 m2', 'E)31 m2']", "role": "user", "uuid": "08ba5e16-b5f3-4642-80f1-01b214a28512" }, { "content": "1/2 * 8 * 4 = 16 m2\nAnswer: C", "role": "assistant", "uuid": "0eaf3cb1-6229-430b-a6d4-5963d9a7373a" } ]

{ "coherence": 2.82, "complexity": 0.63, "correctness": 2.59, "helpfulness": 2.82, "instruction-following": 3.72, "safety": 4.66, "verbosity": 0.42, "verbosity-coeff": -0.1021 }

[ { "content": "Arun purchased 30 kg of wheat at the rate of Rs. 11.50 per kg and 20 kg of wheat at the rate of 14.25 per kg. He mixed the two and sold the mixture. Approximately what price per kg should be sell the mixture to make 20% profit?\n\n['A)15.12', 'B)16.33', 'C)16.35', 'D)16.3', 'E)16.32']", "role": "user", "uuid": "7671976d-6c26-4c94-ad96-9376b7fb5d0a" }, { "content": "C.P. of 50 kg wheat = (30 * 11.50 + 20 * 14.25) = Rs. 630.\nS.P. of 50 kg wheat = 120% of Rs. 630 = 120/100 * 630 = Rs. 756\nS.P. per kg = 756/50 = Rs. 15.12\nAnswer: A", "role": "assistant", "uuid": "077b1556-c9ab-4823-9145-b1fea3d530bf" } ]

{ "coherence": 2.86, "complexity": 1.79, "correctness": 1.98, "helpfulness": 2.25, "instruction-following": 3.46, "safety": 4.7, "verbosity": 1.35, "verbosity-coeff": -0.1528 }

[ { "content": "One years ago,Promila was four times as old as her daughter Sakshi.Six years hence,Promila’s age will excepted her daughter’s age by 9 years.The ratio of the present ages of Promila and her daughter is\n\n['A)9 : 2', 'B)11 : 3', 'C)12 : 5', 'D)13 : 4', 'E)None of these']", "role": "user", "uuid": "e7c0998a-008a-437e-876b-2e9625dbe89d" }, { "content": "Solution\nLet the ages of Promila and Sakshi 1 year ago be 4x and x years respectively.\nThen,[(4x +1)+6]-[(x + 4)+ 4]=64 ⇔ 4x = 48 ⇔ x =12.\n∴ Required ratio =(4x +1 ) : (x + 1) : 13 : 4. Answer D", "role": "assistant", "uuid": "eb207b43-b450-4332-84a9-449233b189c6" } ]

{ "coherence": 2.29, "complexity": 1.29, "correctness": 1.51, "helpfulness": 1.47, "instruction-following": 2.68, "safety": 6.45, "verbosity": 0.56, "verbosity-coeff": -0.1274 }

[ { "content": "Marketing executives for a certain chewing gum company projected a 30 percent increase in revenue this year over that of last year, but revenue this year actually decreased by 25%. What percent of the projected revenue was the actual revenue ?\n\n['A)53%', 'B)57.7%', 'C)62.5%', 'D)64%', 'E)75%']", "role": "user", "uuid": "e651e74f-28b9-4d15-8d68-126ca1c67742" }, { "content": "Last year revenue = 100 (assume);\nThis year revenue = 75;\nProjected revenue = 130.\nActual/Projected*100=75/130*100 = 57.7%.\nAnswer: B.", "role": "assistant", "uuid": "5e37df86-401d-40af-a7b9-c76015965baf" } ]

{ "coherence": 2.98, "complexity": 0.77, "correctness": 2.64, "helpfulness": 2.7, "instruction-following": 3.95, "safety": 4.4, "verbosity": 0.33, "verbosity-coeff": -0.1513 }

[ { "content": "A motorist knows four different routes from Bristol to Birmingham. From Birmingham to Sheffield he knows three different routes and from Sheffield to Carlisle he knows two different routes. How many routes does he know from Bristol to Carlisle ?\n\n['A)4', 'B)8', 'C)12', 'D)24', 'E)26']", "role": "user", "uuid": "c063d2d8-d59c-4501-a1a4-747f07d74412" }, { "content": "Explanation:\nTotal number of routes from Bristol to Carlisle = (4 x 3 x 2) = 24.\nAnswer: D", "role": "assistant", "uuid": "6b36b441-c115-489d-bfa7-70212ec2a1b5" } ]

{ "coherence": 2.9, "complexity": 1.23, "correctness": 2.49, "helpfulness": 2.76, "instruction-following": 3.58, "safety": 5.2, "verbosity": 0.89, "verbosity-coeff": -0.1485 }

[ { "content": "If difference between compound interest and simple interest on a sum at 10% P.a. for 2 years is Rs.51 then sum is\n\n['A)Rs.5000', 'B)Rs.5100', 'C)Rs.5800', 'D)Rs.6000', 'E)Rs.6200']", "role": "user", "uuid": "3ed4b8de-68e0-40c4-a06d-42be2aeda0c8" }, { "content": "p(r/100)^2=C.I-S.I\nP(10/100)^2=51\n5100\nANSWER:B", "role": "assistant", "uuid": "de9d272e-97b2-4a6b-b30b-b21176ea27fe" } ]

{ "coherence": 2.55, "complexity": 1.57, "correctness": 2.12, "helpfulness": 2.41, "instruction-following": 2.98, "safety": 5.24, "verbosity": 0.88, "verbosity-coeff": -0.1135 }

[ { "content": "Double of Quarter of 4 percent written as a decimal is :\n\n['A)0.003', 'B)0.0005', 'C)0.25', 'D)0.02', 'E)None of these']", "role": "user", "uuid": "93cf0a28-d6f0-4470-a222-c1ecf2dbe844" }, { "content": "Explanation :\nSolution: (2)*(1/4)*4% = 2*(1/4 * 1/100)= 0.02.\nAnswer : D", "role": "assistant", "uuid": "8dda3e31-36a2-4b50-a70a-9b674d23c217" } ]

{ "coherence": 2.55, "complexity": 1.79, "correctness": 2.59, "helpfulness": 2.53, "instruction-following": 3.43, "safety": 5.09, "verbosity": 1.01, "verbosity-coeff": -0.1102 }

[ { "content": "When Jessica withdrew $400 from her bank account, her account balance decreased by 2/5. If she deposits an amount equal to 1/4 of the remaining balance, what will be the final balance in her bank account?\n\n['A)300', 'B)375', 'C)400', 'D)500', 'E)750']", "role": "user", "uuid": "a4c3fcf7-15b6-40a8-8f4d-7d5f684cd89c" }, { "content": "As per the question 400=2a/5\nthus- a which is the total amount =1000\nThe amount thus left =600\nShe then deposited 1/4 of 600=150\ntotal amount in her account =750\nanswer E", "role": "assistant", "uuid": "29dd6b07-4959-4bce-aaae-4645e2202c5d" } ]

{ "coherence": 2.47, "complexity": 0.95, "correctness": 1.73, "helpfulness": 2, "instruction-following": 2.37, "safety": 5.98, "verbosity": 0.76, "verbosity-coeff": -0.1558 }

[ { "content": "A single discount equivalent to the discount series of 20%, 10% and 5% is?\n\n['A)31.9', 'B)31.7', 'C)31.6', 'D)31.54', 'E)31.1']", "role": "user", "uuid": "bb468445-3bea-434f-a03b-28caf3f54e15" }, { "content": "100*(80/100)*(90/100)*(95/100) = 68.4\n100 - 68.4 = 31.6\nAnswer:C", "role": "assistant", "uuid": "73f4c082-25ac-4365-bbb8-716ac951c3f3" } ]

{ "coherence": 3, "complexity": 1.51, "correctness": 2.21, "helpfulness": 2.25, "instruction-following": 3.52, "safety": 4.89, "verbosity": 0.96, "verbosity-coeff": -0.097 }

[ { "content": "If logx y = 10 and log2 x = 1000, what is the value of y?\n\n['A)2100', 'B)21000', 'C)210000', 'D)210', 'E)21100']", "role": "user", "uuid": "e99295a4-433d-4b4b-bdad-60e764ef6ba3" }, { "content": "log2 x = 1000\n=> x = 21000\nlogx y = 10\n=> y = x10\n= (21000)10\n= 2(1000 × 10)\n= 210000\nAnswer: Option C", "role": "assistant", "uuid": "5b231675-bfa3-41dd-9eaa-90f17d8532fa" } ]

{ "coherence": 2.68, "complexity": 2.21, "correctness": 2.37, "helpfulness": 2.53, "instruction-following": 3.04, "safety": 5.01, "verbosity": 1.12, "verbosity-coeff": -0.1085 }

[ { "content": "Two trains of equal are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 72 sec. The length of each train is?\n\n['A)50', 'B)26', 'C)27', 'D)28', 'E)100']", "role": "user", "uuid": "0d847723-a39c-46a3-9785-fc7f23f580c8" }, { "content": "Let the length of each train be x m.\nThen, distance covered = 2x m.\nRelative speed = 46 - 36 = 10 km/hr.\n= 10 * 5/18 = 25/9 m/sec.\n2x/72 = 25/9 => x = 100.\nAnswer: E", "role": "assistant", "uuid": "ac1b468f-58f0-47a6-a585-bb2d622ea74e" } ]

{ "coherence": 2.98, "complexity": 1.44, "correctness": 2.68, "helpfulness": 2.84, "instruction-following": 4.03, "safety": 5.63, "verbosity": 0.91, "verbosity-coeff": -0.1207 }

[ { "content": "A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform?\n\n['A)327', 'B)350', 'C)276', 'D)287', 'E)261']", "role": "user", "uuid": "33ba1f66-5578-4351-ade2-c5c9f2c1b5f9" }, { "content": "Speed = 300/18 = 50/3 m/sec.\nLet the length of the platform be x meters.\nThen, (x + 300)/39 = 50/3\n3x + 900 = 1950 => x = 350 m.\nAnswer: B", "role": "assistant", "uuid": "d91c06b2-72d2-45c9-8b26-de92c3befa65" } ]

{ "coherence": 2.62, "complexity": 1.74, "correctness": 2.08, "helpfulness": 2.39, "instruction-following": 3.68, "safety": 4.85, "verbosity": 1.37, "verbosity-coeff": -0.1216 }

[ { "content": "In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 4 boys when No boy gets more than one prize?\n\n['A)16', 'B)18', 'C)20', 'D)24', 'E)26']", "role": "user", "uuid": "2c86ac87-d0b4-4554-a2a0-2bdfeb8f8fa8" }, { "content": "Sol. In this case, repetitions are not allowed. So, the first prize can be given in 4 ways. The second in 3 ways and the third in 2 ways. But fundamental principle, (4 x 3 x 2) ways = 24 ways\n4: Or 4p = — 4:- 4X3X2X1- 24 ways\nD", "role": "assistant", "uuid": "9c812721-573a-4a31-a82c-ca5ed854d078" } ]

{ "coherence": 2.62, "complexity": 1.49, "correctness": 2.21, "helpfulness": 2.23, "instruction-following": 3.07, "safety": 4.73, "verbosity": 1, "verbosity-coeff": -0.1384 }

[ { "content": "What percent of 500 is 125?\n\n['A)0.25%', 'B)4%', 'C)25%', 'D)40%', 'E)250%']", "role": "user", "uuid": "385edcef-79b6-4978-8221-c4d7af7e22ef" }, { "content": "500*x /100 = 125\nx = 125/5\nx = 25\nAns: C", "role": "assistant", "uuid": "c793d110-561c-4094-823d-5374e01b9192" } ]

{ "coherence": 3.15, "complexity": 1.6, "correctness": 3.09, "helpfulness": 2.92, "instruction-following": 3.45, "safety": 5.2, "verbosity": 0.79, "verbosity-coeff": -0.1368 }

[ { "content": "Find the nearest to 25268 which is exactly divisible by 467?\n\n['A)1278', 'B)8100', 'C)1287', 'D)1771', 'E)1221']", "role": "user", "uuid": "99296718-9a2d-459a-9903-c2e5a4339073" }, { "content": "Explanation:\n900 * 3 * 3 = 8100\nAnswer: B", "role": "assistant", "uuid": "896ae9de-0eca-4945-b45a-b97f1d606f24" } ]

{ "coherence": 2.18, "complexity": 0.86, "correctness": 1.28, "helpfulness": 1.55, "instruction-following": 1.31, "safety": 4.85, "verbosity": 0.45, "verbosity-coeff": -0.1591 }

[ { "content": "Sonia's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?\n\n['A)8 Years', 'B)6 Years', 'C)4 Years', 'D)2 Years', 'E)None']", "role": "user", "uuid": "e3331b21-239f-4863-9c7b-460f38766a4a" }, { "content": "Explanation:\nMother's age when Sonia's brother was born = 36 years.\nFather's age when Sonia's brother was born = (38 + 4) years = 42 years.\nRequired difference = (42 - 36) years = 6 years.\nAnswer: B", "role": "assistant", "uuid": "ae9a068b-c7da-4ec2-af26-9eea34a14ebc" } ]

{ "coherence": 2.68, "complexity": 1.38, "correctness": 2.14, "helpfulness": 2.49, "instruction-following": 3.07, "safety": 5.48, "verbosity": 0.93, "verbosity-coeff": -0.1346 }

[ { "content": "An equity analyst needs to select 5 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 10, in how many ways can she choose and rank her top 5 picks?\n\n['A)21548', 'B)31502', 'C)21250', 'D)30240', 'E)84045']", "role": "user", "uuid": "8d855a37-9117-4343-9dff-40f77bab1820" }, { "content": "Number of ways of choosing 5 stocks = 10C5\nNumber of ways of ranking the chosen stocks = 5!\nHence total ways of chosing and ranking = 10C5 * 5! = 30240\nCorrect Option: D", "role": "assistant", "uuid": "2e30cec3-237e-4a4e-a594-ca09913fa2a1" } ]

{ "coherence": 3, "complexity": 2.08, "correctness": 2.78, "helpfulness": 3.15, "instruction-following": 4.07, "safety": 5.75, "verbosity": 1.04, "verbosity-coeff": -0.1136 }

[ { "content": "Find the invalid no.from the following series 15, 16, 34, 105, 424, 2124, 12756\n\n['A)1200', 'B)1465', 'C)1765', 'D)1900', 'E)2124']", "role": "user", "uuid": "420b9db9-fd88-4462-b3b9-670185298cb9" }, { "content": "2nd term = (1st term) * 1 + 1 = 15 *1 + 1 = 16.\n3rd term = (2nd term) * 2 + 2 = 16 * 2 + 2 = 34\n4th term = (3th term) *3 + 3 = 34 * 3 + 3 = 105\n5th term = (4th term) * 4 + 4 = 105 * 4 + 4 = 424\n6th term = (5th term) * 5 + 5 = 424 * 5 + 5 = 2125\n6th term should 2125 instead of 2124.\nE", "role": "assistant", "uuid": "e14c62d4-6f33-4a3e-8e2f-ecb138464dcd" } ]

{ "coherence": 2.49, "complexity": 1.89, "correctness": 2.12, "helpfulness": 2.18, "instruction-following": 2.25, "safety": 2.82, "verbosity": 1.29, "verbosity-coeff": -0.0971 }

[ { "content": "How many 4-letter words with or without meaning can be formed out of the letters of the word,'LOGARITHMS',if repetition of letters is not allowed?\n\n['A)5040', 'B)2520', 'C)400', 'D)40', 'E)1502']", "role": "user", "uuid": "855bd5aa-7de7-48c9-ae19-b443902d9fed" }, { "content": "'LOGARITHMS' contains 10 different letters\nRequired number of words=Number of arrangements of 10 letters taking 4 at a time\n=10P4\n=10*9*8*7\n=5040\nOption A", "role": "assistant", "uuid": "7918ddb0-4622-4cba-b183-f5ac621c772d" } ]

{ "coherence": 2.82, "complexity": 1.47, "correctness": 1.97, "helpfulness": 2.18, "instruction-following": 2.06, "safety": 5.48, "verbosity": 1.16, "verbosity-coeff": -0.1178 }

[ { "content": "A pupil's marks were wrongly entered as 83 instead of 63. Due to the average marks for the class got increased by half. The number of pupils in the class is?\n\n['A)33', 'B)38', 'C)40', 'D)21', 'E)25']", "role": "user", "uuid": "8b505afb-7c23-4abe-89ac-597f5018135f" }, { "content": "Let there be x pupils in the class.\nTotal increase in marks = (x * 1/2)\n= x/2\nx/2 = (83 - 63) => x/2 = 20 => x\n= 40.\nAnswer:C", "role": "assistant", "uuid": "adb8b537-8f12-495c-8407-cbf58bfb6a22" } ]

{ "coherence": 2.9, "complexity": 2.2, "correctness": 2.82, "helpfulness": 2.84, "instruction-following": 3.46, "safety": 4.54, "verbosity": 1.21, "verbosity-coeff": -0.1244 }

[ { "content": "Find the odd man out\n3, 8, 15, 24, 34, 48, 63\n\n['A)15', 'B)24', 'C)34', 'D)48', 'E)58']", "role": "user", "uuid": "4fdc7579-3d04-4f4d-887e-4a2b999f8b26" }, { "content": "difference between numbers are 5, 7, 9, 11, 13, 15\n3+5=8\n8+7=15\n15+9=24\n24+11=35\n35+13=48\n48+15=63\nANSWER:C", "role": "assistant", "uuid": "b0d66e52-9e3b-450b-81bc-a6320b369d27" } ]

{ "coherence": 2.45, "complexity": 1.44, "correctness": 2.29, "helpfulness": 2.41, "instruction-following": 2.35, "safety": 3.8, "verbosity": 1.55, "verbosity-coeff": -0.0773 }

[ { "content": "The average of the marks of 12 students in a class is 36. If the marks of each student are doubled, find the new average?\n\n['A)72', 'B)77', 'C)26', 'D)27', 'E)29']", "role": "user", "uuid": "65ad44b8-3266-47dd-9525-96d36f1d8125" }, { "content": "Sum of the marks for the 12 students\n= 12 * 36 = 432. The marks of each student are doubled, the sum also will be doubled.\nThe new sum = 432 * 2 = 864. So, the new average\n= 864/12 = 72.\nAnswer:A", "role": "assistant", "uuid": "0bb3f56a-554e-4431-9b02-ab91c4277081" } ]

{ "coherence": 3.15, "complexity": 1.49, "correctness": 3.21, "helpfulness": 3.33, "instruction-following": 4.17, "safety": 4.21, "verbosity": 1.7, "verbosity-coeff": -0.1195 }

[ { "content": "Train X crosses a stationary train Y in 60 seconds and a pole in 25 seconds with the same speed. The length of the train X is 300 m. What is the length of the stationary train Y?\n\n['A)185 m', 'B)420 m', 'C)167 m', 'D)176 m', 'E)168 m']", "role": "user", "uuid": "25d0aa47-9b4a-45ab-93d4-46fce23c5ee4" }, { "content": "Let the length of the stationary train Y be LY\nGiven that length of train X, LX = 300 m\nLet the speed of Train X be V.\nSince the train X crosses train Y and a pole in 60 seconds and 25 seconds respectively.\n=> 300/V = 25 ---> ( 1 )\n(300 + LY) / V = 60 ---> ( 2 )\nFrom (1) V = 300/25 = 12 m/sec.\nFrom (2) (300 + LY)/12 = 60\n=> 300 + LY = 60 (12) = 720\n=> LY = 720 - 300 = 420 m\nLength of the stationary train = 420 m\nAnswer:B", "role": "assistant", "uuid": "5e61c19f-8707-4c19-a27d-7e0bea9c7b70" } ]

{ "coherence": 2.96, "complexity": 1.7, "correctness": 2.51, "helpfulness": 2.76, "instruction-following": 3.84, "safety": 4.97, "verbosity": 1.2, "verbosity-coeff": -0.1144 }

[ { "content": "Find the value of (X) in the given equation ?\n35% of 1500 + X = 45% of 4200 – 320\n\n['A)910', 'B)980', 'C)1012', 'D)1045', 'E)None of these']", "role": "user", "uuid": "68a5bdfa-1fc2-4f2d-932b-67975bf6c73b" }, { "content": "Explanation:\n35% of 1500 + X = 45% of 4200 – 320\n(35/100 * 1500) + X = (45/100 * 4200) – 320\n525 + X = 1890 – 320\nX = 1890 – 320 – 525\nX = 1890 – 845\nX = 1045\nANSWER: D", "role": "assistant", "uuid": "3c2ceebd-816c-42d2-a3f7-719d56376311" } ]

{ "coherence": 2.86, "complexity": 1.79, "correctness": 2.43, "helpfulness": 2.7, "instruction-following": 4.32, "safety": 4.25, "verbosity": 1.07, "verbosity-coeff": -0.1148 }

[ { "content": "A and B put in Rs.300 and Rs.400 respectively into a business. A reinvests into the business his share of the first year's profit of Rs.210 where as B does not. In what ratio should they divide the second year's profit?\n\n['A)39:40', 'B)39:47', 'C)39:50', 'D)39:44', 'E)39:41']", "role": "user", "uuid": "fcd1cef2-d5dc-4bd8-8298-4ce9dee9f1c2" }, { "content": "3: 4\nA = 3/7*210 = 90\n390: 400\n39:40.Answer:A", "role": "assistant", "uuid": "cc2142d8-680f-4d3b-bb9d-15f9ae7798e1" } ]

{ "coherence": 2.51, "complexity": 1.42, "correctness": 2.04, "helpfulness": 2.18, "instruction-following": 2.39, "safety": 4.85, "verbosity": 0.41, "verbosity-coeff": -0.1629 }

[ { "content": "Three numbers are in the ratio 4 : 5 : 6 and their average is 25 . The largest number is:\n\n['A)28', 'B)30', 'C)36', 'D)42', 'E)45']", "role": "user", "uuid": "15b487a3-b589-4380-bbad-192625676455" }, { "content": "Explanation:\nLet the numbers be 4x, 5x and 6x. Therefore,\n(4x+5x+6x)/3 = 25\n15x = 75\nx = 5\nLargest number = 6x = 30.\nANSWER B", "role": "assistant", "uuid": "f4bbdfb6-bd32-4cdd-9990-4b618b946a09" } ]

{ "coherence": 3.05, "complexity": 1.42, "correctness": 2.92, "helpfulness": 3.17, "instruction-following": 3.97, "safety": 4.97, "verbosity": 1.09, "verbosity-coeff": -0.114 }

[ { "content": "What Is The Next Number\n12 13 15 17 111 113 117 119 123 ?\n\n['A)212', 'B)321', 'C)129', 'D)234', 'E)654']", "role": "user", "uuid": "a3184a28-2fab-42dd-b085-14b35f6d1867" }, { "content": "C\n129.\nThese are the first 10 prime numbers (2, 3, 5...) prefixed with a 1", "role": "assistant", "uuid": "d9c673a4-895f-43d4-8a25-ccc0cacb8cbf" } ]

{ "coherence": 2.41, "complexity": 1.09, "correctness": 1.42, "helpfulness": 1.65, "instruction-following": 1.52, "safety": 3.05, "verbosity": 0.32, "verbosity-coeff": -0.0863 }

[ { "content": "Country C imposes a two-tiered tax on imported cars: the first tier imposes a tax of 12% of the car's price up to a certain price level. If the car's price is higher than the first tier's level, the tax on the portion of the price that exceeds this value is 8%. If Ron imported a $14,000 imported car and ended up paying $1640 in taxes, what is the first tier's price level?\n\n['A)$1600', 'B)$6000', 'C)$6050', 'D)$7050', 'E)$13000']", "role": "user", "uuid": "305da4c7-3c31-4a89-8087-e4b0503dce74" }, { "content": "Let T be the tier price, P be total price = 14000\nPer the given conditions:\n0.12T + 0.08(P-T) = 1640 ----> T= 13000. E is the correct answer.", "role": "assistant", "uuid": "d1b23cba-ca80-4d64-9f3c-7dd67be00c3e" } ]

{ "coherence": 2.98, "complexity": 1.11, "correctness": 1.49, "helpfulness": 1.77, "instruction-following": 2, "safety": 5.01, "verbosity": 0.21, "verbosity-coeff": -0.2098 }

[ { "content": "In traveling from a dormitory to a certain city, a student went 1/5 of the way by foot, 2/3 of the way by bus, and the remaining 12 kilometers by car. What is the distance, in kilometers, from the dormitory to the city?\n\n['A)30', 'B)45', 'C)60', 'D)90', 'E)120']", "role": "user", "uuid": "dea9000a-8aee-4e2d-87d6-1e03d2a74154" }, { "content": "Whole trip = distance by foot + distance by bus + distance by car\nx = 1/5x + 2/3x + 12\nx - 13/15x = 12\n2/15x = 12 => so x = (15/2)*12 = 90Km\nAnswer D", "role": "assistant", "uuid": "56a116c8-741d-48e5-88e9-a2b8b40b6bf2" } ]

{ "coherence": 3.02, "complexity": 1.28, "correctness": 2.7, "helpfulness": 2.68, "instruction-following": 3.66, "safety": 5.01, "verbosity": 0.76, "verbosity-coeff": -0.2461 }

[ { "content": "AMS employs 7 professors on their staff. Their respective probability of remaining in employment for 10 years are, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9. The probability that after 10 years all 7 of them still work in AMS is ?\n\n['A)0.19', 'B)0.018144', 'C)0.1', 'D)0.16', 'E)none of these']", "role": "user", "uuid": "a58e08a6-471a-454a-9797-4845c057dca6" }, { "content": "Asking atleast 6 of them continue ,\nit has 3 cases.\n1 all 7 professors continue.\nall 7 continues - 0.3*0.4*.0.5*0.6*0.7*0.8*0.9 =0.018144\nB", "role": "assistant", "uuid": "c16ba638-894c-4846-819c-2936cecdee9b" } ]

{ "coherence": 2.45, "complexity": 1.4, "correctness": 1.77, "helpfulness": 1.76, "instruction-following": 2.45, "safety": 4.32, "verbosity": 1.27, "verbosity-coeff": -0.1136 }

[ { "content": "1/3 +1/2 - 5/6 + 1/5 + 1/4 - 9/20 -9/20=\n\n['A)0', 'B)2/15', 'C)2/5', 'D)9/20', 'E)5/6']", "role": "user", "uuid": "f53e2c0c-e1ae-428a-b6e9-8fc3085e683a" }, { "content": "We need to determine the result of 1/3 + 1/2 - 5/6 + 1/5 + 1/4 - 9/20\nLet’s add the given fractions in two groups. In the group of the first three fractions, notice that1/3 and 1/2 share a common denominator of 6 with 5/6.\n1/2 + 1/3 = 3/6 + 2/6 = 5/6\nThus, 5/6 – 5/6 = 0\nLooking at the 2nd group of the fractions (1/5, 1/4, and 9/20), notice that1/5 and 1/4 share a common denominator of 20 with 9/20.\n1/5 + 1/4 = 4/20 + 5/20 = 9/20\nThus, 9/20 – 9/20 = 0.\nThus, the result of 1/3 + 1/2 – 5/6 + 1/5 + 1/4 – 9/20 is 9/20.\nAnswer: D", "role": "assistant", "uuid": "784b8b72-6de6-4ed0-a07d-ec0612f22322" } ]

{ "coherence": 2.94, "complexity": 2.02, "correctness": 2.53, "helpfulness": 2.61, "instruction-following": 3, "safety": 3.82, "verbosity": 1.58, "verbosity-coeff": -0.1085 }

[ { "content": "Find out the C.I on Rs.1000 at 4% p.a. compound half-yearly for 1 1/2 years.\n\n['A)A)Rs.41.20', 'B)B)Rs.51.20', 'C)C)Rs.61.20', 'D)D)Rs.71.20', 'E)E)Rs.81.20']", "role": "user", "uuid": "c499305c-d933-47e5-b644-18147eac856f" }, { "content": "A = 1000(51/50)3\n= 1061.20\n1000\n-----------\n61.20\nANSWER:C", "role": "assistant", "uuid": "aefe0b52-be9f-46d8-9862-a0690df148fc" } ]

{ "coherence": 2.59, "complexity": 1.37, "correctness": 1.68, "helpfulness": 1.79, "instruction-following": 3.13, "safety": 6.18, "verbosity": 1.27, "verbosity-coeff": -0.1221 }

[ { "content": "On a certain Monday, Carlos drove to work at an average speed of 10 miles per hour and home from work along exactly the same route at an average speed of 20 miles per hour. Which of the following is closest to his average speed for both trips combined?\n\n['A)17', 'B)16', 'C)15', 'D)14', 'E)13.33']", "role": "user", "uuid": "2be8368f-1c2b-49ec-ac95-af063d82211d" }, { "content": "To solve the average speed questions, we need to know the total distance and the total time.\nLet us assume that the distance from work = D\nThis will also be the distance from work to home\nHence total distance travelled = 2D\nTime in going to work = D/10,\nTime in coming back from work = D/20\nHence average speed of both the trips = 2D/ (D/10 + D/20)\n= 2*20/3 = 13.33\nE", "role": "assistant", "uuid": "8f5d0504-eb18-4527-88cd-e8024f7ce8f0" } ]

{ "coherence": 2.64, "complexity": 1.83, "correctness": 2.21, "helpfulness": 2.31, "instruction-following": 2.86, "safety": 4.73, "verbosity": 1.3, "verbosity-coeff": -0.2094 }

[ { "content": "A sum of money is put out at compound interest for 2 years at 20%. It would fetch Rs.723 more if the interest were payable half-yearly, then it were pay able yearly. Find the sum.\n\n['A)22200', 'B)21897', 'C)28799', 'D)30000', 'E)32782']", "role": "user", "uuid": "c0aa08e5-3e62-4ecd-981b-def76341f9d9" }, { "content": "P(11/10)^4 - P(6/5)^2 = 723\nP = 30000\nAnswer: D", "role": "assistant", "uuid": "fc895bf2-64d1-4ebc-92ed-739fcd59100d" } ]

{ "coherence": 3.02, "complexity": 1.4, "correctness": 2.39, "helpfulness": 2.47, "instruction-following": 3.56, "safety": 5.52, "verbosity": 0.74, "verbosity-coeff": -0.127 }

[ { "content": "15 men take 21 days of 8 hrs. each to do a piece of work. How many days of 2 hrs. each would it take for 21 women if 3 women do as much work as 2 men?\n\n['A)30', 'B)20', 'C)40', 'D)60', 'E)90']", "role": "user", "uuid": "48374a66-831e-4447-9756-a0cb2921e291" }, { "content": "Let 1Man does 1unit/hr of work\n15M in 21 days of 8hrs will do (15*21*8) units\n3W = 2M\n1W=(2/3)units/hr\n21W with 2hrs a day will take (15*21*8)/(21*2*(2/3)) days\n=> 90 Days\nANSWER:E", "role": "assistant", "uuid": "2b81ec8c-3249-46e7-be07-d5535f7c1c58" } ]

{ "coherence": 2.45, "complexity": 1.58, "correctness": 1.98, "helpfulness": 2.02, "instruction-following": 3.04, "safety": 5.63, "verbosity": 1.1, "verbosity-coeff": -0.1154 }

[ { "content": "If A lends Rs.3500 to B at 10% per annum and B lends the same sum to C at 11.5% per annum then the gain of B in a period of 3 years is?\n\n['A)157.78', 'B)157.98', 'C)157.5', 'D)157.19', 'E)157.12']", "role": "user", "uuid": "b795403d-2258-46f2-8c19-a5f7daa57030" }, { "content": "(3500*1.5*3)/100\n=> 157.50\nAnswer: C", "role": "assistant", "uuid": "94b851fe-0d18-44b7-8e9d-2b62b30f6341" } ]

{ "coherence": 2.78, "complexity": 0.78, "correctness": 1.68, "helpfulness": 1.99, "instruction-following": 3.31, "safety": 6.18, "verbosity": 0.21, "verbosity-coeff": -0.1183 }

[ { "content": "200 hundred multiples of seven are chosen at random, and 500 multiples of eight are chosen at random. Approximately what percentage of the 700 selected numbers are odd?\n\n['A)14.29%', 'B)15.29%', 'C)16.29%', 'D)17.29%', 'E)18.29%']", "role": "user", "uuid": "dd10149d-2ab0-43ae-93df-dba3ad286fbb" }, { "content": "--> Multiples of 7 are 7, 14, 21, 28, 35, 42....\nOut of first 4 multiples, 2 are odd; out of first 6 multiples, 3 are odd.\nSo approx. 50 % of the 200 multiples are odd i.e 100 multiples.\n--> Similalrly, for 8 multiples are:8,16,24...\nAll are even so 0 % are odd.\nTotal odd= (100+0)/(200+500)= 100/700=1/7 = 14.29%\nAnswer A", "role": "assistant", "uuid": "e1118393-2d93-48b0-894d-df47aea25ca9" } ]

{ "coherence": 2.9, "complexity": 1.55, "correctness": 2.41, "helpfulness": 2.2, "instruction-following": 2.57, "safety": 4.85, "verbosity": 1.58, "verbosity-coeff": -0.23 }

[ { "content": "In the formula V = 1/(2r)^3, if r is halved, then V is multiplied by?\n\n['A)16', 'B)8', 'C)1', 'D)1/8', 'E)1/64']", "role": "user", "uuid": "b79c9a71-7f96-46bb-a6fb-23654d53eb88" }, { "content": "Say r=1 => V1 = 1/8\nwhen r=1/2; V2 = 1\nV2 = 1*V1.\nAnswer : B", "role": "assistant", "uuid": "4fdff5c5-34f0-4864-80af-bbd9bc3ea420" } ]

{ "coherence": 2.62, "complexity": 1.45, "correctness": 1.95, "helpfulness": 1.92, "instruction-following": 2, "safety": 5.28, "verbosity": 0.57, "verbosity-coeff": -0.1372 }

[ { "content": "If a = 105 and a^3= 21 * 35 * 45 * b, what is the value of b?\n\n['A)35', 'B)42', 'C)45', 'D)49', 'E)54']", "role": "user", "uuid": "3fd797b9-869a-41f2-9166-4c5087265d43" }, { "content": "First step will be to break down all the numbers into their prime factors.\n105 = 3 * 5 * 7\n21 = 7 * 3\n35 = 7 * 5\n45 = 3 * 3 * 5\nso, (105)^3 = 3 * 7 * 7 * 5 * 3 *3 *5 *b\nTherefore (3 * 5 * 7) ^ 3 = 3^3 * 5^2 * 7^2 *b\nTherefore, b = 3^3 * 5^3 * 7 ^3/3 ^3 * 5 ^2 * 7^2\nb = 5*7 = 35\nCorrect answer A.", "role": "assistant", "uuid": "181212c7-6069-4a29-b1f5-b6dbad17e946" } ]

{ "coherence": 2.98, "complexity": 1.83, "correctness": 2.37, "helpfulness": 2.55, "instruction-following": 2.49, "safety": 4.11, "verbosity": 0.9, "verbosity-coeff": -0.1101 }

[ { "content": "The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is?\n\n['A)27', 'B)82', 'C)245', 'D)288', 'E)232']", "role": "user", "uuid": "6dba9c2f-6c43-466d-8320-4124b374a063" }, { "content": "Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2 ==> 2(130 + X) = 750 ==> X = 245 m.\nAnswer:C", "role": "assistant", "uuid": "977e2447-448a-4a64-9d27-ef1234e744f9" } ]

{ "coherence": 3.05, "complexity": 1.78, "correctness": 2.86, "helpfulness": 2.96, "instruction-following": 4.46, "safety": 5.28, "verbosity": 1.52, "verbosity-coeff": -0.109 }

[ { "content": "The average marks of a class of 30 students is 40 and that of another class of 50 students is 80. Find the average marks of all the students?\n\n['A)52.5', 'B)52.9', 'C)52.1', 'D)52.3', 'E)65']", "role": "user", "uuid": "c2c16ef3-a616-4504-8073-a66a89d35cd9" }, { "content": "Sum of the marks for the class of 30 students = 30 * 40 = 1200\nSum of the marks for the class of 50 students = 50 * 80 = 4000\nSum of the marks for the class of 80 students =\n1200 + 4000 = 5200\nAverage marks of all the students = 5200/80\n= 65\nAnswer:E", "role": "assistant", "uuid": "924b7772-c508-466e-85d2-4a689f4fdef8" } ]

{ "coherence": 3.13, "complexity": 1.39, "correctness": 2.66, "helpfulness": 2.8, "instruction-following": 3.66, "safety": 5.4, "verbosity": 1.49, "verbosity-coeff": -0.1236 }

[ { "content": "You are renting an apartment and you need √729 for each side, how many feet are you looking to measure?\n\n['A)21', 'B)22', 'C)23', 'D)24', 'E)27']", "role": "user", "uuid": "49d3e556-0d70-490d-9a84-f91dce9207d9" }, { "content": "Try filling the numbers into the answer y x y =\nFind the closest to 729\nAnswer E", "role": "assistant", "uuid": "8f66ca4c-fdc6-499d-9635-8dced48dcaf9" } ]

{ "coherence": 1.95, "complexity": 1.1, "correctness": 1.34, "helpfulness": 1.4, "instruction-following": 1.71, "safety": 4.4, "verbosity": 0.63, "verbosity-coeff": -0.0923 }

[ { "content": "The total marks obtained by a student in Mathematics and Physics is 60 and his score in Chemistry is 20 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together?\n\n['A)40', 'B)98', 'C)27', 'D)29', 'E)22']", "role": "user", "uuid": "26457c09-8b38-4854-92a3-34d5be3eb6a9" }, { "content": "Let the marks obtained by the student in Mathematics, Physics and Chemistry be M, P and C respectively.\nGiven , M + C = 60 and C - P = 20 M + C / 2 = [(M + P) + (C - P)] / 2\n= (60 + 20) / 2\n= 40.\nAnswer:A", "role": "assistant", "uuid": "885e6648-6a14-42a5-a156-49824485b8f0" } ]

{ "coherence": 3.05, "complexity": 1.6, "correctness": 2.7, "helpfulness": 2.94, "instruction-following": 3.19, "safety": 5.05, "verbosity": 1.5, "verbosity-coeff": -0.1069 }

[ { "content": "A present value of a machine is $128000. Its value depletiation rate is 25% per annum then find the machine value after 3 years\n\n['A)A)$48000', 'B)B)$54000', 'C)C)$36520', 'D)D)$32450', 'E)E)$42500']", "role": "user", "uuid": "af03338e-d55e-4708-a3bb-bfa09f925e1c" }, { "content": "P= $128000\nR = 25%\nT = 3 years\nMachine value after 3years = P/(1-R/100)^T\n=128000*3/4 * 3/4 * 3/4\n=$54000\nAnswer is B", "role": "assistant", "uuid": "7d85fab2-bb75-413d-ba0b-a9db4624764a" } ]

{ "coherence": 2.82, "complexity": 1.46, "correctness": 2.66, "helpfulness": 2.59, "instruction-following": 3.66, "safety": 4.01, "verbosity": 1.59, "verbosity-coeff": -0.1176 }

[ { "content": "Find out the C.I on Rs.5000 at 4% p.a. compound half-yearly for 1 1/2 years.\n\n['A)Rs.420.20', 'B)Rs.319.06', 'C)Rs.306.04', 'D)Rs.294.75', 'E)Rs.295.75']", "role": "user", "uuid": "a45cfb1d-7a4f-4e4b-91b3-a2474a0af39b" }, { "content": "A = 5000(51/50)3\n= 5306.04\n5000\n-----------\n306.04\nANSWER:C", "role": "assistant", "uuid": "b1ae53dd-d538-450f-85b9-d94b51e11bd4" } ]

{ "coherence": 2.61, "complexity": 1.29, "correctness": 1.83, "helpfulness": 1.94, "instruction-following": 3.27, "safety": 5.87, "verbosity": 0.82, "verbosity-coeff": -0.1186 }

[ { "content": "Mother is aged thrice than her daughter Silvia. After 8 years, he would be 2(1/2) times of Silvia’s age. After 8 years, how many times would she be of Silvia’s age?\n\n['A)2 years', 'B)4 years', 'C)3 years', 'D)5 years', 'E)6 years']", "role": "user", "uuid": "1b7e24a0-8bd8-48c4-837f-108e058a10d6" }, { "content": "A\n2 years\nLet Silvia’s current age is A years.\nThen, mom’s current age = (A + 3A) years = 4A years.\n(4A + 8) = (5/2) (A + 8)\n=> 8A + 16 = 5A + 40\n=> 3A = 24\nA = 8\nNeeded ratio = { (4A + 16)/(A+16) }\n= 48/24\n= 2", "role": "assistant", "uuid": "7f63595f-9d2c-4922-90d5-4d5264cdbbe8" } ]

{ "coherence": 2.82, "complexity": 2.02, "correctness": 2.37, "helpfulness": 2.59, "instruction-following": 3.29, "safety": 4.29, "verbosity": 1.6, "verbosity-coeff": -0.1274 }

[ { "content": "X is a positive number which when increased by 17 is equal to 60 times the reciprocal of the number. Find value of X?\n\n['A)3', 'B)4', 'C)6', 'D)7', 'E)8']", "role": "user", "uuid": "504915f2-5770-493b-9dc9-8855fc689ecb" }, { "content": "Let the number be x.\nThen, x + 17 =\t60\nx\nx2 + 17x - 60 = 0\n(x + 20)(x - 3) = 0\nx = 3\nA", "role": "assistant", "uuid": "268f04c2-0400-421d-9aba-4a658f3505a3" } ]

{ "coherence": 2.41, "complexity": 2.25, "correctness": 1.31, "helpfulness": 1.46, "instruction-following": 2.7, "safety": 5.09, "verbosity": 0.96, "verbosity-coeff": -0.1451 }

[ { "content": "A picture is copied onto a sheet of paper 8.5 inches by 10 inches. A 1.5 inch margin is left all around. What area in square inches does the picture cover?\n\n['A)76', 'B)65', 'C)59.5', 'D)49', 'E)38.5']", "role": "user", "uuid": "70d0a23a-d05f-413e-ab84-e7faf79208de" }, { "content": "Area covered by picture = (8.5-3)*(10-3)\n=5.5*7\n=38.5\nAnswer E", "role": "assistant", "uuid": "662b7260-ec66-4e70-858f-f27bbd0faf55" } ]

{ "coherence": 2.8, "complexity": 0.99, "correctness": 2.39, "helpfulness": 2.49, "instruction-following": 3.56, "safety": 5.09, "verbosity": 0.8, "verbosity-coeff": -0.2188 }

[ { "content": "A researcher computed the mean, the median, and the standard deviation R for a set of performance scores. If 5 were to be added to each score, which of these three statistics would change?\n\n['A)The mean only', 'B)The median only', 'C)The standard deviation only', 'D)The mean and the median', 'E)The mean and the standard deviation']", "role": "user", "uuid": "62e9d555-a273-4816-9286-6419100fad9f" }, { "content": "If we add or subtract a constant to each term in a set the standard deviation R will not change..\nIf we add (or subtract) a constant to each term in a set the mean and the median will increase (decrease) by the value of that constant.\nAnswer: D.", "role": "assistant", "uuid": "df7e2a86-8a40-4b6e-a840-f5214a09dd73" } ]

{ "coherence": 3.04, "complexity": 1.29, "correctness": 2.2, "helpfulness": 2.27, "instruction-following": 2.33, "safety": 5.83, "verbosity": 1.15, "verbosity-coeff": -0.1816 }

[ { "content": "To be eligible for retirement benefits at the Norman Corporation, the sum of an employee's age, in years, and the number of years employment must be at least 68. If x, where x <68, is a certain employee's age when hired and y is the minimum number of years of employment required for the employee to be eligible for retirement benefits, which of the following equations represents the relationship between x and y?\n\n['A)xy=68', 'B)x+y=68', 'C)2x+y=68', 'D)2x+2y=68', 'E)x+2y=68']", "role": "user", "uuid": "3d5b9cac-7017-4201-af14-a2794769379b" }, { "content": "We are told that when a certain employee was hired he was x years old and that the he needed minimum y years to be eligible for benefits.\nNow,after y years of employment, when the employee will be be eligible for benefits, the employee will be x+y years old and will have y years of employment, thus{age after y years}+{employment years}=(x+y)+y=x+2y=68.\nAnswer: E", "role": "assistant", "uuid": "c0c5bf35-de71-4c76-b36a-9c58bd241b7e" } ]

{ "coherence": 2.72, "complexity": 1.21, "correctness": 2.12, "helpfulness": 2.2, "instruction-following": 2.31, "safety": 4.4, "verbosity": 0.7, "verbosity-coeff": -0.2207 }

[ { "content": "A train is 360 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)20 seconds', 'B)30 seconds', 'C)40 seconds', 'D)50 seconds', 'E)None of these']", "role": "user", "uuid": "4aac4f16-22c7-49c0-8ea7-5bac14f13d63" }, { "content": "Explanation:\nSpeed = 45 Km/hr = 45*(5/18) m/sec\n= 25/2 m/sec\nTotal distance = 360+140 = 500 meter\nTime = Distance/speed\n=500∗2/25=40seconds\nOption C", "role": "assistant", "uuid": "0395d435-65a0-4ae9-a026-3e6893d26454" } ]

{ "coherence": 2.86, "complexity": 2.12, "correctness": 2.59, "helpfulness": 2.59, "instruction-following": 3.62, "safety": 6.1, "verbosity": 1.71, "verbosity-coeff": -0.1171 }

[ { "content": "A father and his son are waiting at a bus stop in the evening. There is a lamp post behind them. The lamp post, the father and his son stand on the same straight line. The father observes that the shadows of his head and his son’s head are incident at the same point on the ground. If the heights of the lamp post, the father and his son are 6 metres, 1.8 metres and 0.9 metres respectively, and the father is standing 2.1 metres away from the post, then how far (in metres) is the son standing from his father?\n\n['A)0.9', 'B)0.75', 'C)0.6', 'D)0.45', 'E)None of these']", "role": "user", "uuid": "a216bf94-d689-4140-81b4-8ecf7415b9d7" }, { "content": "Explanation :\nL is the lamp post position, F is father and S is son’s position. X is the point where the shadow falls.\nLD = 0.9 = Son’s height , LB = 1.8 = Father’s height.\nSo AB = 6 – 1.8 = 4.2 Also BC = LF = 2.1\nWe observe that ∆ABC ~ ∆ADE (two triangles are similar).\nHence, the corresponding sides are proportional.\nSo, AB/AD = DC/DE.\n4.2/5.1 = 2.1/DE.\nDE = 5.1*2.1/4.2 = 5.1/2 = 2.55.\nLS = DE = 2.55\nFS = LS – LF = 2.55 – 2.1 = 0.45.\nAnswer : D", "role": "assistant", "uuid": "25be29a3-81c5-49f9-adc0-627be0e5d50b" } ]

{ "coherence": 2.66, "complexity": 1.98, "correctness": 2.33, "helpfulness": 2.49, "instruction-following": 3.19, "safety": 4.15, "verbosity": 1.24, "verbosity-coeff": -0.1241 }

[ { "content": "A train 600m long is running at 54km/hr. How much time will it take to cross a pole?\n\n['A)30 secs.', 'B)42 secs.', 'C)35 secs.', 'D)45 secs.', 'E)40 secs.']", "role": "user", "uuid": "ed4d3783-54a7-40cc-a9c7-18630cb53ed5" }, { "content": "Distance covered =600m =3/5km speed =54km/hr. Time =3/5*54 =1/90hrs. =1/90*3600 =40 secs. Answer : E", "role": "assistant", "uuid": "91ca61e8-a184-4587-b1c7-339afff25891" } ]

{ "coherence": 2.25, "complexity": 1.1, "correctness": 1.87, "helpfulness": 1.73, "instruction-following": 2.33, "safety": 6.45, "verbosity": 0.85, "verbosity-coeff": -0.1194 }

[ { "content": "Free notebooks were distributed equally among children of a class. The number of notebooks each child got was one-eighth of the number of children. Had the number of children been half, each child would have got 16 notebooks. How many notebooks were distributed in all?\n\n['A)432', 'B)640', 'C)256', 'D)512', 'E)None of these']", "role": "user", "uuid": "ec64493a-8202-4e19-8319-baff22aced43" }, { "content": "In case I: Let the no. of children = x.\nHence, total no. of notebooks distributed\n1⁄8x.x or x2⁄8.......(i)\nIn case II: no.of children = x⁄2\nNow, the total no. of notebooks\n= 16 × x⁄2 .......(ii)\nComparing (i) & (ii), we get\nx2⁄8 = 8x\nor, x = 64\nHence, total no. of notebooks\n= 64×64/8=512\nAnswer D", "role": "assistant", "uuid": "a6cace87-a9f8-4118-b986-5ef0a8870856" } ]

{ "coherence": 2.66, "complexity": 1.48, "correctness": 2.39, "helpfulness": 2.49, "instruction-following": 3.6, "safety": 5.63, "verbosity": 1.16, "verbosity-coeff": -0.1277 }

[ { "content": "What is the sum of the first 25 natural numbers (starting from 1)?\n\n['A)325', 'B)350', 'C)375', 'D)400', 'E)425']", "role": "user", "uuid": "23413f5a-0810-49b8-a2c3-9cde8c65b949" }, { "content": "The sum of n natural numbers = n*(n+1) / 2 = 25*26/2 = 325\nThe answer is A.", "role": "assistant", "uuid": "51728c24-0189-4d6f-a545-a3c1712e1739" } ]

{ "coherence": 3.07, "complexity": 1.44, "correctness": 2.82, "helpfulness": 2.9, "instruction-following": 3.56, "safety": 4.27, "verbosity": 0.99, "verbosity-coeff": -0.1278 }

[ { "content": "A solution is 90% glycerin. If there are 4 gallons of the solution, how much water, in gallons must be addded to make a 75% glycerin solution\n\n['A)1.8', 'B)1.4', 'C)1.2', 'D)1.0', 'E)0.8']", "role": "user", "uuid": "db8501a4-5f84-4096-8d9b-c0bd1ad54fc8" }, { "content": "In 4 gallons of the solution there are 0.9∗4=3.80 gallons of glycerin. We want to add ww gallons of water to 4 gallons of solution so that these 3.6 gallons of glycerin to be 75% of new solution: 0.9∗4=0.75(4+w) --> w=0.8\nAnswer: E.", "role": "assistant", "uuid": "86d4d848-1694-4394-8845-d5c22eddd47e" } ]

{ "coherence": 2.64, "complexity": 1.05, "correctness": 1.62, "helpfulness": 1.5, "instruction-following": 2.02, "safety": 3.7, "verbosity": 0.6, "verbosity-coeff": -0.1189 }

[ { "content": "In how many different ways can the letters of the word ‘RED’ be arranged ?\n\n['A)0', 'B)6', 'C)24', 'D)120', 'E)720']", "role": "user", "uuid": "00300b60-1f74-4b7e-b79b-c40118ec6755" }, { "content": "B\n6\nRequired number of arrangements = 3! = 6", "role": "assistant", "uuid": "c135d0c0-c5ce-45db-8ee5-203ae9e5bc6f" } ]

{ "coherence": 2.72, "complexity": 1.35, "correctness": 2.47, "helpfulness": 2.7, "instruction-following": 2.66, "safety": 3.39, "verbosity": 1.13, "verbosity-coeff": -0.1106 }

[ { "content": "The average salary of the employees in a office is Rs.120/month.The avg salary of officers is Rs.470 and of non officers is Rs 110. If the no.of officers is 15,then find the No of nonofficers in the office.\n\n['A)400', 'B)420', 'C)430', 'D)450', 'E)525']", "role": "user", "uuid": "c0f9601f-61f9-4818-a506-cf7fca9cb569" }, { "content": "Let no. of non- officers be x\n15 * 470 + x * 110 = (x + 15) 120\nx = 525\nE", "role": "assistant", "uuid": "60cb828b-78a8-464e-a63c-8ceddc6483ef" } ]

{ "coherence": 2.68, "complexity": 1.32, "correctness": 2, "helpfulness": 2.2, "instruction-following": 3.31, "safety": 4.81, "verbosity": 0.52, "verbosity-coeff": -0.119 }

[ { "content": "If n = (33)^43 + (23)^33 what is the units digit of n?\n\n['A)0', 'B)2', 'C)4', 'D)6', 'E)8']", "role": "user", "uuid": "63cf6aae-fe95-4908-a35c-43be7b708bcf" }, { "content": "First of all, the units digit of (33)^23 is the same as that of 3^23 and the units digit of (23)^33 is the same as that of 3^33. So, we need to find the units digit of 3^23 + 3^33.\nNext, the units digit of 3 in positive integer power repeats in blocks of four {3, 9, 7, 1}:\n3^1=3 (the units digit is 3)\n3^2=9 (the units digit is 9)\n3^3=27 (the units digit is 7)\n3^4=81 (the units digit is 1)\n3^5=243 (the units digit is 3 again!)\n...\nThus:\nThe units digit of 3^23 is the same as the units digit of 3^3, so 7 (43 divided by the cyclicity of 4 gives the remainder of 3).\nThe units digit of 3^33 is the same as the units digit of 3^1, so 3 (33 divided by the cyclicity of 4 gives the remainder of 1).\nTherefore the units digit of (33)^23 + (23)^33 is 3 + 3 = 6.\nAnswer: D.", "role": "assistant", "uuid": "1c63097d-7be1-4feb-bf55-7ffea7ed91bb" } ]

{ "coherence": 3.17, "complexity": 2.31, "correctness": 2.45, "helpfulness": 2.47, "instruction-following": 2.7, "safety": 5.16, "verbosity": 1.66, "verbosity-coeff": -0.1839 }

[ { "content": "In covering a distance of 15 km, A takes 2 hours more than B. If A doubles his speed, then he would take 1 hour less than B. A's speed is:\n\n['A)5 km/h', 'B)8 km/h', 'C)10 km/h', 'D)15 km/h', 'E)2.5 km/h']", "role": "user", "uuid": "8e962225-ff38-48cd-9074-3b54639e5b80" }, { "content": "Let A's speed be X km/hr.\nThen, 15/x - 15/2x = 3\n7.5/x = 3\nx = 2.5 km/hr.\nAnswer : E", "role": "assistant", "uuid": "85d2676e-98f8-4409-bcaf-ace8b3dfc61b" } ]

{ "coherence": 2.7, "complexity": 1.23, "correctness": 2, "helpfulness": 2.12, "instruction-following": 3.09, "safety": 5.28, "verbosity": 0.19, "verbosity-coeff": -0.1236 }

[ { "content": "Evaluate: 45678 * 8*4*8 = ?\n\n['A)730848', 'B)705265', 'C)730846', 'D)730596', 'E)731848']", "role": "user", "uuid": "9b94677c-2465-4e25-b911-d025c477c276" }, { "content": "According to order of operations, 8?4?8 (division and multiplication) is done first from left to right\n8/4 = 2* 8 = 16\nHence\n45678 * 8*4*8 = 45678 * 16 = 730848\ncorrect answer A", "role": "assistant", "uuid": "85151567-b397-4a2f-86bb-8cf4879261a6" } ]

{ "coherence": 2.47, "complexity": 1.71, "correctness": 1.98, "helpfulness": 2.12, "instruction-following": 2.23, "safety": 3.48, "verbosity": 1.32, "verbosity-coeff": -0.1032 }

[ { "content": "A, B two inlet pipes takes 15,18 minutes to fill the tank and C an oulet pipe takes 45 minutes to empty the tank respectively. In what time the tank be filled if all of them are operated together?\n\n['A)11 minutes', 'B)10 minutes', 'C)12 minutes', 'D)13 minutes', 'E)14 minutes']", "role": "user", "uuid": "06c1b72e-fd37-4d01-b4b6-4ed4812702c8" }, { "content": "LCM=90\nNo of days= [90/(90/15 + 90/18 - 90/45)\n= [90/(6+5-2)]\n= [90/9]\n= 10 minutes\nANSWER:B", "role": "assistant", "uuid": "f33a05c4-28bd-42ab-af40-8382034a7204" } ]

{ "coherence": 2.43, "complexity": 1.41, "correctness": 2.04, "helpfulness": 2.14, "instruction-following": 2.66, "safety": 5.55, "verbosity": 1.19, "verbosity-coeff": -0.114 }

[ { "content": "The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is:\n\n['A)Rs. 3500', 'B)Rs. 3750', 'C)Rs. 3840', 'D)Rs. 3900', 'E)Rs. 4900']", "role": "user", "uuid": "1a6aa3fb-e330-4945-83c8-90afd7e0c2ac" }, { "content": "Let the cost of chairs be 'x' and tables be 'y'.\n10x=4y i.e., x=(2/5)y\nand given that 15x+2y=4000\n15((2/5)y)+2y=4000\n8y=4000 i.e., y=500 and x=200\nThe total price of 12 chairs and 3 tables is: 12*(200)+3*500=2400+1500=3900\nANSWER:D", "role": "assistant", "uuid": "876d9c91-dad1-4049-851d-0ad68a3a0a30" } ]

{ "coherence": 3.11, "complexity": 2.04, "correctness": 2.57, "helpfulness": 2.64, "instruction-following": 3.68, "safety": 4.73, "verbosity": 1.64, "verbosity-coeff": -0.1132 }

[ { "content": "X starts a business with Rs.77000. Y joins in the business after 5 months with Rs.42000. What will be the ratio in which they should share the profit at the end of the year?\n\n['A)21:23', 'B)23:45', 'C)22:7', 'D)25:29', 'E)None of these']", "role": "user", "uuid": "e1dc622a-bb85-4666-a5c5-33b3bb12e5cb" }, { "content": "Explanation :\nRatio in which they should share the profit\n= Ratio of the investments multiplied by the time period\n= 77000 * 12: 42000 * 7\n= 77 * 12: 42 * 7\n= 11*2: 7\n= 22:7.\nAnswer : Option C", "role": "assistant", "uuid": "2912a38d-6ba7-4230-b138-e8f845dc8436" } ]

{ "coherence": 2.84, "complexity": 1.65, "correctness": 2.59, "helpfulness": 2.96, "instruction-following": 3.31, "safety": 5.63, "verbosity": 0.95, "verbosity-coeff": -0.125 }

[ { "content": "If the sum of two numbers is 55 and the H.C.F. and L.C.M of these numbers are 5 and 120 respectively, then the sum of the reciprocals of the numbers is equal to:\n\n['A)55/601', 'B)601/55', 'C)11/120', 'D)120/11', 'E)120/13']", "role": "user", "uuid": "eaade050-6b1f-4117-b617-d1be8c27c289" }, { "content": "given a+b=55,hcm and lcm is 5 and 120\naxb=lcmx hcf\n600=120x5\n1/a+1/b=a+b/ab=>55/600=>11/120\nANSWER:C", "role": "assistant", "uuid": "a5eea0ea-34cc-4e1d-b267-a945a5fdadad" } ]

{ "coherence": 2.43, "complexity": 1.93, "correctness": 2.12, "helpfulness": 2.23, "instruction-following": 2.55, "safety": 5.79, "verbosity": 1.41, "verbosity-coeff": -0.1431 }

[ { "content": "A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current?\n\n['A)3 kmph', 'B)1.5 kmph', 'C)13 kmph', 'D)6.5 kmph', 'E)7.5 kmph']", "role": "user", "uuid": "a98dc19f-09dd-41f4-afea-97c69b5ec9d0" }, { "content": "72 --- 9 DS = 8\n? ---- 1\n45 ---- 9 US = 5\n? ---- 1 S = ?\nS = (8 - 5)/2 = 1.5\nANSWER:B", "role": "assistant", "uuid": "44502706-9d1b-44ae-9da4-5f0098e628ea" } ]

{ "coherence": 3.02, "complexity": 1.01, "correctness": 2.51, "helpfulness": 2.66, "instruction-following": 3.21, "safety": 5.12, "verbosity": 0.65, "verbosity-coeff": -0.1137 }

[ { "content": "The length of a train and that of a platform are equal. If with a speed of 90 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?\n\n['A)177', 'B)156', 'C)199', 'D)750', 'E)155']", "role": "user", "uuid": "6398a559-60fd-4a4e-8605-706735615e96" }, { "content": "Speed = [90 * 5/18] m/sec = 25 m/sec; Time = 1 min. = 60 sec.\nLet the length of the train and that of the platform be x meters.\nThen, 2x/60 = 25 è x = 25 * 60 / 2 = 750\nAnswer:D", "role": "assistant", "uuid": "300b9e79-5693-48ec-9a22-c5d07466ee7b" } ]

{ "coherence": 3.11, "complexity": 1.79, "correctness": 2.74, "helpfulness": 2.92, "instruction-following": 4.03, "safety": 5.01, "verbosity": 1.56, "verbosity-coeff": -0.1175 }

[ { "content": "The sum of three consecutive odd natural numbers, each divisible by 3 is 66. What is the largest among them?\n\n['A)21', 'B)24', 'C)25', 'D)36', 'E)57']", "role": "user", "uuid": "33ccd5f8-cdd5-4f9a-876a-bf8c33b218e3" }, { "content": "Let the 3 consecutive odd numbers each divisible by 3 be X, X+3, X+6\nGiven, X + X+3 + X+6 = 66\n3X = 57\nX = 19\nThe numbers are 19, 22, 25\nTherefore the largest number is 25\nAnswer C.", "role": "assistant", "uuid": "823d6a90-1de7-4e3b-850a-8c7711eb9028" } ]

{ "coherence": 2.9, "complexity": 1.36, "correctness": 2.16, "helpfulness": 2.64, "instruction-following": 3.35, "safety": 4.93, "verbosity": 1.03, "verbosity-coeff": -0.1785 }

[ { "content": "A garden has 50,000 trees. 12% of the trees are guava trees, 15% are orange trees, 10% are coconut trees and the rest are mango trees. Find the number of mango trees.\n\n['A)30000', 'B)30200', 'C)30800', 'D)31200', 'E)31500']", "role": "user", "uuid": "652a1928-a933-4ae0-8bcd-693efa25ab3c" }, { "content": "Mango Trees = (100 - 12 - 15 - 10) = 63%.\nNumber of Mango trees = 63% of 50000 = 31,500.\nANSWER : OPTION E", "role": "assistant", "uuid": "e14bd061-5f04-4003-9926-22ca9fa55dc8" } ]

{ "coherence": 2.82, "complexity": 1.26, "correctness": 2.76, "helpfulness": 2.94, "instruction-following": 3.29, "safety": 4.77, "verbosity": 1.22, "verbosity-coeff": -0.1197 }

[ { "content": "In a class there are 55 pupil, out of them 10 are in debate only and 18 in singing only. Then how many in both?\n\n['A)132', 'B)26', 'C)17', 'D)11', 'E)12']", "role": "user", "uuid": "7010de04-ed55-4feb-bc89-117669c9e48b" }, { "content": "Explanation:Total pupil = 55\nDebate + Singing = 10 + 18 = 28\nThe intersection for two = 55 – 10 – 28 = 17 play both games.\nAnswer: C", "role": "assistant", "uuid": "0e249d12-7f2e-400b-b46f-5729f7a8c54f" } ]

{ "coherence": 2.66, "complexity": 1.38, "correctness": 2.04, "helpfulness": 2.33, "instruction-following": 2.82, "safety": 5.52, "verbosity": 1.15, "verbosity-coeff": -0.109 }

[ { "content": "Mona and Donald fly to Rome for the weekend. They take cash only in notes of $10 and notes of €10. Mona carries three times the amount of euros Donald carries. She also carries as many dollars as Donald carries. The number of €10 notes they take is double the number of $10 notes they take. If Donald carries a total of 33 notes (of either $10 or €10,) then what is the total number of notes (of either $10 or €10,) they take?\n\n['A)70', 'B)110', 'C)100', 'D)120', 'E)150']", "role": "user", "uuid": "4952ab31-4640-48a8-85d5-cd5ee2c4cf9c" }, { "content": "let e10 =x no. d10 =y no. donald is having x+y notes mona carries 3x+y again x =2y or donald x+y =33\nor 3y =33 y =11 ;x =22 , total notes they carry = 4x+2y = 88+22 =110\nB", "role": "assistant", "uuid": "b58ccb3e-7f05-45e7-9ddd-e8633cd7350e" } ]

{ "coherence": 2.41, "complexity": 1.37, "correctness": 1.82, "helpfulness": 1.87, "instruction-following": 2.02, "safety": 5.59, "verbosity": 1, "verbosity-coeff": -0.1529 }

[ { "content": "If (5!)^2–(4!)^2=2^a3^b13^c and a, b, and c are integers, then what is the value of a + b + c?\n\n['A)12', 'B)10', 'C)2', 'D)1', 'E)0']", "role": "user", "uuid": "c4887f5d-e05a-4cf9-bbf5-0ff403a4532b" }, { "content": "(5!)^2 -(4!)^2=2^a3^b13^c\n= [5^2*(4!)^2]-(4!)^2\n=[25*(4!)^2]-(4!)^2=24*(4!)^2\n= 24*(24^2)=24^3\n=[2^3*3]^3=2^9*3^3\nso a=9 b=3 c=0\nhence a+b+c=9+3+0=12\nanswer=A", "role": "assistant", "uuid": "f4707586-d537-47be-b2f7-1d996c5cc5d9" } ]

{ "coherence": 2.86, "complexity": 1.93, "correctness": 2.21, "helpfulness": 2.12, "instruction-following": 2.78, "safety": 5.44, "verbosity": 1.15, "verbosity-coeff": -0.1771 }

[ { "content": "A train of 35 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.5 km long?\n\n['A)6', 'B)3', 'C)4', 'D)9', 'E)3.6']", "role": "user", "uuid": "77454075-6a9e-4b1f-ba1a-3223e80d8e37" }, { "content": "D = 35 * 60 + 1500 = 3600 m\nT = 3600/60 * 18/5 = 216 sec = 3.6 mins\nAnswer:E", "role": "assistant", "uuid": "c4375760-a827-4717-97e9-fc60fb43a379" } ]

{ "coherence": 2.29, "complexity": 1.54, "correctness": 1.6, "helpfulness": 1.74, "instruction-following": 2.84, "safety": 5.91, "verbosity": 1.37, "verbosity-coeff": -0.1213 }

[ { "content": "A bag contains 7 red, 9 blue and 5 green balls. If 3 balls are picked at random, what is the probability that both are red?\n\n['A)2/21', 'B)3/41', 'C)5/26', 'D)1/38', 'E)5/32']", "role": "user", "uuid": "4cadaa12-93ee-46e0-af7f-6c0455ce664c" }, { "content": "P(Both are red),\n=7C3/21C3=(7*6*5)/21*20*19\n=1/38\nD", "role": "assistant", "uuid": "9656a96c-6ec5-4f77-9162-c22f55238a26" } ]

{ "coherence": 2.68, "complexity": 1.14, "correctness": 1.64, "helpfulness": 1.87, "instruction-following": 2.08, "safety": 5.05, "verbosity": 0.96, "verbosity-coeff": -0.1524 }

[ { "content": "Last year, the price per transaction of certain company increases P percent from the year before, and the number of transactions increase N percent from the year before. Total revenue is simply the number of transactions times the price per transaction. Assume this one transaction is this company's only source of revenue. Which of the following is the percent increase in revenue last year, from the year before?\n\n['A)P∗N %', 'B)(P+N)', 'C)(P+N+P∗N/100) %', 'D)(P+N-P∗N/100) %', 'E)(P+N+P∗N/100)^2 %']", "role": "user", "uuid": "2fcd78f0-4a48-443e-be5b-01a9758f149b" }, { "content": "Assume\nx = price per transaction for previous year\ny = price per transaction for this year\nRelationship between x and y\ny =x (1+P/100)\nSimilarly, if\nn1= no. of transactions for last year\nn2 = no. of transactions for this year\nn2 = n1(1+N/100)\nNow, the question is [(n2y- n1x) /n1x] * 100\nn2y = n1x(1+P/100)(1+N/100)\nSo, [(n2y - n1x)/n1x] * 100 = (n1x[(1+P/100) (1+N/100) - 1]/ n1x) * 100\nD is the answer.", "role": "assistant", "uuid": "204f73d8-c0e5-48c5-ba61-416e1bd5ac58" } ]

{ "coherence": 2.62, "complexity": 2.04, "correctness": 2.18, "helpfulness": 2.2, "instruction-following": 2.39, "safety": 4.54, "verbosity": 1.6, "verbosity-coeff": -0.157 }

[ { "content": "nd the area of trapezium whose parallel sides are 20 cm and 16 cm long, and the distance between them is 15 cm?\n\n['A)270cm2', 'B)275cm2', 'C)280cm2', 'D)285cm2', 'E)290cm2']", "role": "user", "uuid": "610c1418-61a9-4ba9-9b23-812a57087df4" }, { "content": "Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)\n= 1/2 (20 + 16) * (15)\n= 270 cm2\nAnswer:A", "role": "assistant", "uuid": "155ea946-7f0e-4b09-b991-9a2d3461a1d0" } ]

{ "coherence": 3.17, "complexity": 1.02, "correctness": 2.2, "helpfulness": 2.62, "instruction-following": 4.15, "safety": 5.2, "verbosity": 0.98, "verbosity-coeff": -0.1064 }

[ { "content": "A certain university will select 1 of 4 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?\n\n['A)42', 'B)70', 'C)140', 'D)180', 'E)315']", "role": "user", "uuid": "6bf78acf-8a78-4ccc-a2c1-35df24d5b365" }, { "content": "1 of 7 will be chosen for the math\n2 of 10 will be chosen for the computer\nNone of the 3 chosen people can be in more thn one deparments.\nWe can choose any of the 4 candidates for the math dep., which gives as 4 selections.\nWe can choose 2 of the 10 candidates for the computer dep., which gives us 2 selections and 8 rejections.\nSo, the way to find how many different selections of 2 candidates we can have for the computer dep., we do:\n10! /2!*8!= (9*10) / 2 = 90 / 2 = 45.\nWe are multiplying our individual selections: 4*45 = 180\nIn the bolded part, we don't have to multiply all of the numbers, as those in 8! are included in 10!, so we simplify instead.\nAns D", "role": "assistant", "uuid": "18892372-7de0-43aa-b05e-33745f262841" } ]

{ "coherence": 2.8, "complexity": 1.34, "correctness": 2.33, "helpfulness": 2.29, "instruction-following": 2.27, "safety": 4.89, "verbosity": 1.68, "verbosity-coeff": -0.2448 }

[ { "content": "A child must place 7 different toys in 4 different bins. If any of the toys can go in any of the bins, in how many ways can the child place the toys into the bins?\n\n['A)6^6', 'B)6^4', 'C)4^7', 'D)4^4', 'E)6^4-4^6']", "role": "user", "uuid": "e38df7e8-af6e-4733-a941-1e97c5b84ab9" }, { "content": "there are 4 different bins and each of the toy can go to any of these bins..\nso answer 7∗7∗7∗7∗7∗7∗7=4^7\nANSWER:C", "role": "assistant", "uuid": "19b47744-ad65-4346-9279-867efac0c1c9" } ]

{ "coherence": 2.16, "complexity": 1.82, "correctness": 1.58, "helpfulness": 1.9, "instruction-following": 2.62, "safety": 4.73, "verbosity": 1.38, "verbosity-coeff": -0.2115 }