Cheukting/mathqa huggingface dataset:
Question (general): an engineer designed a ball so that when it was dropped , it rose with each bounce exactly one - half as high as it had fallen . the engineer dropped the ball from a 20 - meter platform and caught it after it had traveled 55 meters . how many times did the ball bounce ?
Options: a ) 5 , b ) 6 , c ) 3 , d ) 8 , e ) 9
Rationale: "going down = 20 m going up = 10 - - > total = 30 going down = 10 - - > total = 40 going up = 5 - - > total = 45 going down = 5 - - > total = 50 going up = 2.5 - - > total = 52.5 going down = 2.5 - - > total = 55 ( caught ) no of bouncing = 3 answer : c"
Answer: c
Question (general): find the value of 582964 x 99999 = m ?
Options: a ) 58210607666 , b ) 58310607896 , c ) 58295817036 , d ) 58591650836 , e ) 58310692816
Rationale: "582964 x 99999 = 582964 x ( 10000 - 1 ) = 582964 x 100000 - 582964 x 1 = 58296400000 - 582964 = 58295817036 c"
Answer: c
Question (general): a big container is 30 % full with water . if 18 liters of water is added , the container becomes 3 / 4 full . what is the capacity of the big container ?
Options: a ) 36 liters , b ) 40 liters , c ) 45 liters , d ) 54 liters , e ) 60 liters
Rationale: "a big container is 30 % full with water and after 18 liters of water is added , the container becomes 75 % full . hence these 18 liters account for 45 % of the container , which means that the capacity of it is 18 / 0.45 = 40 liters . or : if the capacity of the container is x liters then : 0.3 x + 18 = 0.75 x - - > x = 40 liters . answer : b ."
Answer: b
Question (general): ( 18.6 x 17.2 ÷ 0.6 ) x 27.5 = ?
Options: a ) 12132 , b ) 14678 , c ) 12708 , d ) 14663 , e ) 15688
Rationale: "explanation : ( 319.92 ÷ 0.6 ) x 27.5 = 533.2 x 27.5 = 14663 answer : option d"
Answer: d
Question (physics): a 300 m long train crosses a platform in 51 sec while it crosses a signal pole in 18 sec . what is the length of the platform ?
Options: a ) 287 , b ) 350 , c ) 828 , d ) 277 , e ) 550
Rationale: "speed = 300 / 18 = 50 / 3 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 5 a = 50 / 3 3 x + 900 = 2550 = > x = 550 m . answer : e"
Answer: e
Question (general): 16.02 ã — 0.0001 = ?
Options: a ) 0.1602 , b ) 0.001602 , c ) 1.6021 , d ) 0.01602 , e ) none of these
Rationale: "16.02 ã — 0.0001 = 0.001602 the answer is b ."
Answer: b
Question (gain): at an election 2 candidates are participated and a candidate got 30 % of votes and defeated by 1000 . and 100 votes are invalid . find the total polled votes ?
Options: a ) 2150 , b ) 2600 , c ) 3120 , d ) 1500 , e ) 1895
Rationale: "winner votes = 100 - 30 = 70 polled votes = [ ( 100 * 1000 ) / 2 * 70 - 100 ] + 100 = 2600 answer is b"
Answer: b
Question (physics): find avrg speed if a man travels at speed of 32 km / hr up and 48 km / hr dawn at an altitude of 230 m .
Options: a ) 25.8 , b ) 26.8 , c ) 38.4 , d ) 34.4 , e ) 29.8
Rationale: "avg speed = 2 * x * y / ( x + y ) = 2 * 32 * 48 ( 32 + 48 ) = 38.4 answer : c"
Answer: c
Question (general): what is the least integer greater than – 1 + 0.5 ?
Options: a ) – 2 , b ) – 1 , c ) 0 , d ) 1 , e ) 2
Rationale: "this question is just about doing careful arithmetic and remembering what makes a numberbiggerorsmallercompared to another number . first , let ' s take care of the arithmetic : ( - 1 ) + ( 0.5 ) = - 0.5 on a number line , since we ' re adding + . 5 to a number , the total moves to the right ( so we ' re moving from - 1 to - 0.5 ) . next , the question asks for the least integer that is greater than - 0.5 again , we can use a number line . numbers become greater as you move to the right . the first integer to the right of - 0.5 is 0 . final answer : c"
Answer: c
Question (general): the average age of 15 students of a class is 15 years . out of these , the average age of 7 students is 14 years and that of the other 7 students is 16 years , the age of the 15 th student is
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "explanation : age of the 15 th student = [ 15 * 15 - ( 14 * 7 + 16 * 7 ) ] = 15 years . answer : e"
Answer: e
Question (gain): joe invested a certain sum of money in a simple interest bond whose value grew to $ 400 at the end of 3 years and to $ 500 at the end of another 5 years . what was the rate of interest in which he invested his sum ?
Options: a ) 4.76 % , b ) 5.88 % , c ) 6.33 % , d ) 7.75 % , e ) 8.33 %
Rationale: in 5 years , the value grew $ 100 , so the simple interest was $ 20 per year . in 3 years , the total interest was 3 * $ 20 = $ 60 the principal is $ 400 - $ 60 = 340 . the interest rate is $ 20 / $ 340 = 1 / 17 which is about 5.88 % the answer is b .
Answer: b
Question (gain): a doctor prescribed 24 cubic centimeters of a certain drug to a patient whose body weight was 120 pounds . if the typical dosage is 2 cubic centimeters per 15 pounds of the body weight , by what percent was the prescribed dosage greater than the typical dosage ?
Options: a ) 8 % , b ) 9 % , c ) 50 % , d ) 12.5 % , e ) 14.8 %
Rationale: "typical dosage per 15 pound of the body weight = 2 c . c typical dosage per 120 pound of the body weight = 2 * ( 120 / 15 ) = 2 * 8 = 16 c . c dosage prescribed by doctor for 120 pound patient = 24 c . c % prescribed dosage greater than the typical dosage = ( 24 - 16 / 16 ) * 100 % = ( 8 / 16 ) * 100 % = 50 % answer d"
Answer: d
Question (general): in february wilson ’ s earnings were 40 percent of his family ’ s total income . in march wilson earned 25 percent less than in february . if the rest of his family ’ s income was the same in both months , then , in march , wilson ’ s earnings were approximately what percent z of his family ’ s total income ?
Options: a ) 15 % , b ) 17 % , c ) 24 % , d ) 30 % , e ) 33 %
Rationale: "lets suppose the total family income in feb = 100 x wilson ' s earning in feb = 40 % of 100 x = 40 x earnings of remaining family in feb = 100 x - 40 x = 60 x wilson ' s earning in march = 75 % of wilson ' s feb earnings = 75 % of 40 x = 30 x earnings of remaining family in march = earnings of remaining family in feb = 60 x thus wilson ' s earning as % of total family income in march z = 30 x / ( 30 + 60 ) x = 30 x / 90 x = 33.33 % thus answer is e"
Answer: e
Question (other): how many different positive integers are factors of 324 ?
Options: a ) 9 , b ) 16 , c ) 25 , d ) 36 , e ) 49
Rationale: "18 × 18 = 6 ^ 2 × 3 ^ 2 so total factors = ( 5 + 1 ) ( 5 + 1 ) = 36 answer : d"
Answer: d
Question (gain): a reduction in the price of petrol by 10 % enables a motorist to buy 5 gallons more for $ 250 . find the original price of petrol ?
Options: a ) $ 11 , b ) $ 5 , c ) $ 45 , d ) $ 400 , e ) $ 5.5
Rationale: "price decreased by 10 % , so 9 / 10 times , which means that original gallons bought increased 10 / 9 times . since this increase equals to 5 gallons then 45 gallons were bought originally ( 45 * 10 / 9 = 50 - - > increase 5 gallons ) . hence original price was 250 / 45 = $ 5.5 answer : e ."
Answer: e
Question (general): ( 258 % of 1265 ) ÷ 6 = ?
Options: a ) a ) 125 , b ) b ) 175 , c ) c ) 225 , d ) d ) 375 , e ) e ) 544
Rationale: "explanation : ? = ( 258 x 1265 / 100 ) ÷ 6 = 326370 / 600 = 544 answer : option e"
Answer: e
Question (general): if ( 1 / 5 ) ^ n * ( 1 / 4 ) ^ 18 = 1 / ( 2 * ( 10 ) ^ 35 ) , then n =
Options: a ) 40 , b ) 45 , c ) 35 , d ) 30 , e ) 25
Rationale: ( 1 / 5 ) ^ m ( 1 / 4 ) ^ 18 = 1 / { 2 ( 10 ) ^ 35 } 2 ( 10 ) ^ 35 / 4 ^ 18 = 5 ^ m [ 2 ( 2 ^ 35 ) ( 5 ^ 35 ) ] / [ 2 ^ 36 ] = 5 ^ m 5 ^ 35 = 5 ^ m n = 35 c
Answer: c
Question (general): let exp ( m , n ) = m to the power n . if exp ( 10 , m ) = n exp ( 22 ) where m and n are integers then n = ___ ?
Options: a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 28
Rationale: 10 ^ m = n * ( 2 ^ 2 ) ( 2 * 5 ) ^ m = n * ( 2 ^ 2 ) ( 2 ^ m ) * ( 5 ^ m ) = n * ( 2 ^ 2 ) now equate both side we get m = 2 and ( 5 ^ m ) = n ( 5 ^ 2 ) = n = > n = 25 answer : b
Answer: b
Question (general): if [ x ] is the greatest integer less than or equal to x , what is the value of [ - 5.6 ] + [ 3.4 ] + [ 12.7 ] ?
Options: a ) 3 , b ) 5 , c ) 7 , d ) 9 , e ) 10
Rationale: "you are asked what the closest lesser integer value to [ x ] is . [ - 5.6 ] = - 6.0 [ 3.4 ] = 3.0 [ 12.7 ] = 12.0 therefore , answer is : - 6.0 + 3.0 + 12.0 = 9.0 option d ."
Answer: a
Question (general): in a forest 150 deer were caught , tagged with electronic markers , then released . a week later , 50 deer were captured in the same forest . of these 50 deer , it was found that 5 had been tagged with the electronic markers . if the percentage of tagged deer in the second sample approximates the percentage of tagged deer in the forest , and if no deer had either left or entered the forest over the preceding week , what is the approximate number of deer in the forest ?
Options: a ) 150 , b ) 750 , c ) 1,250 , d ) 1,500 , e ) 2,500
Rationale: "given 150 deers were caught and they are tagged in the first slot . in the second slot , 50 were caught and 5 we tagged then 10 % of them are tagged . given this 10 % approximates the percentage of tagged deer in the forest . . here number is 150 . . then 100 % is 1500 . . is the number of deers population in the forest . . answer : d is correct answer . ."
Answer: d
Question (physics): the sum of four consecutive even numbers is 84 . what would be the smallest number ?
Options: a ) 33 , b ) 88 , c ) 70 , d ) 123 , e ) 18
Rationale: "let the four consecutive even numbers be 2 ( x - 2 ) , 2 ( x - 1 ) , 2 x , 2 ( x + 1 ) their sum = 8 x - 4 = 84 = > x = 11 smallest number is : 2 ( x - 2 ) = 18 . answer : e"
Answer: e
Question (general): for the past n days , the average ( arithmetic mean ) daily production at a company was 50 units . if today ' s production of 90 units raises the average to 52 units per day , what is the value of n ?
Options: a ) 30 , b ) 19 , c ) 10 , d ) 9 , e ) 7
Rationale: "( average production for n days ) * n = ( total production for n days ) - - > 50 n = ( total production for n days ) ; ( total production for n days ) + 90 = ( average production for n + 1 days ) * ( n + 1 ) - - > 50 n + 90 = 52 * ( n + 1 ) - - > n = 19 . or as 40 extra units increased the average for n + 1 days by 2 units per day then 40 / ( n + 1 ) = 2 - - > n = 19 . answer : b ."
Answer: b
Question (gain): an escalator moves towards the top level at the rate of 8 ft . sec and its length is 160 feet . if a person walks on the moving escalator at the rate of 2 feet per second towards the top level , how much time does he take to cover the entire length .
Options: a ) 14 sec , b ) 10 sec , c ) 16 sec , d ) 8 sec , e ) 9 sec
Rationale: "time taken to cover the entire length = tot . dist / resultant speed = 160 / ( 8 + 2 ) = 16 sec answer : c"
Answer: c
Question (geometry): a photograph 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 ?
Options: a ) 76
b ) 65
c ) 59.5
d ) 49
e ) 38.5
Rationale: area covered by photograph = ( 8.5 - 3 ) * ( 10 - 3 ) = 5.5 * 7 = 38.5 answer e
Answer: e
Question (general): ( 1000 ) 7 ÷ ( 10 ) 15 = ?
Options: a ) 10 , b ) 100 , c ) 1000000 , d ) 10000 , e ) none of these
Rationale: "explanation : = ( 103 ) 7 / ( 10 ) 15 = ( 10 ) 21 / ( 10 ) 15 = 10 ( 6 ) = 1000000 option c"
Answer: c
Question (gain): a person spends 40 % of his salary on food , 25 % on house rent , 15 % on entertainment and 5 % on conveyance . if his savings at the end of the month is rs . 3000 , then his salary per month in rupees is :
Options: a ) 20000 , b ) 6000 , c ) 8000 , d ) 10000 , e ) none of these
Rationale: "total expenditure = 40 + 25 + 15 + 5 = 85 % saving = ( 100 - 85 ) = 15 % 15 / 100 × salary = 3000 , salary = 20000 rs . answer : a"
Answer: a
Question (other): the l . c . m of two numbers is 48 . the numbers are in the ratio 8 : 3 . the sum of numbers is :
Options: a ) 22 , b ) 30 , c ) 40 , d ) 50 , e ) 60
Rationale: "let the numbers be 8 x and 3 x . then , their l . c . m = 24 x . so , 24 x = 48 or x = 2 . the numbers are 16 and 6 . hence , required sum = ( 16 + 6 ) = 22 . answer : a"
Answer: a
Question (general): when positive integer e is divided by 13 , the remainder is 2 . when n is divided by 8 , the remainder is 5 . how many such values are less than 180 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: the equation that can be formed e is 13 x + 2 = 8 y + 5 . . 13 x - 3 = 8 y . . . as we can see x can take only odd values as the rhs will always be even . . also x can take values till 13 as 13 * 14 > 180 . . now we have to substitue x as 1 , 35 , 79 , 1113 . . . once we find 7 fitting in , any other value need not be checked as every 4 th value will give us answer so next value will be 15 . . ans 1 . . b
Answer: b
Question (general): on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.48 per glass on the first day , what was the price per glass on the second day ?
Options: a ) $ 015 , b ) $ 0.20 , c ) $ 0.30 , d ) $ 0.32 , e ) $ 0.45
Rationale: "on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.48 = 3 * x - - > x = $ 0.32 . answer : d ."
Answer: d
Question (general): if sharon ' s weekly salary increased by 16 percent , she would earn $ 406 per week . if instead , her weekly salary were to decreased by 10 percent , how much would she earn per week ?
Options: a ) rs . 415 , b ) rs . 325 , c ) rs . 352 , d ) rs . 315 , e ) rs . 425
Rationale: "soln : - ( 406 / 116 ) 90 = 315 in this case long division does not take much time . ( 406 / 116 ) = 3.5 3.5 * 90 = rs . 315 answer : d"
Answer: d
Question (general): amit , sumit and pramit go to a seaside town to spend a vacation there and on the first day everybody decides to visit different tourist locations . after breakfast , each of them boards a different tourist vehicle from the nearest bus - depot . after 3 hours , sumit who had gone to a famous beach , calls on the mobile of pramit and claims that he has observed a shark in the waters . pramit learns from the local guide that at that time of the year , only 8 sea - creatures ( including a shark ) are observable and the probability of observing any creature is equal . however , amit and pramit later recall during their discussion that sumit has a reputation for not telling the truth 5 out of 6 times . what is the probability that sumit actually observed a shark in the waters ?
Options: a ) 1 / 36 , b ) 1 / 30 , c ) 5 / 36 , d ) 1 / 24 , e ) 1 / 28
Rationale: explanation : the probability that sumit actually sees a shark , given that he claimed to have seen one . = > p ( he actually sees the shark and reports truth ) / p ( he claims of seeing a shark ) . = > p ( sees the shark ) p ( reports truth ) / ( p ( he sees a shark ) p ( reports truth ) + p ( does n ' t see ) p ( reports false ) . = > ( 1 / 8 × 1 / 6 ) / ( 1 / 8 × 1.6 + 7 / 8 × 5 / 6 ) = > 1 / 36 . answer : a
Answer: a
Question (gain): a certain sum is invested at simple interest at 15 % p . a . for two years instead of investing at 10 % p . a . for the same time period . therefore the interest received is more by rs . 840 . find the sum ?
Options: a ) s . 8400 , b ) s . 9000 , c ) s . 14000 , d ) s . 17000 , e ) s . 27000
Rationale: "let the sum be rs . x . ( x * 15 * 2 ) / 100 - ( x * 10 * 2 ) / 100 = 840 = > 30 x / 100 - 20 x / 100 = 840 = > 10 x / 100 = 840 = > x = 8400 . answer : a"
Answer: a
Question (gain): a dishonest shopkeeper professes to sell pulses at the cost price , but he uses a false weight of 950 gm . for a kg . his gain is … % .
Options: a ) 5.3 % , b ) 8.2 % , c ) 4.3 % , d ) 8.3 % , e ) 8.0 %
Rationale: he sells 950 grams of pulses and gains 50 grams . if he sells 100 grams of pulses then he will gain ( 50 / 950 ) * 100 = 5.26 4 . a software engineer has the capability of thinking 100 lines of code in five minutes and can type 100 lines of code in 10 minutes . he takes a break for five minutes after every ten minutes . how many lines of codes will he complete typing after an hour ? answer : a
Answer: a
Question (general): there are 7 players in a bowling team with an average weight of 121 kg . if two new players join the team , one weighs 110 kg and the second weighs 60 kg , what will be the new average weight ?
Options: a ) 115 kg . , b ) 118 kg . , c ) 113 kg . , d ) 110 kg . , e ) 112 kg .
Rationale: the new average will be = ( 121 * 7 + 110 + 60 ) / 9 = 113 kgs c is the answer
Answer: c
Question (general): a student scored an average of 70 marks in 3 subjects : physics , chemistry and mathematics . if the average marks in physics and mathematics is 90 and that in physics and chemistry is 70 , what are the marks in physics ?
Options: a ) 130 , b ) 120 , c ) 110 , d ) 180 , e ) 150
Rationale: "given m + p + c = 70 * 3 = 210 - - - ( 1 ) m + p = 90 * 2 = 180 - - - ( 2 ) p + c = 70 * 2 = 140 - - - ( 3 ) where m , p and c are marks obtained by the student in mathematics , physics and chemistry . p = ( 2 ) + ( 3 ) - ( 1 ) = 180 + 140 - 210 = 110 answer : c"
Answer: c
Question (general): a box contains 3 pairs of blue gloves and two pairs of green gloves . each pair consists of a left - hand glove and a right - hand glove . each of the gloves is separate from its mate and thoroughly mixed together with the others in the box . if 3 gloves are randomly selected from the box , what is the probability that a matched set ( i . e . , a left - and right - hand glove of the same color ) will be among the 3 gloves selected ?
Options: a ) 3 / 10 , b ) 23 / 60 , c ) 7 / 12 , d ) 41 / 60 , e ) 5 / 6
Rationale: you can use the ' calculating the reverse ' method used by bunuel above or if you would like to calculate the probability of getting a matched set in the usual way , you can think of it in this way : bleft ( 3 ) , bright ( 3 ) , gleft ( 2 ) , gright ( 2 ) bleft , bright , g get a bleft and bright in ( 3 / 10 ) * ( 3 / 9 ) ways . then get any green in 4 / 8 ways . probability of getting b pair and a g = ( 3 / 10 ) * ( 3 / 9 ) * ( 4 / 8 ) * 3 ! ( you multiply by 3 ! here because you could pick in some other order e . g . bright , bleft , g or bleft , g , bright etc ) bleft , bright , b get a bleft and bright in ( 3 / 10 ) * ( 3 / 9 ) ways . then get any blue in 4 / 8 ways . probability of getting b pair and another b = ( 3 / 10 ) * ( 3 / 9 ) * ( 4 / 8 ) * 3 ! / 2 ! ( you multiply by 3 ! here to account for the order e . g . bright , bleft , bleft or bleft , bright , bright etc but two gloves will be identical so you divide by 2 ! ) gleft , gright , b get a gleft and gright in ( 2 / 10 ) * ( 2 / 9 ) ways . then get any blue in 6 / 8 ways . probability of getting g pair and a b = ( 2 / 10 ) * ( 2 / 9 ) * ( 6 / 8 ) * 3 ! gleft , gright , g get a gleft and gright in ( 2 / 10 ) * ( 2 / 9 ) ways . then get any other g in 2 / 8 ways . probability of getting g pair and a g = ( 2 / 10 ) * ( 2 / 9 ) * ( 2 / 8 ) * 3 ! / 2 ! adding them all up , you get 41 / 60 . answer : d
Answer: d
Question (general): the output of a factory is increased by 10 % to keep up with rising demand . to handle the holiday rush , this new output is increased by 30 % . by approximately what percent would the output of the factory now have to be decreased in order to restore the original output ?
Options: a ) 20 % , b ) 24 % , c ) 30 % , d ) 32 % , e ) 79 %
Rationale: take it as original output = 100 . to meet demand increase by 10 % , then output = 110 . to meet holiday demand , new output increase by 30 % then output equals 143 to restore new holidy demand output to original 100 . final - initial / final * 100 = 43 / 143 * 100 = 30 % approxiamately . option c is correct .
Answer: c
Question (physics): a 300 meter long train crosses a platform in 54 seconds while it crosses a signal pole in 18 seconds . what is the length of the platform ?
Options: a ) 99 , b ) 289 , c ) 350 , d ) 882 , e ) 600
Rationale: speed = [ 300 / 18 ] m / sec = 50 / 3 m / sec . let the length of the platform be x meters . then , x + 300 / 54 = 50 / 3 3 ( x + 300 ) = 2700 è x = 350 m . answer : e
Answer: e
Question (general): 150 ml of 30 % sulphuric acid was added to approximate 400 ml of 12 % sulphuric acid solution . find the approximate concentration e of the acid in the mixture ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 6 , e ) 1 / 5
Rationale: "do not need any computation 30 % - - - - - - - - - - - 21 % - - - - - - - - - 12 % if volume of both sol . were equal the concentration e would be 21 % = 1 / 5 , but 12 % is more than 3 times only possibility is 1 / 6 d"
Answer: d
Question (general): what is the smallest integer k for which 64 ^ k > 4 ^ 19 ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: 64 ^ k > 4 ^ 19 4 ^ ( 3 k ) > 4 ^ 19 3 k > 19 k = 7 the answer is d .
Answer: d
Question (physics): a cistern 6 m long and 5 m wide contains water up to a depth of 1 m 25 cm . the total area of the wet surface is :
Options: a ) 49 m 2 , b ) 50 m 2 , c ) 53.5 m 2 , d ) 55 m 2 , e ) 57.5 m 2
Rationale: "area of the wet surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 5 x 1.25 + 6 x 1.25 ) + 6 x 5 ] m 2 = 57.5 m 2 . answer : option e"
Answer: e
Question (geometry): there are 6 equally spaced points a , b , c , d , e and f marked on a circle with radius r . how many convex pentagons of distinctly different areas can be drawn using these points as vertices ?
Options: a ) 6 p 5
b ) 1
c ) 5
d ) none of these
e ) can not be determined
Rationale: solution : since , all the points are equally spaced ; hence the area of all the convex pentagons will be same . answer : option d
Answer: d
Question (physics): a train 1600 m long can cross a pole in 40 sec and then find the speed of the train ?
Options: a ) 140 , b ) 142 , c ) 144 , d ) 146 , e ) 148
Rationale: "length = speed * time speed = l / t s = 1600 / 40 s = 40 m / sec speed = 40 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 144 kmph answer : c"
Answer: c
Question (general): if 4 log ( 4 * 5 ^ 2 ) = x , find x
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "4 ( log 2 ^ 2 * 5 ^ 2 ) = x 4 log ( 5 * 2 ) ^ 2 = x 4 * 2 log ( 5 * 2 ) = x 8 log 10 = x log 10 base 10 = 1 so 8 * 1 = x x = 8 answer : d"
Answer: d
Question (general): if x is real , find the maximum value of the expression - 2 x ^ 2 + 9 x + 11 .
Options: a ) 12.125 , b ) 15.125 , c ) 18.125 , d ) 21.125 , e ) 24.125
Rationale: "this is an equation of a downward facing parabola . the maximum value is the top point of the parabola . - 2 x ^ 2 + 9 x + 11 = ( - 2 x + 11 ) ( x + 1 ) the roots are 11 / 2 and - 1 . the maximum value must be when x is halfway between these two points . x = 2.25 the maximum value is - 2 ( 2.25 ) ^ 2 + 9 ( 2.25 ) + 11 = 21.125 the answer is d ."
Answer: d
Question (physics): find the l . c . m of 12 , 8 , 24 and 16 .
Options: a ) 48 , b ) 96 , c ) 80 , d ) 44 , e ) 140
Rationale: "explanation : 2 x 3 x 2 x 2 x 2 = 48 answer : option a"
Answer: a
Question (general): if [ x ] is the greatest integer less than or equal to x , what is the value of [ - 11.6 ] + [ 13.4 ] + [ 12.7 ] ?
Options: a ) 3 , b ) 10 , c ) 13 , d ) 16 , e ) 17
Rationale: "you are asked what the closest lesser integer value to [ x ] is . [ - 11.6 ] = - 12.0 [ 13.4 ] = 13.0 [ 12.7 ] = 12.0 therefore , answer is : - 12.0 + 13.0 + 12.0 = 13.0 option a ."
Answer: c