Cheukting/mathqa huggingface dataset:
Question (gain): if rs . 7500 are borrowed at c . i at the rate of 4 % per annum , then after 2 years the amount to be paid is :
Options: a ) rs . 8082 , b ) rs . 7800 , c ) rs . 8100 , d ) rs . 8112 , e ) none
Rationale: "explanation : amount = rs . [ 7500 ( 1 + 4 / 100 ) 2 ] = rs . [ 7500 × 26 / 25 × 26 / 25 ] = rs . 8112 . correct option : d"
Answer: d
Question (gain): a and b invests rs . 10000 each , a investing for 4 months and b investing for all the 12 months in the year . if the total profit at the end of the year is rs . 4000 , find their shares ?
Options: a ) 1000,3500 , b ) 1000,3000 , c ) 1000,2000 , d ) 1000,5000 , e ) 1000,2500
Rationale: the ratio of their profits a : b = 4 : 12 = 1 : 3 share of a in the total profit = 1 / 4 * 4000 = rs . 1000 share of b in the total profit = 3 / 4 * 4000 = rs . 3000 answer : b
Answer: b
Question (general): for all even integers n , h ( n ) is defined to be the sum of the even integers between 2 and n , inclusive . what is the value of h ( 18 ) / h ( 10 ) ?
Options: a ) 1.8 , b ) 3 , c ) 6 , d ) 18 , e ) 60
Rationale: "mean = median = ( first + last ) / 2 and sum = mean * number of terms h ( 18 ) = [ ( 2 + 18 ) / 2 ] * 9 = 90 h ( 10 ) = ( 2 + 10 ) / 2 ] * 5 = 30 h ( 18 ) / h ( 10 ) = ( 90 ) / ( 30 ) = 3 answer : b"
Answer: b
Question (general): in how many ways can an answer key for a quiz be written if the quiz contains 5 true - false questions followed by 2 multiples - choice questions with 4 answer choices each , if the correct answers to all true - false questions can not be the same ?
Options: a ) 160 , b ) 320 , c ) 480 , d ) 600 , e ) 720
Rationale: there are 2 ^ 5 = 32 possibilities for the true - false answers . however we need to remove two cases for ttttt and fffff . there are 4 * 4 = 16 possibilities for the multiple choice questions . the total number of possibilities is 30 * 16 = 480 . the answer is c .
Answer: c
Question (gain): the difference between simple and compound interest on rs . 1600 for one year at 10 % per annum reckoned half - yearly is ?
Options: a ) 8 , b ) 3 , c ) 9 , d ) 4 , e ) 2
Rationale: "s . i . = ( 1600 * 10 * 1 ) / 100 = rs . 160 c . i . = [ 1600 * ( 1 + 5 / 100 ) 2 - 1600 ] = rs . 164 difference = ( 164 - 160 ) = rs . 4 . answer : d"
Answer: d
Question (physics): a person travels equal distances with speeds of 4 km / hr , 5 km / hr and 6 km / hr and takes a total time of 47 minutes . the total distance is ?
Options: a ) 2 km , b ) 4 km , c ) 7 km , d ) 9 km , e ) 5 km
Rationale: "let the total distance be 3 x km . then , x / 4 + x / 5 + x / 6 = 47 / 60 37 x / 60 = 47 / 60 = > x = 1.27 total distance = 3 * 1.27 = 3.81 km . answer : b"
Answer: b
Question (physics): one hour after yolanda started walking from x to y , a distance of 10 miles , bob started walking along the same road from y to x . if yolanda ' s walking rate was 3 miles per hour and bob т ' s was 4 miles per hour , how many miles had bob walked when they met ?
Options: a ) 24 , b ) 23 , c ) 22 , d ) 21 , e ) 4
Rationale: "when b started walking y already has covered 3 miles out of 10 , hence the distance at that time between them was 10 - 3 = 7 miles . combined rate of b and y was 3 + 4 = 7 miles per hour , hence they would meet each other in 7 / 7 = 1 hours . in 6 hours b walked 1 * 4 = 4 miles . answer : e ."
Answer: e
Question (gain): a person borrows rs . 5000 for 2 years at 4 % p . a . simple interest . he immediately lends it to another person at 7 % p . a for 2 years . find his gain in the transaction per year .
Options: a ) 167.5 , b ) 150 , c ) 225 , d ) 112.5 , e ) 212.5
Rationale: "explanation : the person borrows rs . 5000 for 2 years at 4 % p . a . simple interest simple interest that he needs to pay = prt / 100 = 5000 × 4 × 2 / 100 = 400 he also lends it at 7 % p . a for 2 years simple interest that he gets = prt / 100 = 5000 × 7 × 2 / 100 = 700 his overall gain in 2 years = rs . 700 - rs . 400 = rs . 300 his overall gain in 1 year = 300 / 2 = rs . 150 answer : option b"
Answer: b
Question (gain): one fourth of one third of two fifth of a number is 14 . what will be 40 % of that number
Options: a ) 168 , b ) 150 , c ) 180 , d ) 200 , e ) 250
Rationale: "explanation : ( 1 / 4 ) * ( 1 / 3 ) * ( 2 / 5 ) * x = 14 then x = 14 * 30 = 420 40 % of 420 = 168 answer : option a"
Answer: a
Question (physics): a vantakes 6 hours to cover a distance of 540 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 60 kmph , b ) 61 kmph , c ) 62 kmph , d ) 64 kmph , e ) 66 kmph
Rationale: time = 6 distence = 540 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 540 / 9 = 60 kmph a )
Answer: a
Question (other): a certain fruit stand sold apples for $ 0.80 each and bananas for $ 0.70 each . if a customer purchased both apples and bananas from the stand for a total of $ 7.30 , what total number of apples and bananas did the customer purchase ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "let ' s start with 1 apple for $ 0.80 . let ' s subtract $ 0.80 from $ 7.30 until we get a multiple of $ 0.70 . $ 7.30 , $ 6.50 , $ 5.70 , $ 4.90 = 7 * $ 0.70 the customer purchased 7 bananas and 3 apples . the answer is b ."
Answer: b
Question (physics): a can do a piece of work in 4 days . b can do it in 9 days . with the assistance of c they completed the work in 2 days . find in how many days can c alone do it ?
Options: a ) 22 days , b ) 36 / 5 days , c ) 67 days , d ) 17 / 7 days , e ) 18 days
Rationale: "c = 1 / 2 - 1 / 4 - 1 / 9 = 5 / 36 = > 36 / 5 days answer : b"
Answer: b
Question (general): a number when divided by a certain divisor left remainder 255 , when twice the number was divided by the same divisor , the remainder was 112 . find the divisor ?
Options: a ) 370 , b ) 365 , c ) 398 , d ) 456 , e ) 460
Rationale: easy solution : n = dq 1 + 255 2 n = 2 dq 1 + 51 0 - ( 1 ) 2 n = dq 2 + 112 - ( 2 ) as ( 1 ) = ( 2 ) = 2 n d * ( q 2 - 2 q 1 ) = 398 d * some integer = 398 checking all options only ( c ) syncs with it . answer c
Answer: c
Question (gain): if 30 % of a number is 12.6 , find the number ?
Options: a ) 42 , b ) 40 , c ) 26 , d ) 36 , e ) 66
Rationale: "a 40"
Answer: a
Question (general): 5 + 3
Options: a ) 8 , b ) 13 , c ) 28 , d ) 6 , e ) 2
Rationale: a
Answer: a
Question (general): find the number , difference between number and its 3 / 5 is 60 .
Options: a ) 150 , b ) 153 , c ) 154 , d ) 155 , e ) 156
Rationale: "explanation : let the number = x , then , x - ( 3 / 5 ) x = 60 , = > ( 2 / 5 ) x = 60 = > 2 x = 60 * 5 , = > x = 150 answer : option a"
Answer: a
Question (physics): x can do a piece of work in 40 days . he works at it for 8 days and then y finished it in 16 days . how long will y take to complete the work ?
Options: a ) 10 , b ) 12 , c ) 15 , d ) 18 , e ) 20
Rationale: "work done by x in 8 days = 8 * 1 / 40 = 1 / 5 remaining work = 1 - 1 / 5 = 4 / 5 4 / 5 work is done by y in 16 days whole work will be done by y in 16 * 5 / 4 = 20 days answer is e"
Answer: e
Question (general): a positive number x is multiplied by 3 , and this product is then divided by 3 . if the positive square root of the result of these two operations equals x , what is the value of x ?
Options: a ) 9 / 4 , b ) 3 / 2 , c ) 4 / 3 , d ) 2 / 3 , e ) 1 / 2
Rationale: "we need to produce an equation from the information given in the problem stem . we are first given that x is multiplied by 2 and then the product is divided by 3 . this gives us : 2 x / 3 next we are given that the positive square root of the result ( which is 2 x / 3 ) is equal to x . this gives us √ ( 2 x / 3 ) = x 2 x / 3 = x ^ 2 2 x = 3 x ^ 2 3 x ^ 2 – 2 x = 0 x ( 3 x – 2 ) = 0 x = 0 or 3 x – 2 = 0 3 x = 2 x = 4 / 3 because x is positive , x = 4 / 3 . the answer is c ."
Answer: c
Question (physics): 10 men do a work in 10 days . how many men are needed to finish the work in 4 days ?
Options: a ) 25 , b ) 20 , c ) 30 , d ) 10 , e ) 15
Rationale: "men required to finish the work in 4 days = 10 * 10 / 4 = 25 answer is a"
Answer: a
Question (physics): a trader sells 80 meters of cloth for rs . 6900 at the profit of rs . 20 per metre of cloth . what is the cost price of one metre of cloth ?
Options: a ) 22 , b ) 75 , c ) 90 , d ) 78 , e ) 66
Rationale: "sp of 1 m of cloth = 6900 / 80 = rs . 86 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 86 - rs . 20 = rs . 66 . answer : e"
Answer: e
Question (general): during a certain two - week period , 80 percent of the movies rented from a video store were comedies , and of the remaining movies rented , there were 4 times as many dramas as action movies . if no other movies were rented during that two - week period and there were a action movies rented , then how many comedies , in terms of a , were rented during that two - week period ?
Options: a ) 5 a , b ) 15 a , c ) 20 a , d ) 1 / 25 a , e ) 30 a
Rationale: "movies : 80 % comedies . 20 % remaining genre . now in this 20 % , there are only 2 categories . action movies and drama movies . if action = x ; drama movies = 4 x . total 5 x . 5 x = 20 ; x = 4 action movies : 4 % drama movies : 16 % we can say that out of 100 z , : comedies : 80 z action : 4 z drama : 16 z now action movies werea this means : a = 4 z . z = ( a / 4 ) comedies : 80 z = 80 * ( a / 4 ) 20 a c is the answer ."
Answer: c
Question (general): ( 100 x 60 ) + ( 138 x 400 ) = ? x 60
Options: a ) 880 , b ) 550 , c ) 1100 , d ) 1020 , e ) 600
Rationale: "explanation : ? = ( 100 x 60 ) + ( 138 x 400 ) / 60 = 6000 + 55200 / 60 = 1020 answer : option d"
Answer: d
Question (physics): the speed of the boat in still water in 12 kmph . it can travel downstream through 42 kms in 3 hrs . in what time would it cover the same distance upstream ?
Options: a ) 8 hours , b ) 6 hours , c ) 4.2 hours , d ) 5 hours , e ) 6 hours
Rationale: "still water = 12 km / hr downstream = 42 / 3 = 14 km / hr upstream = > > still water = ( u + v / 2 ) = > > 12 = u + 14 / 2 = 10 km / hr so time taken in upstream = 42 / 10 = 4.2 hrs answer : c"
Answer: c
Question (general): tickets numbered from 1 to 20 are mixed and then a ticket is selected randomly . what is the probability that the selected ticket bearsa number which is a multiple of 3 ?
Options: a ) 1 / 5 , b ) 2 / 5 , c ) 3 / 10 , d ) 3 / 7 , e ) 1 / 7
Rationale: "here , s = [ 1 , 2 , 3 , 4 , … . , 19 , 20 ] let e = event of getting a multiple of 3 = [ 3 , 6 , 9 , 12 , 15 , 18 ] p ( e ) = n ( e ) / n ( s ) = 6 / 20 = 3 / 10 c"
Answer: c
Question (general): two equally sized jugs full of water are each emptied into two separate unequally sized empty jugs , x and y . now , jug x is 1 / 4 full , while jug y is 2 / 3 full . if water is poured from jug x into jug y until jug y is filled , what fraction of jug x then contains water ?
Options: a ) 0 , b ) 1 / 15 , c ) 2 / 15 , d ) 1 / 8 , e ) 2 / 10
Rationale: "suppose the water in each jug is l liters cx x ( 1 / 4 ) = l cx = 4 l liters cx is capacity of x cy x ( 2 / 3 ) = l cy = 3 l / 2 liters cy is capacity of y now , y is 3 l / 2 - l empty = l / 2 empty so , we can put only l / 2 water in jug y from jug x jug x ' s remaining water = l - l / 2 = l / 2 fraction of x which contains water = water / cx = ( l / 2 ) / 4 l = 1 / 8 answer will be d"
Answer: d
Question (physics): harry started a 6 - mile hike with a full 7 - cup canteen of water and finished the hike in 2 hours with 1 cup of water remaining in the canteen . if the canteen leaked at the rate of 1 cup per hour and harry drank 1 cups of water during the last mile , how many cups did he drink per mile during the first 5 miles of the hike ?
Options: a ) 1 / 5 , b ) 2 / 3 , c ) 1 / 3 , d ) 3 / 5 , e ) 4 / 5
Rationale: "a . no of cups leaked during the trip = 2 cups . no of cups harry drank = 4 cups . no of cups harry drank during the first 5 miles = 4 . drink / mile = 4 / 5 answer : e"
Answer: e
Question (general): the average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 60 kg . what is the correct weight ?
Options: a ) 58.6 kgs , b ) 58.85 kgs , c ) 58.95 kgs , d ) 59 kgs , e ) 59.85 kgs
Rationale: actual total weight is ( 20 x 58.4 - 56 + 60 ) = 1172 kgs actual average weight is 1172 / 20 = 58.6 kgs a
Answer: a
Question (general): hillary and eddy are climbing to the summit of mt . everest from a base camp 4,700 ft from the summit . when they depart for the summit at 06 : 00 , hillary climbs at a rate of 800 ft / hr with eddy lagging behind at a slower rate of 500 ft / hr . if hillary stops 700 ft short of the summit and then descends at a rate of 1,000 ft / hr , at what time do hillary and eddy pass each other on her return trip ?
Options: a ) 14.0 , b ) 13.0 , c ) 12.0 , d ) 11.0 , e ) 10.0
Rationale: "solution : h stopped 700 ft before reaching the final point , time taken to reach 4000 ft = 4000 / 800 = 5 hrs . this means she reached there at 11 : 00 . speed difference between them is 800 - 500 = 300 ft / hr so by the time h stops they have 1500 ft of distance so now here we use relative speed formula they both are travelling toward each other with speed of 1000 and 500 total 1500 ft / hr and distance bwn them is 1500 ft so time taken to meet = 1 hr from 11 : 00 means 12 : 00 is the answer . c"
Answer: c
Question (general): p and q are the only two applicants qualified for a short - term research project that pays 420 dollars in total . candidate p has more experience and , if hired , would be paid 50 percent more per hour than candidate q would be paid . candidate q , if hired , would require 10 hours more than candidate p to do the job . candidate p ’ s hourly wage is how many dollars greater than candidate q ’ s hourly wage ?
Options: a ) $ 3 , b ) $ 5 , c ) $ 7 , d ) $ 9 , e ) $ 11
Rationale: let q ' s hourly wage be x , then p ' s hourly wage is 1.5 x let t be the number of hours that q needs , then p needs t - 10 hours to do the job . since they both are paid an equal total amount of $ 420 : x * t = 1.5 x * ( t - 10 ) t = 30 hours and q ' s hourly wage is 420 / 30 = $ 14 p ' s hourly wage is 420 / ( t - 10 ) = $ 21 which is $ 7 per hour more . the answer is c .
Answer: c
Question (general): log ( a ( a ( a ) ^ 1 / 4 ) ^ 1 / 4 ) ^ 1 / 4 here base is a .
Options: a ) 0 , b ) 21 / 64 , c ) 1 , d ) 22 / 63 , e ) 23 / 65
Rationale: log ( a ( a ( a ^ 1 / 4 ) ^ 1 / 4 ) ^ 1 / 4 = > log ( a ( a ^ 1 + 1 / 4 ) ^ 1 / 4 ) ^ 1 / 4 = > log ( a ( a ^ 5 / 4 ) ^ 1 / 4 ) ^ 1 / 4 = > log ( a ( a ^ 5 / 16 ) ^ 1 / 4 = > log ( a ^ 1 + 5 / 16 ) ^ 1 / 4 = > log ( a ^ 21 / 16 ) ^ 1 / 4 = > log ( a ^ 21 / 64 ) = > 21 / 64 log ( a ) = > 21 / 64 answer : b
Answer: b
Question (general): rahul is 30 years older than his daughter mary . in 20 years rahul will be twice as old as mary . what is mary current age .
Options: a ) 12 , b ) 14 , c ) 10 , d ) 16 , e ) 18
Rationale: now : mary = x , rahul = x + 30 in 20 years mary = x + 20 , rahul = x + 30 + 20 or 2 ( x + 20 ) x + 30 + 20 = 2 ( x + 20 ) x + 50 = 2 x + 40 50 - 40 = 2 x - x x = 10 mary is 10 years old answer : c
Answer: c
Question (geometry): a rectangular field has to be fenced on three sides leaving a side of 2020 feet uncovered . if the area of the field is 680680 sq . feet , how many feet of fencing will be required ?
Options: a ) 95 , b ) 92 , c ) 88 , d ) 82 , e ) 80
Rationale: "explanation : area of the field = 680 sq . feet . length of the adjacent sides are 20 feet and 680 / 20 = 34 feet . required length of the fencing = 20 + 34 + 34 = 88 feet answer : option c"
Answer: c
Question (gain): if a lends rs . 3500 to b at 10 % per annum and b lends the same sum to c at 13 % per annum then the gain of b in a period of 3 years is ?
Options: a ) 320 , b ) 300 , c ) 310 , d ) 315 , e ) 330
Rationale: "( 3500 * 3 * 3 ) / 100 = > 315 answer : d"
Answer: d
Question (probability): what is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular 11 - sided polygon ) ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 8 , e ) 1 / 11
Rationale: "from any vertex , there are two vertices on sides , which do not make a diagonal but a side . so the remaining n - 3 vertices make diagonals . there are 2 of these diagonals which are the shortest . the probability of choosing one of the shortest diagonals is 2 / 8 = 1 / 4 . the answer is c ."
Answer: c
Question (gain): a particular store purchased a stock of turtleneck sweaters and marked up its cost by 20 % . during the new year season , it further marked up its prices by 25 % of the original retail price . in february , the store then offered a discount of 6 % . what was its profit on the items sold in february ?
Options: a ) 27.5 % , b ) 30 % , c ) 35 % , d ) 37.5 % , e ) 41 %
Rationale: "assume the total price = 100 x price after 20 % markup = 120 x price after 25 % further markup = 1.25 * 120 x = 150 x price after the discount = 0.94 * 150 x = 141 x hence total profit = 41 % option e"
Answer: e
Question (physics): the perimeter of a semi circle is 144 cm then the radius is ?
Options: a ) 22
b ) 28
c ) 99
d ) 77
e ) 16
Rationale: 36 / 7 r = 144 = > r = 28 answer : b
Answer: b
Question (geometry): find the area of the square , one of whose diagonals is 3.8 m long ?
Options: a ) 7.22 m ^ 2
b ) 3.86 m ^ 2
c ) 8.96 m ^ 2
d ) 2.68 m ^ 2
e ) 7.89 m ^ 2
Rationale: area of the square = 1 / 2 ( diagonal ) ^ 2 = ( 1 / 2 * 3.8 * 3.8 ) m ^ 2 = 7.22 m ^ 2 answer ( a )
Answer: a
Question (gain): in an election between two candidates , the winner has a margin of 10 % of the votes polled . if 1500 people change their mind and vote for the loser , the loser would have won by a margin of 10 % of the votes polled . find the total number of votes polled in the election ?
Options: a ) 30,000 , b ) 15,450 , c ) 45,000 , d ) 60,000 , e ) 15,000
Rationale: "total # of votes cast = 100 x , out of these , let the # of votes won by the winner = w , and for the loser ( l ) = 100 x - w . given that w - ( 100 x - w ) = 10 % of total votes cast = 10 x thus , 2 w - 100 x = 10 x → → w = 55 x and l = 100 x - 55 x = 45 x . according to the new condition , if the loser had won 45 x + 1500 votes , then , ( 45 x + 1500 ) - ( 55 x - 1500 ) = 10 % of total votes cast = 10 x thus , 3000 = 20 x and 100 x = 15000 answer : e"
Answer: e
Question (general): in a certain game of dice , the player ’ s score is determined as a sum of three throws of a single die . the player with the highest score wins the round . if more than one player has the highest score , the winnings of the round are divided equally among these players . if john plays this game against 22 other players , what is the probability of the minimum score that will guarantee john some monetary payoff ?
Options: a ) 41 / 50 , b ) 1 / 216 , c ) 1 / 221 , d ) 1 / 84 , e ) 1 / 42
Rationale: "to guarantee that john will get some monetary payoff he must score the maximum score of 6 + 6 + 6 = 18 , because if he gets even one less than that so 17 , someone can get 18 and john will get nothing . p ( 18 ) = 1 / 6 ^ 3 = 1 / 216 . answer : b ."
Answer: b
Question (general): line m lies in the xy - plane . the y - intercept of line m is - 2 , and line m passes through the midpoint of the line segment whose endpoints are ( 2 , 8 ) and ( 8 , - 2 ) . what is the slope of line m ?
Options: a ) - 2 , b ) - 1 , c ) 0 , d ) 1 , e ) 2
Rationale: "the midpoint of ( 2,8 ) and ( 8 , - 2 ) is ( 5,3 ) . the slope of a line through ( 0 , - 2 ) and ( 5,3 ) is ( 3 - ( - 2 ) ) / ( 5 - 0 ) = 5 / 5 = 1 the answer is d ."
Answer: d
Question (gain): the sale price sarees listed for rs . 340 after successive discount is 20 % and 15 % is ?
Options: a ) 298 , b ) 231 , c ) 342 , d ) 876 , e ) 291
Rationale: "340 * ( 80 / 100 ) * ( 85 / 100 ) = 231 answer : b"
Answer: b
Question (general): what is 5 + 7
Options: a ) 2 , b ) 4 , c ) 10 , d ) 12 , e ) 11
Rationale: d
Answer: d
Question (physics): a train crosses a platform of 100 m in 15 sec , same train crosses another platform of length 250 m in 20 sec . then find the length of the train ?
Options: a ) 150 , b ) 88 , c ) 77 , d ) 62 , e ) 350
Rationale: "length of the train be â € ˜ x â € ™ x + 100 / 15 = x + 250 / 20 4 x + 400 = 3 x + 750 x = 350 m answer : e"
Answer: e
Question (general): if 0.75 : x : : 5 : 9 , then x is equal to :
Options: a ) 1.12 , b ) 1.16 , c ) 1.2 , d ) 1.35 , e ) none of these
Rationale: "explanation : ( x * 5 ) = ( 0.75 * 9 ) x = 6.75 / 5 = 1.35 answer : d"
Answer: d
Question (general): in the xy - plane , the point ( 3 , 1 ) is the center of a circle . the point ( 3 , - 2 ) lies inside the circle and the point ( - 2 , 1 ) lies outside the circle . if the radius r of the circle is an integer , then r =
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "an easy way to solve this question will be just to mark the points on the coordinate plane . you ' ll see that the distance between the center ( 3 , 1 ) and the point inside the circle ( 3 , - 2 ) is 3 units ( both points are on x = 3 line so the distance will simply be 1 - ( - 2 ) = 3 ) so the radius must be more than 3 units . the distance between the center ( 3,1 ) and the point outside the circle ( - 2,1 ) is 5 units ( both points are on y = 1 line so the distance will simply be 3 - ( - 2 ) = 5 ) so the radius must be less than 5 units , which implies 3 < r < 5 , thus as r is an integer then r = 4 . answer : c ."
Answer: c
Question (general): s ( n ) is a n - digit number formed by attaching the first n perfect squares , in order , into one integer . for example , s ( 1 ) = 1 , s ( 2 ) = 14 , s ( 3 ) = 149 , s ( 4 ) = 14916 , s ( 5 ) = 1491625 , etc . how many digits t are in s ( 99 ) ?
Options: a ) t = 350 , b ) t = 353 , c ) t = 354 , d ) t = 356 , e ) 357
Rationale: "focus on the points where the number of digits in squares change : 1 , 2 , 3 - single digit squares . first 2 digit number is 10 . 4 , 5 , . . . 9 - two digit squares . to get 9 , the last number with two digit square , think that first 3 digit number is 100 which is 10 ^ 2 . so 9 ^ 2 must be the last 2 digit square . 10 , 11 , 12 , . . . 31 - three digit squares . to get 31 , think of 1000 - the first 4 digit number . it is not a perfect square but 900 is 30 ^ 2 . 32 ^ 2 = 2 ^ 10 = 1024 , the first 4 digit square . 32 - 99 - four digit squares . to get 99 , think of 10,000 - the first 5 digit number which is 100 ^ 2 . so number of digits in s ( 99 ) = 3 * 1 + 6 * 2 + 22 * 3 + 68 * 4 = 3 + 12 + 66 + 272 = 353 . b"
Answer: b
Question (general): you have been given a physical balance and 7 weights of 57 , 55 , 45 , 44 , 43 , 41 and 85 kgs . keeping weights on one pan and object on the other , what is the maximum you can weigh less than 199 kgs .
Options: a ) 198 , b ) 195 , c ) 196 , d ) 197 , e ) 200
Rationale: "85 + 55 + 57 = 197 answer : d"
Answer: d
Question (general): the average age of 7 men increases by 4 years when two women are included in place of two men of ages 26 and 30 years . find the average age of the women ?
Options: a ) 42 , b ) 40 , c ) 30 , d ) 18 , e ) 11
Rationale: "explanation : 26 + 30 + 7 * 4 = 84 / 2 = 42 answer : a"
Answer: a
Question (geometry): what is the area of the square with the following coordinates : ( x , y ) , ( 20 , 20 ) , ( 20 , 9 ) , ( x , 9 ) ?
Options: a ) 121
b ) 132
c ) 144
d ) 156
e ) 169
Rationale: to find the area of a square , knowing the length of one side is sufficient . from the coordinates given , we can see that one side equals 11 . the area is 11 * 11 = 121 . the answer is a .
Answer: a
Question (general): 450.271 + 369.422 ÷ 0.03 - 108.612 x 2.001 = ?
Options: a ) 12980 , b ) 12532 , c ) 12610 , d ) 12430 , e ) 12560
Rationale: "explanation : ? = 450.271 + ( 369.422 ÷ 0.03 ) - ( 108.612 x 2.001 ) ≈ 450 + 369 / 0.03 - ( 109 x 2 ) ≈ 450 + 12300 - 218 ≈ 12532 answer : option b"
Answer: b
Question (general): how many 3 - digit numerals begin with a digit that represents a prime number ?
Options: a ) 16 , b ) 80 , c ) 400 , d ) 180 , e ) 240
Rationale: prime digits 2 , 35 and 7 . three digit numbers _ _ _ 1 st place can be filled in 4 ways 2 nd place can be filled in 10 ways 3 rd place can be filled in 10 ways total = 4 * 10 * 10 = 400 ans : c
Answer: c