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[ { "content": "A rectangular lawn of dimensions 80 m * 50 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?\n\n['A)A)3820', 'B)B)930', 'C)C)9309', 'D)D)3600', 'E)E)8302']", "role": "user", "uuid": "a669040c-6baa-4307-be9a-d4f2ff22ff25" }, { "content": "Explanation:\nArea = (l + b – d) d\n(80 + 50 – 10)10 => 1200 m2\n1200 * 3 = Rs.3600\nAnswer: Option D", "role": "assistant", "uuid": "5bbd80b7-f2a1-483b-ba30-a9a48a7c4fcd" } ]

{ "coherence": 2.51, "complexity": 1.39, "correctness": 1.92, "helpfulness": 2.27, "instruction-following": 2.96, "safety": 5.63, "verbosity": 0.87, "verbosity-coeff": -0.1204 }

[ { "content": "If b < 2 and 2x - 2b = 0, which of the following must be true?\n\n['A)x > -3', 'B)x < 2', 'C)x = 3', 'D)x < 3', 'E)D. x > 3']", "role": "user", "uuid": "1e4da1c0-7b54-493d-9455-e97fdeee97b8" }, { "content": "2x - 2b = 0\nTherefore, 2x = 2b\nAs, b<2\n2x < 2(2)\ni.e x < 2\nAnswer : B", "role": "assistant", "uuid": "9842e294-d82d-4b91-9e2d-3c0225f4e07e" } ]

{ "coherence": 3.05, "complexity": 1.84, "correctness": 2.92, "helpfulness": 3.04, "instruction-following": 3.33, "safety": 4.97, "verbosity": 0.93, "verbosity-coeff": -0.1943 }

[ { "content": "An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq m?\n\n['A)Rs.4082.21', 'B)Rs.4082.98', 'C)Rs.4032.40', 'D)Rs.4282.40', 'E)Rs.4082.40']", "role": "user", "uuid": "9a520976-2259-4878-93f5-fa692f2b60ac" }, { "content": "Length of the first carpet\n= (1.44)(6) = 8.64 cm\nArea of the second carpet\n= 8.64(1 + 40/100) 6 (1 + 25/100)\n= 51.84(1.4)(5/4) sq m\n= (12.96)(7) sq m\nCost of the second carpet = (45)(12.96 * 7)\n= 315 (13 - 0.04) = 4095 - 12.6\n= Rs.4082.40\nAnswer:E", "role": "assistant", "uuid": "cc1b0a8a-4664-4a72-8253-44c025aafda2" } ]

{ "coherence": 2.61, "complexity": 1.44, "correctness": 1.89, "helpfulness": 2.23, "instruction-following": 3.5, "safety": 4.7, "verbosity": 1.22, "verbosity-coeff": -0.1194 }

[ { "content": "A “Sophie Germain” prime is any positive prime number p for which 2p + 1 is also prime. The product of all the possible units digits of Sophie Germain primes greater than 6 is\n\n['A)3', 'B)7', 'C)21', 'D)189', 'E)198']", "role": "user", "uuid": "2eca732b-46b4-4af6-956b-bf9bad037009" }, { "content": "In that case, the Sophie prime numbers greater than 6 are 7,11,23,47,59, .. which yields units digit as 1,3,7 and 9\nProduct would be 1 x 3 x 7x9 =189 Answer should be D", "role": "assistant", "uuid": "009e8731-96df-4d9b-89a9-d1fa3d1d985e" } ]

{ "coherence": 2.82, "complexity": 1.69, "correctness": 2.16, "helpfulness": 2.14, "instruction-following": 2.18, "safety": 4.81, "verbosity": 1.1, "verbosity-coeff": -0.1556 }

[ { "content": "The length of rectangle is thrice its breadth and its perimeter is 96 m, find the area of the rectangle?\n\n['A)432', 'B)212', 'C)252', 'D)992', 'E)212']", "role": "user", "uuid": "a3cb2279-7b3a-4934-856e-7d9ae8443c78" }, { "content": "2(3x + x) = 96\nl = 36 b = 12\nlb = 36 * 12 = 432 Answer:A", "role": "assistant", "uuid": "8da41406-49cc-4638-89bc-7d7583289872" } ]

{ "coherence": 2.8, "complexity": 1.2, "correctness": 2.43, "helpfulness": 2.43, "instruction-following": 3.11, "safety": 5.2, "verbosity": 0.58, "verbosity-coeff": -0.1014 }

[ { "content": "A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.900, what is the reduced price for kg?\n\n['A)s.40', 'B)s.46', 'C)s.49', 'D)s.45', 'E)s.42']", "role": "user", "uuid": "a150fbc0-6025-4d24-8944-7eda236a2ac9" }, { "content": "900*(25/100) = 225 ---- 5\n? ---- 1\n=> Rs.45\nAnswer: D", "role": "assistant", "uuid": "f1d86290-d9a1-4347-841c-511031c33d15" } ]

{ "coherence": 2.68, "complexity": 1.35, "correctness": 2.43, "helpfulness": 2.72, "instruction-following": 3.35, "safety": 3.86, "verbosity": 0.82, "verbosity-coeff": -0.115 }

[ { "content": "The circumferences of two circles are 264 meters and 704 meters. Find the difference between the areas of the larger and the smaller circles?\n\n['A)29960 sq m', 'B)33880 sq m', 'C)43120 sq m', 'D)27680 sq m', 'E)12786 sq m']", "role": "user", "uuid": "a85acd7b-3676-42e6-b10d-bc55b7dd5fe6" }, { "content": "Let the radii of the smaller and the larger circles be s m and l m respectively.\n2∏s = 264 and 2∏l = 704\ns = 264/2∏ and l = 704/2∏\nDifference between the areas = ∏l^2 - ∏s^2\n= ∏{132^2/∏^2 - 352^2/∏^2}\n= 132^2/∏ - 352^2/∏\n= (132 - 352)(132 + 352)/∏\n= (220)(484)/(22/7)\n= 33880 sq m\nAnswer:B", "role": "assistant", "uuid": "ba3337c8-25e1-4fe7-b162-a7eae5d10595" } ]

{ "coherence": 3.05, "complexity": 1.73, "correctness": 2.61, "helpfulness": 2.8, "instruction-following": 3.52, "safety": 4.3, "verbosity": 1.68, "verbosity-coeff": -0.1091 }

[ { "content": "700 + 6 × 4 = ?\n\n['A)820', 'B)202', 'C)420', 'D)724', 'E)None of these']", "role": "user", "uuid": "92ef7166-9d0f-475c-bc20-b15daaba4bcf" }, { "content": "700 + 6 × 4 = ?\nor, ? = 700 + 24 = 724\nAnswer D", "role": "assistant", "uuid": "59413670-5cb1-4dd6-87e0-95a459b7c04c" } ]

{ "coherence": 2.88, "complexity": 0.96, "correctness": 2.59, "helpfulness": 2.7, "instruction-following": 3.48, "safety": 3.84, "verbosity": 1.36, "verbosity-coeff": -0.1141 }

[ { "content": "If from a group of 5 people, an old member is replaced by a new one, the average age is same as it was 3 years ago. What is the difference between the ages of the old member and the new one?\n\n['A)12', 'B)15', 'C)11', 'D)18', 'E)16']", "role": "user", "uuid": "f2bc0900-161c-432e-a98d-614129312605" }, { "content": "Explanation:\nThe present average age is (x + 3) when the old member is present and it equals to x when an old member is replaced by a new one.\nThe difference in the ages of the old member and the new one is equal to the difference in the total age before and after the replacement = 15 years.\nANSWER: B", "role": "assistant", "uuid": "3e04fa83-ec8a-46ac-bbf8-de9522c54c57" } ]

{ "coherence": 2.35, "complexity": 1.65, "correctness": 1.88, "helpfulness": 2.12, "instruction-following": 2.57, "safety": 5.79, "verbosity": 1, "verbosity-coeff": -0.1324 }

[ { "content": "If 12/x is an integer and 4/x is an integer, which of the following must be true? I. 4/x is an integer II. 18/x is an integer III. 3/x is an integer\n\n['A)III only', 'B)II only', 'C)II,III only', 'D)I,III only', 'E)I only']", "role": "user", "uuid": "0bf7c19f-f330-49d6-b7db-2edf8f2f8467" }, { "content": "The question asks which of the following MUST be true, not COULD be true. The largest possible value of x is 4, GCD of 12 and 4, and if x=4 then ONLY I is true.\nAnswer: E", "role": "assistant", "uuid": "9f338c55-31d8-4559-8f0b-24da873e306f" } ]

{ "coherence": 2.68, "complexity": 1.74, "correctness": 1.91, "helpfulness": 1.86, "instruction-following": 2.55, "safety": 5.71, "verbosity": 1.03, "verbosity-coeff": -0.2076 }

[ { "content": "A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr The man's speed against the current is\n\n['A)8.5 km/hr', 'B)9 km/hr', 'C)10 km/hr', 'D)12.5 km/hr', 'E)None']", "role": "user", "uuid": "b406d948-f6a8-4698-9aa1-c64a4d26654c" }, { "content": "Solution\nMan's rate in still water\t= (15 - 2.5) km/hr\n= 12.5 km/hr.\nMan's rate against the current\t= (12.5 - 2.5) km/hr\n= 10 km/hr.\nAnswer C", "role": "assistant", "uuid": "b648a49a-b827-4a6c-8aed-0e62605e344d" } ]

{ "coherence": 3.23, "complexity": 1.06, "correctness": 2.66, "helpfulness": 2.57, "instruction-following": 3.23, "safety": 5.09, "verbosity": 1.05, "verbosity-coeff": -0.1182 }

[ { "content": "A tradesman is marketing his goods 20% above the cost price of the goods. He gives 10% discount on cash payment, find his gain percent.\n\n['A)12%', 'B)8%', 'C)15%', 'D)18%', 'E)None of these']", "role": "user", "uuid": "1f6d6882-8b45-4ee6-899f-ac9829572d41" }, { "content": "Let the C.P. of the goods be 100\n⇒ Marked price of the goods = 120\nDiscount = 10% ⇒ S.P. is 90% of 120 = 108\n∴ Gain = (108 – 100) i.e. 8%.\nAnswer B", "role": "assistant", "uuid": "8f7a11a8-2f1e-4efb-aa95-41b52f1a0955" } ]

{ "coherence": 3.02, "complexity": 1.73, "correctness": 3.07, "helpfulness": 3.15, "instruction-following": 3.74, "safety": 5.59, "verbosity": 1.64, "verbosity-coeff": -0.118 }

[ { "content": "A man invested Rs. 4455 in Rs. 10 shares quoted at Rs. 8.25. If the rate of dividend be 12%, his annual income is:\n\n['A)233', 'B)648', 'C)366', 'D)266', 'E)991']", "role": "user", "uuid": "69c44d81-56ef-4cf5-b82e-415a2f75a735" }, { "content": "Explanation:\nNumber of shares = = 540.\nFace value = Rs. (540 x 10) = Rs. 5400.\nAnnual income = = Rs. 648.\nAnswer: B) 648", "role": "assistant", "uuid": "7ab8f875-0fb1-4ad8-9db0-3db278412d3f" } ]

{ "coherence": 3.04, "complexity": 0.67, "correctness": 2.55, "helpfulness": 2.96, "instruction-following": 2.84, "safety": 4.81, "verbosity": 0.12, "verbosity-coeff": -0.0974 }

[ { "content": "Tom found a box of 220 baseball cards. Being a thoughtful older brother, he wanted to save at least 40 percent of the cards for himself and split the remaining cards evenly among his 4 younger brothers. What is the lowest possible number of cards that Tom can save for himself that will also allow each of his 4 younger brothers to get an equal number of cards?\n\n['A)110', 'B)112', 'C)116', 'D)118', 'E)122']", "role": "user", "uuid": "0ad968ac-c4ef-4571-8e8b-2c06051eecdb" }, { "content": "This question can be easily solved by looking at the options.\nAssuming number of cards to be x\nWe need to find the option for which (1/4)*(2x/5) is an integer\nOr x/10 is an integer.\nHence we need the lowest multiple of 10 from the given options.\nLet us start from the lowest value:\nOption A: 110. This is not a multiple of 10\nOption B: 112 = 10*11. This is a multiple of 10. Hence the correct answer.\nCorrect Option: A", "role": "assistant", "uuid": "2c10985c-a535-48b4-94cf-e87d95c21304" } ]

{ "coherence": 2.51, "complexity": 1.91, "correctness": 1.84, "helpfulness": 1.79, "instruction-following": 1.52, "safety": 4.7, "verbosity": 1.42, "verbosity-coeff": -0.2053 }

[ { "content": "A ship 77 km from the shore, springs a leak which admits to 9/4 tonnes of water in 11/2 minutes. 92 tonnes of water would sink it. But the pumps can throw out 12 tonnes of water per hour. Find the average rate of sailing so that the ship may just reach the shore as it begins to sink.\n\n['A)10.5', 'B)11', 'C)12', 'D)13', 'E)15']", "role": "user", "uuid": "1b224647-abe1-4576-8bdf-25d6fae95275" }, { "content": "Leak admits 9/4 tonnes water in 11/2 min\n=11/2 * 4/9 = 22/9\nleak admits 9/22 tonne of water in 5 min\nin 1 min in thrws 1/5 tonne of water = 9/22 - 1/5 = 23/110\n92/23/11 min = 440 min\n22/3 min=7/22/22/3 => 10.5 km/hr\nANSWER A", "role": "assistant", "uuid": "e336ccf0-1e06-45a7-b30e-120d0455099c" } ]

{ "coherence": 2.35, "complexity": 1.69, "correctness": 2.1, "helpfulness": 2.02, "instruction-following": 2.35, "safety": 5.44, "verbosity": 1.16, "verbosity-coeff": -0.1465 }

[ { "content": "The security gate at a storage facility requires a Six-digit lock code. If the lock code must consist only of digits from 1 through 9, inclusive, with no repeated digits, and the first and last digits of the code must be odd, how many lock codes are possible?\n\n['A)120', 'B)240', 'C)360', 'D)720', 'E)16800']", "role": "user", "uuid": "c5344a45-0c5e-42d8-a86d-b659ef4e3fdb" }, { "content": "X-X-X-X-X --> there are 5 odd digits from 1 to 9, inclusive thus options for the first and the last X's are: 5-X-X-X-X-4. Other X's can take following values: 5-7-6-5-4-4 -> 5*7*6*5*4*4=16800.\nAnswer: E.", "role": "assistant", "uuid": "82a67688-18bd-442e-9ad3-a9cfa79b63bf" } ]

{ "coherence": 2.37, "complexity": 1.28, "correctness": 2.04, "helpfulness": 2.02, "instruction-following": 2.61, "safety": 5.52, "verbosity": 0.84, "verbosity-coeff": -0.2257 }

[ { "content": "If (x × 10^q) – (y × 10^r) = 10^r, where q, r, x, and y are positive integers and q > r, then what is the units digit of y?\n\n['A)0', 'B)1', 'C)5', 'D)7', 'E)9']", "role": "user", "uuid": "be4181b2-ff63-41b8-aac7-5f9493fbd575" }, { "content": "Group the 10^r terms on one side of the equal sign.\n(x × 10^q) – (y × 10^r) = 10^r\nx × 10^q = (y × 10^r) + (1 × 10^r)\nx × 10^q = (y + 1) × 10^r\nNow, solve for y.\nx∗10 q=(y+1)∗10 rx∗10 q=(y+1)∗10r\nx∗10q10r=y+1x∗10q10r=y+1\nx∗10 q−r=y+1x∗10 q−r=y+1\nx∗10q−r−1=yx∗10 q−r−1=y\nSince q > r, the exponent on 10^(q-r) is positive. Since x is a positive integer, x*10^(q-r) is a multiple of 10 and therefore ends 0. Any multiple of 10 minus 1 yields an integer with a units digit of 9.\nThe correct answer is E.", "role": "assistant", "uuid": "7380550b-a435-4b89-a9f3-ee016d03c681" } ]

{ "coherence": 2.68, "complexity": 2.9, "correctness": 2.06, "helpfulness": 1.83, "instruction-following": 2.1, "safety": 5.79, "verbosity": 1.36, "verbosity-coeff": -0.2027 }

[ { "content": "Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is?\n\n['A)2/9', 'B)3/2', 'C)2/1', 'D)2/7', 'E)2/6']", "role": "user", "uuid": "c1e63030-5933-4fe9-8440-85ae5df66733" }, { "content": "Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y) = 23 ==> 27 x + 17 y = 23 x + 23 y ==> 4 x = 6 y ==> x/y = 3/2.\nAnswer:B", "role": "assistant", "uuid": "9ed5284b-bbde-47fb-a054-5276ee1ee7e0" } ]

{ "coherence": 2.78, "complexity": 1.79, "correctness": 2.23, "helpfulness": 2.33, "instruction-following": 3.39, "safety": 6.77, "verbosity": 1.29, "verbosity-coeff": -0.1169 }

[ { "content": "Find the invalid no.from the following series 3, 7, 15, 31 , 63, 127, 257\n\n['A)3', 'B)7', 'C)257', 'D)63', 'E)31']", "role": "user", "uuid": "9178357f-6429-4f47-9102-9df791e77a20" }, { "content": "Go on multiplying the number by 2 and adding 1 to it to get the next number.So, 257 is wrong.\nC", "role": "assistant", "uuid": "5eee0531-8fe6-4c0f-9ad5-b2b7a1d478bd" } ]

{ "coherence": 2.76, "complexity": 1.17, "correctness": 2.47, "helpfulness": 2.33, "instruction-following": 3.02, "safety": 3.35, "verbosity": 0.79, "verbosity-coeff": -0.0919 }

[ { "content": "How many different ways can you select a pilot and a co pilot if you have 80 people to choose from?\n\n['A) 199', 'B) 200', 'C) 398', 'D) 6320', 'E) 9900']", "role": "user", "uuid": "4f01a59c-c26b-499f-be6e-6d8577251ab7" }, { "content": "You are not just choosing two from 80. Each of the two people chosen fills a particular slot. The first filling the pilot slot and the second filling the copilot slot is different from the first filling the copilot slot and the second filling the pilot slot.\nSo the answer is in a sense (80C2) x 2 = 6320.\nAns D", "role": "assistant", "uuid": "cc666840-7669-477c-8236-36e70371300f" } ]

{ "coherence": 2.8, "complexity": 1.57, "correctness": 2.55, "helpfulness": 2.41, "instruction-following": 3.19, "safety": 4.97, "verbosity": 1.8, "verbosity-coeff": -0.1155 }

[ { "content": "If x and y are integers such that x^2= 2y and xy = 256, then x – y = ?\n\n['A)-30', 'B)-24', 'C)-5', 'D)5', 'E)20']", "role": "user", "uuid": "dc6108a7-9589-4fbf-b593-edff83d13c0a" }, { "content": "here x and y are integers .\nx^2=2y,xy =256.\nsubstitute (x^2)/2=y in xy => x^3=256*2=>x^3=512.\nhere x^3 is positive ,\nx is also positive.\nx=8 then y=32.\nx-y=-24\nso option B is correct", "role": "assistant", "uuid": "fcba7bc5-0b52-48b2-95b7-006e478bfce4" } ]

{ "coherence": 3.07, "complexity": 2.14, "correctness": 2.35, "helpfulness": 2.47, "instruction-following": 2.45, "safety": 5.59, "verbosity": 1.47, "verbosity-coeff": -0.1572 }

[ { "content": "There is a square with sides of 12. What is the circumference of the biggest circle that can be cut out of this square?\n\n['A)75.4', 'B)31.42', 'C)36', 'D)18.85', 'E)37.7']", "role": "user", "uuid": "ed606cfb-b780-47a3-bdcf-7e732942f7db" }, { "content": "Circumference of a circle = C=2Ï€r\nSquare is 12 wide, so circle's diameter would be 12, and radius would be 6\nC=2Ï€6 which is approximately 37.7\nAnswer is E", "role": "assistant", "uuid": "b8a7df7a-729c-4b6d-b615-d1cb2e46240f" } ]

{ "coherence": 2.84, "complexity": 1.79, "correctness": 2.29, "helpfulness": 2.41, "instruction-following": 2.78, "safety": 4.38, "verbosity": 1.29, "verbosity-coeff": -0.1205 }

[ { "content": "The Racing magic takes 60 seconds to circle the racing track once. The Charging bull makes 40 rounds of the track in an hour. If they left the starting point together, how many minutes will it take for them to meet at the starting point for the second time?\n\n['A)3', 'B)6', 'C)9', 'D)12', 'E)15']", "role": "user", "uuid": "ce36bbd5-abd1-48cd-8a39-eac1a1bf1a63" }, { "content": "Time taken by Racing magic to make one circle = 60 seconds\nTime taken byCharging bullto make one circle = 60 mins / 40 = 1.5 mins = 90 seconds\nLCM of 90 and 60 seconds = 180 seconds\nTime taken for them to meet at the starting point for the second time = 180 *2 =360 seconds= 6 mins\nAnswer B", "role": "assistant", "uuid": "1ff74b22-63dc-4ec9-8bd9-4b5224ecc62c" } ]

{ "coherence": 2.86, "complexity": 1.4, "correctness": 2.92, "helpfulness": 3.04, "instruction-following": 3.43, "safety": 5.67, "verbosity": 1.57, "verbosity-coeff": -0.1404 }

[ { "content": "A group of 12 girl scouts had enough food to last for 8 days when they arrived in camp. However, 4 more scouts joined them without the amount of food being increased. How long will the food last if each scout is given the same daily ration as originally planned?\n\n['A)2', 'B)3', 'C)4', 'D)5', 'E)6']", "role": "user", "uuid": "218d5e30-5155-4904-8b64-323881de44f5" }, { "content": "(M1*D1)/W1 = (M2*D2)/W2\nhere W1 = W2 (food)\nM1 = 12\nD1 = 8\nM2 = 12+4 = 16\nso (12*8)= (16*D2)\nD2 = 6\nANSWER:E", "role": "assistant", "uuid": "3513ba33-566b-4f36-ac62-3c5a35c83930" } ]

{ "coherence": 2.66, "complexity": 1.19, "correctness": 2.14, "helpfulness": 2.23, "instruction-following": 3.23, "safety": 5.52, "verbosity": 0.57, "verbosity-coeff": -0.1507 }

[ { "content": "A is a working partner and B is a sleeping partner in the business. A puts in Rs.15000 and B Rs.25000, A receives 10% of the profit for managing the business the rest being divided in proportion of their capitals. Out of a total profit of Rs.9600, money received by A is?\n\n['A)1797', 'B)2970', 'C)2782', 'D)4200', 'E)2081']", "role": "user", "uuid": "b35eca91-7825-44da-9dd6-ca746037fea3" }, { "content": "15:25 => 3:5\n9600*10/100 = 960\n9600 - 960 = 8640\n8640*3/8 = 3240 + 960\n= 4200\nAnswer:D", "role": "assistant", "uuid": "4cd5da3b-ef8e-444a-9267-e7c79dd1ba1e" } ]

{ "coherence": 2.45, "complexity": 1.32, "correctness": 2.1, "helpfulness": 2.39, "instruction-following": 3.43, "safety": 5.87, "verbosity": 1.16, "verbosity-coeff": -0.1221 }

[ { "content": "If M is the sum of consecutive even integers w, x, y, and z, where w < x < y < z, all of the following must be true EXCEPT\n\n['A)z - w = 3(y - x)', 'B)M is divisible by 8', 'C)The average of w, x, y, and z is odd', 'D)M is divisible by 4', 'E)w + x + 8 = y + z']", "role": "user", "uuid": "5fa687ec-768c-47b0-89c4-6b9fa345b4c9" }, { "content": "Just assume that the numbers are 2a, 2a+2, 2a+4 and 2a+6.\nM = 2a + 2a+2 + 2a+4 + 2a+6 = 8a + 12\nFocus on the easiest options first. You see that M is not divisible by 8. Answer (B)", "role": "assistant", "uuid": "e643b847-a1c4-4e09-a16b-7d04b2c53ebd" } ]

{ "coherence": 2.64, "complexity": 1.79, "correctness": 2.02, "helpfulness": 1.96, "instruction-following": 1.89, "safety": 5.48, "verbosity": 0.55, "verbosity-coeff": -0.2285 }

[ { "content": "If y ¤ z = y^(2z) for all positive integers, then (3 ¤ 4) ¤ 2 =\n\n['A)3^8', 'B)3^12', 'C)3^16', 'D)3^24', 'E)3^32']", "role": "user", "uuid": "fa3c582b-d750-4741-ae49-e480d754514e" }, { "content": "y ¤ z = y^(2z)\n3 ¤ 4 = 3^(8)\n(3 ¤ 4) ¤ 2 = (3^8) ¤ 2 = (3^8)^4 = 3^32\nCorrect Option: E", "role": "assistant", "uuid": "0c580ff8-c88d-4b17-9327-3810c804686d" } ]

{ "coherence": 3.35, "complexity": 2.06, "correctness": 2.84, "helpfulness": 2.92, "instruction-following": 3.6, "safety": 4.7, "verbosity": 1.3, "verbosity-coeff": -0.1733 }

[ { "content": "If a × b = 2a - 3b + ab, then 4 × 5 + 5 × 4 is equal to :\n\n['A)31', 'B)32', 'C)43', 'D)45', 'E)26']", "role": "user", "uuid": "dcd20fff-1632-4bed-99d5-b9ec929d753f" }, { "content": "Explanation:\n4 × 5 + 5 × 4 = (2 × 4 - 3 × 5 + 4 × 5) + ( 2 × 5 - 3 × 4 + 5 × 4)\n= (8 -15 + 20 + 10 - 12 +20) = 31.\nAnswer: A", "role": "assistant", "uuid": "3a8ca595-e5a4-4103-9b27-fb04069ccb24" } ]

{ "coherence": 3.13, "complexity": 2.08, "correctness": 2.86, "helpfulness": 2.92, "instruction-following": 3.93, "safety": 4.48, "verbosity": 1.77, "verbosity-coeff": -0.1164 }

[ { "content": "A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of this son is\n\n['A)21 years', 'B)22 years', 'C)23 years', 'D)24 years', 'E)26 years']", "role": "user", "uuid": "0d214041-ce4f-4c32-a663-17e2d03ab2eb" }, { "content": "Explanation:\nLet's Son age is x, then Father age is x+24.\n=> 2(x+2) = (x+24+2)\n=> 2x+4 = x+26\n=> x = 22 years\nOption B", "role": "assistant", "uuid": "fd0f901a-b965-4068-aab8-fd133907fb50" } ]

{ "coherence": 3.33, "complexity": 0.97, "correctness": 2.94, "helpfulness": 3.27, "instruction-following": 3.52, "safety": 4.62, "verbosity": 0.52, "verbosity-coeff": -0.1486 }

[ { "content": "A grocer has a sale of Rs. 435, Rs. 927, Rs. 855, Rs. 230 and Rs. 562 for 5 consecutive days. How much sale must he have in the sixth day so that he gets an average sale of Rs. 625?\n\n['A)Rs 741', 'B)Rs 5991', 'C)Rs 6001', 'D)Rs 6991', 'E)None of these']", "role": "user", "uuid": "4929432e-1b69-4643-8758-81b0376d4ef0" }, { "content": "Explanation :\nTotal sale for 5 days = Rs. (435 + 927 + 855 + 230 + 562)\n= Rs. 3009.\nRequired sale = Rs. [ (625 x 6) - 3009 ]\n= Rs. (3750 - 3009)\n= Rs. 741.\nAnswer : A", "role": "assistant", "uuid": "67c98473-d99a-4177-bc2f-f219eca183c6" } ]

{ "coherence": 3.07, "complexity": 1.24, "correctness": 2.51, "helpfulness": 2.98, "instruction-following": 3.88, "safety": 4.97, "verbosity": 1.2, "verbosity-coeff": -0.1274 }

[ { "content": "A man took some money for borrowed, for 3 years the total will be Rs.6500 and 5 years it will be Rs.7500/-. Then how much amount he borrowed?\n\n['A)s.5000/-', 'B)s.5500/-', 'C)s.5770/-', 'D)s.5800/-', 'E)s.5820/-']", "role": "user", "uuid": "a9b3a114-4612-4971-bbd9-dfdfcce02b9b" }, { "content": "3 years --------> Rs.6500/-\n5 years --------> Rs.7500/-\n~ ~\n------------------------------\n2 years ---------> Rs.1000/-\n1 year ----------> Rs.500/-\n3years * Rs.500/- = Rs.1500/-\nP = Rs.6500/- - Rs.1500/- = Rs.5000/-\nP = Rs.5000/-\nA", "role": "assistant", "uuid": "9bd8f44f-acbc-4f67-98db-52e67edac8bc" } ]

{ "coherence": 2.61, "complexity": 1.22, "correctness": 2.12, "helpfulness": 2.12, "instruction-following": 3.11, "safety": 3.7, "verbosity": 0.67, "verbosity-coeff": -0.0968 }

[ { "content": "Set X consists of 15 integers and has median of 20 and a range of 20. What is the value of the greatest possible integer that can be present in the set?\n\n['A)32', 'B)37', 'C)C.40', 'D)60', 'E)50']", "role": "user", "uuid": "2f822133-5a56-464b-b5a3-5601d594b607" }, { "content": "Note that both median and range do not restrict too many numbers in the set. Range is only concerned with the smallest and greatest. Median only cares about the middle.\nQuick check of each option starting from the largest:\n(E) 50\nRange of 20 means the smallest integer will be 30. So 20 cannot lie in between and hence cannot be the median.\n(D) 43\nRange of 20 means the smallest integer will be 23. So 20 cannot lie in between and hence cannot be the median.\n(C) 40\nRange of 20 means the smallest integer will be 20. 20 can lie in between such as:\n20, 20, 20, 20, 20, 20, 20, 20, 20, 40, 40, 40, 50, 60\nThis is possible. Hence it is the greatest such number.\nAnswer (D)", "role": "assistant", "uuid": "b2e602e2-1d01-4f9f-9585-f882a0a87337" } ]

{ "coherence": 2.57, "complexity": 1.48, "correctness": 2.02, "helpfulness": 2, "instruction-following": 2.16, "safety": 5.09, "verbosity": 1.24, "verbosity-coeff": -0.1283 }

[ { "content": "One computer can upload 100 megabytes worth of data in 5 seconds. Two computers, including this one, working together, can upload 1300 megabytes worth of data in 40 seconds. How long would it take for the second computer, working on its own, to upload 100 megabytes of data?\n\n['A) 6', 'B) 8', 'C) 9', 'D) 11', 'E) 13']", "role": "user", "uuid": "ddef1a70-792d-4647-879d-2a78381dcc89" }, { "content": "Since the first computer can upload 100 megabytes worth of data in 5 seconds then in 5*8=40 seconds it can upload 8*100=800 megabytes worth of data, hence the second computer in 40 seconds uploads 1300-800=500 megabytes worth of data. The second computer can upload 100 megabytes of data in 8 seconds.\nAnswer: B.", "role": "assistant", "uuid": "aad60674-11d4-4507-a152-ffc9123f1945" } ]

{ "coherence": 3.23, "complexity": 1.02, "correctness": 2.45, "helpfulness": 2.57, "instruction-following": 2.98, "safety": 5.55, "verbosity": 0.46, "verbosity-coeff": -0.1596 }

[ { "content": "The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?\n\n['A)18/35', 'B)18/38', 'C)18/34', 'D)18/31', 'E)18/30']", "role": "user", "uuid": "d7276201-dd92-4170-9684-2a4e83c88d95" }, { "content": "If both agree stating the same fact, either both of them speak truth of both speak false.\nProbability = 3/5 * 4/7 + 2/5 * 3/7\n= 12/35 + 6/35 = 18/35.\nAnswer:A", "role": "assistant", "uuid": "fbc0f4af-93cc-4ef3-9cfc-6dbbd087b6e4" } ]

{ "coherence": 3.31, "complexity": 1.84, "correctness": 2.92, "helpfulness": 3.15, "instruction-following": 3.99, "safety": 4.21, "verbosity": 1.49, "verbosity-coeff": -0.1734 }

[ { "content": "A mobile battery in 1 hour charges to 20 percent.How much time (in minute) will it require more to charge to 30 percent.\n\n['A)145', 'B)90', 'C)175', 'D)160', 'E)130']", "role": "user", "uuid": "3620ad23-5a8e-4553-8895-ccb064f2121c" }, { "content": "1 hr =20 percent.Thus 15 min=5 percent .Now to charge 30 percent 90 min.Answer:B", "role": "assistant", "uuid": "78a71717-0a9b-4b51-9e85-4e5687af38ae" } ]

{ "coherence": 2.61, "complexity": 0.97, "correctness": 1.79, "helpfulness": 1.79, "instruction-following": 2.33, "safety": 6.14, "verbosity": 0.81, "verbosity-coeff": -0.1214 }

[ { "content": "A 25 cm wide path is to be made around a circular garden having a diameter of 4 meters. Approximate area of the path is square meters is?\n\n['A)3.34 sq m', 'B)98.8 sq m', 'C)67.8 sq m', 'D)27.9 sq m', 'E)19.9 sq m']", "role": "user", "uuid": "4e5dde36-d8b7-42b2-bce5-c75a6a71211c" }, { "content": "Area of the path = Area of the outer circle - Area of the inner circle\n= ∏{4/2 + 25/100}2 - ∏[4/2]2\n= ∏[2.252 - 22] = ∏(0.25)(4.25) { (a2 - b2 = (a - b)(a + b) }\n= (3.14)(1/4)(17/4) = 53.38/16\n= 3.34 sq m\nAnswer: A", "role": "assistant", "uuid": "808c3fb8-e04d-4326-8e7c-2cd709beb2ac" } ]

{ "coherence": 2.92, "complexity": 1.38, "correctness": 2.31, "helpfulness": 2.43, "instruction-following": 3.54, "safety": 3.95, "verbosity": 1.3, "verbosity-coeff": -0.1146 }

[ { "content": "In a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl ande 2 boys are selected is:\n\n['A)21/46', 'B)25/117', 'C)1/50', 'D)3/25', 'E)7/15']", "role": "user", "uuid": "71c48ec6-4b03-4a16-a799-6bd1be009e7b" }, { "content": "Let S be sample space and E be event of selecting 1 girl and 2 boys\nThen n(S)=25c3\n=2300\nn(E)=10c1x15c2=1050\nP(E)=2300/1050=21/46\nANSWER A 21/46", "role": "assistant", "uuid": "004dde54-b747-4049-9d14-c9e4b0fc226a" } ]

{ "coherence": 2.9, "complexity": 1.39, "correctness": 2.08, "helpfulness": 2.31, "instruction-following": 2.45, "safety": 5.44, "verbosity": 0.9, "verbosity-coeff": -0.142 }

[ { "content": "In what time will a train 120 meters long completely pass an electric pole, if it travels at a speed of 60kmph.\n\n['A)6.18', 'B)5.18', 'C)4.18', 'D)4.18', 'E)7.18']", "role": "user", "uuid": "72917904-1037-478c-9ed2-c57003d29b48" }, { "content": "Sol.\nSpeed = [ 60x5/18] m/sec =16.7 m / sec.\nTime taken = (120/16.7)sec = 7.18 sec.\nAnswer E", "role": "assistant", "uuid": "ef8d6e3c-ead6-4ca8-8b7e-ffb3703c2397" } ]

{ "coherence": 2.57, "complexity": 1.6, "correctness": 2.31, "helpfulness": 2.02, "instruction-following": 3.48, "safety": 5.24, "verbosity": 1.59, "verbosity-coeff": -0.1008 }

[ { "content": "Find the value of x from the below equation? : 3x^2+5x+2 = 0\n\n['A)-1', 'B)-2', 'C)1', 'D)2', 'E)3']", "role": "user", "uuid": "c600aef2-3a37-4088-9b74-78abf3fbcf60" }, { "content": "a = 3, b = 5, c = 2\nx1,2 = (-5 ± √(52 - 4×3×2)) / (2×3) = (-5 ± √(25-24)) / 6 = (-5 ± 1) / 6\nx1 = (-5 + 1)/6 = -4/6 = -2/3\nx2 = (-5 - 1)/6 = -6/6 = -1\nA", "role": "assistant", "uuid": "010c2a10-f30a-40ba-ad25-d109e32fe588" } ]

{ "coherence": 2.86, "complexity": 1.59, "correctness": 2.59, "helpfulness": 2.64, "instruction-following": 3.07, "safety": 4.13, "verbosity": 1.14, "verbosity-coeff": -0.0969 }

[ { "content": "If the average of 5 positive integers is 50 and the difference between the largest and the smallest of these 5 numbers is 10, what is the maximum value possible for the largest of these 5 integers?\n\n['A)50', 'B)58', 'C)49', 'D)48', 'E)44']", "role": "user", "uuid": "c8e8a3ca-32f2-4a5b-a764-7f2edfcb4ab4" }, { "content": "Sum of 5 Integer (a, b, c, d, e) = 5*50 = 250\ne - a = 10\ni.e. e = a+10\nFor e to be maximum remaining 4 MUST be as small as possible\nSince smallest of 5 numbers is a so to minimize other numbers we can take them equal to the smallest of 5 numbers\ni.e. a+a+a+a+(a+10) = 250\ni.e. 5a = 240\ni.e. a =48\ni.e. Largest e = 48+10 = 58\nAnswer: option B", "role": "assistant", "uuid": "101f5a44-8a1c-4c44-ab64-6b2ba1690128" } ]

{ "coherence": 2.94, "complexity": 1.66, "correctness": 2.18, "helpfulness": 2.45, "instruction-following": 2.51, "safety": 6.1, "verbosity": 1.35, "verbosity-coeff": -0.2397 }

[ { "content": "The price of an article has been reduced by 25%. In order to restore the original price the new price must be increased by?\n\n['A)33 1/3%', 'B)43 1/3%', 'C)83 1/3%', 'D)36 1/3%', 'E)33 1/7%']", "role": "user", "uuid": "a2e8ef71-ef2b-4978-bc52-4bb91d3ad0f8" }, { "content": "100\n75\n-------\n75 ------- 25\n100 ------ ? => 33 1/3%\nAnswer:A", "role": "assistant", "uuid": "60984a5b-95ad-44fd-aee4-a18c5245e982" } ]

{ "coherence": 2.78, "complexity": 1.47, "correctness": 2.35, "helpfulness": 2.41, "instruction-following": 2.94, "safety": 5.05, "verbosity": 1.03, "verbosity-coeff": -0.1158 }

[ { "content": "Suppose you want to arrange your English, Hindi, Mathematics, History, Geography and Science books on a shelf. In how many ways can you do it?\n\n['A)700', 'B)710', 'C)720', 'D)740', 'E)750']", "role": "user", "uuid": "fb570915-2849-44ae-8f54-e25a45e3d459" }, { "content": "We have to arrange 6 books.\nThe number of permutations of n objects isn!=n.(n−1).(n−2)...2.1n!=n.(n−1).(n−2)...2.1\nHere n=6n=6 and therefore, number of permutations is 6.5.4.3.2.1=6.5.4.3.2.1= 720\nOption is C", "role": "assistant", "uuid": "16d4d277-5391-499b-87f0-dd5ae2e64c70" } ]

{ "coherence": 2.68, "complexity": 1.8, "correctness": 2.51, "helpfulness": 2.57, "instruction-following": 3.05, "safety": 5.05, "verbosity": 1.45, "verbosity-coeff": -0.1941 }

[ { "content": "Six cards numbered from 1 to 6 are placed in a cardboard box . First one card is drawn and then put back into the bowl; then a second card is drawn. If the cards are drawn at random and if the sum of the numbers on the cards is 10, what is the probability that one of the two cards drawn is numbered 5 ?\n\n['A)1/2', 'B)1/4', 'C)1/5', 'D)1/6', 'E)1/3']", "role": "user", "uuid": "25e275df-5600-46e0-850b-d1d7bd902925" }, { "content": "(6,4) (4,6) (5,5) – only 3 possible scenarios for sum to be 10. One from this 5 has already happened.\nFrom this three cases, only in one we have 5. So, the probability is 1 chances out of 3 that the one that occurred had 5: P=1/3.\nAnswer: E.", "role": "assistant", "uuid": "2c3fe17e-36b2-4186-9dd8-9b4c40f39caa" } ]

{ "coherence": 2.96, "complexity": 1.26, "correctness": 2.35, "helpfulness": 2.25, "instruction-following": 2.88, "safety": 5.91, "verbosity": 0.8, "verbosity-coeff": -0.15 }

[ { "content": "After doing 3/5 of the Biology homework on Monday night, Sanjay did 1/3 of the remaining homework on Tuesday night. What fraction of the original homework would Sanjay have to do on Wednesday night to complete the Biology assignment ?\n\n['A)1/15', 'B)2/15', 'C)4/15', 'D)2/5', 'E)None of these']", "role": "user", "uuid": "f6c7bfd2-f3dd-44d7-8e5d-8d1c11adc1e2" }, { "content": "Sol.(c) Remaining homework on Monday night\n= 1 - (3/5) = 2/5\nWork done on Tuesday night\n= 1/3 of 2/5 = 2/15\nRemaining homework to complete the biology assignment\n= 2/5 - 2/15 = (6 - 2)/15 = 4/15\nAnswer C", "role": "assistant", "uuid": "aeb173ad-3c70-4669-95f6-eb295cb5b2bb" } ]

{ "coherence": 2.88, "complexity": 1.96, "correctness": 2.8, "helpfulness": 2.86, "instruction-following": 3.66, "safety": 4.54, "verbosity": 1.25, "verbosity-coeff": -0.1573 }

[ { "content": "96 is divided into two parts in such a way that seventh part of first and ninth part of second are equal. Find the smallest part?\n\n['A)76', 'B)76', 'C)42', 'D)58', 'E)45']", "role": "user", "uuid": "b76f436b-48a5-4cd5-8350-ad00e604483a" }, { "content": "x/7 = y/9\n=> x:y\n= 7:9\n7/16 * 96\n= 42\nAnswer: C", "role": "assistant", "uuid": "551a7436-1719-4dcf-9913-fdec107fac1d" } ]

{ "coherence": 2.49, "complexity": 1.84, "correctness": 2.21, "helpfulness": 2.31, "instruction-following": 2.94, "safety": 6.88, "verbosity": 1.04, "verbosity-coeff": -0.1288 }

[ { "content": "If x is divisible by 3 and 4, which of the following must divide evenly into x?\nI. 2\nII. 38\nIII. 41\n\n['A)I only', 'B)I and II', 'C)II\\u200b and III', 'D)II\\u200b only', 'E)I, II, and III']", "role": "user", "uuid": "f5a61b70-8a73-4b7b-828c-2d1911d0e728" }, { "content": "If x is divisible by 3,4 means it will be = or > 12, 24,48 etc...\nThat are not divisible by 38, 41.\nSo, the answer is A", "role": "assistant", "uuid": "de3ff7e9-1685-4b59-8c6a-142bb211a542" } ]

{ "coherence": 2.18, "complexity": 2.12, "correctness": 1.44, "helpfulness": 1.43, "instruction-following": 1.05, "safety": 5.83, "verbosity": 1.28, "verbosity-coeff": -0.1675 }

[ { "content": "4 dice are thrown simultaneously on the board. Find the probability show the same face.\n\n['A)1/115', 'B)2/115', 'C)1/216', 'D)1/213', 'E)1/215']", "role": "user", "uuid": "6bf408b1-6f4d-45c5-90bd-87c34e61748f" }, { "content": "The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:\n=6×6×6×6=64=6×6×6×6=64\nn(S)=64n(S)=64\nLet XX be the event that all dice show the same face.\nX={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}\nn(X)=6n(X)=6\nHence required probability,\n=n(X)n(S)=664=n(X)n(S)=664\n=1/216\nC", "role": "assistant", "uuid": "2b2bc745-ca46-488c-a3de-dfa91e57721f" } ]

{ "coherence": 2.7, "complexity": 1.91, "correctness": 2.64, "helpfulness": 2.53, "instruction-following": 3.62, "safety": 5.05, "verbosity": 1.95, "verbosity-coeff": -0.0801 }

[ { "content": "What is the probability for a family with four children to have two boys and two girls (assuming the probability of having a boy or a girl is equal)?\n\n['A)1/2', 'B)1/4', 'C)1/8', 'D)3/8', 'E)5/16']", "role": "user", "uuid": "bb248e05-fdfa-4692-a630-47ca20e074b9" }, { "content": "One possible case is: girl - girl - boy - boy\nThe probability of this is 1/2*1/2*1/2*1/2 = 1/16\nThere are 4C2 = 6 such cases so we should multiply by 6.\nP(two boys and two girls) = 6/16 = 3/8\nThe answer is D.", "role": "assistant", "uuid": "639bb06b-3194-41db-8e3c-e6442ba1453b" } ]

{ "coherence": 3.33, "complexity": 1.93, "correctness": 3.02, "helpfulness": 3.09, "instruction-following": 3.5, "safety": 5.05, "verbosity": 1.24, "verbosity-coeff": -0.1361 }

[ { "content": "in how man ways team of four can be formed from four boys and three girls such that atleast one boy and one girl should be there?\n\n['A)33', 'B)34', 'C)35', 'D)36', 'E)37']", "role": "user", "uuid": "e8687211-7c91-493c-9717-548b640c899d" }, { "content": "One boy and one girl can be selected as (one boy & three girls) or (two boys & two girls) or (three boys & one girl)=(4C1*3C3)+(4C2*3C2)+(4C3*3C1)=4+18+12=34\nANSWER:B", "role": "assistant", "uuid": "460ac203-23be-4277-9760-b0cff3ef3b1c" } ]

{ "coherence": 2.84, "complexity": 2.02, "correctness": 2.64, "helpfulness": 2.64, "instruction-following": 3.43, "safety": 5.09, "verbosity": 1.52, "verbosity-coeff": -0.0868 }

[ { "content": "A bank pays interest to its customers on the last day of the year. The interest paid to a customer\nis calculated as 10% of the average monthly balance maintained by the customer. John is a customer at the bank. On the last day, when the interest was accumulated into his account, his bank balance doubled to $7540. What is the average monthly balance maintained by John in his account during the year?\n\n['A)2840', 'B)5680', 'C)6840', 'D)7540', 'E)37700']", "role": "user", "uuid": "9376dbe7-b789-4876-b51f-c5f7562db212" }, { "content": "Soln:-\nBank balance is doubled with accumulation of interest to 7540..\nthis means INTEREST is 7540/2=3770 for entire year..\nalthough since interest is 10% of avg MONthly balance, it becomes 37700..\nANSWER:E", "role": "assistant", "uuid": "045aed78-1463-4358-9fa3-fdb8d95ec478" } ]

{ "coherence": 2.62, "complexity": 1.38, "correctness": 2.1, "helpfulness": 2.12, "instruction-following": 3.04, "safety": 5.4, "verbosity": 0.97, "verbosity-coeff": -0.1648 }

[ { "content": "Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 4 hours and 16 hours respectively. The ratio of their speeds is?\n\n['A)4:5', 'B)4:2', 'C)4:4', 'D)4:8', 'E)4:1']", "role": "user", "uuid": "a86b3047-7d35-4893-8403-59fd83bffec9" }, { "content": "Let us name the trains A and B.\nThen, (A's speed) : (B's speed)\n= √b : √a = √16 : √4\n= 4:2\nAnswer: B", "role": "assistant", "uuid": "d73804dd-cad6-4caf-9930-64eec959b66b" } ]

{ "coherence": 2.45, "complexity": 1.78, "correctness": 2.04, "helpfulness": 2.18, "instruction-following": 2.86, "safety": 6.45, "verbosity": 0.94, "verbosity-coeff": -0.1266 }

[ { "content": "The price of a radio was increased by 25 percent. The new price was then increased by 40 percent. A single increase of what percent is equivalent to these two successive increases?\n\n['A)80%', 'B)75%', 'C)65%', 'D)50%', 'E)45%']", "role": "user", "uuid": "114a1057-9757-4f11-8b55-47e004245df4" }, { "content": "consider base price - $100\n25% increase = 1.25*100 = $125\nanother 40% increase on new price = 1.4* 125 = $175\nso final price of radio - $175\ntherefore a 75% increase\ncorrect option - B", "role": "assistant", "uuid": "3dfeba59-4a09-4d2c-bc80-53154c3a532e" } ]

{ "coherence": 2.74, "complexity": 1.61, "correctness": 2.39, "helpfulness": 2.41, "instruction-following": 2.55, "safety": 5.52, "verbosity": 1.23, "verbosity-coeff": -0.2197 }

[ { "content": "A pair of prime numbers that can be expressed in the form R{p, (p + 6)} is defined as a pair of “sexy primes.” A “sexy triplet” is a group of three primes that can be expressed in the form {p, (p + 6), (p + 12)}. All of the following prime numbers are the middle term of a sexy triplet EXCEPT\n\n['A) 11', 'B) 13', 'C) 17', 'D) 19', 'E) 23']", "role": "user", "uuid": "3ea0198d-c13e-4808-b1c0-4530be768759" }, { "content": "definetly a sitter.plug in the values for middle term and calculate.We can see clearly that R for 19 , 19+6 gives 25 which is not a prime\ntherefore correct answer D", "role": "assistant", "uuid": "a9c919dc-e6a4-4fba-960c-e3274021cdc0" } ]

{ "coherence": 2.16, "complexity": 1.55, "correctness": 1.65, "helpfulness": 1.55, "instruction-following": 1.79, "safety": 4.89, "verbosity": 1.12, "verbosity-coeff": -0.0986 }

[ { "content": "Find the altitude of a parallelogram whose are is\n5400cm2 and the base is 45cm\n\n['A)80 cm', 'B)90 cm', 'C)100 cm', 'D)110 cm', 'E)120 cm']", "role": "user", "uuid": "5cf24c69-f516-41a4-b0af-2a7e27d6fa1b" }, { "content": "area of parallelogram =base * hight then 5400 cm2=45cm*h\nh=120 cm\nANSWER:E", "role": "assistant", "uuid": "e450173e-9486-4357-807b-9c2a0587aa56" } ]

{ "coherence": 2.98, "complexity": 0.75, "correctness": 2.76, "helpfulness": 2.88, "instruction-following": 3.41, "safety": 5.71, "verbosity": 0.38, "verbosity-coeff": -0.102 }

[ { "content": "Which is not a leap year?\n\n['A)2004', 'B)2012', 'C)1700', 'D)1704', 'E)2008']", "role": "user", "uuid": "17b3335e-c261-454e-9673-93f588fccd01" }, { "content": "the answer is 1700,\nbecz if the year is centurial ,that should be divisible by 400 for leap year\nex:400,800,1200\nANSWER:C", "role": "assistant", "uuid": "a34e5a10-1032-4e1e-b47a-2bbdb7f5989d" } ]

{ "coherence": 2.86, "complexity": 1.3, "correctness": 2.66, "helpfulness": 2.57, "instruction-following": 3.11, "safety": 4.21, "verbosity": 1.44, "verbosity-coeff": -0.0976 }

[ { "content": "Faiza has 9 purses, she gives 3 purse as gift. Now how many purse did she have?\n\n['A)2', 'B)6', 'C)11', 'D)9', 'E)4']", "role": "user", "uuid": "dda923c6-bc8b-465b-a37b-f6b4e5d9b380" }, { "content": "9-3=6. Answer is B", "role": "assistant", "uuid": "5b3ef82c-f5a0-4b1e-aaf6-4dc482242a2e" } ]

{ "coherence": 2.76, "complexity": 0.2, "correctness": 2.92, "helpfulness": 3.09, "instruction-following": 3.74, "safety": 5.52, "verbosity": 0.48, "verbosity-coeff": -0.0835 }

[ { "content": "Find (7x + 8y ) / (x-2y) if x/2y = 3/2 ?\n\n['A)24', 'B)25', 'C)26', 'D)27', 'E)29']", "role": "user", "uuid": "41b5ba3b-9292-4a30-a066-399e22d811e4" }, { "content": "x/2y=3/2\n=>x=6y/2=3y\n=>(7x+8y)/(x-2y)=((7*(3y))+8y)/(3y-2y)\n=>29y/y=29\nANSWER:E", "role": "assistant", "uuid": "4de45922-0400-4cfb-8c1f-53df33e19203" } ]

{ "coherence": 2.82, "complexity": 2.08, "correctness": 1.96, "helpfulness": 1.85, "instruction-following": 3.04, "safety": 4.77, "verbosity": 1.3, "verbosity-coeff": -0.1321 }

[ { "content": "Average of first six multiples of 15 is\n\n['A)9.5', 'B)44.5', 'C)52.5', 'D)15.75', 'E)17.7']", "role": "user", "uuid": "b60052fa-9648-4c74-ba22-a658a75ab063" }, { "content": "Explanation:\nAverage=15(1+2+3+4+5+6) / 6=315 / 6=52.5\nOption C", "role": "assistant", "uuid": "60f936f5-05d9-48a5-b1c5-d404cafac60c" } ]

{ "coherence": 2.96, "complexity": 1.38, "correctness": 2.31, "helpfulness": 2.47, "instruction-following": 2.98, "safety": 4.89, "verbosity": 0.88, "verbosity-coeff": -0.1017 }

[ { "content": "If t = 20! + 17, then t is divisible by which of the following?\nI. 15\nII. 17\nIII. 19\n\n['A) None', 'B) I only', 'C) II only', 'D) I and II', 'E) II and II']", "role": "user", "uuid": "efc435be-8e53-464c-81e7-8cd7eecd6937" }, { "content": "Another crude way to answer this, if you did not know the properties above would be to consider that that 20! will have the number ending in 00 due to 10 and 20 being included.\nSo t!+17 = xxxx00 +17 = xxxx17 which is only possibly divisible by 17. Hence Option C is the answer.", "role": "assistant", "uuid": "9a2a818c-3b81-4f2d-8bfc-d143b14ffc1f" } ]

{ "coherence": 2.61, "complexity": 2.35, "correctness": 1.43, "helpfulness": 1.24, "instruction-following": 1.42, "safety": 4.01, "verbosity": 1.53, "verbosity-coeff": -0.2109 }

[ { "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)3500', 'B)3750', 'C)3800', 'D)3840', 'E)3900']", "role": "user", "uuid": "524a63e3-5a44-49d4-9d91-50e6290beb40" }, { "content": "Let the cost of a chair and that of a table be Rs. x and Rs. y respectively.\nThen, 10x = 4y or y =\t5/2x.\n15x + 2y = 4000\n15x + 2 x\t(5/2)\tx = 4000\n20x = 4000\nx = 200.\nSo, y =(5/2)x 200= 500.\nHence, the cost of 12 chairs and 3 tables = 12x + 3y\n= Rs. (2400 + 1500)\n= Rs. 3900.\nOption E", "role": "assistant", "uuid": "f3379010-f8b4-4263-a230-85d892474edc" } ]

{ "coherence": 3.11, "complexity": 2.16, "correctness": 2.62, "helpfulness": 2.76, "instruction-following": 3.82, "safety": 4.11, "verbosity": 1.5, "verbosity-coeff": -0.1161 }

[ { "content": "Of the 11 members of a football team in school, 9 are trained to play the offensive position, 6 can play defensive position, and 4 can play both position. If one member is chosen at random, what is the probability that the member chosen will be someone who play either position ?\n\n['A)a) 3/11', 'B)b) 4/11', 'C)c) 0', 'D)d) 6/11', 'E)e) 7/11']", "role": "user", "uuid": "e9831e0b-8d8a-4151-8320-58f1ac73273b" }, { "content": "You know how to solve for Total number of people who can play at one position:\nTotal = n(A) + n(B) - n(A and B)\nTotal people who can play at least one position = 9+6-4=11\nSo all 11 people know how to play at least one position. Hence, if you pick anyone, the probability is 0 that he wouldn't know how to play any position\nAnswer (C)", "role": "assistant", "uuid": "b1724458-9927-4368-9d87-faf8b8bd1782" } ]

{ "coherence": 2.37, "complexity": 1.75, "correctness": 1.28, "helpfulness": 1.15, "instruction-following": 1.47, "safety": 5.55, "verbosity": 1.38, "verbosity-coeff": -0.2133 }

[ { "content": "Find the C.I. on a sum of Rs.1600 for 9 months at 20% per annum, interest being compounded quarterly?\n\n['A)2888', 'B)2689', 'C)2522', 'D)277', 'E)2911']", "role": "user", "uuid": "992ccea2-2d6a-4cb7-a55e-2e1ab94ba431" }, { "content": "A = 1600(21/20)3 = 2522.Answer: C", "role": "assistant", "uuid": "27ec399e-4a85-4ff5-b169-3e865e8f58eb" } ]

{ "coherence": 2.8, "complexity": 0.87, "correctness": 2.04, "helpfulness": 2.21, "instruction-following": 3.5, "safety": 5.44, "verbosity": 0.34, "verbosity-coeff": -0.106 }

[ { "content": "If 2x + y = 7 and x + 2y = 5, then 7xy/3 =?\n\n['A)A) 1', 'B)B) 2', 'C)C) 7', 'D)D) 18/5', 'E)E) 4']", "role": "user", "uuid": "70606d81-ae1d-4c82-8519-97a6e4e5e63a" }, { "content": "2*(x+2y = 5) equals 2x+4y=10\n2x+4y=10\n- 2x + y= 7\n= 3y=3\nTherefore Y = 1\nPlug and solve...\n2x + 1 = 7\n2x=6\nx=3\n(7*3*1)/3\n= 21/3\n=7\nC", "role": "assistant", "uuid": "63916937-967f-4876-8ff7-799f92a315ef" } ]

{ "coherence": 2.7, "complexity": 1.86, "correctness": 1.81, "helpfulness": 1.78, "instruction-following": 2.55, "safety": 5.52, "verbosity": 0.9, "verbosity-coeff": -0.1237 }

[ { "content": "Kyle is a lumberjack with 12 trees to cut down. How many ways can he cut down one or more of the trees today?\n\n['A)255', 'B)4095', 'C)1023', 'D)8125', 'E)513']", "role": "user", "uuid": "e4285aae-6d68-484b-8171-2ec07339146b" }, { "content": "Kyle can cut down one or more of 12 trees\n=> 2 ^ 12 - 1 = 4095\nB", "role": "assistant", "uuid": "df25204d-7f86-46f7-8472-743c67e68629" } ]

{ "coherence": 3, "complexity": 0.83, "correctness": 2.59, "helpfulness": 2.72, "instruction-following": 3.15, "safety": 4.62, "verbosity": 0.69, "verbosity-coeff": -0.1123 }

[ { "content": "The average age of 8 men increases by 2 years when two women are included in place of two men of ages 20 and 24 years. Find the average age of the women?\n\n['A)25 years', 'B)20 years', 'C)30 years', 'D)15 years', 'E)10 years']", "role": "user", "uuid": "806d5f18-abbd-4314-8433-ac9e6df46c54" }, { "content": "Answer: Option C\n20 + 24 + 8 * 2 = 60/2 = 30", "role": "assistant", "uuid": "b86a163d-fb6b-4315-96be-bff1d8f6b1f0" } ]

{ "coherence": 2.61, "complexity": 0.94, "correctness": 1.5, "helpfulness": 1.74, "instruction-following": 1.36, "safety": 4.58, "verbosity": 0.22, "verbosity-coeff": -0.1387 }

[ { "content": "when i was of 2 years old, my sister's age was half of mine..\nnow i am of 100..\nwhat is the age of my sister??\n\n['A)98', 'B)99', 'C)97', 'D)95', 'E)94']", "role": "user", "uuid": "78a0d169-b621-4587-83e0-bc97bc4b2eca" }, { "content": "99,one less than me.\nANSWER:B", "role": "assistant", "uuid": "951f30e8-0474-4a91-8354-b8f46a145ef8" } ]

{ "coherence": 2.74, "complexity": 0.69, "correctness": 2.08, "helpfulness": 2.29, "instruction-following": 2.35, "safety": 4.93, "verbosity": 0.74, "verbosity-coeff": -0.1022 }

[ { "content": "Sachin can cover a distance in 1hr 24 min by covering 2/3 of the distance at 4 kmph and the rest at 5 kmph. The total distance is?\n\n['A)8 km', 'B)7 km', 'C)5 km', 'D)6 km', 'E)4 km']", "role": "user", "uuid": "28bd1276-834e-4d58-8198-270ba87288c7" }, { "content": "dist travelled at 4 kmph speed = 2/3\ndist at 5 kmph speed = (1-2/3)d=(1/3)d\ntot time = 1 hr 24 min =(64+24) min=84/60hr=>21/15 hr\ntime = dist/speed\n21/15=2/3/4d+1/3/5d\nd=6 km\nANSWER D", "role": "assistant", "uuid": "f1c96f73-603e-45cb-9792-348082ebd72c" } ]

{ "coherence": 2.43, "complexity": 1.72, "correctness": 2.06, "helpfulness": 2.12, "instruction-following": 3.19, "safety": 6.02, "verbosity": 0.83, "verbosity-coeff": -0.1252 }

[ { "content": "Mixture A is 40 percent alcohol, and mixture B is 80 percent alcohol. If the two are poured together to create a 4-gallon mixture that contains 50 percent alcohol, approximately how many gallons of mixture A are in the mixture?\n\n['A)1.5', 'B)1.7', 'C)2.3', 'D)2.5', 'E)2.4']", "role": "user", "uuid": "51435e3e-e092-4bb1-a007-7b6cfdbd15bf" }, { "content": "(80-50)/(50-40) = Qa/Qb\n30/10 = Qa/Qb\n3/1 = Qa/Qb\nQa = (3/5) * 4 = 12/5 = 2.4 approx\nAnswer : E", "role": "assistant", "uuid": "12195b5f-f114-4d07-9f87-98ff9f25a8e3" } ]

{ "coherence": 2.64, "complexity": 1.34, "correctness": 1.9, "helpfulness": 1.87, "instruction-following": 2.78, "safety": 4.32, "verbosity": 0.54, "verbosity-coeff": -0.1653 }

[ { "content": "On flipping 2 coins together what is the outcomes for at least two heads?\n\n['A){HH}', 'B){TT}', 'C){HT}', 'D){TH}', 'E)None']", "role": "user", "uuid": "5bf39b8e-4c37-4c81-94b7-e2fb05bd2c05" }, { "content": "Sample space, S = {HH, TH, TH, TT}\nFavorable outcomes for at least two heads\n= favorable outcomes for exactly two heads and favorable outcomes for more than two heads\n= {HH}\nA", "role": "assistant", "uuid": "02f69ae9-b589-4e6b-944f-21bd9ea6d555" } ]

{ "coherence": 2.29, "complexity": 1.63, "correctness": 1.76, "helpfulness": 1.56, "instruction-following": 2, "safety": 4.66, "verbosity": 1.38, "verbosity-coeff": -0.0861 }

[ { "content": "The distance between Delhi and Mathura is 110 kms. A starts from Delhi with a speed of 20 kmph at 7 a.m. for Mathura and B starts from Mathura with a speed of 25 kmph at 8 p.m. from Delhi. When will they meet?\n\n['A)08 a.m.', 'B)09 a.m.', 'C)12 a.m.', 'D)10 a.m.', 'E)07 a.m.']", "role": "user", "uuid": "5bacc637-004f-4854-98cf-b4078db801d6" }, { "content": "D\n10 a.m.\nD = 110 – 20 = 90\nRS = 20 + 25 = 45\nT = 90/45 = 2 hours\n8 a.m. + 2 = 10 a.m.", "role": "assistant", "uuid": "642614d5-b47c-40e0-a109-ccc90fef0cd1" } ]

{ "coherence": 2.82, "complexity": 1.45, "correctness": 2.33, "helpfulness": 2.57, "instruction-following": 2.82, "safety": 5.12, "verbosity": 0.81, "verbosity-coeff": -0.1046 }

[ { "content": "If r and s are positive integers, and r^2 + r/s is an odd integer, which of the following cannot be even?\n\n['A)3r + 2s', 'B)(r-1)(s+2)', 'C)r^(s+1) + s^r', 'D)r^3 +3', 'E)s^4 +4']", "role": "user", "uuid": "f0888b2c-69e3-4137-a503-a56b519dba5d" }, { "content": "Given: r and s are positive integers, and r2r2 + r/s is an odd integer\nWhat are some \"nice\" values that make this true?\nHow about r = 2 and s = 2. We get: 2222 + 2/2 = 4 + 1 = 5, which IS an odd integer\nGreat, now let's plug r = 2 and s = 2 into each answer choice.\nA. 3(2) + 2(2) = 10, which is even. so ELIMINATE A\nB. (2 - 1)(2 + 2) = 4, which is even. so ELIMINATE B\nC. 2^(2+1) + 2^2 = 12, which is even. so ELIMINATE C\nD. 23+323+3 = 11, which is odd. so KEEP D for now\nE. 24+424+4 = 20, which is even. so ELIMINATE E\nBy the process of elimination, the answer must be D", "role": "assistant", "uuid": "6421f101-2762-43fe-8c5f-52bc9b67c4fc" } ]

{ "coherence": 2.78, "complexity": 2.04, "correctness": 2.21, "helpfulness": 2.02, "instruction-following": 1.96, "safety": 4.29, "verbosity": 1.49, "verbosity-coeff": -0.2296 }

[ { "content": "Ross has 80 shirts, 3/4 of the shirts are green and 1/10 is without buttons. Therefore Ross has between ___ and ___ shirts with buttons that are not green.\n\n['A)12 ; 20.', 'B)12 ; 19.', 'C)12 ; 18.', 'D)12 ; 17.', 'E)12 ; 16.']", "role": "user", "uuid": "77e4b881-86b9-49d0-aa10-5076173b4752" }, { "content": "Total shirts = 80\nGreen shirts = 3/4*80 = 60, Non green shirts = 20\nShirts without button = 1/10*80 = 8, shirts with button = 72\nRequired: Range of shirts with buttons that are not green.\nMaximum non green shirts with buttons = number of non green shirts = 20\nMinimum non green shirts with buttons (All without button shirts are non green) = Non green shirts - shirts without button = 20 - 8 = 12\nHence the range would be (12, 20)\nCorrect Option: A", "role": "assistant", "uuid": "4598b4b3-9adb-40dc-8071-47c3359d8aec" } ]

{ "coherence": 3.25, "complexity": 1.25, "correctness": 2.88, "helpfulness": 3.07, "instruction-following": 3.72, "safety": 5.75, "verbosity": 0.92, "verbosity-coeff": -0.1147 }

[ { "content": "A coin is tossed live times. What is the probability that there is at the least one tail?\n\n['A)31/32', 'B)31/38', 'C)31/31', 'D)61/38', 'E)31/35']", "role": "user", "uuid": "22b63d4d-2662-4f66-91bc-1e2427f9caf5" }, { "content": "Let P(T) be the probability of getting least one tail when the coin is tossed five times.\n= There is not even a single tail.\ni.e. all the outcomes are heads.\n= 1/32 ; P(T) = 1 - 1/32 = 31/32\nAnswer: A", "role": "assistant", "uuid": "a9c59dd5-2c78-4132-8cfc-226225496c54" } ]

{ "coherence": 2.84, "complexity": 1.44, "correctness": 2.55, "helpfulness": 2.88, "instruction-following": 3.58, "safety": 5.01, "verbosity": 1.17, "verbosity-coeff": -0.1419 }

[ { "content": "A and B complete a work in 20 days. A alone can do it in 40 days. If both together can do the work in how many days?\n\n['A)1.0875 days', 'B)0.1875 days', 'C)0.0675 days', 'D)0.075 days', 'E)0.0175 days']", "role": "user", "uuid": "f49a176b-cbca-4f97-a495-62a0b83514bc" }, { "content": "1/20 + 1/40 = 0.075 days\nANSWER:D", "role": "assistant", "uuid": "3baf6ee8-0f76-4140-873d-e90c2bac8dab" } ]

{ "coherence": 2.74, "complexity": 1.08, "correctness": 2.16, "helpfulness": 2.29, "instruction-following": 2.64, "safety": 4.54, "verbosity": 0.48, "verbosity-coeff": -0.1194 }

[ { "content": "A 60 cm long wire is to be cut into two pieces so that one piece will be 2/4th of the other, how many centimeters will the shorter piece be?\n\n['A)A)73', 'B)B)20', 'C)C)83', 'D)D)21', 'E)E)52']", "role": "user", "uuid": "8adbcf84-31c5-49b1-92bf-df8ccfa890b3" }, { "content": "Explanation:\n1: 2/4 = 4: 2\n2/6* 60 = 20\nAnswer: Option B", "role": "assistant", "uuid": "ab1cac43-ac59-4077-b789-83ace4a80cfd" } ]

{ "coherence": 2.55, "complexity": 0.82, "correctness": 1.92, "helpfulness": 2.12, "instruction-following": 2.21, "safety": 6.34, "verbosity": 0.06, "verbosity-coeff": -0.1221 }

[ { "content": "A bookshop had science and art books in the ratio of 2:5. By the end of the week, 20% of both type of books were sold and 2240 books were unsold. How many art books were there at the starting?\n\n['A)1000', 'B)1200', 'C)1500', 'D)1600', 'E)2000']", "role": "user", "uuid": "6b4e32be-e73f-4fb3-950d-c6946371be21" }, { "content": "science books sold = 2x × 0.2 = 0.4x\nscience books unsold = 2x – 0.4x = 1.6x\nart books sold = 5x × 0.2 = x\nart books unsold = 5x – x = 4x\ntotal books unsold = 1.6x + 4x = 5.6x\n5.6x = 2240\nx = 400\n2x science = 800\nand 5x art books = 2000\nE", "role": "assistant", "uuid": "383a4f5a-dd68-4765-bce9-faf94aa430d9" } ]

{ "coherence": 2.9, "complexity": 1.59, "correctness": 2.45, "helpfulness": 2.55, "instruction-following": 3.05, "safety": 4.93, "verbosity": 0.91, "verbosity-coeff": -0.1145 }

[ { "content": "We are required to form different words with the help of letters of the word INTEGER. Let m1 be the number of words in which I and N are never together and m2 be the number of words which begin with I and end with R, then what is the value if m1/m2?\n\n['A)18', 'B)24', 'C)30', 'D)36', 'E)40']", "role": "user", "uuid": "ee3c6685-af08-4436-8f83-21718fe1b4e2" }, { "content": "Total possible combination without any restriction:- 7!/2! (E is mentioned two times in the word INTEGER, hence we are dividing by 2!)\nTotal Possible combination when letter 'I' and 'N' are together- 6!*2/2! (Think of I and N as one, hence total letters are 6, but I and N can be written in two ways- IN and NI- that is why we multiplied 6!*2)\nTotal possible combination when letter 'I' and 'N' are not together, i.e. m1= 7!/2! - 6!*2/2!= 6!*5/2\nNow fix 'I' and 'R', then total possible combination, i.e m2, are= 5!/2!\nm1/m2= 6!*5/2/5!/2= 30\nAnswer is 'C'", "role": "assistant", "uuid": "f82825f3-e2d3-4aa9-ad63-06d2221c1665" } ]

{ "coherence": 2.66, "complexity": 2.53, "correctness": 2.39, "helpfulness": 2.62, "instruction-following": 3.07, "safety": 4.93, "verbosity": 1.61, "verbosity-coeff": -0.1099 }

[ { "content": "A coin is tossed four times. What is the probability that there is at the least one tail?\n\n['A)15/16', 'B)15/37', 'C)15/67', 'D)15/17', 'E)15/31']", "role": "user", "uuid": "8a50def3-ad1f-4dca-af65-f6dd05176445" }, { "content": "Let P(T) be the probability of getting least one tail when the coin is tossed four times.\n= There is not even a single tail.\ni.e. all the outcomes are heads.\n= 1/16 ; P(T) = 1 - 1/16\n= 15/16\nAnswer: A", "role": "assistant", "uuid": "4bb2f5f3-3823-4849-8964-4bbea6da366c" } ]

{ "coherence": 3.04, "complexity": 1.46, "correctness": 2.68, "helpfulness": 2.9, "instruction-following": 3.56, "safety": 5.16, "verbosity": 1.33, "verbosity-coeff": -0.1953 }

[ { "content": "x, y and z are consecutive positive integers such that x < y < z; which of the following must be true?\n1. xyz is divisible by 6\n2. (z-x)(y-x+1) = 4\n3. xy is even\n\n['A)I only', 'B)II only', 'C)III only', 'D)I and II only', 'E)I, II, and III']", "role": "user", "uuid": "6036cbd4-9492-4aed-92ee-f4fd3cd39e20" }, { "content": "Since x, y and z are consecutive integers such that x < y < z, we can say x = y-1 and Z = y+1\nStatement 1 would be true as at least one of the three numbers is divisible by 2 and one by 3 so xyz would be divisible by 6.\nStatement 2 can be simplified if we write everything in terms of y as ((y+1)-(y-1))*(y-(y-1)+1) = 2*2 = 4 So, always true\nStatement 3 talks about xy Since x and y are consecutive integers one of them is odd and other is even so product would always be even and hence true.\nSo, I II and III are always true and hence answer is\nE.", "role": "assistant", "uuid": "761fd163-7910-4af4-a595-1c879e79e0ea" } ]

{ "coherence": 2.82, "complexity": 2.47, "correctness": 2.04, "helpfulness": 2.04, "instruction-following": 2.62, "safety": 5.98, "verbosity": 1.39, "verbosity-coeff": -0.208 }

[ { "content": "If 3a – 2b – 2c = 30 and √3a-√(2b+2c)=4, what is the value of a + b + c?\n\n['A)3', 'B)9', 'C)10', 'D)12', 'E)14']", "role": "user", "uuid": "cabd4a36-d3da-4232-b1f7-e0dc7ac128bf" }, { "content": "when we look at the two equations, we can relize some similarity, so lets work on it..\n3a – 2b – 2c = 32 can be written as √3a^2-√(2b+2c)^2=32\n{√3a-√(2b+2c)}{√3a+√(2b+2c)}=32..\nor 4*√3a+√(2b+2c)=32..\nor √3a+√(2b+2c)=8..\nnow lets work on these two equations\n1)√3a-√(2b+2c)=4..\n2)√3a+√(2b+2c)=8..\nA) add the two eq..\n√3a+√(2b+2c)+√3a-√(2b+2c)=12..\n2√3a=12..\nor √3a=6..\n3a=36..\na=12.\nB) subtract 1 from 2..\n√3a+√(2b+2c)-√3a+√(2b+2c)=4..\n2√(2b+2c)=4..\n√(2b+2c)=2..\n2b+2c=4..\nor b+c=2..\nfrom A and B a+b+c=12+2=14..\nC", "role": "assistant", "uuid": "b48a89db-76bc-4434-b773-3a2f869d4791" } ]

{ "coherence": 2.37, "complexity": 2.16, "correctness": 1.46, "helpfulness": 1.31, "instruction-following": 1.72, "safety": 5.52, "verbosity": 1.75, "verbosity-coeff": -0.1474 }

[ { "content": "A man leaves a point P at 6 a.m. and reaches the point Q at 10 a.m. another man leaves the point give at 8 a.m. and reaches the point P at 12 noon. At what time do they meet?\n\n['A)9 a.m', 'B)8 a.m', 'C)7 a.m', 'D)6 a.m', 'E)5 a.m']", "role": "user", "uuid": "3ac77e2b-4a16-4a63-9e08-ab19708b2bcd" }, { "content": "A\n9 a.m.", "role": "assistant", "uuid": "e467875b-ef69-4ca9-8fbb-4f9b74b23d82" } ]

{ "coherence": 2.66, "complexity": 1, "correctness": 1.53, "helpfulness": 1.66, "instruction-following": 1.69, "safety": 4.93, "verbosity": 0.62, "verbosity-coeff": -0.1236 }

[ { "content": "Find the area of a parallelogram with base 28 cm and height 32 cm.\n\n['A)200', 'B)384', 'C)345', 'D)244', 'E)896']", "role": "user", "uuid": "443fcf79-ea50-4f27-9712-ee336784c1ec" }, { "content": "Area of a parallelogram = base * height = 28 * 32 = 896 cm2\nAnswer: Option E", "role": "assistant", "uuid": "86b027ef-8e17-4408-9424-9d1f9459cfe2" } ]

{ "coherence": 2.92, "complexity": 0.97, "correctness": 2.12, "helpfulness": 2.51, "instruction-following": 3.46, "safety": 4.58, "verbosity": 0.49, "verbosity-coeff": -0.1288 }

[ { "content": "5^100 is divided by 18. Then what is the remainder?\n\n['A)10', 'B)11', 'C)13', 'D)15', 'E)19']", "role": "user", "uuid": "b2067f03-b61e-4a11-9c54-67b51a937bfc" }, { "content": "Here N = 18=2×32\nϕ(18)=18(1−12)(1−13) = 6\nSo 56 when divided by 18, remainder is 1.\nSo we can write the given expression 5100=(56)16×54 = (1)16×54 = 52×52=7×7=49\nNow 49 when divided by 18, remainder is 13.\nC", "role": "assistant", "uuid": "7b6df0f7-62bc-4d13-8bff-fab0274f1685" } ]

{ "coherence": 2.41, "complexity": 2.43, "correctness": 1.55, "helpfulness": 1.45, "instruction-following": 1.64, "safety": 5.2, "verbosity": 1.29, "verbosity-coeff": -0.1536 }

[ { "content": "The rate of spin of a certain gyroscope doubled every 10 seconds from the moment a particular stopwatch started. If after a minute and a half the gyroscope reached a speed of 6400 meters per second, what was the speed, in meters per second, when the stopwatch was started?\n\n['A)25/2', 'B)25/4', 'C)25/8', 'D)25/16', 'E)25/32']", "role": "user", "uuid": "7e093347-477e-40ec-a14c-43ab27233a3a" }, { "content": "Let x be the original speed when the stopwatch was started.\nIn 90 seconds, the speed doubled 9 times.\n2^9 * x = 6400\nx = (2^8 * 25) / 2^9 = 25/2\nThe answer is A.", "role": "assistant", "uuid": "7bdba2e6-dcfa-45c1-99fd-0d57a8eca0a9" } ]

{ "coherence": 3.29, "complexity": 1.86, "correctness": 2.41, "helpfulness": 2.35, "instruction-following": 2.72, "safety": 4.77, "verbosity": 0.92, "verbosity-coeff": -0.218 }

[ { "content": "John makes $60 a week from his job. He earns a raise andnow makes $72 a week. What is the % increase?\n\n['A)20%', 'B)16.66%', 'C)16.56%', 'D)17.66%', 'E)18.1%']", "role": "user", "uuid": "36e59373-dc22-4abf-b8b6-afbbb2b48c2e" }, { "content": "Increase = (12/60)*100 = (1/5)*100 = 20%.\nA", "role": "assistant", "uuid": "2f332494-c0a0-4cf0-9bb3-a146c90f9979" } ]

{ "coherence": 2.94, "complexity": 1.19, "correctness": 2.51, "helpfulness": 2.25, "instruction-following": 2.35, "safety": 3.13, "verbosity": 0.75, "verbosity-coeff": -0.1118 }

[ { "content": "At the wholesale store you can buy an 8-pack of hot dogs for $1.55, a 20-pack for $3.05, and a 250-pack for $22.95. What is the greatest number of hot dogs you can buy at this store with $208?\n\n['A)1,108', 'B)2,100', 'C)2,108', 'D)2,160', 'E)2,256']", "role": "user", "uuid": "7ed4eb5f-de1a-4381-83c5-ef1fec6e24d3" }, { "content": "I think it should be D.\nI can buy 8 250-pack for Rs 22.95*8 = $183.60\nNow, I can buy 8 20-pack for 3.05*8 = $24.40\nNow, I am left with only $1.15. I cannot but anything with this.\nHence Total Hotdogs = 250*8 + 20*5 = 2160", "role": "assistant", "uuid": "38b3c6ed-2a59-4eb5-9baa-86401bfc9db2" } ]

{ "coherence": 2.82, "complexity": 0.81, "correctness": 1.53, "helpfulness": 1.83, "instruction-following": 1.36, "safety": 3.8, "verbosity": 0.96, "verbosity-coeff": -0.1616 }

[ { "content": "A sum of money is to be distributed among A, B, C, D in the proportion of 5:2:4:3. If C gets Rs. 2500 more than D, what is B's share?\n\n['A)A)8239', 'B)B)2900', 'C)C)4500', 'D)D)2393', 'E)E)5000']", "role": "user", "uuid": "6f5db5ec-5609-4a3c-8f24-f43dd3fe4cb7" }, { "content": "Let the shares of A, B, C and D be 5x, 2x, 4x and 3x Rs. respectively.\nThen, 4x - 3x = 2500 => x = 2500.\nB's share = Rs. 2x = 2 * 2500 = Rs. 5000.\nAnswer: E", "role": "assistant", "uuid": "bd5a8b26-e0b0-479c-9566-f5bcc803ef2b" } ]

{ "coherence": 2.98, "complexity": 0.89, "correctness": 2.23, "helpfulness": 2.7, "instruction-following": 3.37, "safety": 4.81, "verbosity": 0.68, "verbosity-coeff": -0.1232 }

[ { "content": "A, B, K start from the same place and travel in the same direction at speeds of 30 km/hr, 40 km/hr, 120 km/hr respectively. B starts two hours after A. If B and K overtake A at the same instant, how many hours after A did K start?\n\n['A)3', 'B)4', 'C)6', 'D)8', 'E)10']", "role": "user", "uuid": "89e43202-4f40-49c7-babe-ee4c081eb95e" }, { "content": "In 2 hours, A travels 60 km.\nB can catch A at a rate of 10 km/hr, so B catches A 6 hours after B starts.\nSo A and B both travel a distance of 240 km.\nC needs 2 hours to travel 240 km, so C leaves 6 hours after A.\nThe answer is C.", "role": "assistant", "uuid": "74446acd-7f4c-4c3e-9816-3f69ca9c2ffe" } ]

{ "coherence": 2.9, "complexity": 1.58, "correctness": 1.98, "helpfulness": 2.31, "instruction-following": 3.04, "safety": 5.98, "verbosity": 1.28, "verbosity-coeff": -0.2004 }

[ { "content": "A shopkeeper sold an article offering a discount of 4% and earned a profit of 38%. What would have been the percentage of profit earned if no discount was offered?\n\n['A)24', 'B)28', 'C)30', 'D)32', 'E)44']", "role": "user", "uuid": "8a4fec19-e3a2-4176-9340-11dbf7e650e7" }, { "content": "Let C.P. be Rs. 100.\nThen, S.P. = Rs. 138\nLet marked price be Rs. x. Then, 96/100 x = 138\nx = 13800/96 = Rs. 143.75\nNow, S.P. = Rs. 143.75, C.P. = Rs. 100\nProfit % = 44%.\nANSWER:E", "role": "assistant", "uuid": "3de91f00-fc31-447f-b3b8-4225c46ec276" } ]

{ "coherence": 3.11, "complexity": 2.29, "correctness": 3.04, "helpfulness": 3.05, "instruction-following": 3.8, "safety": 4.36, "verbosity": 2.04, "verbosity-coeff": -0.1385 }

[ { "content": "If r and h are two positive integers and r/h = 1.60, then r can equal which one of the following?\n\n['A) 9', 'B) 24', 'C) 20', 'D) 22', 'E) 23']", "role": "user", "uuid": "ab06e748-624c-4fd6-ba00-b06dfb6d9e11" }, { "content": "r/h = 1.60 = 160/100 = 8/5\nSo, r COULD equal 24\nAnswer: B", "role": "assistant", "uuid": "c9284d7a-61ca-40d4-a8bb-ccffd70dc21a" } ]

{ "coherence": 2.88, "complexity": 1.22, "correctness": 2.64, "helpfulness": 2.96, "instruction-following": 2.98, "safety": 5.79, "verbosity": 0.46, "verbosity-coeff": -0.2009 }

[ { "content": "X and Y started a business with capitals Rs. 20000 and Rs. 25000. After few months Z joined them with a capital of Rs. 30000. If the share of Z in the annual profit of Rs. 50000 is Rs. 14000, then after how many months from the beginning did Z join?\n\n['A)2', 'B)6', 'C)7', 'D)8', 'E)5']", "role": "user", "uuid": "0cfbf2ec-ec75-407b-84a6-89b184584c23" }, { "content": "Investments of X, Y and Z respectively are Rs. 20000, Rs. 25000 and Rs. 30000\nLet investment period of Z be x months.\nRatio of annual investments of X, Y and Z is (20000 * 12) : (25000 * 12) : (30000 * x)\n= 240 : 300 : 30x = 8 : 10 : x\nThe share of Z in the annual profit of Rs. 50000 is Rs. 14000.\n=> [x/ (18 + x)] 50000 = 14000 => [x/ (18 + x)] 25 = 7\n=> 25x = 7x + (18 * 7) => x = 7 months.\nZ joined the business after (12 - 7) months. i.e., 5 months.\nAnswer: E", "role": "assistant", "uuid": "6513486a-edd3-4e7d-ab5b-617186978e15" } ]

{ "coherence": 2.96, "complexity": 1.58, "correctness": 2.25, "helpfulness": 2.59, "instruction-following": 3.05, "safety": 4.19, "verbosity": 1.04, "verbosity-coeff": -0.151 }

[ { "content": "A boy wants to go abroad by boat and return by flight. He has a choice of 4 different boat to go and 5 flight to return. In how many ways, can the boy perform his journey?\n\n['A)20', 'B)30', 'C)43', 'D)45', 'E)80']", "role": "user", "uuid": "f943cf80-e5c8-40db-877a-09be7479e974" }, { "content": "Ans.(a)\nSol. Number of choices to go by ship = 4 Number of choices to return by airline = 5 From, fundamental principle, total number of ways of performing the journey = 4 x 5 = 20 ways", "role": "assistant", "uuid": "f2b99858-5abb-4a32-9561-edf292d58333" } ]

{ "coherence": 2.88, "complexity": 1.24, "correctness": 2.49, "helpfulness": 2.66, "instruction-following": 3.13, "safety": 5.24, "verbosity": 1.1, "verbosity-coeff": -0.1105 }

[ { "content": "Cecilia, Robbie, and Briony all bought stamps. The number of stamps Cecilia purchased was equal to a single digit. The number of stamps only one of them purchased was divisible by 5. The number of stamps one of them bought was an even number. Which of the following could represent the numbers of stamps each purchased?\n\n['A)3, 8, 24', 'B)7, 9, 17', 'C)6, 9, 12', 'D)5, 15, 18', 'E)9, 10, 13']", "role": "user", "uuid": "e871d582-503c-4373-adec-409b88b0bebb" }, { "content": "I didnt get your point on eliminating C.\nThe number of stamps only one purchased was divisible by 5.Could that not be Cecilia with 9 stamps.\nI choose this and marked C.", "role": "assistant", "uuid": "d57d9e5c-47a0-4228-b25e-814c0632e15e" } ]

{ "coherence": 1.89, "complexity": 0.9, "correctness": 0.77, "helpfulness": 0.75, "instruction-following": 0.67, "safety": 4.38, "verbosity": 0.42, "verbosity-coeff": -0.205 }

[ { "content": "A grocer has a sale of Rs. 5266, Rs. 5744, Rs. 5864, Rs. 6122 and Rs. 6588 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 5750?\n\n['A)4016', 'B)4076', 'C)4816', 'D)4916', 'E)5916']", "role": "user", "uuid": "eb66460e-9f9c-40e2-aa8c-48c7e7dec96a" }, { "content": "Total sale for 5 months = Rs. (5266 + 5744 + 5864 + 6122+ 6588) = Rs. 29584.\nRequired sale = Rs. [ (5750 x 6) - 34500 ]\n= Rs. (34500 - 29584)\n= Rs. 4916.\nANSWER:D", "role": "assistant", "uuid": "14d7c5b5-f03e-4562-84a8-355bd3adb3cf" } ]

{ "coherence": 3, "complexity": 1.31, "correctness": 2.1, "helpfulness": 2.59, "instruction-following": 3.54, "safety": 5.24, "verbosity": 1.23, "verbosity-coeff": -0.1294 }

[ { "content": "Set S consists of integers {6, 7, 10, 12, 15}. If integer n is included in the set, the average (arithmetic mean) of set S will increase by 40%. What is the value of integer n?\n\n['A)26', 'B)30', 'C)34', 'D)38', 'E)42']", "role": "user", "uuid": "975c0607-8f65-4862-b68a-cc765a730c21" }, { "content": "The average of the numbers in set S is 10.\nIf we increase the mean by 40%, the new mean is 14.\nThus, on average, 5 numbers increase by 4.\nTherefore n = 14+20 = 34\nThe answer is C.", "role": "assistant", "uuid": "c2eca086-9084-48e1-9f92-def4c334eae2" } ]

{ "coherence": 2.53, "complexity": 1.43, "correctness": 1.65, "helpfulness": 1.94, "instruction-following": 2.33, "safety": 5.59, "verbosity": 0.55, "verbosity-coeff": -0.1952 }

[ { "content": "Eight friends go to see a movie at the local movie theater and sit in a row together. If there are two friends who refuse to sit next to each other, how many 8-person seating arrangements are possible?\n\n['A)5040', 'B)15,120', 'C)30,240', 'D)35,280', 'E)40,320']", "role": "user", "uuid": "1a05a1c8-df0b-41d7-a59d-25e7c0a57cf1" }, { "content": "The number of ways to arrange 8 people in a row is 8!\nFrom this we want to subtract all the arrangements where the two friends are next to each other. If we consider them as one unit, then the number of arrangements of this 2-person unit and the 6 other friends is 7! And the number of arrangements of the two friends within this unit are 2 because the two friends can switch places. So the total number of arrangements of the 8 friends with the 2-person unit together is 7!*2\nThe total number of permutations where these two friends are not seated next to each other is 8! - 7!*2 = 6*7! = 30,240\nThe answer is C.", "role": "assistant", "uuid": "d2fd9bb7-d268-4620-9af3-cbcad6941cc5" } ]

{ "coherence": 3.13, "complexity": 1.79, "correctness": 2.78, "helpfulness": 2.88, "instruction-following": 3.37, "safety": 5.16, "verbosity": 1.78, "verbosity-coeff": -0.2318 }

[ { "content": "A man leaves a point P at 6 a.m. and reaches the point Q at 10 a.m. another man leaves the point give at 8 a.m. and reaches the point P at 12 noon. At what time do they meet?\n\n['A)2', 'B)5', 'C)9', 'D)6', 'E)3']", "role": "user", "uuid": "0df38e97-17ad-48b2-93f5-95639ea697fa" }, { "content": "9 a.m.\nAnswer: C", "role": "assistant", "uuid": "603888af-e61e-456c-a346-d48327bd4cd7" } ]

{ "coherence": 2.53, "complexity": 0.8, "correctness": 1.68, "helpfulness": 1.74, "instruction-following": 2.29, "safety": 5.67, "verbosity": 0.61, "verbosity-coeff": -0.1246 }

[ { "content": "seven friends met for lunch at an expensive restaurant, and everyone decided to contribute equally to the total bill of $530. If one of the friends had a coupon for 32% off the total bill, and if each friend still contributed equally after the coupon was applied to the bill, how much did each friend pay?\n\n['A)$90', 'B)$70', 'C)$51', 'D)$37', 'E)$35']", "role": "user", "uuid": "78607581-1dea-4746-a57b-2162a098640a" }, { "content": "530 * 0,32 = 169\n530 - 169 = 361\n361 / 7 = 51\nAnswer C", "role": "assistant", "uuid": "3170dd46-1d63-493e-b23e-954ed9414b3b" } ]

{ "coherence": 2.72, "complexity": 0.15, "correctness": 2.45, "helpfulness": 2.55, "instruction-following": 3.33, "safety": 4.23, "verbosity": 0.47, "verbosity-coeff": -0.1573 }

[ { "content": "Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.\n\n['A)2', 'B)3', 'C)4', 'D)5', 'E)6']", "role": "user", "uuid": "32325bc0-791b-45d2-9743-ff3af33c4aa8" }, { "content": "Required number = H.C.F. of (91 - 43), (183 - 91) and (183 - 43)\n= H.C.F. of 48, 92 and 140 = 4.\nanswer :C", "role": "assistant", "uuid": "81755ddb-8cb5-4a15-9fea-ea84beb168b9" } ]

{ "coherence": 2.72, "complexity": 2.04, "correctness": 1.96, "helpfulness": 2.1, "instruction-following": 3.13, "safety": 6.26, "verbosity": 1.46, "verbosity-coeff": -0.2152 }

[ { "content": "2+2+2²+2³ ... +2^11\n\n['A)2^9', 'B)2^10', 'C)2^16', 'D)2^12', 'E)2^37']", "role": "user", "uuid": "3b6c7cbf-18bb-480c-ae80-2328b029b07b" }, { "content": "2+2=2^2\n2^2+2^2=(2^2)*(1+1)=2^3\n2^3+2^3=(2^3)*(1+1)=2^4\nso you can notice the pattern... in the end you will have 2^11+2^11, which will give you 2^12\nAnswer D", "role": "assistant", "uuid": "b551def1-afd6-48f8-bda7-ca799e3ef485" } ]

{ "coherence": 2.66, "complexity": 1.71, "correctness": 2.27, "helpfulness": 2.2, "instruction-following": 2.33, "safety": 4.77, "verbosity": 1.21, "verbosity-coeff": -0.119 }