Cheukting/mathqa huggingface dataset:
Question (physics): how long does a train 60 m long travelling at 60 kmph takes to cross a bridge of 80 m in length ?
Options: a ) 5.8 sec , b ) 8.4 sec , c ) 12.4 sec , d ) 6.8 sec , e ) 1.8 sec
Rationale: "b 16.8 sec d = 60 + 80 = 140 m s = 60 * 5 / 18 = 50 / 3 t = 140 * 3 / 50 = 8.4 sec answer is b"
Answer: b
Question (geometry): a circle graph shows how the budget of a certain company was spent : 55 percent for salaries , 9 percent for research and development , 5 percent for utilities , 4 percent for equipment , 2 percent for supplies , and the remainder for transportation . if the area of each sector of the graph is proportional to the percent of the budget it represents , how many degrees of the circle are used to represent transportation ?
Options: a ) 18 ° , b ) 36 ° , c ) 54 ° , d ) 72 ° , e ) 90 °
Rationale: "the percent of the budget for transportation is 100 - ( 55 + 9 + 5 + 4 + 2 ) = 25 % 100 % of the circle is 360 degrees . then ( 25 % / 100 % ) * 360 = 90 degrees the answer is e ."
Answer: e
Question (general): how many integers are between 5 and 96 / 7 , inclusive ?
Options: a ) 7 , b ) 9 , c ) 10 , d ) 12 , e ) 15
Rationale: "96 / 7 = 13 . xx we are not concerned about the exact value of 96 / 7 as we just need the integers . since the values are small , we can write down the integers . the different integers between 5 and 96 / 7 would be 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12,13 total number of integers = 9 option b"
Answer: b
Question (general): simplify : 256 x 256 - 144 x 144
Options: a ) 761200 , b ) 44800 , c ) 761800 , d ) 761500 , e ) none of them
Rationale: "( 256 ) ^ 2 - ( 144 ) ^ 2 = ( 256 + 144 ) ( 256 - 144 ) = 400 x 112 = 44800 answer is b"
Answer: b
Question (geometry): the area of a square garden is a square feet and the perimeter is p feet . if a = 2 p + 20 , what is the perimeter of the garden , in feet ?
Options: a ) 28 , b ) 36 , c ) 40 , d ) 56 , e ) 64
Rationale: "perimeter of square = p side of square = p / 4 area of square = ( p ^ 2 ) / 16 = a given that a = 2 p + 20 ( p ^ 2 ) / 16 = 2 p + 20 p ^ 2 = 32 p + 320 p ^ 2 - 32 p - 320 = 0 p ^ 2 - 40 p + 8 p - 320 = 0 p ( p - 40 ) + 8 ( p + 40 ) = 0 ( p - 40 ) ( p + 8 ) = 0 p = 40 or - 8 discarding negative value , p = 40 answer is c"
Answer: c
Question (general): which is the least number that must be subtracted from 1856 so that the remainder when divided by 7 , 12 , 10 is 4 ?
Options: a ) 168 , b ) 172 , c ) 182 , d ) 140 , e ) 160
Rationale: first we need to figure out what numbers are exactly divisible by 7 , 12,10 . this will be the set { lcm , lcmx 2 , lcmx 3 , . . . } lcm ( 7 , 12,10 ) = 42 * 10 = 420 the numbers which will leave remainder 4 will be { 420 + 4 , 420 x 2 + 4 , , . . . } the largest such number less than or equal to 1856 is 420 * 4 + 4 or 1684 to obtain this you need to subtract 172 . b
Answer: b
Question (general): find the average of first 3 multiples of 5 ?
Options: a ) 10 , b ) 15 , c ) 12.5 , d ) 13 , e ) 21
Rationale: "average = ( 5 + 10 + 15 ) / 3 = 10 answer is a"
Answer: a
Question (general): the population of a town increased from 1 , 34,800 to 2 , 42,500 in a decade . the average percent increase of population per year is :
Options: a ) 4.37 % , b ) 7.9 % , c ) 6.8 % , d ) 8.75 % , e ) none
Rationale: "explanation : increase in 10 years = ( 242500 - 134800 ) = 107700 increase % = ( 107700 / 134800 x 100 ) % = 79 % . required average = ( 79 / 10 ) % = 7.9 % . answer : option b"
Answer: b
Question (physics): how many bricks , each measuring 25 cm * 11.25 cm * 6 cm , will be needed to build a wall 8 m * 6 m * 22.5 m
Options: a ) 6400 , b ) 3777 , c ) 2679 , d ) 2667 , e ) 1997
Rationale: "to solve this type of question , simply divide the volume of wall with the volume of brick to get the numbers of required bricks so lets solve this number of bricks = volume of wall / volume of 1 brick = 800 ∗ 600 ∗ 22.5 / 25 ∗ 11.25 ∗ 6 = 6400 answer : a"
Answer: a
Question (gain): a soccer team played 160 games and won 65 percent of them . how many games did it win ?
Options: a ) 84 , b ) 94 , c ) 104 , d ) 114 , e ) 124
Rationale: "65 % of 160 = x 0.65 * 160 = x 104 = x answer : c"
Answer: c
Question (general): a certain no . when divided by 80 leaves a remainder 25 , what is the remainder if the same no . be divided by 15 ?
Options: a ) 3 , b ) 4 , c ) 6 , d ) 7 , e ) 9
Rationale: "explanation : 80 + 25 = 105 / 15 = 7 ( remainder ) d"
Answer: d
Question (physics): a trader sells 80 meters of cloth for rs . 9000 at the profit of rs . 23.5 per metre of cloth . what is the cost price of one metre of cloth ?
Options: a ) 22 , b ) 89 , c ) 90 , d ) 78 , e ) 80
Rationale: "sp of 1 m of cloth = 9000 / 80 = rs . 112.5 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 112.5 - rs . 23.5 = rs . 89 . answer : b"
Answer: b
Question (general): a farm has chickens , cows and sheep . there are 6 times the number of chickens and cows than sheep . if there are more cows than chickens or sheep , and together , cows and chickens have a total of 100 feet and heads , how many sheep live at the farm ?
Options: a ) 5 , b ) 8 , c ) 10 , d ) 4 , e ) 17
Rationale: chicken - ch cows - c sheep - s ch + c = 6 s c > ch and c > s each cow has 4 legs and 1 head each chicken has 2 legs and 1 head so 5 c + 3 ch = 100 ( sum of legs and head ) there are 2 possible solutions to this equation c = 11 and ch = 9 or c = 14 and ch = 10 since from first equation where ch + c = 6 s the sum of ch and c should be divisbile by 6 . 20 is not so the only possible solution is c = 14 and ch = 10 . so s = 4 answer : d
Answer: d
Question (gain): in a certain city , 60 percent of the registered voters are democrats and the rest are republicans . in a mayoral race , if 75 percent of the registered voters who are democrats and 25 percent of the registered voters who are republicans are expected to vote for candidate a , what percent of the registered voters are expected to vote for candidate a ?
Options: a ) 50 % , b ) 53 % , c ) 54 % , d ) 55 % , e ) 57 %
Rationale: "say there are total of 100 registered voters in that city . thus 60 are democrats and 40 are republicans . 60 * 0.75 = 45 democrats are expected to vote for candidate a ; 40 * 0.25 = 10 republicans are expected to vote for candidate a . thus total of 45 + 10 = 55 registered voters are expected to vote for candidate a , which is 55 % of the total number of registered voters . answer : d ."
Answer: d
Question (physics): a rower can row 5 km / h in still water . when the river is running at 2 km / h , it takes the rower 1 hour to row to big rock and back . how many kilometers is it to big rock ?
Options: a ) 1.5 , b ) 1.8 , c ) 2.1 , d ) 2.4 , e ) 2.7
Rationale: "let x be the distance to big rock . time = x / 3 + x / 7 = 1 x = 21 / 10 = 2.1 km the answer is c ."
Answer: c
Question (physics): a brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 24 m * 2 m * 0.75 m ?
Options: a ) 29798 , b ) 27908 , c ) 24000 , d ) 25000 , e ) 27991
Rationale: "24 * 2 * 0.75 = 20 / 100 * 10 / 100 * 7.5 / 100 * x 24 = 1 / 100 * x = > x = 24000 answer : c"
Answer: c
Question (gain): thirty percent of the members of a swim club have passed the lifesaving test . among the members who have not passed the test , 26 have taken the preparatory course and 65 have not taken the course . how many members are there in the swim club ?
Options: a ) 60 , b ) 80 , c ) 100 , d ) 130 , e ) 140
Rationale: "30 % of the members have passed the test , thus 70 % have not passed the test . we also know that 65 + 26 = 91 members have not passed the test , thus 0.7 * total = 91 - - > total = 130 . answer : d ."
Answer: d
Question (general): if 12 x = 16 y = 28 z , then what is a possible sum of positive integers x , y , and z ?
Options: a ) 52 , b ) 58 , c ) 122 , d ) 84 , e ) 168
Rationale: "12 x = 16 y = 28 z 3 x = 4 y = 7 z 3 ( 4 * 7 ) = 4 ( 3 * 7 ) = 7 ( 3 * 4 ) addition = 28 + 21 + 12 = 61 answer would be multiple of 61 which is 122 answer : c"
Answer: c
Question (gain): a salesperson received a commission of 3 percent of the sale price for each of the first 100 machines that she sold and 4 percent of the sale price for each machine that she sold after the first 100 . if the sale price of each machine was $ 10,000 and the salesperson received a $ 32,000 commission , how many machines did she sell ?
Options: a ) 90 , b ) 110 , c ) 105 , d ) 115 , e ) 120
Rationale: "first 100 machines = 3 % commission = 0.03 * 100 * 10000 = 30000 commission from sale of next machines = 34000 - 30000 = 4000 so 10 more machines . . total = 110 machines imo b . ."
Answer: b
Question (general): in a group of ducks and cows , the total number of legs are 28 more than twice the no . of heads . find the total no . of buffaloes .
Options: a ) 11 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 28 = > 2 x = 28 = > x = 14 c"
Answer: c
Question (gain): a producer of tea blends two varieties of tea from two tea gardens one costing rs 18 per kg and another rs 20 per kg in the ratio 5 : 3 . if he sells the blended variety at rs 26 per kg , then his gain percent is
Options: a ) 12 % , b ) 39 % , c ) 14 % , d ) 15 % , e ) 16 %
Rationale: "explanation : suppose he bought 5 kg and 3 kg of tea . cost price = rs . ( 5 x 18 + 3 x 20 ) = rs . 150 . selling price = rs . ( 8 x 26 ) = rs . 208 . profit = 208 - 150 = 58 so , profit % = ( 58 / 150 ) * 100 = 39 % option b"
Answer: b
Question (physics): abel can complete a work in 10 days , ben in 12 days and carla in 16 days . all of them began the work together , but abel had to leave after 2 days and ben 4 days before the completion of the work . how long did the work last ?
Options: a ) 6 , b ) 7 , c ) 7 2 / 3 , d ) 9 , e ) 10
Rationale: abel in the 2 days that he worked completed 1 / 5 of the job = 4 / 5 remains then if ben had to leave 4 days before the completion , this means that carla had to work alone for these 4 days in which she completed 1 / 4 of the job . now together , ben and carla completed the job in ( 1 / 12 + 1 / 15 ) ( t ) = 11 / 20 3 / 20 ( t ) = 11 / 20 - - - > t = 3 2 / 3 therefore , these 3 2 / 3 days worked plus the 4 days that carla had to work by herself add to 7 2 / 3 days answer : c
Answer: c
Question (physics): joe needs to paint all the airplane hangars at the airport , so he buys 360 gallons of paint to do the job . during the first week , he uses 1 / 4 of all the paint . during the second week , he uses 1 / 4 of the remaining paint . how many gallons of paint has joe used ?
Options: a ) 18 , b ) 157 , c ) 175 , d ) 216 , e ) 250
Rationale: "total paint initially = 360 gallons paint used in the first week = ( 1 / 4 ) * 360 = 90 gallons . remaning paint = 270 gallons paint used in the second week = ( 1 / 4 ) * 270 = 67 gallons total paint used = 157 gallons . option b"
Answer: b
Question (general): 0,2 , 6 , 12 , 20 , 30 , 42 , ___
Options: a ) 55 , b ) 85 , c ) 59 , d ) 63 , e ) 56
Rationale: "0 = 1 * 1 - 1 2 = 2 * 2 - 2 6 = 3 * 3 - 3 12 = 4 * 4 - 4 20 = 5 * 5 - 5 30 = 6 * 6 - 6 42 = 7 * 7 - 7 similarly 8 * 8 - 8 = 56 answer : e"
Answer: e
Question (physics): the diameter of the driving wheel of a bus in 140 cm . how many revolutions per minute must the wheel make in order to keep a speed of 66 kmph ?
Options: a ) 210 , b ) 220 , c ) 230 , d ) 240 , e ) 250
Rationale: "distance covered in 1 min = ( 66 * 1000 ) / 60 = 1100 m circumference of the wheel = ( 2 * ( 22 / 7 ) * . 70 ) = 4.4 m no of revolution per min = 1100 / 4.4 = 250 answer : e"
Answer: e
Question (general): a man has some hens and cows . if the number of heads be 50 and the number of feet equals 160 , then the number of hens will be :
Options: a ) 22 , b ) 23 , c ) 24 , d ) 20 , e ) 28
Rationale: "explanation : let the number of hens be x and the number of cows be y . then , x + y = 50 . . . . ( i ) and 2 x + 4 y = 160 x + 2 y = 80 . . . . ( ii ) solving ( i ) and ( ii ) we get : x = 20 , y = 30 the required answer = 20 . answer : d"
Answer: d
Question (gain): if a population of women in a town is 50 % of men . what is the population of men as a percentage of population of women ?
Options: a ) 100 % , b ) 120 % , c ) 200 % , d ) 150 % , e ) 180 %
Rationale: "we ' re told that the number of women in a town is equal to 50 % of the number of men in that town . men = 10 women = 5 we ' re asked for the number of men , as a percentage of the number of women . m / w % = 10 / 5 = 200 % answer is c"
Answer: c
Question (general): how many even multiples of 65 are there between 649 and 1301 ?
Options: a ) 5 , b ) 6 , c ) 9 , d ) 10 , e ) 11
Rationale: "650 = 10 * 65 1300 = 20 * 65 the even multiples are 65 multiplied by 10 , 12 , 14 , 16 , 18 , and 20 for a total of 6 . the answer is b ."
Answer: b
Question (physics): two trains are moving in opposite directions with speed of 70 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 ) 45 , c ) 47 , d ) 26 , e ) 25
Rationale: "explanation : relative speed = 70 + 90 = 160 km / hr ( since both trains are moving in opposite directions ) total distance = 1.1 + . 9 = 2 km time = 2 / 160 hr = 1 / 80 hr = 3600 / 80 seconds = = 45 seconds answer : option b"
Answer: b
Question (gain): in 1998 the profits of company n were 10 percent of revenues . in 1999 , the revenues of company n fell by 20 percent , but profits were 10 percent of revenues . the profits in 1999 were what percent of the profits in 1998 ?
Options: a ) 80 % , b ) 105 % , c ) 120 % , d ) 124.2 % , e ) 138 %
Rationale: "0,08 r = x / 100 * 0.1 r answer a"
Answer: a
Question (general): a certain experimental mathematics program was tried out in 2 classes in each of 26 elementary schools and involved 32 teachers . each of the classes had 1 teacher and each of the teachers taught at least 1 , but not more than 3 , of the classes . if the number of teachers who taught 3 classes is n , then the least and greatest possible values of n , respectively , are
Options: a ) 0 and 13 , b ) 0 and 14 , c ) 1 and 10 , d ) 1 and 9 , e ) 2 and 8
Rationale: "one may notice that greatest possible values differ in each answer choice in contrast to the least values , which repeat . to find out the greatest value you should count the total classes ( 26 * 2 = 52 ) , then subtract the total # of teachers since we know from the question that each teacher taught at least one class ( 52 - 32 = 20 ) . thus we get a number of the available extra - classes for teachers , and all that we need is just to count how many teachers could take 2 more classes , which is 20 / 2 = 10 . so the greatest possible value of the # of teachers who had 3 classes is 10 . only answer c has this option ."
Answer: c
Question (general): if ( 2 to the x ) - ( 2 to the ( x - 2 ) ) = 3 ( 2 to the 5 ) , what is the value of x ?
Options: a ) 7 , b ) 11 , c ) 13 , d ) 15 , e ) 17
Rationale: "( 2 to the power x ) - ( 2 to the power ( x - 2 ) ) = 3 ( 2 to the power 5 ) 2 ^ x - 2 ^ ( x - 2 ) = 3 . 2 ^ 5 hence x = 7 . answer is a"
Answer: a
Question (physics): convert 1.8 hectares in ares
Options: a ) 130 ares . , b ) 160 ares . , c ) 180 ares . , d ) 230 ares . , e ) 250 ares .
Rationale: "1.8 hectares in ares 1 hectare = 100 ares therefore , 1.8 hectares = 1.8 × 100 ares = 180 ares . answer - c"
Answer: c
Question (general): in an examination , the percentage of students qualified to the students appeared from school ' p ' is 70 % . in school ' q ' , the number of students appeared is 30 % more than the students appeared from school ' p ' and the number of students qualified from school ' q ' is 50 % more than the students qualified from school ' p ' . what is the % of students qualified to the number of students appeared from school ' q ' ?
Options: a ) 80.78 % , b ) 80.76 % , c ) 80.72 % , d ) 80.79 % , e ) 80.74 %
Rationale: explanation : number of students appeared from school ' p ' = 100 , say number of students qualified from school ' p ' = 70 and number of students appeared from school ' q ' = 130 number of students qualified from school ' q ' = 50 % more than those qualified from school ' p ' . = 70 + 35 = 105 % of students qualified to the number of students appeared from school b = 105 / 130 * 100 = 80.76 % answer : b
Answer: b
Question (general): there are 4 people of different heights standing in order of increasing height . the difference is 2 inches between the first person and the second person , and also between the second person and the third person . the difference between the third person and the fourth person is 6 inches and the average height is 75 . how tall is the fourth person ?
Options: a ) 73 , b ) 75 , c ) 77 , d ) 79 , e ) 81
Rationale: let x be the height of the first person . then the heights are x , x + 2 , x + 4 , and x + 10 . 4 x + 16 = 4 ( 75 ) = 300 x = 71 and the fourth person has a height of 71 + 10 = 81 inches the answer is e .
Answer: e
Question (general): if the angles of an n sided polygon are in a . p and a > = 20 and d > = 20 then wat is the maximum possible value of n ?
Options: a ) 12 , b ) 14 , c ) 21 , d ) 25 , e ) cant determine
Rationale: sum of interior angles of a polygon = ( n - 2 ) × 180 ° where n = number of sides there will be n angles which are in a . p . therefore , since we need to find maximum value of n , put minimum value for a and d . i . e . , take a = 20 and d = 20 then sum of the angles = n / 2 [ 2 × 20 + ( n − 1 ) 20 ] therefore , 10 n ( n + 1 ) = ( n − 2 ) 180 n = 14.52 since number of sides must be a positive integer , maximum value of n = 14 answer : b
Answer: b
Question (general): the average of 9 numbers is 23 . if each number is increased by 4 , what will the new average be ?
Options: a ) 25 , b ) 26 , c ) 27 , d ) 28 , e ) 29
Rationale: "sum of the 9 numbers = 207 if each number is increased by 4 , the total increase = 4 * 9 = 36 the new sum = 207 + 36 = 243 the new average = 243 / 9 = 27 . answer : c"
Answer: c
Question (gain): a shopkeeper forced to sell at cost price , uses a 800 grams weight for a kilogram . what is his gain percent ?
Options: a ) 10 % , b ) 25 % , c ) 11.11 % , d ) 12 % , e ) none of these
Rationale: "shopkeeper sells 800 g instead of 1000 g . so , his gain = 1000 - 800 = 200 g . thus , % gain = 200 * 100 ) / 800 = 25 % . answer : option b"
Answer: b
Question (general): company z has 58 employees . if the number of employees having birthdays on wednesday is more than the number of employees having birthdays on any other day of the week , each of which have same number of birth - days , what is the minimum number of employees having birthdays on wednesday .
Options: a ) 6 , b ) 10 , c ) 8 , d ) 9 , e ) 12
Rationale: "say the number of people having birthdays on wednesday is x and the number of people having birthdays on each of the other 6 days is y . then x + 6 y = 54 . now , plug options for x . only b and e give an integer value for y . but only for b x > y as needed . answer : b ."
Answer: b
Question (general): if there are only 2 wheelers and 4 wheelers parked in a school located at the heart of the city , find the number of 4 wheelers parked there if the total number of wheels is 82 ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 20 , e ) 25
Rationale: "four wheeler = 20 * 4 = 80 ( max ) 2 wheel = 1 so no of 4 wheeler = 20 answer : d"
Answer: d
Question (general): if 50 % of x is 25 less than 25 % of 2500 , then x is ?
Options: a ) 1880 , b ) 2160 , c ) 1200 , d ) 8400 , e ) 1210
Rationale: "50 % of x = x / 2 ; 25 % of 2500 = 25 / 100 * 2500 = 625 given that , x / 2 = 625 - 25 = > x / 2 = 600 = > x = 1200 . answer : c"
Answer: c
Question (physics): a contractor undertakes to built a walls in 50 days . he employs 30 peoples for the same . however after 25 days he finds that only 40 % of the work is complete . how many more man need to be employed to complete the work in time ?
Options: a ) 25 , b ) 30 , c ) 45 , d ) 20 , e ) none of these
Rationale: "30 men complete 0.4 work in 25 days . applying the work rule , m 1 × d 1 × w 2 = m 2 × d 2 × w 1 we have , 30 × 25 × 0.6 = m 2 × 25 × 0.4 or m 2 = 30 × 25 × 0.6 / 25 × 0.4 = 45 men answerc"
Answer: c
Question (general): in an examination , 30 % of total students failed in hindi , 35 % failed in english and 35 % in both . the percentage of these who passed in both the subjects is :
Options: a ) 10 % , b ) 20 % , c ) 30 % , d ) 70 % , e ) 50 %
Rationale: "pass percentage = 100 - ( 30 + 35 - 35 ) = 100 - 30 = 70 answer : d"
Answer: d
Question (gain): in a shop , the profit is 320 % of the cost . if the cost increases by 25 % but the selling price remains constant , find out approximately what percentage of the selling price is the profit ?
Options: a ) 180 % , b ) 120 % , c ) 90 % , d ) 80 % , e ) 70 %
Rationale: let the cp = 100 profit = ( 320 / 100 ) × 100 = 320 sp = cp + profit = 100 + 320 = 420 if the cost increases by 25 % , new cp = ( 125 / 100 ) × 100 = 125 selling price is constant , hence new sp = 420 profit = sp – cp = 420 – 125 = 295 required percentage = ( 295 / 420 ) × 100 = 2950 / 42 = 1475 / 21 ≈ 70 answer : e
Answer: e
Question (gain): a person spends 40 % of his salary on food , 25 % on house rent , 15 % on entertainment and 10 % on conveyance . if his savings at the end of the month is rs . 1200 , then his salary per month in rupees is :
Options: a ) 12000 , b ) 6000 , c ) 8000 , d ) 10000 , e ) none of these
Rationale: total expenditure = 40 + 25 + 15 + 10 = 90 % saving = ( 100 - 90 ) = 10 % 10 / 100 × salary = 1200 , salary = 12000 rs . answer : a
Answer: a
Question (general): the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 12000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is ?
Options: a ) 76 , b ) 21 , c ) 26 , d ) 28 , e ) 11
Rationale: "explanation : lot the total number of workers be v then , 8 ooov = ( 12000 * 7 ) + 6000 ( v - 7 ) < = > 2000 v = 42000 < = > v = 21 . answer : b"
Answer: b
Question (general): a student chose a number , multiplied it by 2 , then subtracted 138 from the result and got 108 . what was the number he chose ?
Options: a ) 123 , b ) 267 , c ) 277 , d ) 267 , e ) 120
Rationale: "let xx be the number he chose , then 2 â ‹ … x â ˆ ’ 138 = 108 x = 123 answer : a"
Answer: a
Question (gain): two numbers are less than third number by 30 % and 37 % respectively . how much percent is the second number less than by the first
Options: a ) 8 % , b ) 10 % , c ) 9 % , d ) 11 % , e ) 12 %
Rationale: "let the third number is x . then first number = ( 100 - 30 ) % of x = 70 % of x = 7 x / 10 second number is ( 63 x / 100 ) difference = 7 x / 10 - 63 x / 100 = 7 x / 10 so required percentage is , difference is what percent of first number ( 7 x / 100 * 10 / 7 x * 100 ) % = 10 % answer : b"
Answer: b
Question (physics): express 30 mps in kmph ?
Options: a ) 122 , b ) 108 , c ) 110 , d ) 150 , e ) 100
Rationale: "30 * 18 / 5 = 108 kmph answer : b"
Answer: b
Question (general): in a group of ducks and cows , the total number of legs are 8 more than twice the no . of heads . find the total no . of buffaloes .
Options: a ) 5 , b ) 4 , c ) 6 , d ) 3 , e ) 2
Rationale: "let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 8 = > 2 x = 8 = > x = 4 b"
Answer: b
Question (gain): a merchant gets a 5 % discount on each meter of fabric he buys after the first 2,000 meters and a 7 % discount on every meter after the next 1,500 meters . the price , before discount , of one meter of fabric is $ 2 , what is the total amount of money the merchant spends on 5,000 meters of fabric ?
Options: a ) $ 8280 , b ) $ 8520 , c ) $ 8710 , d ) $ 8930 , e ) $ 9640
Rationale: "for first 2000 meters he does not get any discount . the price is 2 * 2000 = $ 4000 for next 1500 meters , he gets a 5 % discount . the price is 1.9 * 1500 = $ 2850 for the next 1500 meters , he gets a 7 % discount . the price is 1.86 * 1500 = $ 2790 the total price is $ 4000 + $ 2850 + $ 2790 = $ 9640 the answer is e ."
Answer: e