Cheukting/mathqa huggingface dataset:
Question (gain): in a certain city , 70 percent of the registered voters are democrats and the rest are republicans . in a mayoral race , if 80 percent of the registered voters who are democrats and 30 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 ) 65 % , b ) 52 % , c ) 85 % , d ) 69 % , e ) 75 %
Rationale: "say there are total of 100 registered voters in that city . thus 70 are democrats and 30 are republicans . 70 * 0.80 = 56 democrats are expected to vote for candidate a ; 30 * 0.30 = 9 republicans are expected to vote for candidate a . thus total of 56 + 9 = 65 registered voters are expected to vote for candidate a , which is 65 % of the total number of registered voters . answer : a"
Answer: a
Question (physics): a and b can do a piece of work in 7 days . with the help of c they finish the work in 4 days . c alone can do that piece of work in ?
Options: a ) 33 , b ) 9 1 / 3 , c ) 30 , d ) 88 , e ) 11
Rationale: "c = 1 / 4 â € “ 1 / 7 = 3 / 28 = > 28 / 3 = 9 1 / 3 days answer : b"
Answer: b
Question (physics): the ratio between the length and the breadth of a rectangular park is 3 : 2 . if a man cycling along the boundary of the park at the speed of 12 km / hr completes one round in 9 minutes , then the area of the park ( in sq . m ) is :
Options: a ) 153601 , b ) 153600 , c ) 153602 , d ) 153603 , e ) 194400
Rationale: "perimeter = distance covered in 9 min . = ( 12000 / 60 ) x 9 m = 1800 m . let length = 3 x metres and breadth = 2 x metres . then , 2 ( 3 x + 2 x ) = 1800 or x = 180 . length = 540 m and breadth = 360 m . area = ( 540 x 360 ) m 2 = 194400 m 2 . answer : e"
Answer: e
Question (gain): a broker invested her own money in the stock market . during the first year , she increased her stock market wealth by 80 percent . in the second year , largely as a result of a slump in the stock market , she suffered a 30 percent decrease in the value of her stock investments . what was the net increase or decrease on her overall stock investment wealth by the end of the second year ?
Options: a ) − 5 % , b ) 5 % , c ) 15 % , d ) 26 % , e ) 80 %
Rationale: "the actual answer is obtained by multiplying 180 % by 70 % and subtracting 100 % from this total . that is : 180 % × 70 % = 126 % ; 126 % − 100 % = 26 % . answer : d"
Answer: d
Question (physics): pipe a can fill a tank in 16 hrs and pipe b can fill it in 24 hrs . if both the pipes are opened in the empty tank . in how many hours will it be fill 5 / 4 th of that tank ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: part filled a in 1 hr = ( 1 / 16 ) part filled b in 1 hr = ( 1 / 24 ) part filled by ( a + b ) together in 1 hr = ( 1 / 16 ) + ( 1 / 24 ) = 5 / 48 so , the tank will be full in 48 / 5 hrs time taken to fill exact quarter tank = ( 48 / 5 ) * ( 5 / 4 ) = 12 hrs answer : b
Answer: b
Question (gain): a certain sum is invested at simple interest at 18 % p . a . for two years instead of investing at 12 % p . a . for the same time period . therefore the interest received is more by rs . 504 . find the sum ?
Options: a ) 7000 , b ) 7029 , c ) 2778 , d ) 4200 , e ) 2791
Rationale: "let the sum be rs . x . ( x * 18 * 2 ) / 100 - ( x * 12 * 2 ) / 100 = 504 = > 36 x / 100 - 24 x / 100 = 504 = > 12 x / 100 = 840 = > x = 4200 . answer : d"
Answer: d
Question (general): the average age of 8 men is increased by years when two of them whose ages are 21 years and 23 years are replaced by two new men . the average age of the two new men is
Options: a ) 22 , b ) 30 , c ) 99 , d ) 38 , e ) 27
Rationale: "total age increased = ( 8 * 2 ) years = 16 years . sum of ages of two new men = ( 21 + 23 + 16 ) years = 60 years average age of two new men = ( 60 / 2 ) years = 30 years . answer : b"
Answer: b
Question (physics): a boy traveled from the village to the post - office at the rate of 12.5 kmph and walked back at the rate of 2 kmph . if the whole journey took 5 hours 48 minutes , find the distance of the post - office from the village .
Options: a ) 5 km , b ) 7 km , c ) 9 km , d ) 10 km , e ) 12 km
Rationale: explanation : solution : average speed = 2 xy / ( x + y ) km / hr = ( 2 * 12.5 * 2 ) / ( 12.5 + 2 ) km / hr = 50 / 14.5 km / hr . total distance = ( 50 / 14.5 * 29 / 5 ) km . = 20 km . required distance = 20 / 2 = 10 km . answer : d
Answer: d
Question (other): the sum of the numbers is 177 . if the ratio between the first and the second be 5 : 3 and that between the second and third be 4 : 9 , then find the second number ?
Options: a ) 12 , b ) 20 , c ) 45 , d ) 60 , e ) 52
Rationale: "given ratios 5 : 3 4 : 9 20 : 12 : 27 the second number = 177 / ( 20 + 12 + 27 ) * 15 = 45 answer is c"
Answer: c
Question (geometry): if the height of a cone is increased by 190 % then its volume is increased by ?
Options: a ) 100 , b ) 777 , c ) 998 , d ) 190 , e ) 2879
Rationale: "100 % answer : d"
Answer: d
Question (gain): a green lizard can travel from the green cave to the blue cave in 108 minutes ; the blue lizard can travel from the blue cave to the green cave in 25 % less time . if the green lizard started to travel 7.5 minutes before the blue lizard , how many minutes after the blue lizard , will the green lizard pass the middle line ?
Options: a ) 2 . , b ) 3.5 . , c ) 4 . , d ) 5.5 . , e ) 6 .
Rationale: time take by the green lizard to cover the distance between the caves = 108 mins time take by the green lizard to cover half the distance = 108 / 2 = 54 mins time take by the blue lizard to cover the distance between the caves = 108 x 3 / 4 = 81 mins time take by the blue lizard to cover half the distance = 81 / 2 = 40.5 mins now the green lizard had been travelling for 7.5 mins when the blue lizard started . therefore when the blue lizard starts to move the green lizard will have to cover 54 - 7.5 = 46.5 mins worth of distance at its current speed . difference in time when they both reach the mid point = 46.5 - 40.5 = 6 mins . e is the correct answer .
Answer: e
Question (general): working alone , printers x , y , and z can do a certain printing job , consisting of a large number of pages , in 12 , 16 , and 18 hours , respectively . what is the ratio of the time it takes printer x to do the job , working alone at its rate , to the time it takes printers y and z to do the job , working together at their individual rates ?
Options: a ) 4 / 11 , b ) 1 / 2 , c ) 15 / 22 , d ) 144 / 17 , e ) 11 / 4
Rationale: "p 1 takes 12 hrs rate for p 2 p 3 together = 1 / 16 + 1 / 18 = 17 / 144 therefore they take 144 / 17 ratio = 144 / 17 = d"
Answer: d
Question (general): the first year , two cows produced 8100 litres of milk . the second year their production increased by 15 % and 10 % respectively , and the total amount of milk increased to 9100 litres a year . how many litres were milked from each cow each year ?
Options: a ) 3472 , b ) 8222 , c ) 4370 , d ) 26777 , e ) 8222
Rationale: let x be the amount of milk the first cow produced during the first year . then the second cow produced ( 8100 − x ) ( 8100 − x ) litres of milk that year . the second year , each cow produced the same amount of milk as they did the first year plus the increase of 15 % 15 % or 10 % 10 % . so 8100 + 15100 ⋅ x + 10100 ⋅ ( 8100 − x ) = 91008100 + 15100 ⋅ x + 10100 ⋅ ( 8100 − x ) = 9100 therefore 8100 + 320 x + 110 ( 8100 − x ) = 91008100 + 320 x + 110 ( 8100 − x ) = 9100 120 x = 190120 x = 190 x = 3800 x = 3800 therefore , the cows produced 3800 and 4300 litres of milk the first year , and 4370 and 4730 litres of milk the second year , respectively . answer : c
Answer: c
Question (other): sara bought both german chocolate and swiss chocolate for some cakes she was baking . the swiss chocolate cost $ 2.5 per pound , and german chocolate cost $ 1.5 per pound . if the total the she spent on chocolate was $ 15 and both types of chocolate were purchased in whole number of pounds , how many total pounds of chocolate she purchased ?
Options: a ) 9 , b ) 8 , c ) 10 , d ) 12 , e ) 15
Rationale: "if there were all the expensive ones 2.5 . . . . there would be 15 / 2.5 or 6 of them but since 1.5 $ ones are also there , answer has to be > 6 . . . . if all were 1.5 $ ones , there will be 15 / 1.5 or 10 . . . so only 8 is left ans b . ."
Answer: b
Question (general): an integer n between 1 and 99 , inclusive , is to be chosen at random . what is the probability that n ( n + 2 ) will be divisible by 3 ?
Options: a ) 1 / 9 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6
Rationale: n ( n + 2 ) to be divisible by 3 either n or n + 2 must be a multiples of 3 . in each following group of numbers : { 1 , 2 , 3 } , { 4 , 5 , 6 } , { 7 , 8 , 9 } , . . . , { 97 , 98 , 99 } there are exactly 2 numbers out of 3 satisfying the above condition . for example in { 1 , 2 , 3 } n can be : 1 , or 3 . thus , the overall probability is 2 / 3 . answer : d .
Answer: d
Question (physics): find the expenditure on digging a well 14 m deep and of 3 m diameter at rs . 15 per cubic meter ?
Options: a ) 2998 , b ) 2799 , c ) 2890 , d ) 1485 , e ) 2780
Rationale: "22 / 7 * 14 * 3 / 2 * 3 / 2 = 99 m 2 99 * 15 = 1485 answer : d"
Answer: d
Question (physics): a car started running at a speed of 28 km / hr and the speed of the car was increased by 2 km / hr at the end of every hour . find the total distance covered by the car in the first 10 hours of the journey .
Options: a ) 37 km , b ) 76 km , c ) 25 km , d ) 15 km , e ) 30 km
Rationale: "a 37 km the total distance covered by the car in the first 10 hours = 28 + 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44 + 46 = sum of 10 terms in ap whose first term is 28 and last term is 46 = 10 / 2 [ 28 + 46 ] = 370 km ."
Answer: a
Question (general): find the total number of prime factors in the expression ( 4 ) ^ 11 x ( 7 ) ^ 3 x ( 11 ) ^ 2
Options: a ) 26 , b ) 22 , c ) 25 , d ) 27 , e ) 29
Rationale: "( 4 ) ^ 11 x ( 7 ) ^ 3 x ( 11 ) ^ 2 = ( 2 x 2 ) ^ 11 x ( 7 ) ^ 3 x ( 11 ) ^ 2 = 2 ^ 11 x 2 ^ 11 x 7 ^ 3 x 11 ^ 2 = 2 ^ 22 x 7 ^ 3 x 11 ^ 2 total number of prime factors = ( 22 + 3 + 2 ) = 27 . answer is d ."
Answer: d
Question (general): for a group of n people , k of whom are of the same sex , the ( n - k ) / n expression yields an index for a certain phenomenon in group dynamics for members of that sex . for a group that consists of 20 people , 7 of whom are females , by how much does the index for the females exceed the index for the males in the group ?
Options: a ) 0.05 , b ) 0.0625 , c ) 0.2 , d ) 0.3 , e ) 0.6
Rationale: "index for females = ( 20 - 7 ) / 20 = 13 / 20 = 0.65 index for males = ( 20 - 13 / 20 = 7 / 20 = 0.35 index for females exceeds males by 0.65 - 0.35 = 0.3 answer : d"
Answer: d
Question (general): the sum of the squares of three numbers is 138 , while the sum of their products taken two at a time is 131 . their sum is :
Options: a ) 20 , b ) 98 , c ) 37 , d ) 26 , e ) 17
Rationale: "explanation : let the numbers be a , b and c . then , a 2 + b 2 + c 2 = 138 and ( ab + bc + ca ) = 131 ( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) 138 + 2 * 131 = 400 ( a + b + c ) = â ˆ š 400 = 20 answer : a"
Answer: a
Question (gain): the cost price of an article is 64 % of the marked price . calculate the gain percent after allowing a discount of 14 % ?
Options: a ) 34.375 % , b ) 48 % , c ) 50.5 % , d ) 52 % , e ) 56 %
Rationale: "explanation : let marked price = rs . 100 . then , c . p . = rs . 64 , s . p . = rs . 86 gain % = 22 / 64 * 100 = 34.375 % . answer : option a"
Answer: a
Question (geometry): the parameter of a square is equal to the perimeter of a rectangle of length 16 cm and breadth 14 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places )
Options: a ) 77.14 cm
b ) 47.14 cm
c ) 84.92 cm
d ) 94.94 cm
e ) 23.57 cm
Rationale: let the side of the square be a cm . parameter of the rectangle = 2 ( 16 + 14 ) = 60 cm parameter of the square = 60 cm i . e . 4 a = 60 a = 15 diameter of the semicircle = 15 cm circimference of the semicircle = 1 / 2 ( ∏ ) ( 15 ) = 1 / 2 ( 22 / 7 ) ( 15 ) = 330 / 14 = 23.57 cm to two decimal places answer : e
Answer: e
Question (general): in a graduating class , the difference between the highest and lowest salaries is $ 100000 . the median salary is $ 50000 higher than the lowest salary and the average salary is $ 20000 higher than the median . what is the minimum number of students e in the class ?
Options: a ) a ) 10 , b ) b ) 12 , c ) c ) 15 , d ) d ) 20 , e ) e ) 25
Rationale: the difference between the highest and lowest salaries is $ 100000 . so there are at least 2 people - say one with salary 0 and the other with 100 k . no salary will be outside this range . median = 50 k more than lowest . so median is right in the center of lowest and highest since lowest and highest differ by 100 k . in our example , median = 50 k . since there are more than 2 people , there would probably be a person at 50 k . mean = 20 k more than median so in our example , mean salary = 70 k on the number line , 0 . . . . . . . . 50 k ( median ) . . . . . . . . 100 k mean = 70 k so there must be people more toward 100 k to bring the mean up to 70 k . since we want to add minimum people , we will add people at 100 k to quickly make up the right side deficit . 0 and 50 k are ( 70 k + 20 k ) = 90 k away from 70 k . 100 k is 30 k away from 70 k . to bring the mean to 70 k , we will add two people at 100 k each to get : 0 . . . . 50 k . . . . . 100 k , 100 k , 100 k but when we add more people to the right of 70 k , the median will shift to the right . we need to keep the median at 50 k . so every time we add people to the right of 70 k , we need to add people at 50 k too to balance the median . 50 k is 20 k less than 70 k while 100 k is 30 k more than 70 k . to keep the mean same , we need to add 2 people at 100 k for every 3 people we add at 50 k . so if we add 3 people at 50 k and 2 people at 100 k , we get : 0 , . . . 50 k , 50 k , 50 k , 50 k , . . . 100 k , 100 k , 100 k , 100 k , 100 k the median is not at 50 k yet . add another 3 people at 50 k and another 2 at 100 k to get 0 , 50 k , 50 k , 50 k , 50 k , 50 k , 50 k , 50 k , 100 k , 100 k , 100 k , 100 k , 100 k , 100 k , 100 k now the median is 50 k and mean is 70 k . total number of people is 15 . answer ( c )
Answer: c
Question (general): a car travels first 160 km at 64 km / hr and the next 160 km at 80 km / hr . what is the average speed for the first 320 km of the tour ?
Options: a ) 71.11 , b ) 71.12 , c ) 71.1 , d ) 71.17 , e ) 71.13
Rationale: "car travels first 160 km at 64 km / hr time taken to travel first 160 km = distancespeed = 16064 car travels next 160 km at 80 km / hr time taken to travel next 160 km = distancespeed = 16080 total distance traveled = 160 + 160 = 2 × 160 total time taken = 16064 + 16080 average speed = total distance traveledtotal time taken = 2 × 16016064 + 16080 = 2164 + 180 = 2 × 64 × 8080 + 64 = 2 × 64 × 80144 = 2 × 8 × 8018 = 6409 = 71.11 km / hr answer : a"
Answer: a
Question (general): a prize of $ 800 is to be distributed among 20 winners , each of whom must be awarded at least $ 20 . if 2 / 5 of the prize will be distributed to 3 / 5 of the winners , what is the greatest possible individual award ?
Options: a ) $ 200 , b ) $ 220 , c ) $ 280 , d ) $ 300 , e ) $ 340
Rationale: "total value of the prize = $ 800 number of people = 20 2 / 5 of 800 ( = $ 320 ) should be distributed among 3 / 5 of 20 ( = 12 people ) with each getting $ 20 each . remaining money = 800 - 320 = $ 480 . now in order to ' maximize ' 1 prize , we need to minimise the others and we have been given that each should get $ 20 . thus , minimising the remaining 7 people ( = 20 - 12 - 1 . ' - 1 ' to exclude 1 that needs to be maximised ) = 7 * 20 = 140 . thus the maximum award can be = 480 - 140 = $ 340 , hence e is the correct answer ."
Answer: e
Question (gain): simple interest on a certain sum of money for 3 years at 10 % per annum is half the compound interest on rs . 6500 for 2 years at 14 % per annum . the sum placed on simple interest is
Options: a ) rs . 6500 , b ) rs . 1947.4 , c ) rs . 973.7 , d ) rs . 2000 , e ) none
Rationale: "solution c . i . = rs [ 6500 x ( 1 + 14 / 100 ) â ² - 6500 ] rs . ( 6500 x 114 / 100 x 114 / 100 - 6500 ) = rs . 1947.4 . sum = rs . [ 973.7 x 100 / 3 x 10 ] = rs . 3245.67 . answer e"
Answer: e
Question (gain): mary works in a restaurant a maximum of 50 hours . for the first 20 hours , she is paid $ 8 per hour . for each overtime hour , she is paid at a rate which is 25 % higher than her regular rate . how much mary can earn in a week ?
Options: a ) 300 , b ) 420 , c ) 460 , d ) 320 , e ) 400
Rationale: "mary receives $ 8 ( 20 ) = $ 160 for the first 20 hours . for the 30 overtime hours , she receives $ 8 ( 0.25 ) + $ 8 = $ 10 per hour , that is $ 10 ( 30 ) = $ 300 . the total amount is $ 160 + $ 300 = $ 460 answer c 460 ."
Answer: c
Question (physics): an outlet pipe empties a tank which is full in 5 hours . if the inlet pipe is kept open , which lets water in at the rate of 4 litres / min then outlet pipe would take 3 hours longer . find the capacity of the tank .
Options: a ) 8600 litres , b ) 3200 litres , c ) 12800 litres , d ) 11200 litres , e ) 13200 litres
Rationale: let the rate of outlet pipe be x liters / hour ; rate of inlet pipe is 8 litres / min , or 4 * 60 = 240 liters / hour ; net outflow rate when both pipes operate would be x - 240 liters / hour . capacity of the tank = x * 5 hours = ( x - 240 ) * ( 5 + 3 ) hours 5 x = ( x - 240 ) * 8 - - > x = 640 - - > capacity = 5 x = 3200 liters . answer : b .
Answer: b
Question (geometry): you buy a piece of land with an area of â ˆ š 625 , how long is one side of the land plot ?
Options: a ) 28 , b ) 29 , c ) 30 , d ) 31 , e ) 25
Rationale: "try filling the numbers into the answer y x y = find the closest to 625 . answer e"
Answer: e
Question (general): in a division sum , the remainder is 4 and the divisor is 2 times the quotient and is obtained by adding 2 to the thrice of the remainder . the dividend is :
Options: a ) 72 , b ) 90 , c ) 100 , d ) 110 , e ) 120
Rationale: "diver = ( 4 * 3 ) + 2 = 14 2 * quotient = 14 quotient = 7 dividend = ( divisor * quotient ) + remainder dividend = ( 14 * 7 ) + 2 = 100 c"
Answer: c
Question (general): if the sum of two numbers is 42 and their product is 437 , then find the absolute difference between the numbers .
Options: a ) 2 , b ) 4 , c ) 3 , d ) 1 , e ) 0
Rationale: let the numbers be x and y . then , x + y = 42 and xy = 437 x - y = sqrt [ ( x + y ) 2 - 4 xy ] = sqrt [ ( 42 ) 2 - 4 x 437 ] = sqrt [ 1764 – 1748 ] = sqrt [ 16 ] = 4 . required difference = 4 . answer is b .
Answer: b
Question (general): for dinner , cara ate 240 grams of bread which was 8 times as much bread as she ate for lunch , and 6 times as much bread as she ate for breakfast . how much bread did cara eat in total ?
Options: a ) 300 , b ) 310 , c ) 320 , d ) 330 , e ) 340
Rationale: for breakfast , cara ate 240 / 6 = 40 grams . for lunch , cara ate 240 / 8 = 30 grams . for dinner , cara ate 240 grams . the total is 40 + 30 + 240 = 310 grams . the answer is b .
Answer: b
Question (geometry): a rectangular box 60 m long and 40 m wide has two concrete crossroads running in the middle of the box and rest of the box has been used as a lawn . the area of the lawn is 2109 sq . m . what is the width of the road ?
Options: a ) 3 m
b ) 4 m
c ) 5 m
d ) 6 m
e ) 2 m
Rationale: total area of cross roads = 60 x + 40 x − x 2 but total area of the cross roads = 291 m 2 hence , 60 x + 40 x − x 2 = 291 ⇒ 100 x − x 2 = 291 ⇒ x 2 − 100 x + 291 = 0 ⇒ ( x − 97 ) ( x − 3 ) = 0 ⇒ x = 3 answer : a
Answer: a
Question (general): if 50 % of a number is equal to one - third of another number , what is the ratio of first number to the second number ?
Options: a ) 2 : 5 , b ) 1 : 4 , c ) 3 : 7 , d ) 6 : 11 , e ) 2 : 3
Rationale: "let 50 % of a = 1 / 3 b then 50 a / 100 = 1 b / 3 a / 2 = b / 3 a / b = 2 / 3 a : b = 2 : 3 answer is e"
Answer: e
Question (physics): the megatek corporation is displaying its distribution of employees by department in a circle graph . the size of each sector of the graph representing a department is proportional to the percentage of total employees in that department . if the section of the circle graph representing the manufacturing department takes up 180 ° of the circle , what percentage of megatek employees are in manufacturing ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 50 %
Rationale: "answer : e 180 ° divided by 360 ° equals 0.5 , therefore the sector is equal to 50 % of the total"
Answer: e
Question (physics): the speed at which a man can row a boat in still water is 25 kmph . if he rows downstream , where the speed of current is 11 kmph , what time will he take to cover 80 metres ?
Options: a ) 18 seconds , b ) 27 seconds , c ) 26 seconds , d ) 12 seconds , e ) 8 seconds
Rationale: "speed of the boat downstream = 25 + 11 = 36 kmph = 36 * 5 / 18 = 10 m / s hence time taken to cover 80 m = 80 / 10 = 8 seconds . answer : e"
Answer: e
Question (general): for a particular american football game , the probability of a team ' s quarterback throwing a completed pass on each throw is 3 / 10 . what is the least number of times that the quarterback should throw the ball that will increase the probability of getting a completed pass at least once to more than 50 % .
Options: a ) 10 , b ) 5 , c ) 2 , d ) 3 , e ) 1
Rationale: rule of subtraction : p ( a ) = 1 - p ( a ' ) rule of multiplication : p ( a ∩ b ) = p ( a ) p ( b ) the probability that the quarterback throws a completed pass at least once in 2 throws is 1 - ( 7 / 10 ) ^ 2 = 1 - 49 / 100 = 51 / 100 > 50 % answer : c
Answer: c
Question (physics): a and b can do a work in 8 hours and 12 hours respectively . a starts the work at 6 am and they work alternately for one hour each . when will the work be completed ?
Options: a ) 9.6 days , b ) 7.6 days , c ) 4 days , d ) 8.6 days , e ) 6.6 days
Rationale: work done by a and b in the first two hours , working alternately = first hour a + second hour b = 1 / 8 + 1 / 12 = 5 / 24 . total time required to complete the work = 2 * 24 / 5 = 9.6 days . answer : a
Answer: a
Question (general): in a weight - lifting competition , the total weight of joe ' s two lifts was 1800 pounds . if twice the weight of his first lift was 300 pounds more than the weight of his second lift , what was the weight , in pounds , of his first lift ?
Options: a ) 225 , b ) 275 , c ) 325 , d ) 350 , e ) 700
Rationale: this problem is a general word translation . we first define variables and then set up equations . we can define the following variables : f = the weight of the first lift s = the weight of the second lift we are given that the total weight of joe ' s two lifts was 1800 pounds . we sum the two variables to obtain : f + s = 1800 we are also given that twice the weight of his first lift was 300 pounds more than the weight of his second lift . we express this as : 2 f = 300 + s 2 f – 300 = s we can now plug in ( 2 f – 300 ) for s into the first equation , so we have : f + 2 f – 300 = 1800 3 f = 2100 f = 700 answer is e .
Answer: e
Question (physics): a train covers a distance of 12 km in 10 min . if it takes 1 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 15 , e ) 45
Rationale: "speed = ( 12 / 10 * 60 ) km / hr = ( 72 * 5 / 18 ) m / sec = 20 m / sec . length of the train = 20 * 1 = 20 m . answer : option b"
Answer: b
Question (general): in a division , divident is 729 , divisior is 38 and quotient is 19 . find the remainder .
Options: a ) a ) 4 , b ) b ) 3 , c ) c ) 2 , d ) d ) 5 , e ) e ) 7
Rationale: "explanation : 729 = 38 x 19 + r 729 = 722 + r r = 729 - 722 = 7 answer : option e"
Answer: e
Question (other): compound x contains elements a and b at an approximate ratio , by weight , of 2 : 10 . approximately how many grams of element b are there in 330 grams of compound x ?
Options: a ) 54 , b ) 162 , c ) 250 , d ) 275 , e ) 322
Rationale: total number of fractions = 2 + 10 = 12 element b constitutes = 10 out of 12 parts of x so in 330 gms of x have 330 * 10 / 12 = 275 gms of b and 330 - 275 = 55 gms of a . cross check : - a / b = 55 / 275 = 2 / 10 ( as given ) ans d
Answer: d