Cheukting/mathqa huggingface dataset:
Question (physics): a and b can finish a work in 10 days while b and c can do it in 18 days . a started the work , worked for 5 days , then b worked for 10 days and the remaining work was finished by c in 15 days . in how many days could c alone have finished the whole work ?
Options: a ) 30 days , b ) 15 days , c ) 45 days , d ) 24 days , e ) none of these
Rationale: let c completes the work in x days . work done by ( a + b ) in 1 day = 1 ⁄ 10 work done by ( b + c ) in 1 day = 1 ⁄ 18 a ’ s 5 days ’ work + b ’ s 10 days ’ work + c ’ s 15 days ’ work = 1 or ( a + b ) ’ s 5 days ’ work + ( b + c ) ’ s 5 days ’ work + c ’ s 10 days ’ work = 1 or 5 ⁄ 10 + 5 ⁄ 18 + 10 ⁄ x = 1 or x = 45 days answer c
Answer: c
Question (physics): a boat running upstream takes 8 hours 48 minutes to cover a certain distance , while it take 4 hours to cover the same distance running downstream . what is the ratio between the speed of the boat and speed of the water current respectively ?
Options: a ) 1 : 3 , b ) 3 : 8 , c ) 6 : 3 , d ) 8 : 3 , e ) none
Rationale: "sol . let the man rate upstream be x kmph and that downstream be y kmph . then , distance coverd upstream in 8 hrs 48 min . = distance coverd downstream in 4 hrs . ⇒ [ x 8 4 / 5 ] = ( y * 4 ) ⇒ 44 / 5 x = 4 y ⇒ y = 11 / 5 x . ∴ required ratio = [ y + x / 2 ] : [ 6 x / 5 * 1 / 2 ] : [ 6 x / 5 * 1 / 2 ] = 8 / 5 : 3 / 5 = 8 : 3 . answer d"
Answer: d
Question (general): if 2 ^ x + 2 ^ y = 10 ^ 0 + 90 ^ 0 , where x and y are non negative integers , what is the greatest possible value of | x â € “ y | ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: | x â € “ y | for x and y 2 ^ x + 2 ^ y = 10 ^ 0 + 90 ^ 0 a . x = y x = y = 0 1 + 1 = 1 + 1 right b . 1 x = 2 , y = 1 4 + 2 = 1 + 1 wrong c . 2 x = 3 , y = 1 8 + 2 = 1 + 1 wrong d . 3 x = 4 , y = 1 16 + 2 = 1 + 1 wrong e . 4 x = 5 , y = 1 32 + 2 = 1 + 1 wrong my answer is a .
Answer: a
Question (general): a certain bus driver is paid a regular rate of $ 16 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 1032 in total compensation , how many total hours did he work that week ?
Options: a ) 36 , b ) 40 , c ) 44 , d ) 48 , e ) 54
Rationale: for 40 hrs = 40 * 16 = 640 excess = 1032 - 640 = 392 for extra hours = . 75 ( 16 ) = 12 + 16 = 28 number of extra hrs = 392 / 28 = 98 / 7 = 14 total hrs = 40 + 14 = 54 answer e 52
Answer: e
Question (physics): find the length of the wire required to go 15 times round a square field containing 69696 m 2 ?
Options: a ) 15840 , b ) 19879 , c ) 27997 , d ) 15842 , e ) 15823
Rationale: "a 2 = 69696 = > a = 264 4 a = 1056 1056 * 15 = 15840 answer : a"
Answer: a
Question (general): p , q and r have rs . 7000 among themselves . r has two - thirds of the total amount with p and q . find the amount with r ?
Options: a ) rs . 3000 , b ) rs . 3600 , c ) rs . 2400 , d ) rs . 2800 , e ) none of these
Rationale: "let the amount with r be rs . r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 7000 - r ) = > 3 r = 14000 - 2 r = > 5 r = 14000 = > r = 2800 . answer : d"
Answer: d
Question (physics): rahul put his timepiece on the table in such a way that at 6 p . m . hour hand points to north . in which direction the minute hand will point at 9.15 p . m . ?
Options: a ) 233 , b ) 37 , c ) 27 , d ) west , e ) 271
Rationale: explanation : at 9.15 p . m . , the minute hand will point towards west . answer : d ) west
Answer: d
Question (gain): in the first 10 overs of a cricket game , the run rate was only 3.2 . what should be the run rate in the remaining 40 overs to reach a target of 282 runs ?
Options: a ) 6.25 , b ) 6.5 , c ) 6.75 , d ) 7.0 , e ) none of the above
Rationale: "total runs in the first 10 overs = 10 × 3.2 = 32 run rate required in the remaining 40 overs = 282 − 32 / 40 = 250 / 40 = 6.25 runs per over . answer a"
Answer: a
Question (physics): a and b together can complete a piece of work in 10 days . if a alone can complete the same work in 15 days , in how many days , in how many days can b alone complete that work ?
Options: a ) 10 , b ) 30 , c ) 25 , d ) 15 , e ) 45
Rationale: ( a + b ) ' s 1 day ' s work = 1 / 10 a ' s 1 day ' s work = 1 / 15 b ' s 1 days ' s work = ( 1 / 10 ) - ( 1 / 15 ) = 1 / 30 hence , b alone can complete the work in 30 days . answer is b
Answer: b
Question (other): the triplicate ratio of 2 : 4 is ?
Options: a ) 1 : 64 , b ) 1 : 8 , c ) 1 : 34 , d ) 3 : 64 , e ) 5 : 64
Rationale: "2 ^ 3 : 4 ^ 3 = 8 : 64 = 1 : 8 answer : b"
Answer: b
Question (gain): how many liters of a 40 % iodine solution need to be mixed with 35 liters of a 20 % iodine solution to create a 32 % iodine solution ?
Options: a ) 35 , b ) 49 , c ) 100 , d ) 102 , e ) 140
Rationale: "solution 1 : assume the iodine solution to be mixed = x lts . iodine = 0.4 x lts , water = 0.6 x lts . solution 2 : 35 liters of a 20 % iodine solution iodine = 7 lts , water = 28 lts . total iodine = 0.4 x + 7 total water = 0.6 x + 28 the resultant is a 35 % idoine solution . hence ( 0.4 x + 7 ) / ( x + 35 ) = 32 / 100 40 x + 700 = 32 x + 1120 8 x = 820 x = 102 lts correct option : d"
Answer: d
Question (physics): a garrison of 2000 men has provisions for 54 days . at the end of 18 days , a reinforcement arrives , and it is now found that the provisions will last only for 20 days more . what is the reinforcement ?
Options: a ) 1977 , b ) 1600 , c ) 1979 , d ) 1900 , e ) 1278
Rationale: "2000 - - - - 54 2000 - - - - 36 x - - - - - 20 x * 20 = 2000 * 36 x = 3600 2000 - - - - - - - 1600 answer : b"
Answer: b
Question (general): the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 75 kg . what might be the weight of the new person ?
Options: a ) 95 kg , b ) 90 kg , c ) 85 kg , d ) data inadequate , e ) none of these
Rationale: "a 95 kg total weight increased = ( 8 x 2.5 ) kg = 20 kg . weight of new person = ( 75 + 20 ) kg = 95 kg ."
Answer: a
Question (general): when a merchant imported a certain item , she paid a 7 percent import tax on the portion of the total value of the item in excess of $ 1,000 . if the amount of the import tax that the merchant paid was $ 109.20 , what was the total value of the item ?
Options: a ) $ 1,600 , b ) $ 1,850 , c ) $ 2,250 , d ) $ 2,440 , e ) $ 2,560
Rationale: "let x be the value of the item . 0.07 * ( x - 1000 ) = 109.20 x = 2560 the answer is e ."
Answer: e
Question (general): the “ length of integer x ” refers to the number of prime factors , not necessarily distinct , that x has . ( if x = 60 , the length of x would be 4 because 60 = 2 × 2 × 3 × 5 . ) what is the greatest possible length of integer z if z < 1,080 ?
Options: a ) 13 , b ) 10 , c ) 9 , d ) 7 , e ) 6
Rationale: to maximize the length of z we should minimize its prime base . the smallest prime is 2 and since 2 ^ 10 = 1,024 < 1,080 then the greatest possible length of integer z is 10 . answer : b .
Answer: b
Question (general): how many multiples of 3 are less than 6500 , and also multiples of 7 ?
Options: a ) 104 , b ) 208 , c ) 310 , d ) 340 , e ) 454
Rationale: "lcm of 3 & 7 = 21 tried dividing 6500 by 21 got quotient 309.5 ' so c is answer"
Answer: c
Question (physics): a can finish a piece of work in 4 days . b can do it in 10 days . they work together for two days and then a goes away . in how many days will b finish the work ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: 2 / 4 + ( 2 + x ) / 10 = 1 = > x = 3 days answer : a
Answer: a
Question (geometry): if the sides of a triangle are 26 cm , 24 cm and 15 cm , what is its area ?
Options: a ) 120 , b ) 772 , c ) 180 , d ) 266 , e ) 2848
Rationale: "the triangle with sides 26 cm , 24 cm and 15 cm is right angled , where the hypotenuse is 26 cm . area of the triangle = 1 / 2 * 24 * 15 = 180 cm 2 answer : c"
Answer: c
Question (physics): two trains , a and b , started simultaneously from opposite ends of a 125 - mile route and traveled toward each other on parallel tracks . train a , traveling at a constant rate , completed the 125 - mile trip in 12 hours ; train b , traveling at a constant rate , completed the 125 - mile trip in 8 hours . how many miles had train a traveled when it met train b ?
Options: a ) 25 , b ) 37.5 , c ) 40 , d ) 45.5 , e ) 50
Rationale: as the ratio of the rates of a and b is 8 to 12 then the distance covered at the time of the meeting ( so after traveling the same time interval ) would also be in that ratio , which means that a would cover 8 / ( 8 + 12 ) = 8 / 20 of 125 miles : 125 * 8 / 20 = 50 miles . answer : e .
Answer: e
Question (gain): if the simple interest on a certain amount in at 4 % rate 5 years amounted to rs . 2400 less than the principal . what was the principal ?
Options: a ) 1500 , b ) 2500 , c ) 2507 , d ) 3000 , e ) 11500
Rationale: "p - 2400 = ( p * 5 * 4 ) / 100 p = 3000 answer : d"
Answer: d
Question (other): out of 250 students of a college , 160 play football , 90 play cricket and 50 neither play football nor cricket . how many students play both football and cricket ?
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70
Rationale: explanation : solution : n ( a ) = 160 , n ( b ) = 90 , n ( a u b ) = 250 - 50 = 200 . required number = > n ( a ^ b ) = n ( a ) + n ( b ) - n ( a u b ) = 160 + 90 - 200 = 250 - 200 = 50 . answer : c
Answer: c
Question (geometry): what is the area a of the square with the following coordinates : ( x , y ) , ( 20 , 20 ) , ( 20 , 5 ) , ( x , 5 ) ?
Options: a ) 60 .
b ) 85 .
c ) 125 .
d ) 225 .
e ) it can not be determined from the information given
Rationale: length of one side = 15 ( 20 - 5 ) since , its a square , the area will be a = 15 ^ 2 = 225 d is the answer
Answer: d
Question (physics): a van takes 5 hours to cover a distance of 495 km . what speed in kph should the van maintain to cover the same distance in 3 / 2 of the previous time ?
Options: a ) 60 , b ) 63 , c ) 66 , d ) 69 , e ) 72
Rationale: "( 3 / 2 ) * 5 = 7.5 hours 495 / 7.5 = 66 kph the answer is c ."
Answer: c
Question (probability): what is the probability of getting a queen or spade from a set of cards ?
Options: a ) 3 / 13 , b ) 4 / 13 , c ) 5 / 13 , d ) 6 / 13 , e ) 7 / 13
Rationale: "no . of spade = 13 no . of queen = 3 ( excluding queen of spade ) no . of possible outcome = 13 + 3 = 16 probability = no . of favorable outcome / total possible outcomes = 16 / 52 = 4 / 13 answer : b"
Answer: b
Question (gain): find the compound interest on $ 1000 in 2 years at 4 % per annum , the interest being compounded half - yearly ?
Options: a ) $ 645.56 , b ) $ 82.43 , c ) $ 954.26 , d ) $ 745.69 , e ) $ 1020.45
Rationale: "principle = $ 10000 rate = 2 % half yearly = 4 half years amount = 1000 * ( 1 + 2 / 100 ) ^ 4 = 1000 * 51 / 50 * 51 / 50 * 51 / 50 * 51 / 50 = $ 1082.43 c . i . = 1082.43 - 1000 = $ 82.43 answer is b"
Answer: b
Question (general): if n is a positive integer and n ^ 2 is divisible by 36 , then the largest positive integer that must divide n is
Options: a ) 6 , b ) 12 , c ) 24 , d ) 36 , e ) 48
Rationale: "the question asks aboutthe largest positive integer that must divide n , not could divide n . since the least value of n for which n ^ 2 is a multiple of 72 is 12 then the largest positive integer that must divide n is 12 . complete solution of this question is given above . please ask if anything remains unclear . i spent a few hours on this one alone and i ' m still not clear . i chose 12 at first , but then changed to 48 . i ' m not a native speaker , so here is how i interpreted this question : the largest positive integer that must divide n = the largest positive factor of n . since n is a variable ( i . e . n is moving ) , so is its largest factor . please correct if i ' m wrong here . i know that if n = 12 , n ^ 2 = 144 = 2 * 72 ( satisfy the condition ) . when n = 12 , the largest factor of n is n itself , which is 12 . check : 12 is the largest positive number that must divide 12 - - > true however if n = 48 , n ^ 2 = 48 * 48 = 32 * 72 ( satisfy the condition too ) . when n = 48 , the largest factor of n is n itself , which is 48 . check : 48 is the largest positive number that must divide 48 - - > true so , i also notice that the keyword ismust , notcould . the question is , why is 48 notmust divide 48 , but instead onlycould divide 48 ? i ' m not clear right here . why is 12 must divide 12 ? what ' s the difference between them ? only restriction we have on positive integer n is that n ^ 2 is divisible by 72 . the least value of n for which n ^ 2 is divisible by 72 is 12 , thus nmustbe divisible by 12 ( n is in any case divisible by 12 ) . for all other values of n , for which n ^ 2 is divisible by 72 , n will still be divisible by 12 . this means that n is always divisible by 12 if n ^ 2 is divisible by 72 . now , ask yourself : if n = 6 , is n divisible by 48 ? no . so , n is not always divisible by 48 . a"
Answer: a
Question (gain): the population of a town is 8000 . it decreases annually at the rate of 10 % p . a . what was its population 2 years ago ?
Options: a ) 9876 , b ) 8000 , c ) 8500 , d ) 9500 , e ) 10000
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 8000 ã — 100 / 90 ã — 100 / 90 = 9876 a )"
Answer: a
Question (general): sum of two numbers is 40 and their difference is 4 . the ratio of the numbers is
Options: a ) 10 : 3 , b ) 5 : 9 , c ) 11 : 9 , d ) 13 : 9 , e ) none of these
Rationale: "explanation : = > ( x + y ) / ( x − y ) = 40 / 4 = > ( x + y ) = 10 ( x − y ) = > 9 x = 11 y = > x / y = 11 / 9 option c"
Answer: c
Question (physics): a man sitting in a train which is traveling at 36 kmph observes that a goods train , traveling in opposite direction , takes 10 seconds to pass him . if the goods train is 240 m long , find its speed
Options: a ) 50 kmph , b ) 56 kmph , c ) 58 kmph , d ) 62 kmph , e ) 72 kmph
Rationale: "explanation : relative speed = 240 / 10 m / sec = ( ( 240 / 10 ) × ( 18 / 5 ) ) kmph = 86 kmph . speed of goods train = ( 86 - 36 ) kmph = 50 kmph answer : option a"
Answer: a
Question (physics): a train traveling at 72 kmph crosses a platform in 30 seconds and a man standing on the platform in 15 seconds . what is the length of the platform in meters ?
Options: a ) 240 meters , b ) 360 meters , c ) 300 meters , d ) 600 meters , e ) can not be determined
Rationale: speed of the train in metres / sec = 72000 / 3600 = 20 distance travelled by train to cross the platform = 30 * 20 = 600 = length of train + length of platform distance travelled by train to cross the man = 15 * 20 = 300 = length of train length of platform = 600 - 300 = 300 answer : c
Answer: c
Question (physics): brenda and sally run in opposite direction on a circular track , starting at diametrically opposite points . they first meet after brenda has run 50 meters . they next meet after sally has run 150 meters past their first meeting point . each girl runs at a constant speed . what is the length of the track in meters ?
Options: a ) 250 , b ) 300 , c ) 350 , d ) 400 , e ) 500
Rationale: "nice problem . + 1 . first timetogetherthey run half of the circumference . second timetogetherthey run full circumference . first time brenda runs 50 meters , thus second time she runs 2 * 50 = 100 meters . since second time ( when they run full circumference ) brenda runs 200 meters and sally runs 150 meters , thus the circumference is 100 + 150 = 250 meters . answer : a ."
Answer: a
Question (gain): a man buys a cycle for rs . 1900 and sells it at a loss of 18 % . what is the selling price of the cycle ?
Options: a ) s . 1590 , b ) s . 1560 , c ) s . 1558 , d ) s . 1252 , e ) s . 1062
Rationale: "s . p . = 82 % of rs . 1900 = rs . 82 x 1900 / 100 = rs . 1558 answer : option c"
Answer: c
Question (general): at the end of the day , february 14 th , a florist had 120 roses left in his shop , all of which were red , white or pink in color and either long or short - stemmed . a third of the roses were short - stemmed , 20 of which were white and 10 of which were pink . the percentage of pink roses that were short - stemmed equaled the percentage of red roses that were short - stemmed . if none of the long - stemmed roses were white , what percentage of the long - stemmed roses were red ?
Options: a ) 20 % , b ) 50 % , c ) 55 % , d ) 75 % , e ) 80 %
Rationale: "r + w + p = 120 s + l = 120 1 / 3 * 120 = 40 short - stemmed white = 20 short - stemmed pink = 10 = > short - stemmed red = 10 10 / p = 10 / r = > r = p so total long stemmed = 80 and long stemmed red + long stemmed pink = 80 so long stemmed red / long stemmed = ? total white = 20 ( as no long stemmed white ) = > r + r + 20 = 120 = > 2 r = 100 and r = 50 long stemmed r = 50 - 10 = 40 so long stemmed red / r = 40 / 80 = 50 % answer - b"
Answer: b
Question (general): the difference between a two - digit number and the number obtained by interchanging the positions of its digits is 27 . what is the difference between the two digits of that number ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: "sol . let the ten ’ s digit be x and unit ’ s digit be y , then , ( 10 x + y ) - ( 10 y + x ) = 27 ⇔ 9 ( x - y ) = 27 ⇔ x - y = 3 answer a"
Answer: a
Question (gain): a fair price shopkeeper takes 10 % profit on his goods . he lost 60 % goods during theft . his loss percent is :
Options: a ) 72 % , b ) 42 % , c ) 56 % , d ) 12 % , e ) 22 %
Rationale: "explanation : suppose he has 100 items . let c . p . of each item be re . 1 . total cost = rs . 100 . number of items left after theft = 40 . s . p . of each item = rs . 1.10 total sale = 1.10 * 40 = rs . 44 hence , loss % = 56 / 100 * 100 = 56 % answer : c"
Answer: c
Question (general): a corporation that had $ 115.19 billion in profits for the year paid out $ 230.10 million in employee benefits . approximately what percent of the profits were the employee benefits ? ( note : 1 billion = 10 ^ 9 )
Options: a ) 50 % , b ) 20 % , c ) 5 % , d ) 2 % , e ) 0.2 %
Rationale: required answer = [ employee benefit / profit ] * 100 = [ ( 230.10 million ) / ( 115.19 billion ) ] * 100 = [ ( 230.10 * 10 ^ 6 ) / ( 115.19 * 10 ^ 9 ) ] * 100 = ( 2 / 1000 ) * 100 = 0.2 % so answer is ( e )
Answer: e
Question (physics): 39 men can complete a piece of work in 18 days . in how many days will 27 men complete the same work ?
Options: a ) 24 , b ) 77 , c ) 26 , d ) 25 , e ) 13
Rationale: "explanation : less men , means more days { indirect proportion } let the number of days be x then , 27 : 39 : : 18 : x [ please pay attention , we have written 27 : 39 rather than 39 : 27 , in indirect proportion , if you get it then chain rule is clear to you : ) ] { \ color { blue } x = \ frac { 39 \ times 18 } { 27 } } x = 26 so 26 days will be required to get work done by 27 men . answer : c"
Answer: c
Question (physics): two cars a and b start from boston and new york respectively simultaneously and travel towards each other at constant speeds along the same route . after meeting at a point between boston and new york the two cars a and b proceed to their respective destinations of new york and boston . car a reaches new york 80 minutes after the two cars have met and car b reaches boston 90 minutes after they have met . how long did car a take to cover the distance between boston and new york ?
Options: a ) 1 hour , b ) 1 hour 10 minutes , c ) 2 hours 30 minutes , d ) 1 hour 40 minutes , e ) 2 hours 20 minutes
Rationale: both cars leave at the same time both cars travel at constant speed stealing a useful piece of information from paragkan : if two objects a and b start from opposite points and , after having met en route , reach their respective destinations in a and b mins ( or any other measure of time ) respectively , then the ratio of their speeds ratio of speed : ( a / b ) = sq . rt ( b / a ) sq . rt ( b / a ) sq . rt ( 90 / 80 ) sq . rt ( 3 / 2 ) so , for every three units of distance a travels , b travels two . because we know the ratio of speed and the time it took b to travel the distance a has n ' t yet covered , we can find the time it took a to cover the distance b did in 90 minutes . 90 * ( 2 / 3 ) where 2 / 3 represents the lesser amount of time it took a to travel the distance b did in 90 minutes . = 60 minutes . therefore , a took 80 minutes to travel the first portion then 60 minutes to travel the distance b did in 90 minutes . a spent ( 80 + 60 ) = 140 minutes on the road . e . 2 hours 20 minutes
Answer: e
Question (physics): a metallic sphere of radius 24 cm is melted and drawn into a wire , whose radius of cross section is 16 cm . what is the length of the wire ?
Options: a ) 26 cm , b ) 45 cm , c ) 58 cm , d ) 63 cm , e ) 72 cm
Rationale: "volume of the wire ( in cylindrical shape ) is equal to the volume of the sphere . π ( 16 ) ^ 2 * h = ( 4 / 3 ) π ( 24 ) ^ 3 = > h = 72 cm answer : e"
Answer: e
Question (physics): two pipes can fill a tank in 18 minutes and 6 minutes . an outlet pipe can empty the tank in 45 minutes . if all the pipes are opened when the tank is empty , then how many minutes will it take to fill the tank ?
Options: a ) 1 / 15 , b ) 1 / 6 , c ) 1 / 11 , d ) 1 / 10 , e ) 1 / 12
Rationale: "part of the filled by all the three pipes in one minute = 1 / 18 + 1 / 6 - 1 / 45 = 1 / 6 so , the tank becomes full in 6 minutes . answer : b"
Answer: b
Question (general): how many multiples of 4 are there between 32 and 252 ?
Options: a ) 67 , b ) 64 , c ) 54 , d ) 56 , e ) 60
Rationale: "it should be mentioned whether 32 and 252 are inclusive . if 32 and 252 are inclusive , then the answer is ( 252 - 32 ) / 4 + 1 = 56 . if 32 and 252 are not inclusive , then the answer is ( 248 - 36 ) / 4 + 1 = 54 . since oa is c , then we have not inclusive case ."
Answer: c
Question (physics): a train 260 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 140 m long ?
Options: a ) 40 , b ) 32 , c ) 26 , d ) 21 , e ) 14
Rationale: "speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 260 + 140 = 400 m required time = 400 * 2 / 25 = 32 sec answer : b"
Answer: b
Question (general): set # 1 = { a , b , c , d , e , f } set # 2 = { k , l , m , n , o , p } there are these two sets of letters , and you are going to pick exactly one letter from each set . what is the probability of picking at least one vowel ?
Options: a ) 1 / 6 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 4 / 9
Rationale: so not a vowel in set - 1 : 4 / 6 and not a vowel in ser - 2 : 5 / 6 now , 4 / 6 ∗ 5 / 6 = 5 / 9 this is for not a vowel . then for at least one vowel will be = 1 − 5 / 9 = 4 / 9 answer will be e .
Answer: e
Question (general): if a no . when divided by 44 , gives 432 as quotient and 0 as remainder . what will be the remainder when dividing thesame no . by 31
Options: a ) 2 , b ) 4 , c ) 5 , d ) 7 , e ) 8
Rationale: p ÷ 44 = 432 = > p = 432 * 44 = 19008 p / 31 = 19008 / 31 = 613 , remainder = 5 c
Answer: c
Question (general): the age of somu is one - third his father ' s . 7 years back he was one - fifth of his father ' s age . what is his persent age ?
Options: a ) 11 , b ) 13 , c ) 14 , d ) 12 , e ) 10
Rationale: "explanation : let somu ' s age be x and that of his father be 3 x . so , x - 7 = 3 x - 7 / 5 = x = 14 answer : option c"
Answer: c
Question (general): sam ’ s car was fined when he gave joe and peter a ride , so they decided to help sam pay the fine . joe paid $ 6 more than 1 / 4 of the fine and peter paid $ 6 less than 1 / 3 of the fine , leaving pay $ 10 less than 1 / 2 the fine to complete the payment . what fraction of the fine did sam pay ?
Options: a ) $ 50 , b ) $ 40 , c ) $ 35 , d ) $ 44 , e ) $ 45
Rationale: "call the fine f . joe paid ( 1 / 4 ) f + 4 and peter paid ( 1 / 3 ) f – 4 , leaving ( 1 / 2 ) f – 5 left . if we add those three up , they should add up to f . f = [ ( 1 / 4 ) f + 6 ] + [ ( 1 / 3 ) f – 6 ] + [ ( 1 / 2 ) f – 10 ] f = ( 1 / 4 ) f + ( 1 / 3 ) f + ( 1 / 2 ) f – 10 multiply all terms by 12 to clear the fractions . 12 f = 3 f + 4 f + 6 f – 120 12 f = 13 f – 120 – f = – 120 f = 120 well , if the fine cost $ 120 , then sam paid the part not covered by joe or peter . half the fine is $ 60 , and sam paid $ 10 less than this : $ 50 . answer = a"
Answer: a