Cheukting/mathqa huggingface dataset:
Question (physics): a train running at the speed of 120 km / hr crosses a pole in 9 seconds . find the length of the train .
Options: a ) 100 meter , b ) 150 meter , c ) 200 meter , d ) 250 meter , e ) 300 meter
Rationale: "speed = 120 * ( 5 / 18 ) m / sec = 200 / 6 m / sec length of train ( distance ) = speed * time ( 200 / 6 ) * 9 = 300 meter answer : e"
Answer: e
Question (general): marts income is 60 percent more than tims income and tims income is 50 percent less than juans income . what percentage of juans income is marts income
Options: a ) 124 % , b ) b ) 120 % , c ) c ) 96 % , d ) d ) 80 % , e ) e ) 64 %
Rationale: "m = ( 160 / 100 ) t t = ( 50 / 100 ) j = > m = ( 80 / 100 ) j answer d ."
Answer: d
Question (general): 155 liters of a mixture of milk and water contains in the ratio 3 : 2 . how much water should now be added so that the ratio of milk and water becomes 3 : 4 ?
Options: a ) 12 liters , b ) 62 liters , c ) 41 liters , d ) 50 liters , e ) 34 liters
Rationale: milk = 3 / 5 * 155 = 93 liters water = 62 liters 93 : ( 62 + p ) = 3 : 4 186 + 3 p = 372 = > p = 62 62 liters of water are to be added for the ratio become 3 : 4 . answer : b
Answer: b
Question (physics): the center of a circle lies on the origin of the coordinate plane . if a point ( x , y ) is randomly selected inside of the circle , what is the probability that y > 0 and y > x ?
Options: a ) 1 / 8 , b ) 1 / 6 , c ) 3 / 8 , d ) 1 / 2 , e ) 3 / 4
Rationale: the line y = x divides the circle into two equal areas . all the points above the line y = x satisfy the condition that y > x . all the points above the x - axis satisfy the condition that y > 0 . the intersection of these two areas is 3 / 8 of the circle . the answer is c .
Answer: c
Question (other): how many different positive integers are factors of 196 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 49 , e ) 36
Rationale: "15 , 14 × 15 , 14 = 7 ^ 2 × 2 ^ 2 so total factors = ( 6 + 1 ) ( 6 + 1 ) = 49 answer : d"
Answer: d
Question (general): the product of two numbers is 266 and their difference is 5 . what is the bigger number ?
Options: a ) 13 , b ) 15 , c ) 19 , d ) 24 , e ) none of these
Rationale: "explanation : let the two numbers be a and b , here a > b ab = 266 b = 266 / a - - - - - - - - - - - - - - - - - ( i ) given , a – b = 5 - - - - - - - - - - - ( ii ) substitute from ( i ) in ( ii ) , we get a – 266 / a = 5 a 2 – 5 a + 266 = 0 ( a – 19 ) ( a – 14 ) = 0 therefore , a = 19 or a = 14 hence , bigger number = a = 19 answer : c"
Answer: c
Question (general): if 821562 is to be divisible by 5 , what is the least whole number that should be added to it ?
Options: a ) 6 , b ) 4 , c ) 5 , d ) 2 , e ) 3
Rationale: a number is divisible by 8 if the number formed by the last three digits is divisible by 8 . here , 821562 = 562 , the next multiple of 9 is 568 . 6 must be added to 821562 to make it divisible by 8 a
Answer: a
Question (gain): in 2008 , the profits of company n were 10 percent of revenues . in 2009 , the revenues of company n fell by 20 percent , but profits were 16 percent of revenues . the profits in 2009 were what percent of the profits in 2008 ?
Options: a ) 80 % , b ) 105 % , c ) 120 % , d ) 124.2 % , e ) 128 %
Rationale: "x = profits r = revenue x / r = 0,1 x = 10 r = 100 2009 : r = 80 x / 80 = 0,16 = 16 / 100 x = 80 * 16 / 100 x = 12.8 12.8 / 10 = 1,28 = 128 % , answer e"
Answer: e
Question (general): the difference between the place values of 8 and 3 in the number 587435 is
Options: a ) 75200 , b ) 79970 , c ) 75460 , d ) 24580 , e ) none
Rationale: sol . = ( place value of 8 ) – ( place value of 3 ) = ( 80000 - 30 ) = 79970 answer b
Answer: b
Question (general): what is the unit digit of 3 ^ 58 ?
Options: a ) 0 , b ) 5 , c ) 7 , d ) 1 , e ) 9
Rationale: "unit digit in 3 ^ 58 = unit digit in [ ( 3 ^ 4 ) ^ 14 ] * 3 ^ 2 = 1 * 9 = 9 answer is e"
Answer: e
Question (general): if the average ( arithmetic mean ) of a and b is 35 and the average of b and c is 80 , what is the value of c − a ?
Options: a ) 25 , b ) 50 , c ) 90 , d ) 140 , e ) it can not be determined from the information given .
Rationale: "- ( a + b = 70 ) b + c = 160 c - a = 90 c . 90"
Answer: c
Question (physics): a group of men decided to do a work in 17 days , but 8 of them became absent . if the rest of the group did the work in 21 days , find the original number of men ?
Options: a ) 15 , b ) 20 , c ) 42 , d ) 25 , e ) 18
Rationale: "original number of men = 8 * 21 / ( 21 - 17 ) = 42 answer is c"
Answer: c
Question (gain): arun purchased 30 kg of wheat at the rate of rs . 11.50 per kg and 20 kg of wheat at the rate of 14.25 per kg . he mixed the two and sold the mixture . approximately what price per kg should be sell the mixture to make 10 % profit ?
Options: a ) 13.86 , b ) 16.33 , c ) 16.35 , d ) 16.3 , e ) 16.32
Rationale: "c . p . of 50 kg wheat = ( 30 * 11.50 + 20 * 14.25 ) = rs . 630 . s . p . of 50 kg wheat = 110 % of rs . 630 = 110 / 100 * 630 = rs . 693 s . p . per kg = 693 / 50 = rs . 13.86 answer : a"
Answer: a
Question (general): in an apartment building that has 490 units , 4 out of every 7 units are currently rented , including 1 / 6 of the one - bedroom units . if , of the rented apartments , there is a 6 : 1 ratio of two - bedroom units to one - bedroom units , and the building only consists of two - bedroom and one - bedroom units , how many two - bedroom units are not rented ?
Options: a ) 50 , b ) 70 , c ) 10 , d ) 105 , e ) 140
Rationale: rented = 4 / 7 * 490 = 280 . rented two - bedroom = 6 / 7 * 280 = 240 ; rented one - bedroom = 1 / 7 * 280 = 40 ( or 280 - 240 = 40 ) . rented one - bedroom units are 1 / 5 of all one - bedroom : 1 / 6 * { all one bedroom } = 40 - - > { all one - bedroom } = 240 . { all two - bedroom } = 490 - 240 = 250 . two - bedroom not rented = 250 - 240 = 10 . answer : c .
Answer: c
Question (general): a certain bus driver is paid a regular rate of $ 16 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 976 in total compensation , how many total hours did he work that week ?
Options: a ) 51 , b ) 52 , c ) 59 , d ) 55 , e ) 56
Rationale: "for 40 hrs = 40 * 16 = 640 excess = 976 - 640 = 336 for extra hours = . 75 ( 16 ) = 12 + 16 = 28 number of extra hrs = 336 / 28 = 12 total hrs = 40 + 12 = 52 answer b"
Answer: b
Question (physics): a works twice as fast as b . if b can complete a work in 18 days independently , the number of days in which a and b can together finish the work is :
Options: a ) 4 days , b ) 6 days , c ) 8 days , d ) 10 days , e ) 12 days
Rationale: "explanation : ratio of rates of working of a and b = 2 : 1 . so , ratio of times taken = 1 : 2 a ' s 1 day ' s work = 1 / 9 b ' s 1 day ' s work = 1 / 18 ( a + b ) ' s 1 day ' s work = ( 1 / 9 + 1 / 18 ) = 3 / 18 = 1 / 6 so , a and b together can finish the work in 6 days answer is b"
Answer: b
Question (general): he average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?
Options: a ) 75 kg , b ) 55 kg , c ) 45 kg , d ) 85 kg , e ) 25 kg
Rationale: explanation : total weight increased = ( 8 x 2.5 ) kg = 20 kg . weight of new person = ( 65 + 20 ) kg = 85 kg . answer : d
Answer: d
Question (gain): a , band c enter into partnership . a invests 3 times as much as b and b invests two - third of what c invests . at the end of the year , the profit earned is rs . 8800 . what is the share of b ?
Options: a ) 1100 , b ) 800 , c ) 1400 , d ) 1200 , e ) 1600
Rationale: "let c ' s capital = rs . x . then , b ' s capital = rs . ( 2 / 3 ) x a ’ s capital = rs . ( 3 x ( 2 / 3 ) . x ) = rs . 2 x . ratio of their capitals = 2 x : ( 2 / 3 ) x : x = 6 : 2 : 3 . hence , b ' s share = rs . ( 8800 x ( 2 / 11 ) ) = rs . 1600 . answer is e"
Answer: e
Question (general): how many numbers are divisible by 4 between 1 and 100 ?
Options: a ) 25 , b ) 24 , c ) 23 , d ) 22 , e ) 20
Rationale: "numbers divisible by 4 till 100 = ( 100 / 4 ) = 25 but we should not consider 100 as we are asked to find the numbers between 1 and 100 which are divisible by 4 . so answer is 24 numbers . answer is option b"
Answer: b
Question (general): a certain city with a population of 120,000 is to be divided into 11 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district what is the minimum possible population that the least populated district could have ?
Options: a ) a ) 10,700 , b ) b ) 10,000 , c ) c ) 10,900 , d ) d ) 11,000 , e ) e ) 11,100
Rationale: "let x = number of people in smallest district x * 1.1 = number of people in largest district x will be minimised when the number of people in largest district is maximised 10 * x * 1.1 = 11 x = total number of people in other districts so we have 11 x + x = 120 k x = 10,000 answer : b"
Answer: b
Question (physics): two trains of length 100 m and 200 m are 100 m apart . they start moving towards each other on parallel tracks , at speeds 54 kmph and 72 kmph . after how much time will the trains meet ?
Options: a ) 20 / 8 sec , b ) 20 / 4 sec , c ) 20 / 7 sec , d ) 22 / 7 sec , e ) 60 / 7 sec
Rationale: "they are moving in opposite directions , relative speed is equal to the sum of their speeds . relative speed = ( 54 + 72 ) * 5 / 18 = 7 * 5 = 35 mps . the time required = d / s = 100 / 35 = 20 / 7 sec . answer : c"
Answer: c
Question (geometry): an oil cylinder was 3 / 4 th full . when 4 bottles of oil is poured into it , it is 4 / 5 th full . how many bottles of oil can the full cylinder hold ?
Options: a ) 90 , b ) 75 , c ) 70 , d ) 80 , e ) 85
Rationale: ( 4 / 5 - 3 / 4 ) cylinder is filled by 4 bottles 0.8 - 0.75 = 0.05 cylinder is filled by 4 bottles 1 cylinder is filled by 4 / 0.05 = 80 bottles answer : d
Answer: d
Question (general): if f ( f ( n ) ) + f ( n ) = 2 n + 3 , f ( 0 ) = 1 then f ( 2013 ) = ?
Options: a ) 2014 , b ) 2088 , c ) 270 , d ) 1881 , e ) 1781
Rationale: "f ( f ( 0 ) ) + f ( 0 ) = 2 ( 0 ) + 3 ⇒ ⇒ f ( 1 ) = 3 - 1 = 2 , f ( 1 ) = 2 f ( f ( 1 ) ) + f ( 1 ) = 2 ( 1 ) + 3 ⇒ ⇒ f ( 2 ) = 5 - 2 = 3 , f ( 2 ) = 3 f ( f ( 2 ) ) + f ( 2 ) = 2 ( 2 ) + 3 ⇒ ⇒ f ( 3 ) = 7 - 3 = 4 , f ( 3 ) = 4 . . . . . . . . . . . . . . f ( 2013 ) = 2014 ans : a"
Answer: a
Question (general): last year manfred received 26 paychecks . each of his first 6 paychecks was $ 750 ; each of his remaining paychecks was $ 50 more than each of his first 6 paychecks . to the nearest dollar , what was the average ( arithmetic mean ) amount of his pay checks for the year ?
Options: a ) $ 752 , b ) $ 755 , c ) $ 765 , d ) $ 788 , e ) $ 775
Rationale: "= ( 750 * 6 + 800 * 20 ) / 26 = 788 answer is d . posted from my mobile device"
Answer: d
Question (general): a certain no . when divided by 110 leaves a remainder 25 , what is the remainder if the same no . be divided by 15 ?
Options: a ) 2 , b ) 4 , c ) 7 , d ) 8 , e ) 9
Rationale: "explanation : 110 + 25 = 135 / 15 = 9 ( remainder ) e"
Answer: e
Question (general): of the final grades received by the students in a certain math course , 1 / 5 are a ' s , 1 / 4 are b ' s , 1 / 2 are c ' s , and the remaining 30 grades are d ' s . what is the number of students in the course ?
Options: a ) 80 , b ) 110 , c ) 160 , d ) 600 , e ) 400
Rationale: "we start by creating a variable for the total number of students in the math course . we can say : t = total number of students in the math course next , we can use variable t in an equation that we translate from the given information . we are given that , of the final grades received by the students in a certain math course , 1 / 5 are a ' s , 1 / 4 are b ' s , 1 / 2 are c ' s , and the remaining 30 grades are d ' s . since this represents all the grades in the class , it represents all the students in the class . thus we know : # a ’ s + # b ’ s + # c ’ s + # d ’ s = total number of students in the class 1 / 5 ( t ) + ¼ ( t ) + ½ ( t ) + 30 = t we can multiply the entire equation by 20 to cancel out the denominators of the fractions and we have : 4 t + 5 t + 10 t + 600 = 20 t 19 t + 600 = 20 t 600 = t there are a total of 600 students in the math class . answer is d ."
Answer: d
Question (physics): a man can row 3 kmph in still water . when the river is running at 1.2 kmph , it takes him 1 hour to row to a place and black . what is the total distance traveled by the man ?
Options: a ) 2.9 , b ) 2.8 , c ) 2.4 , d ) 2.8 , e ) 2.2
Rationale: "m = 3 s = 1.2 ds = 3.6 us = 1.8 x / 3.6 + x / 1.8 = 1 x = 1.2 d = 1.2 * 2 = 2.4 answer : c"
Answer: c
Question (physics): lloyd normally works 7.5 hours per day and earns $ 4.50 per hour . for each hour he works in excess of 7.5 hours on a given day , he is paid 2.5 times his regular rate . if lloyd works 10.5 hours on a given day , how much does he earn for that day ?
Options: a ) $ 33.75 , b ) $ 47.25 , c ) $ 51.75 , d ) $ 54.00 , e ) $ 67.50
Rationale: "daily working hour * regular rate + overtime * increased rate 7.5 * 4.5 + 3 * 4.5 * 2.5 = 67.5 answer e"
Answer: e
Question (gain): if a large pizza has a radius that is 40 % larger that that of a medium pizza , what is the percent increase in area between a medium and a large pizza ?
Options: a ) 40 % , b ) 80 % , c ) 96 % , d ) 112 % , e ) 124 %
Rationale: let the radius of medium pizza be r . then the radius of large pizza is 1.4 r . the area of the medium pizza is pi * r ^ 2 the area of the large pizza is pi * ( 1.4 * r ) ^ 2 = 1.96 * pi * r ^ 2 , an increase of 96 % . the answer is c .
Answer: c
Question (gain): if tim had lunch at $ 60.50 and he gave 20 % tip , how much did he spend ?
Options: a ) $ 30.60 , b ) $ 72.60 , c ) $ 70.60 , d ) $ 40.60 , e ) $ 50.60
Rationale: "the tip is 20 % of what he paid for lunch . hence tip = 20 % of 60.50 = ( 20 / 100 ) * 60.50 = $ 12.1 total spent 60.50 + 12.1 = $ 72.6 correct answer b"
Answer: b
Question (general): the salary of a , b , c , d , e is rs . 8000 , rs . 5000 , rs . 14000 , rs . 7000 , rs . 9000 per month respectively , then the average salary of a , b , c , d , and e per month is
Options: a ) rs . 7000 , b ) rs . 8000 , c ) rs . 8600 , d ) rs . 9000 , e ) none
Rationale: answer average salary = 8000 + 5000 + 14000 + 7000 + 9000 / 5 = rs . 8600 correct option : c
Answer: c
Question (other): water consists of hydrogen and oxygen , and the approximate ratio , by mass , of hydrogen to oxygen is 2 : 16 . approximately how many grams of oxygen are there in 162 grams of water ?
Options: a ) 16 , b ) 72 , c ) 112 , d ) 128 , e ) 144
Rationale: "solution : we are given that the ratio of hydrogen to oxygen in water , by mass , is 2 : 16 . using our ratio multiplier we can re - write this as 2 x : 16 x . we can now use these expressions to determine how much oxygen is in 162 grams of water . 2 x + 16 x = 162 18 x = 162 x = 9 since x is 9 , we know that there are 16 x 9 = 144 grams of oxygen in 162 grams of water . answer e ."
Answer: e
Question (physics): a can do a piece of work in 20 days and b can do it in 30 days and c can do it 10 days . they started the work together and a leaves after 2 days and c leaves after 4 days from the beginning . how long will work lost ?
Options: a ) 13 , b ) 16 , c ) 25 , d ) 14 , e ) 15
Rationale: 2 / 20 + x / 30 + 4 / 10 = 1 x = 300 / 20 = 15 answer : e
Answer: e
Question (general): find the least number which when divided by 18,32 , 48,52 leaves remainder 14,28 , 44,48 respectively .
Options: a ) 2845 , b ) 3250 , c ) 3740 , d ) 4150 , e ) 5140
Rationale: "the difference of 18 - 14 = 4 , 32 - 28 = 4 , 48 - 44 = 4 , 52 - 48 = 4 lcm of 18,32 , 48,52 = 3744 required number = 3744 - 4 = 3740 answer is c"
Answer: c
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 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 = 30 x / ( 30 + 60 ) x = 30 x / 90 x = 33.33 % thus answer is e"
Answer: e
Question (general): if 0.75 : x : : 7 : 8 , then x is equal to :
Options: a ) a ) 1.12 , b ) b ) 1.2 , c ) c ) 0.95 , d ) d ) 0.85 , e ) e ) 0.9
Rationale: "( x * 7 ) = ( 0.75 * 8 ) x = 6 / 7 x = 0.85 answer = d"
Answer: d
Question (physics): tom drives from town r to town b , driving at a constant speed of 60 miles per hour . from town b tom immediately continues to town c . the distance between r and b is twice the distance between b and c . if the average speed of the whole journey was 36 mph , then what is tom ' s speed driving from b to c in miles per hour ?
Options: a ) 12 , b ) 20 , c ) 24 , d ) 30 , e ) 36
Rationale: let ' s assume that it takes 4 hours to go from point r to b . then the distance between them becomes 240 which makes distance between b and c 120 . ( 240 + 120 ) / ( 4 + x ) gives us the average speed which is 36 . you find x = 6 . so the question simplifies itself to 120 / 6 = 20 hence the answer is b .
Answer: b
Question (general): of the 3,600 employees of company x , 1 / 3 are clerical . if the clerical staff were to be reduced by 1 / 3 , what percent of the total number of the remaining employees would then be clerical ?
Options: a ) 25 % , b ) 22.2 % , c ) 20 % , d ) 12.5 % , e ) 11.1 %
Rationale: "let ' s see , the way i did it was 1 / 3 are clerical out of 3600 so 1200 are clerical 1200 reduced by 1 / 3 is 1200 * 1 / 3 so it reduced 400 people , so there is 800 clerical people left but since 400 people left , it also reduced from the total of 3600 so there are 3200 people total since 800 clerical left / 3200 people total you get ( a ) 25 %"
Answer: a
Question (physics): calculate the circumference of a circular field whose radius is 2 centimeters .
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "circumference c is given by c = 2 ï € r = 2 ï € * 2 = 4 ï € cm correct answer b"
Answer: b
Question (physics): a and b can do a piece of work in 6 days , b and c in 7 days , c and a in 8 days . how long will c take to do it ?
Options: a ) 12.6 days , b ) 14.4 days , c ) 15.2 days , d ) 16.8 days , e ) 18.2 days
Rationale: "2 c = 1 / 7 + 1 / 8 – 1 / 6 = 20 / 168 = 10 / 84 c = 5 / 84 = > 84 / 5 = 16.8 days the answer is d ."
Answer: d
Question (physics): two trains are moving in opposite directions with speed of 210 km / hr and 90 km / hr respectively . their lengths are 1.10 km and 0.9 km respectively . the slower train cross the faster train in - - - seconds
Options: a ) 56 , b ) 48 , c ) 47 , d ) 26 , e ) 24
Rationale: explanation : relative speed = 210 + 90 = 300 km / hr ( since both trains are moving in opposite directions ) total distance = 1.1 + . 9 = 2 km time = 2 / 300 hr = 1 / 150 hr = 3600 / 150 seconds = 24 seconds answer : option e
Answer: e
Question (general): pat , kate and mark charged a total of 216 hours to a certain project . if pat charged twice as much time to the project as kate and 1 / 3 as much times as mark , how many more hours did mark charge to the project than kate .
Options: a ) 18 , b ) 36 , c ) 120 , d ) 90 , e ) 108
Rationale: "let kate charge for x hours , then pat charged for 2 x and mat - for 6 x . so , 2 x + 6 x + x = 216 - total hours charged for , x = 24 . mat charged 6 x - x or 5 x for more hours than kate , or for 120 hours . c is correct"
Answer: c
Question (gain): find the principle on a certain sum of money at 5 % per annum for 5 years if the amount being rs . 1120 ?
Options: a ) 896 , b ) 1067 , c ) 1977 , d ) 1056 , e ) 1097
Rationale: "1120 = p [ 1 + ( 5 * 5 ) / 100 ] p = 896 answer : a"
Answer: a
Question (gain): 10 percent of the women in a college class are science majors , and the non - science majors make up 60 % of the class . what percentage of the men are science majors if 40 % of the class are men ?
Options: a ) 45 % , b ) 55 % , c ) 65 % , d ) 75 % , e ) 85 %
Rationale: science majors make up 0.4 of the class . 60 % of the class are women and 0.1 * 0.6 = 0.06 of the class are female science majors . then 0.34 of the class are male science majors . 0.4 x = 0.34 x = 0.85 = 85 % the answer is e .
Answer: e
Question (general): a 40 - liter solution of alcohol and water is 5 percent alcohol . if 6.5 liters of alcohol and 3.5 liters of water are added to this solution , what percent of the solution produced is alcohol ?
Options: a ) 13 % , b ) 14 % , c ) 15 % , d ) 16 % , e ) 17 %
Rationale: "the percent of alcohol in the solution is ( 0.05 ( 40 ) + 6.5 ) / 50 = 8.5 / 50 = 17 % the answer is e ."
Answer: e
Question (geometry): the area of a parallelogram is 243 sq m and its altitude is three times the corresponding base . what is the length of the base ?
Options: a ) 4 , b ) 9 , c ) 10 , d ) 4 , e ) 12
Rationale: "3 x * x = 243 = > x = 9 answer : b"
Answer: b
Question (general): rs . 730 were divided among punith , michael , suresh in such a way that if punith gets rs . 3 , then michael gets rs . 4 and if michael gets rs . 3.50 then suresh gets rs . 3 . the share of michael exceeds that of suresh by
Options: a ) rs 30 , b ) rs 40 , c ) rs 70 , d ) rs 210 , e ) rs 310
Rationale: explanation : let a = punith , b = michael , c = suresh . a : b = 3 : 4 and b : c = 7 / 2 : 3 = ( 8 / 7 ) * ( 7 / 2 ) * ( 8 / 7 ) * 3 = 4 : ( 24 / 7 ) a : b : c = 3 : 4 : 24 / 7 = 21 : 28 : 24 . bs share = rs . [ 730 * ( 28 / 73 ) ] = rs . 280 . cs share = rs . [ 730 * ( 24 / 73 ) ] = rs . 240 . difference of their shares = 40 answer : b
Answer: b
Question (other): the value of log 5 ( 1 / 125 ) is :
Options: a ) 3 , b ) - 3 , c ) 1 / 3 , d ) - 1 / 3 , e ) none of these
Rationale: "log 5 ( 1 / 125 ) = log 5 ( 1 / 5 ) ^ 3 = 3 log 5 ( 1 / 5 ) = 3 ( log 5 1 - log 5 5 ) = 3 ( 0 - 1 ) = - 3 answer : b"
Answer: b
Question (gain): a sells a cricket bat to b at a profit of 20 % . b sells it to c at a profit of 25 % . if c pays $ 222 for it , the cost price of the cricket bat for a is :
Options: a ) 150 , b ) 148 , c ) 130 , d ) 160 , e ) 210
Rationale: "125 % of 120 % of a = 222 125 / 100 * 120 / 100 * a = 222 a = 222 * 2 / 3 = 148 . answer b"
Answer: b
Question (physics): a car traveled 75 % of the way from town a to town b at an average speed of 90 miles per hour . the car travels at an average speed of s miles per hour for the remaining part of the trip . the average speed for the entire trip was 40 miles per hour . what is s ?
Options: a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 37.5
Rationale: "total distance = 100 miles ( easier to work with % ) 75 % of the distance = 75 miles 25 % of the distance = 25 miles 1 st part of the trip → 75 / 90 = 0.833 2 nd part of the trip → 25 / s = t total trip → ( 75 + 25 ) / 40 = 0.833 + t » 100 / 40 = 0.833 + t » 2.5 = 0.833 + t » t = 1.667 back to 2 nd part of the trip formula : 25 / s = 1.667 » s = 15 ans a"
Answer: a
Question (other): there are 190 items that are members of set u . of these items , 49 are members of set b , 59 are not members of either of set a or set b , and 23 are members of both sets a and b . how many of the members of set u are members of set a ?
Options: a ) 72 , b ) 85 , c ) 94 , d ) 105 , e ) 108
Rationale: "you had the answer almost right . the x = 82 refers to only set a . however what ' s being asked is how many members are part of set a . this will include : 1 . only set a 2 . set a and set b so the answer is set a = 82 + set ab = 82 + 23 = 105 d"
Answer: d
Question (physics): in a 240 meters race a beats b by 56 m or 7 seconds . a ' s time over the course is :
Options: a ) 23 seconds , b ) 12 seconds , c ) 10 seconds , d ) 18 seconds , e ) 28 seconds
Rationale: "b runs 56 m in 7 sec . = > b runs 240 m in 7 / 56 * 240 = 30 seconds since a beats b by 7 seconds , a runs 240 m in ( 30 - 7 ) = 23 seconds hence , a ' s time over the course = 23 seconds answer : a"
Answer: a