Cheukting/mathqa huggingface dataset:
Question (physics): a farmer planned to plough a field by doing 120 hectares a day . after two days of work he increased his daily productivity by 25 % and he finished the job two days ahead of schedule . a ) what is the area of the field ? b ) in how many days did the farmer get the job done ? c ) in how many days did the farmer plan to get the job done ?
Options: a ) 2337 , b ) 2667 , c ) 1440 , d ) 2887 , e ) 2661
Rationale: first of all we will find the new daily productivity of the farmer in hectares per day : 25 % of 120 hectares is 25100 ⋅ 120 = 3025100 ⋅ 120 = 30 hectares , therefore 120 + 30 = 150120 + 30 = 150 hectares is the new daily productivity . lets x be the planned number of days allotted for the job . then the farm is 120 ⋅ x 120 ⋅ x hectares . on the other hand , we get the same area if we add 120 ⋅ 2120 ⋅ 2 hectares to 150 ( x − 4 ) 150 ( x − 4 ) hectares . then we get the equation 120 x = 120 ⋅ 2 + 150 ( x − 4 ) 120 x = 120 ⋅ 2 + 150 ( x − 4 ) x = 12 x = 12 so , the job was initially supposed to take 12 days , but actually the field was ploughed in 12 - 2 = 10 days . the field ' s area is 120 ⋅ 12 = 1440120 ⋅ 12 = 1440 hectares . answer : c
Answer: c
Question (physics): 12 men complete a work in 9 days . after they have worked for 6 days , 6 more men join them . how many days will they take to complete the remaining work ?
Options: a ) 2 days , b ) 7 days , c ) 8 days , d ) 9 days , e ) 45 days
Rationale: 1 man ' s 1 day work = 1 / 108 12 men ' s 6 day ' s work = 1 / 9 * 6 = 2 / 3 remaining work = 1 - 2 / 3 = 1 / 3 18 men ' s 1 day work = 1 / 108 * 18 = 1 / 6 1 / 6 work is done by them in 1 day . 1 / 3 work is done by them in 6 * 1 / 3 = 2 days . answer : a
Answer: a
Question (general): joe has a total of $ 200 in his two pockets . he takes one fourth of the money in his left pocket and puts it in his right pocket . he then takes $ 20 from his left pocket and puts it in his right pocket . if he now has an equal amount of money in each pocket , then how much money did he originally have in his left pocket ?
Options: a ) $ 120 , b ) $ 130 , c ) $ 140 , d ) $ 150 , e ) $ 160
Rationale: joe had $ 100 in his left and $ 100 in his right pocket at the end . so , he had $ 120 in his left pocket ( and $ 80 in his right pocket ) before moving $ 20 from his left to his right pocket . thus , he had $ 160 in his left pocket originally ( solve x − x / 4 = 120 ) . correct answer e
Answer: e
Question (physics): if 5 machines can produce 20 units in 10 hours , how long would it take 20 machines to produce 200 units ?
Options: a ) 50 hours , b ) 40 hours , c ) 25 hours , d ) 12 hours , e ) 8 hours
Rationale: here , we ' re told that 5 machines can produce 20 units in 10 hours . . . . that means that each machine works for 10 hours apiece . since there are 5 machines ( and we ' re meant to assume that each machine does the same amount of work ) , then the 5 machines equally created the 20 units . 20 units / 5 machines = 4 units are made by each machine every 10 hours now that we know how long it takes each machine to make 4 units , we can break this down further if we choose to . . . 10 hours / 4 units = 2.5 hours per unit when 1 machine is working . the prompt asks us how long would it take 20 machines to produce 200 units . if 20 machines each work for 2.5 hours , then we ' ll have 20 units . since 200 units is ' 10 times ' 20 , we need ' 10 times ' more time . ( 2.5 hours ) ( 10 times ) = 25 hours final answer : [ reveal ] spoiler : c
Answer: c
Question (general): the price of a cycle is reduced by 25 per cent . the new price is reduced by a further 60 per cent . the two reductions together are equal to a single reduction of
Options: a ) 45 % , b ) 70 % , c ) 35 % , d ) 32.5 % , e ) 30 %
Rationale: "price = p initially price reduced by 25 % which means new price is 3 / 4 p now on this new price further 60 percent is reduced which means the new price is merely 40 percent of 3 / 4 p = = > ( 3 / 4 ) x ( 2 / 5 ) p = 6 / 20 p is the new price after both deduction which is 30 percent of the original value p . this implies this entire series of deduction is worth having discounted 70 % of p . so answer is b = 70 %"
Answer: b
Question (general): given a number , there is an algorithm described here to find it ' s sum and number of factors . for example , let us take the number 1225 ?
Options: a ) 1767 , b ) 1800 , c ) 1812 , d ) 1890 , e ) none
Rationale: solving for 1225 = 52 × 72 sum of divisors = ( ap + 1 – 1 ) / ( a – 1 ) × ( bq + 1 – 1 ) / ( b – 1 ) here a = 5 , b = 7 prime factors p = 2 and q = 2 sum of divisors = ( 53 – 1 ) / ( 5 – 1 ) × ( 73 – 1 ) / ( 7 – 1 ) = ( 124 / 4 ) × ( 342 / 6 ) = ( 31 × 57 ) = 1767 option a
Answer: a
Question (general): total 60 cows 20 cow gives each 2 liter milk 20 cow gives each 3 / 4 liter milk 20 cow gives each 1 / 4 liter milk this is split into 3 son per each 20 cows & 20 liter milk how ?
Options: a ) 20 , b ) 10 , c ) 15 , d ) 16 , e ) 18
Rationale: 20 cow 2 liter each = 40 liter 20 cow 3 / 4 liter each = 3 / 4 = 0.75 * 20 = 15 20 cow 1 / 4 liter each = 1 / 4 = 0.25 * 20 = 5 add 40 + 15 + 5 = 60 milk split into 3 son each 20 liter then 60 / 3 = 20 answer : a
Answer: a
Question (other): x starts a business with rs . 45000 . y joins in the business after 5 months with rs . 30000 . what will be the ratio in which they should share the profit at the end of the year ?
Options: a ) 1 : 2 , b ) 2 : 1 , c ) 1 : 3 , d ) 3 : 1 , e ) 18 : 7
Rationale: explanation : ratio in which they should share the profit = ratio of the investments multiplied by the time period = 45000 ã — 12 : 30000 ã — 7 = 45 ã — 12 : 30 ã — 7 = 3 ã — 12 : 2 ã — 7 = 18 : 7 answer : option e
Answer: e
Question (gain): ashok and pyarelal invested money together in a business and share a capital of ashok is 1 / 9 of that of pyarelal . if the incur a loss of rs 2000 then loss of pyarelal ?
Options: a ) 1600 , b ) 1700 , c ) 1800 , d ) 1900 , e ) 1000
Rationale: "let the capital of pyarelal be x , then capital of ashok = x / 9 so ratio of investment of pyarelal and ashok = x : x / 9 = 9 x : x hence out of the total loss of 2000 , loss of pyarelal = 2000 * 9 x / 10 x = 1800 answer : c"
Answer: c
Question (general): a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets rs . 1200 more than d , what is b ' s share ?
Options: a ) rs . 500 , b ) rs . 1500 , c ) rs . 2000 , d ) rs . 2400 , e ) none of the above
Rationale: "let the shares of a , b , c and d be rs . 5 x , rs . 2 x , rs . 4 x and rs . 3 x respectively . then , 4 x - 3 x = 1200 x = 1200 . b ' s share = rs . 2 x = rs . ( 2 x 1200 ) = rs . 2400 . answer = d"
Answer: d
Question (gain): a store sells chairs and tables . if the price of 2 chairs and 1 table is 60 % of the price of 1 chair and 2 tables , and the price of 1 table and 1 chair is $ 60 , what is the price , in dollars , of 1 table ? ( assume that every chair has the same price and every table has the same price . )
Options: a ) 105 / 2 , b ) 45 , c ) 44 , d ) 52 , e ) 50
Rationale: "let c = chair ; t = table 2 c + 1 t = 0.6 ( 1 c + 2 t ) or c ( 2 - 0.6 ) = 1.2 t - 1 t or 1.4 c = 0.2 t therefore c = 0.2 / 1.4 t = 1 / 7 t ic + 1 t = 60 or 1 / 7 t + 1 t = 60 therefore t = 60 * 7 / 8 = 105 / 2 a"
Answer: a
Question (gain): you hold some gold in a vault as an investment . over the past year the price of gold increases by 60 % . in order to keep your gold in the vault , you must pay 10 % of the total value of the gold per year . what percentage has the value of your holdings changed by over the past year .
Options: a ) 45 % , b ) 46 % , c ) 50 % , d ) 55 % , e ) 44 %
Rationale: "( 100 % + 60 % ) * ( 100 % - 10 % ) = 160 * 0.90 = 144 % an increase of 44 % your gold holdings have increased in value by 44 % . the answer is e"
Answer: e
Question (geometry): there is a square of side 6 cm . a circle is inscribed inside the square . find the ratio of the area of circle to square .
Options: a ) 11 / 14
b ) 1 / 14
c ) 13 / 14
d ) 12 / 14
e ) 5 / 14
Rationale: let the side of square = a unit so area of square = a ^ 2 diameter of inscribed circle = side of square = a radius of circle = a / 2 area of circle = ( 22 / 7 ) ( a / 2 ) ^ 2 ratio of area of circle to square = { ( 22 / 7 ) ( a / 2 ) ^ 2 } / a ^ 2 = 11 / 14 answer : a
Answer: a
Question (general): if p and q are prime numbers , how many divisors does the product p ^ 4 * q ^ 9 have ?
Options: a ) 30 , b ) 35 , c ) 40 , d ) 50 , e ) 60
Rationale: "when a number n = a ^ x * b ^ y , where a and b are prime numbers , and x , y are positive integers , the number of divisors of n = ( x + 1 ) ( y + 1 ) therefore , the answer is d . 5 * 10 = 50"
Answer: d
Question (gain): 30 is subtracted from 40 % of a number , the result is 50 . find the number ?
Options: a ) 200 , b ) 997 , c ) 266 , d ) 288 , e ) 271
Rationale: "( 40 / 100 ) * x – 30 = 50 4 x = 800 x = 200 answer : a"
Answer: a
Question (physics): calculate how many days it will take for 5 boys to paint a 65 m long wall if 2 boys can paint a 40 m long wall in 4 days ,
Options: a ) 2.6 days , b ) 3.6 days , c ) 5.6 days , d ) 6 days , e ) 2 days
Rationale: "the length of wall painted by one boy in one day = 40 / 2 * 1 / 4 = 5 m no . of days required to paint 50 m cloth by 8 boys = 65 / 5 * 1 / 5 = 2.6 days . a"
Answer: a
Question (general): if a - b = 3 and a 2 + b 2 = 29 , find the value of ab ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 17 , e ) 18
Rationale: "2 ab = ( a 2 + b 2 ) - ( a - b ) 2 = 29 - 9 = 20 ab = 10 a )"
Answer: a
Question (gain): mary invested a certain sum of money in a bank that paid simple interest . the amount grew to $ 260 at the end of 2 years . she waited for another 4 years and got a final amount of $ 380 . what was the principal amount that she invested at the beginning ?
Options: a ) $ 200 , b ) $ 220 , c ) $ 230 , d ) $ 240 , e ) $ 250
Rationale: "what shall be the rate of interest . ? does that is not required for the calculation ? not really ! keep in mind that the interest earned each year will be the same in simple interest . at the end of 2 years , amount = $ 260 at the end of 6 years , amount = $ 380 this means she earned an interest of $ 120 in 4 years . or $ 30 in each year . we know that the interest earned each year will be the same . therefore she must have earned $ 60 in 2 years . hence principal amount = $ 260 - $ 60 = $ 200 option a"
Answer: a
Question (physics): pipe a can fill a tank in 32 minutes . pipe b can fill the same tank 5 times faster than pipe a . if both the pipes are connected to the tank so that they fill the tank simultaneously , how long will it take for the empty tank to overflow ?
Options: a ) 4 minutes , b ) 2 / 7 minutes , c ) 32 / 7 minutes , d ) 224 / 7 minutes , e ) 28 minutes
Rationale: "pipe a can fill a tank in 32 minutes - - > the rate of a = 1 / 32 tank / minute ; pipe b can fill the same tank 5 times fasterthan pipe a - - > the rate of b = 1 / 32 + 5 / 32 = 6 / 32 tank / minute . their combined rate = 1 / 32 + 6 / 32 = 7 / 32 tank / minute ; therefore , a and b can fill the tank in 32 / 7 minutes . answer : c"
Answer: c
Question (geometry): one side of a rectangular field is 4 m and its length along diagonal is 5 m . what is the area of the field ?
Options: a ) 12 , b ) 27 , c ) 98 , d ) 27 , e ) 29
Rationale: "lb = 3 * 4 = 12 answer : a"
Answer: a
Question (physics): a taxi company charges $ 1.85 for the first quarter of a mile and fifteen cents for each additional quarter of a mile . what is the maximum distance someone could travel with $ 4.90 ?
Options: a ) 4 miles , b ) 4 1 / 4 miles , c ) 4 3 / 4 miles , d ) 5 1 / 3 miles , e ) 6 1 / 4 miles
Rationale: "if we start out with $ 4.90 and have to spend $ 1.85 for the first quarter - mile , we will have $ 3.05 left to spend on quarter - mile intervals . since $ 3.05 / $ 0.15 = 20.33 , we can buy 20.33 more quarter - miles , and will travel 21.33 quarter miles in all : 21.33 × 1 / 4 = 5 1 / 3 miles . the correct answer is choice ( d ) ."
Answer: d
Question (physics): the speed of a train is 64 kmph . what is the distance covered by it in 9 minutes ?
Options: a ) 10 kmph , b ) 11 kmph , c ) 88 kmph , d ) 18 kmph , e ) 12 kmph
Rationale: "64 * 9 / 60 = 9.6 kmph answer : a"
Answer: a
Question (general): if it is a 3 x 3 matrix , for which elements in first row are ( v , 50 , w ) , second row ( 196 , x , y ) and in third row are ( 269 , z , 123 ) . it is given that the sum of the numbers in each row , column , diagonal are same . then find the value of ( y + z ) .
Options: a ) 1012 , b ) 1011 , c ) 1212 , d ) 1122 , e ) 1021
Rationale: v 50 w 196 x y 269 z 123 in 1 st row and 1 st column v + 196 + 269 = v + 50 + w w = 415 again , in 2 nd column and 3 rd row 50 + x + z = 269 + z + 123 x = 342 as sum of each row column and diagonal are same . so , 269 + 342 + 415 = 1026 415 + y + 123 = 1026 y = 488 269 + z + 123 = 1026 z = 634 y + z = 488 + 634 = 1122 answer : d
Answer: d
Question (gain): in an examination 35 % of the students passed and 455 failed . how many students appeared for the examination ?
Options: a ) 540 , b ) 400 , c ) 700 , d ) 650 , e ) 840
Rationale: "let the number of students appeared be x then , 65 % of x = 455 65 x / 100 = 455 x = 455 * 100 / 65 = 700 answer is c"
Answer: c
Question (general): a bag contains an equal number of one rupee , 50 paise and 25 paise coins respectively . if the total value is 140 , how many coins of each type are there ?
Options: a ) 20 coins , b ) 30 coins , c ) 40 coins , d ) 80 coins , e ) none of these
Rationale: let number of each type of coin = x . then , 1 × x + . 50 × x + . 25 x = 140 ⇒ 1.75 x = 140 ⇒ x = 80 coins answer d
Answer: d
Question (general): a 80 gallon solution of salt and water is 10 % salt . how many gallons of water must be added to the solution in order to decrease the salt to 8 % of the volume ?
Options: a ) 20 , b ) 12 , c ) 13 , d ) 14 , e ) 16
Rationale: "amount of salt = 8.0 assume x gallons of water are added . 8.0 / 80 + x = 8 / 100 800 = 8 x + 640 8 x = 160 x = 20 correct option : a"
Answer: a
Question (general): what least value should be replaced by * in 223431 * so the number become divisible by 5
Options: a ) 0 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: explanation : trick : number is divisible by 5 , if last digit is 0 or 5 so that least number is 0 . answer : option a
Answer: a
Question (general): the average height of 35 boys in a class was calculated as 184 cm . it has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm . find the actual average height of the boys in the class ( round off your answer to two decimal places ?
Options: a ) 187.89 cm , b ) 182.29 cm , c ) 123.98 cm , d ) 149.98 cm , e ) 146.89 cm
Rationale: "calculated average height of 35 boys = 184 cm . wrong total height of 35 boys = 184 * 35 cm . this was as a result of an actual height of 106 cm being wrongly written as 166 cm . correct total height of 35 boys = 183 cm - ( 166 cm + 106 cm ) / 35 = 184 cm - 60 / 35 cm = 184 cm - 1.71 cm = 182.29 cm . answer : b"
Answer: b
Question (general): a certain country had a total annual expenditure of $ 2.4 x 10 ^ 11 last year . if the population of the country was 240 million last year , what was the per capita expenditure ?
Options: a ) $ 500 , b ) $ 1,000 , c ) $ 2,000 , d ) $ 3,000 , e ) $ 5,000
Rationale: "total expenditure / population = per capita expenditure hence , ( 2,4 x 10 ^ 11 ) / 240 000 000 = ( 2,4 x 10 ^ 11 ) / ( 2,4 x 10 ^ 8 ) = 1 x 10 ^ ( 11 - 8 ) = 1 x 10 ^ 3 = 1000 . answer is b ."
Answer: b
Question (gain): there were two candidates in an election . winner candidate received 62 % of votes and won the election by 336 votes . find the number of votes casted to the winning candidate ?
Options: a ) 288 , b ) 744 , c ) 788 , d ) 868 , e ) 177
Rationale: "w = 62 % l = 38 % 62 % - 38 % = 24 % 24 % - - - - - - - - 336 62 % - - - - - - - - ? = > 868 answer : d"
Answer: d
Question (physics): a train running at the speed of 60 km / hr crosses a pole in 3 seconds . what is the length of the train ?
Options: a ) 120 metres , b ) 180 metres , c ) 324 metres , d ) 50 metres , e ) 180 metres
Rationale: "speed = ( 60 x 5 / 18 ) / m / sec = 50 / 3 m / sec . length of the train = ( speed x time ) . length of the train = 50 x 3 / 3 m = 50 m . answer : option d"
Answer: d
Question (general): two positive integers differ by 4 , and sum of their reciprocals is 5 then one of the numbers is
Options: a ) a ) 3 , b ) b ) 1 , c ) c ) 5 , d ) d ) 21 , e ) 4
Rationale: "algebraic approach : let n be the smaller integer = > 1 / n + 1 / ( n + 4 ) = 5 or ( ( n + 4 ) + n ) / n ( n + 4 ) = 6 or ( n ^ 2 + 4 n ) * 5 = 2 n + 4 or n = 2 as n can not be - negative solve for n = > n = 4 . hence , e"
Answer: e
Question (general): jennifer had $ 90 to spend on herself . she spent 1 / 5 of the money on a sandwich , 1 / 6 for a ticket to a museum , and 1 / 2 of it on a book . how much money does jennifer have left over ?
Options: a ) $ 12 , b ) $ 14 , c ) $ 5 , d ) $ 15 , e ) $ 0
Rationale: "1 / 5 x $ 90 = $ 15 for sandwich 1 / 6 x $ 90 = $ 45 for museum 1 / 2 x $ 90 = $ 78 for book $ 15 + $ 45 + $ 18 = $ 78 spent $ 90 - $ 78 = $ 12 left over correct answer a"
Answer: a
Question (geometry): the surface of a cube is 24 sq cm . find its volume ?
Options: a ) 8 , b ) 6 , c ) 4 , d ) 3 , e ) 1
Rationale: "6 a 2 = 24 a = 2 = > a 3 = 8 cc answer : a"
Answer: a
Question (physics): in one hour , a boat goes 11 km along the stream and 5 km against it . find the speed of the boat in still water
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "explanation : we know we can calculate it by 1 / 2 ( a + b ) = > 1 / 2 ( 11 + 5 ) = 1 / 2 ( 16 ) = 8 km / hr answer is c"
Answer: c
Question (physics): how long does a train 145 meters long running at the rate of 54 kmph take to cross a bridge 660 meters in length ?
Options: a ) 52.66 , b ) 53.66 , c ) 54.66 , d ) 58.66 , e ) 59.66
Rationale: "t = ( 660 + 145 ) / 54 * 18 / 5 t = 53.66 answer : b"
Answer: b
Question (general): in a group of ducks and cows , the total number of legs are 36 more than twice the no . of heads . find the total no . of buffaloes .
Options: a ) 10 , b ) 12 , c ) 13 , d ) 15 , e ) 18
Rationale: "let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 36 = > 2 x = 36 = > x = 18 e"
Answer: e
Question (gain): in town x , 60 percent of the population are employed , and 48 percent of the population are employed males . what percent of the employed people in town x are females ?
Options: a ) 16 % , b ) 20 % , c ) 31 % , d ) 40 % , e ) 52 %
Rationale: "we are asked to find the percentage of females in employed people . total employed people 60 % , out of which 48 are employed males , hence 12 % are employed females . ( employed females ) / ( total employed people ) = 12 / 60 = 1 / 5 = 20 % answer : b ."
Answer: b
Question (general): what is the remainder when 1273 * 1275 * 1277 * 1285 is divided by 12 ?
Options: a ) 9 , b ) 1 , c ) 11 , d ) 0 , e ) 7
Rationale: "1271 * 1275 * 1277 * 1285 = ( 1272 + 1 ) ( 1272 + 3 ) ( 1284 - 7 ) ( 1284 + 1 ) = ( multiple of 12 - 1 ) ( multiple of 12 + 3 ) ( multiple of 12 - 7 ) ( multiple of 12 + 1 ) now , if we expand this expression all terms but the last one will have a multiple of 12 in them , thus will leave no remainder upon division by 12 , the last term will be ( 1 ) ( 3 ) ( - 7 ) ( 1 ) = 21 . thus the question becomes : what is the remainder upon division of 21 by 12 ? the answer to this question is 9 . answer : a"
Answer: a
Question (general): find large number from below question the difference of two numbers is 1335 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder
Options: a ) 1254 , b ) 1376 , c ) 1456 , d ) 1599 , e ) 1635
Rationale: "let the smaller number be x . then larger number = ( x + 1335 ) . x + 1335 = 6 x + 15 5 x = 1320 x = 264 large number = 264 + 1335 = 1599 d"
Answer: d
Question (gain): in a sample of college students , 20 percent are third year students and 80 percent are not second - year students . what fraction of those students who are not third - year students are second - year students ?
Options: a ) 1 / 4 , b ) 2 / 3 , c ) 4 / 7 , d ) 1 / 2 , e ) 3 / 7
Rationale: "= 20 / 80 . = 1 / 4 my answer is a too"
Answer: a
Question (general): what is the product of all the possible values of x if x ^ 2 - 9 x + 20 ?
Options: a ) – 29 , b ) – 12 , c ) 12 , d ) 20 , e ) 168
Rationale: "explanation : = > y = x ^ 2 - 9 x + 20 = > y = ( x - 4 ) ( x - 5 ) = > x = 4 , y = 5 product y = ( 4 ) ( 5 ) = 20 answer option 20 answer : d"
Answer: d
Question (general): in a group of ducks and cows , the total number of legs are 28 more than twice the number of heads . find the total number of cows .
Options: a ) 14 , b ) 12 , c ) 16 , d ) 8 , e ) 6
Rationale: "explanation : let the number of ducks be d and number of cows be c then , total number of legs = 2 d + 4 c = 2 ( d + 2 c ) total number of heads = c + d given that total number of legs are 28 more than twice the number of heads = > 2 ( d + 2 c ) = 28 + 2 ( c + d ) = > d + 2 c = 14 + c + d = > 2 c = 14 + c = > c = 14 i . e . , total number of cows = 14 answer : a"
Answer: a
Question (other): a dog takes 3 leaps for every 8 leaps of a hare . if one leap of the dog is equal to 3 leaps of the hare , the ratio of the speed of the dog to that of the hare is :
Options: a ) 9 : 8 , b ) 9 : 9 , c ) 9 : 6 , d ) 9 : 1 , e ) 9 : 2
Rationale: "explanation : dog : hare = ( 3 * 3 ) leaps of hare : 8 leaps of hare = 9 : 5 . answer : a ) 9 : 8"
Answer: a
Question (general): a certain no . when divided by 50 leaves a remainder 25 , what is the remainder if the same no . be divided by 15 ?
Options: a ) 2 , b ) 4 , c ) 5 , d ) 8 , e ) 9
Rationale: "explanation : 50 + 25 = 75 / 15 = 5 ( remainder ) c"
Answer: c
Question (general): a retailer bought a coat at wholesale and marked it up 90 % to its initial price of $ 76 . by how many more dollars does he need to increase the price to achieve a 100 % markup ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: let x be the wholesale price . then 1.9 x = 76 and x = 76 / 1.9 = 40 . to achieve a 100 % markup , the price needs to be $ 80 . the retailer needs to increase the price by $ 4 more . the answer is b .
Answer: b
Question (general): if bat = 58 hat = 52 cat = 57 then whats rat = ?
Options: a ) 42 , b ) 45 , c ) 34 , d ) 76 , e ) 25
Rationale: a 42
Answer: a
Question (general): ( 700 + 200 ) ã — 4 ã — ( 4 + 2 ) = ?
Options: a ) 24500 , b ) 21600 , c ) 36600 , d ) 22400 , e ) 12500
Rationale: "( 700 + 200 ) ã — 4 ã — ( 4 + 2 ) = ? or , ? = 900 ã — 4 ã — 6 = 21600 answer b"
Answer: b
Question (general): there are 5 chess amateurs playing in villa ' s chess club tournament . if each chess amateur plays with exactly 16 other amateurs , what is the total number of chess games possible to be played in the tournament ?
Options: a ) 10 , b ) 20 , c ) 40 , d ) 60 , e ) 120
Rationale: "each person is one participant of 4 games . so there are in all 16 * 5 = 80 instances of one participant games . but each game has 2 participants so total number of games = 80 / 2 = 40 c"
Answer: c
Question (other): find the highest common factor of 36 and 84 .
Options: a ) 12 , b ) 10 , c ) 16 , d ) 19 , e ) 18
Rationale: "36 = 2 ^ 2 x 3 ^ 2 84 = 2 ^ 2 x 3 x 7 h . c . f . = 2 ^ 2 x 3 = 12 . answer : option a"
Answer: a
Question (probability): a basket contains 7 apples , of which 1 is spoiled and the rest are good . if we select 2 apples from the basket simultaneously and at random , what is the probability that the 2 apples selected will include the spoiled apple ?
Options: a ) 1 / 5 , b ) 2 / 7 , c ) 2 / 9 , d ) 3 / 5 , e ) 4 / 11
Rationale: "the total number of ways to choose 2 apples is 7 c 2 = 21 the number of ways that include the spoiled apple is 6 c 1 = 6 p ( the spoiled apple is included ) = 6 / 21 = 2 / 7 the answer is b ."
Answer: b
Question (gain): the cost price of a radio is rs . 1500 and it was sold for rs . 1275 , find the loss % ?
Options: a ) 15 % , b ) 16 % , c ) 17 % , d ) 78 % , e ) 28 %
Rationale: "1500 - - - - 225 100 - - - - ? = > 15 % answer : a"
Answer: a