Cheukting/mathqa huggingface dataset:
Question (physics): how many seconds will a 800 m long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?
Options: a ) 11 , b ) 30 , c ) 99 , d ) 48 , e ) 61
Rationale: speed of train relative to man = 63 - 3 = 60 km / hr . = 60 * 5 / 18 = 50 / 3 m / sec . time taken to pass the man = 800 * 3 / 50 = 48 sec . answer : d
Answer: d
Question (gain): a man cheats while buying as well as while selling . while buying he takes 10 % more than what he pays for and while selling he gives 20 % less than what he claims to . find the profit percent , if he sells at 13 % below the cost price of the claimed weight .
Options: a ) 19.63 % , b ) 20 % , c ) 37.5 % , d ) 25 % , e ) 37.5 %
Rationale: "there is a one step calculation method too . it requires more thought but is faster . the man takes 10 % more than what he pays for . so if he claims to take 100 pounds , he pays $ 100 but he actually takes 110 pounds for which he will take from the customer $ 110 . hence , in effect , there is a 10 % mark up . while selling , he sells 20 % less . this means , he claims to sell 100 pounds and gets $ 100 but actually sells only 80 pounds and should have got only $ 80 for it . so this is again a mark up of $ 20 on $ 80 which is 25 % . but he also sells at 13 % less ( 1 + m 1 % ) ( 1 + m 2 % ) ( 1 - d % ) = ( 1 + p % ) 11 / 10 * 5 / 4 * 87 / 100 = ( 1 + p % ) profit % = 19.63 % a"
Answer: a
Question (general): if log 64 = 1.8061 , then the value of log 16 will be ( approx ) ?
Options: a ) 1.204 , b ) 1.9874 , c ) 1.3564 , d ) 1.2547 , e ) 1.6547
Rationale: "log 64 = 1.8061 log 4 ^ 3 = 1.8061 log 4 = 0.6020 2 log 4 = 1.2040 log 4 ^ 2 = 1.2040 log 16 = 1.2040 ( approx ) answer a"
Answer: a
Question (general): the student manager of the university theater estimated that for every 6 movie tickets sold on valentine ' s weekend , the theater will sell 3 packs of grain crackers at $ 2.25 each , 4 bottles of a beverage at $ 1.50 each , and 4 chocolate bars at $ 1.00 each . find the approximate average ( arithmetic mean ) amount of estimated snack sales per movie ticket sold .
Options: a ) $ 1.40 , b ) $ 1.58 , c ) $ 2.00 , d ) $ 2.64 , e ) $ 2.79
Rationale: 3 * 2.25 + 4 * 1.50 + 4 * 1 = 6.75 + 6 + 4 = 16.75 . this is the sale for 6 tickets avg sale per ticket : 16.75 / 6 = $ 2 . 79 answer : e
Answer: e
Question (general): the sum of the ages of 5 children born at the intervals of 4 years each is 50 years . what is the age of the eldest child ?
Options: a ) 15 , b ) 8 , c ) 18 , d ) none of these , e ) can not be determined
Rationale: "explanation : let x = the youngest child . each of the other four children will then be x + 4 , x + 8 , x + 12 , x + 16 . we know that the sum of their ages is 50 . so , x + ( x + 4 ) + ( x + 8 ) + ( x + 12 ) + ( x + 16 ) = 50 x = 2 the youngest child is 2 years old . age of eldest child is = 2 + 16 = 18 answer : c"
Answer: c
Question (physics): a 28 cm long wire is to be cut into two pieces so that one piece will be 2.00001 / 5 th of the other , how many centimeters will the shorter piece be ?
Options: a ) 12 , b ) 8 , c ) 88 , d ) 77 , e ) 14
Rationale: "1 : 2 / 5 = 5 : 2 2 / 7 * 28 = 8 answer : b"
Answer: b
Question (general): eighteen years ago , a father was 3 times as old as his son . now the father is only twice as old as his son . then the sum of the present ages of the son and the father is :
Options: a ) 120 , b ) 76 , c ) 108 , d ) 105 , e ) 86
Rationale: let the present ages of the father and son be 2 x and x years respectively . then , ( 2 x - 18 ) = 3 ( x - 18 ) x = 36 . required sum = ( 2 x + x ) = 3 x = 108 years . answer is c
Answer: c
Question (gain): the banker ' s gain on a sum due 6 years hence at 12 % per annum is rs . 828 . what is the banker ' s discount ?
Options: a ) 1240 , b ) 1120 , c ) 1190 , d ) 1978 , e ) none of these
Rationale: "explanation : td = ( bg × 100 ) / tr = ( 828 × 100 ) / ( 6 × 12 ) = rs . 1150 bg = bd – td = > 828 = bd - 1150 = > bd = 1978 answer : option d"
Answer: d
Question (physics): a runner runs the 40 miles from marathon to athens at a constant speed . halfway through the run she injures her foot , and continues to run at half her previous speed . if the second half takes her 12 hours longer than the first half , how many hours did it take the runner to run the second half ?
Options: a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 28
Rationale: "the runner runs the first 20 miles at speed v and the second 20 miles at speed v / 2 . the time t 2 to run the second half must be twice the time t 1 to run the first half . t 2 = 2 * t 1 = t 1 + 12 t 1 = 12 and so t 2 = 24 . the answer is c ."
Answer: c
Question (physics): the racing magic takes 40 seconds to circle the racing track once . the charging bull makes 40 rounds of the track in an hour . if they left the starting point together , how many minutes will it take for them to meet at the starting point for the second time ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: "time taken by racing magic to make one circle = 40 seconds time taken bycharging bullto make one circle = 60 mins / 40 = 1.5 mins = 90 seconds lcm of 90 and 40 seconds = 360 seconds = 6 mins time taken for them to meet at the starting point for the second time = 6 mins * 2 = 12 mins answer d"
Answer: d
Question (physics): every day daniel drives 96 miles back from work . on sunday , daniel drove all the way back from work at a constant speed of x miles per hour . on monday , daniel drove the first 32 miles back from work at ( 2 x ) miles per hour , and the rest of the way at ( x / 2 ) miles per hour . the time it took daniel to drive back from work on monday is longer than the time it took him to drive back from work on sunday by what percent ?
Options: a ) 10 % , b ) 20 % , c ) 30 % , d ) 40 % , e ) 50 %
Rationale: "let ' s test x = 4 . . . . on sunday , daniel drove 96 miles at 4 miles / hour . d = ( r ) ( t ) 96 = ( 4 ) ( t ) 96 / 4 = 24 = t it takes 24 hours to drive home on monday , daniel drove the first 32 miles at ( 2 ) ( 4 ) = 8 miles / hour and the rest of the way ( 64 miles ) at 4 / 2 = 2 miles / hour d = ( r ) ( t ) 32 = ( 8 ) ( t ) 32 / 8 = 4 = t it takes 4 hours for the first part d = ( r ) ( t ) 64 = ( 2 ) ( t ) 64 / 2 = 32 = t it takes 32 hours for the second part total time to drive home on monday = 4 + 32 = 36 hours we ' re asked by what percent 36 hours is greater than 32 hours . 36 / 32 = 1.5 , so it is 50 % greater . e"
Answer: e
Question (physics): a train running at the speed of 108 km / hr crosses a pole in 7 seconds . find the length of the train .
Options: a ) 150 meter , b ) 145 meter , c ) 140 meter , d ) 135 meter , e ) 210 meter
Rationale: "explanation : speed = 108 * ( 5 / 18 ) m / sec = 30 m / sec length of train ( distance ) = speed * time = 30 * 7 = 210 meter option e"
Answer: e
Question (physics): a train crosses a bridge of length 2500 m in 120 seconds and a lamp post on the bridge in 30 seconds . what is the length of the train in metres ?
Options: a ) 375 m , b ) 750 / 3 m , c ) 2500 / 3 m , d ) 800 m , e ) 300 m
Rationale: "let length of train = l case - 1 : distance = 2500 + l ( while crossing the bridge ) time = 120 seconds i . e . speed = distance / time = ( 2500 + l ) / 120 case - 2 : distance = l ( while passing the lamp post ) time = 30 seconds i . e . speed = distance / time = ( l ) / 30 but since speed has to be same in both cases so ( 2500 + l ) / 120 = ( l ) / 30 i . e . 4 l = 2500 + l i . e . 3 l = 2500 i . e . l = 2500 / 3 answer : option c"
Answer: c
Question (general): find the sum of all odd number upto 250 .
Options: a ) 15345 , b ) 15645 , c ) 15625 , d ) 15342 , e ) 15683
Rationale: "explanation : number of odd numbers upto 250 = n / 2 = 250 / 2 = 125 sum of first 125 odd numbers = ( 125 ) 2 = 15625 answer : option c"
Answer: c
Question (physics): a wooden box of dimensions 8 m x 7 m x 6 m is to carry rectangularboxes of dimensions 2 cm x 7 cm x 3 cm . the maximum number ofboxes that can be carried in the wooden box , is
Options: a ) 8000000 , b ) 1000000 , c ) 7500000 , d ) 1200000 , e ) none of these
Rationale: explanation : number = ( 800 * 700 * 600 ) / 2 * 7 * 3 = 8000000 answer : a
Answer: a
Question (physics): x can finish a work in 18 days . y can finish the same work in 15 days . yworked for 5 days and left the job . how many days does x alone need to finish the remaining work ?
Options: a ) 12 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: work done by x in 1 day = 1 / 18 work done by y in 1 day = 1 / 15 work done by y in 5 days = 5 / 15 = 1 / 3 remaining work = 1 – 1 / 3 = 2 / 3 number of days in which x can finish the remaining work = ( 2 / 3 ) / ( 1 / 18 ) = 12 a
Answer: a
Question (physics): the diameter of the wheel of a car is 120 m . how many revolution / min mustthe wheel makeing order to keep a speed of 60 km / hour approximately ?
Options: a ) 140 , b ) 160 , c ) 220 , d ) 250 , e ) 265
Rationale: "distance to be covered in 1 min . = ( 60 x 1000 ) / ( 60 ) m = 1000 m . circumference of the wheel = ( 2 x ( 22 / 7 ) x 0.60 ) m = 3.77 m . number of revolutions per min . = ( 1000 / 3.77 ) = 265 e"
Answer: e
Question (physics): a and b together can do a work in 5 days . if a alone can do it in 15 days . in how many days can b alone do it ?
Options: a ) 10 , b ) 99 , c ) 7.5 , d ) 55 , e ) 21
Rationale: "1 / 5 – 1 / 15 = 2 / 15 = > 7.5 answer : c"
Answer: c
Question (general): if a coin has an equal probability of landing heads up or tails up each time it is flipped , what is the probability that the coin will land heads up exectly twice in 3 consecutive flips ?
Options: a ) 0.125 , b ) 0.25 , c ) 0.375 , d ) 0.5 , e ) 0.666
Rationale: "p = ncm * p ^ m * q ^ ( n - m ) n - the total number of trials . m - the number of trials with heads . n - m - the number of trials with tails . p - probability of heads . q - probability of tails . p = 3 c 2 * ( 1 / 2 ) ^ 2 * ( 1 / 2 ) ^ 1 = 3 / 8 = 0.375 answer : c"
Answer: c
Question (physics): the length of the bridge , which a train 110 metres long and travelling at 45 km / hr can cross in 30 seconds , is :
Options: a ) 230 , b ) 240 , c ) 245 , d ) 250 , e ) 265
Rationale: "speed = [ 45 x 5 / 18 ] m / sec = [ 25 / 2 ] m / sec time = 30 sec let the length of bridge be x metres . then , ( 110 + x ) / 30 = 25 / 2 = > 2 ( 110 + x ) = 750 = > x = 265 m . answer : option e"
Answer: e
Question (physics): one hour after yolanda started walking from x to y , a distance of 40 miles , bob started walking along the same road from y to x . if yolanda â s walking rate was 2 miles per hour and bob â s was 4 miles per hour , how many miles had bob walked when they met ?
Options: a ) 24 , b ) 23.5 , c ) 22 , d ) 21.2 , e ) 25.32
Rationale: "let t be the number of hours that bob had walked when he met yolanda . then , when they met , bob had walked 4 t miles and yolanda had walked 2 ( t + 1 ) miles . these distances must sum to 40 miles , so 4 t + 2 ( t + 1 ) = 40 , which may be solved for t as follows 4 t + 2 ( t + 1 ) = 40 4 t + 2 t + 2 = 40 6 t = 38 t = 6.33 ( hours ) therefore , bob had walked 4 t = 4 ( 7.6 ) = 25.32 miles when they met . the best answer is e ."
Answer: e
Question (general): 23 , 29 , 31 , 37 , 41 , 43 , 47 , 53 , ( . . . )
Options: a ) 53 , b ) 47 , c ) 48 , d ) 59 , e ) 45
Rationale: "explanation : all are prime numbers in their order , starting from 23 hence , next number is 59 answer : d"
Answer: d
Question (gain): what is the rate percent when the simple interest on rs . 800 amount to rs . 160 in 4 years ?
Options: a ) 5 % , b ) 7 % , c ) 9 % , d ) 2 % , e ) 4 %
Rationale: "160 = ( 180 * 4 * r ) / 100 r = 5 % answer : a"
Answer: a
Question (physics): a and b can do a piece of work in 4 2 / 3 days and 5 days respectively . they work together for 1 days and then a leaves . in how many days after that b will complete the work alone .
Options: a ) 3.92 days , b ) 1.92 days , c ) 2.12 days , d ) 2.02 days , e ) 2.92 days
Rationale: 3 / 14 * 1 + ( 1 + x ) / 5 = 1 x = 2.92 days answer : e
Answer: e
Question (geometry): a semicircle is drawn with ab as its diameter . from c , a point on ab , a line perpendicular to ab is drawn , meeting the circumference of the semicircle at d . given that ac = 2 cm and cd = 6 cm , the area of the semicircle in square cm will be ?
Options: a ) 30 pi
b ) 40 pi
c ) 50 pi
d ) 60 pi
e ) 70 pi
Rationale: let o be center of circle and radius be x . c can be anywhere on ab . let us suppose that c is somewhere between a and o . ac = 2 cm . . . . so co = ( x - 2 ) do = x , cd = 6 cm cdo form a right angled triangle with right angle at c . using pythagoras theorem , x ^ 2 = 6 ^ 2 + ( x - 2 ) ^ 2 4 x = 40 x = 10 cm area = [ pi ( x ) ^ 2 ] / 2 area = 50 pi answer : c
Answer: c
Question (physics): two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 24 hours and 8 hours respectively . the ratio of their speeds is
Options: a ) 4 : 9 , b ) 4 : 3 , c ) 1 : 3 , d ) 4 : 8 , e ) 4 : 5
Rationale: let us name the trains as a and b . then , ( a ' s speed ) : ( b ' s speed ) = b : a = 8 : 24 = 1 : 3 . answer : c
Answer: c
Question (physics): length of a rectangular plot is 20 mtr more than its breadth . if the cost of fencin gthe plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ?
Options: a ) 50 m , b ) 60 m , c ) 65 m , d ) 75 m , e ) 80 m
Rationale: "let breadth = x metres . then , length = ( x + 20 ) metres . perimeter = 5300 m = 200 m . 26.50 2 [ ( x + 20 ) + x ] = 200 2 x + 20 = 100 2 x = 80 x = 40 . hence , length = x + 20 = 60 m b"
Answer: b
Question (physics): a train is running at a speed of 40 km / hr and it crosses a post in 17.1 seconds . what is the length of the train ?
Options: a ) 190 metres , b ) 160 metres , c ) 200 metres , d ) 120 metres , e ) 250 metres
Rationale: "speed of the train , v = 40 km / hr = 40000 / 3600 m / s = 400 / 36 m / s time taken to cross , t = 17.1 s distance covered , d = vt = ( 400 / 36 ) ã — 17.1 = 190 m distance covered is equal to the length of the train = 190 m correct answer is 190 metres a"
Answer: a
Question (general): of the 160 people at a party , 70 were women , and 50 women tried the appetizer . if 50 people did not try the appetizer , what is the total number of men who tried the appetizer ?
Options: a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80
Rationale: "total people at party = 160 women = 70 so men 160 - 70 = 90 no . of pple who tried appetizer = 160 - 50 ( given info ) = 110 no of women who tried appetizer = 50 so remaining ppl ( men ) who tried the appetizer = 110 - 50 = 60 correct option c"
Answer: c
Question (physics): a 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 20 sec . what is the length of the platform ?
Options: a ) 389 m , b ) 350 m , c ) 285 m , d ) 299 m , e ) 219 m
Rationale: "speed = 300 / 20 = 15 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 39 = 15 = > x = 285 m . answer : c"
Answer: c
Question (geometry): a box measuring 49 inches long by 42 inches wide by 14 inches deep is to be filled entirely with identical cubes . no space is to be left unfilled . what is the smallest number of cubes that can accomplish this objective ?
Options: a ) 78 , b ) 82 , c ) 84 , d ) 86 , e ) 88
Rationale: "least number of cubes will be required when the cubes that could fit in are biggest . 7 is the biggest number that could divide all three , 49 , 42 and 14 . thus side of cube must be 7 , and total number of cubes = 49 / 7 * 42 / 7 * 14 / 7 = 84 ans c ."
Answer: c
Question (geometry): the height of cylinder is 14 cm and its diameter is 10 cm . the volume of the cylinder is :
Options: a ) 4400
b ) 2200
c ) 5500
d ) 1100
e ) 3300
Rationale: h = 14 cm and r = 5 cm cylinder volume = π r ( power 2 ) h = ( 22 / 7 × 5 × 5 × 14 ) cm ( power 3 ) = 1100 cm ( power 3 ) answer is d .
Answer: d
Question (general): if 20 liters of chemical x are added to 80 liters of a mixture that is 20 % chemical x and 80 % chemical y , then what percentage of the resulting mixture is chemical x ?
Options: a ) 30 % , b ) 33 % , c ) 36 % , d ) 39 % , e ) 42 %
Rationale: "the amount of chemical x in the solution is 20 + 0.2 ( 80 ) = 36 liters . 36 liters / 100 liters = 36 % the answer is c ."
Answer: c
Question (physics): working together , jose and jane can complete an assigned task in 20 days . however , if jose worked alone and completed half the work and then jane takes over and completes the second half , the task will be completed in 45 days . how long will jose take to complete the task if he worked alone ? assume that jane is more efficient than jose .
Options: a ) 25 days , b ) 30 days , c ) 60 days , d ) 65 days , e ) 36 days
Rationale: "explanatory answer step 1 : assign variables and frame equations let jose take ' x ' days to complete the task if he worked alone . let jane take ' y ' days to complete the task if she worked alone . statement 1 of the question : they will complete the task in 20 days , if they worked together . in 1 day , jose will complete 1 / x of the task . in 1 day , jane will complete 1 / yof the task . together , in 1 day they will complete 1 / 20 of the task . therefore , 1 / x + 1 / y = 1 / 20 . . . . ( 1 ) statement 2 of the question : if jose worked alone and completed half the work and then jane takes over and completes the second half , the task will be completed in 45 days . jose will complete half the task in x / 2 days . jane will complete half the task in y / 2 days . ∴ x / 2 + y / 2 = 45 or , x + y = 90 or x = 90 - y . . . . ( 2 ) step 2 : solve the two equations and find x and y substitute the value of x as ( 90 - y ) in the first equation 1 / 90 − y + 1 / y = 1 / 20 or y 2 - 90 + 1800 = 0 . the quadratic equation factorizes as ( y - 60 ) ( y - 30 ) = 0 so , y = 60 or y = 30 . if y = 60 , then x = 90 - y = 90 - 60 = 30 and if y = 30 , then x = 90 - y = 90 - 30 = 60 . the question clearly states that jane is more efficient than jose . therefore , jane will take lesser time than jose . hence , jose will take 60 days to complete the task if he worked alone and jane will take 30 days to complete the same task . choice c"
Answer: c
Question (other): a certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 3 of 10 candidates eligible to fill 3 identical positions in the computer science department . if none of the candidates is eligible for a position in both departments , how many different sets of 4 candidates are there to fill the 4 positions ?
Options: a ) 420 , b ) 770 , c ) 840 , d ) 165 , e ) 315
Rationale: "1 of 7 will be chosen for the math 3 of 10 will be chosen for the computer none of the 4 chosen people can be in more than one departments . we can choose any of the 7 candidates for the math dep . , which gives as 7 selections . we can choose 3 of the 10 candidates for the computer dep . , which gives us 3 selections and 7 rejections . so , the way to find how many different selections of 2 candidates we can have for the computer dep . , we do : 10 ! / 3 ! * 7 ! = 120 we are multiplying our individual selections : 7 * 120 = 840 in the bolded part , we do n ' t have to multiply all of the numbers , as those in 8 ! are included in 10 ! , so we simplify instead . ans c"
Answer: c
Question (geometry): the volume of a cube is 343 cc . find its surface .
Options: a ) 864 , b ) 556 , c ) 294 , d ) 287 , e ) 267
Rationale: "a 3 = 343 = > a = 7 6 a 2 = 6 * 7 * 7 = 294 answer : c"
Answer: c
Question (physics): a boeing 757 flies a direct route from dallas , tx , to phoenix , az and then returns to dallas , tx . the flight is 900 miles one way . it took 2 hrs and 15 minutes for the flight to phoenix and 2 hrs for the flight back to dallas . what was the speed of the wind in mph ?
Options: a ) 20 mph , b ) 25 mph , c ) 30 mph , d ) 35 mph , e ) 40 mph
Rationale: explanation : change the times in the problem to minutes first . speed of airplane from dallas to phoenix : ( 900 / 135 ) x 60 = 400 mph speed of airplane from phoenix to dallas : ( 900 / 120 ) x 60 = 450 mph wind speed : 1 / 2 ( 450 - 400 ) = 50 / 2 = 25 mph answer : option b
Answer: b
Question (physics): tanks a and b are each in the shape of a right circular cylinder . the interior of tank a has a height of 5 meters and a circumference of 4 meters , and the interior of tank b has a height of 8 meters and a circumference of 10 meters . the capacity of tank a is what percent of the capacity of tank b ?
Options: a ) 10 %
b ) 80 %
c ) 100 %
d ) 120 %
e ) 125 %
Rationale: for a , r = 4 / 2 pi . its capacity = ( 2 pi ) ^ 2 * 5 = 20 pi for b , r = 10 / pi . its capacity = ( 5 pi ) ^ 2 * 8 = 200 pi a / b = 20 pi / 200 pi = 0.1 a
Answer: a
Question (general): he total marks obtained by a student in physics , chemistry and mathematics is 180 more than the marks obtained by him in physics . what is the average mark obtained by him in chemistry and mathematics ?
Options: a ) 55 , b ) 65 , c ) 75 , d ) 85 , e ) 90
Rationale: let the marks obtained by the student in physics , chemistry and mathematics be p , c and m respectively . p + c + m = 180 + p c + m = 180 average mark obtained by the student in chemistry and mathematics = ( c + m ) / 2 = 180 / 2 = 90 . answer : e
Answer: e
Question (general): rahim bought 27 books for rs . 581 from one shop and 20 books for rs . 594 from another . what is the average price he paid per book ?
Options: a ) 28 , b ) 18 , c ) 27 , d ) 25 , e ) 21
Rationale: "average price per book = ( 581 + 594 ) / ( 27 + 20 ) = 1175 / 47 = rs . 25 answer : d"
Answer: d
Question (gain): a , b and c enter into partnership . a invests some money at the beginning , b invests double the amount after 6 months , and c invests thrice the amount after 8 months . if the annual gain be rs . 24000 . a ' s share is ?
Options: a ) 2999 , b ) 8000 , c ) 6000 , d ) 2889 , e ) 6612
Rationale: "x * 12 : 2 x * 6 : 3 x * 4 1 : 1 : 1 1 / 3 * 24000 = 8000 answer : b"
Answer: b
Question (other): the ratio of flour to water to sugar in a recipe is 10 : 6 : 3 . the ratio in a new recipe calls for a doubling of the ratio of flour to water from the original recipe and a halving of the ratio of flour to sugar . if the new recipe calls for 2 cups of water , how much sugar is required ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "the ratio of flour to water is 10 : 3 . the ratio of flour to sugar is 5 : 3 = 10 : 6 . the new ratio of flour to water to sugar is 10 : 3 : 6 if we need 2 cups of water , then we need 4 cups of sugar . the answer is b ."
Answer: b
Question (geometry): an artist wishes to paint a circular region on a square poster that is 4 feet on a side . if the area of the circular region is to be 1 / 2 the area of the poster , what must be the radius of the circular region in feet ?
Options: a ) 1 / pi , b ) sqrt ( 8 / pi ) , c ) 1 , d ) 2 / sqrt ( pi ) , e ) pi / 2
Rationale: "area of the poster is 4 x 4 = 16 1 / 2 the area = 8 pi * r ^ 2 = 8 r ^ 2 = 8 / pi r = sqrt ( 8 / pi ) answer : c"
Answer: c
Question (general): the smallest number which when diminished by 4 , is divisible by 12 , 16 , 18 , 21 and 28 is
Options: a ) 1008 , b ) 1012 , c ) 1022 , d ) 1032 , e ) 1043
Rationale: "required number = ( l . c . m of 12 , 16 , 18 , 21,28 ) + 4 = 1008 + 4 = 1012 answer : b"
Answer: b
Question (other): two numbers are in the ratio 3 : 5 . if 9 is subtracted from each , the new numbers are in the ratio 12 : 23 . the smaller number is :
Options: a ) 15 , b ) 33 , c ) 58 , d ) 56 , e ) 91
Rationale: "let the numbers be 3 x and 5 x . then , ( 3 x - 9 ) / ( 5 x - 9 ) = 12 / 23 9 x = 99 = > x = 11 the smallest number = 3 * 11 = 33 . answerb"
Answer: b