Cheukting/mathqa huggingface dataset:
Question (physics): a woman complete a journey in 25 hours . she travels first half of the journey at the rate of 21 km / hr and second half at the rate of 24 km / hr . find the total journey in km .
Options: a ) 334 km . , b ) 216 km . , c ) 314 km . , d ) 224 km . , e ) 560 km .
Rationale: 0.5 x / 21 + 0.5 x / 24 = 25 - - > x / 21 + x / 24 = 50 - - > x = 560 km . e
Answer: e
Question (general): set j consists of 10 consecutive even numbers . if the smallest term in the set is - 4 , what is the range of the positive integers in set j ?
Options: a ) 8 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "since there are only 10 integers , another approach is the just list all 10 . we get : - 4 , - 2 , 0,2 , 4 , 6 , 8 , 10 , 12 , 14 range of positive integers = 14 - 2 = 12 answer : b"
Answer: b
Question (gain): a man two flats for $ 675958 each . on one he gains 12 % while on the other he loses 12 % . how much does he gain or lose in the whole transaction ?
Options: a ) 1.44 % , b ) 2.56 % , c ) 3.12 % , d ) 4.65 % , e ) 5.12 %
Rationale: "in such a case there is always a loss loss % = ( 12 / 10 ) ^ 2 = 36 / 25 = 1.44 % answer is a"
Answer: a
Question (gain): in a certain company , a third of the workers do not have a retirement plan . 10 % of the workers who do not have a retirement plan are women , and 40 % of the workers who do have a retirement plan are men . if 120 of the workers of that company are men , how many of the workers are women ?
Options: a ) 80 , b ) 95 , c ) 105 , d ) 120 , e ) 91
Rationale: 20 % of the workerswithoutretirement plan are women , this means 80 % of the workerswithoutretirement plan are men right ? makes 100 % = no retirement plan . then 40 % of those wo have a retirement plan are men , which means 60 % of those who have a retirement plan are women . these percentages are always refering to the subgroupsretirement plan = yesandno retirement plan . make the total workers equal x and work from there and it should be fine > x / 3 have no retirement plan at all . i struggled with the question a lot , it was hard for me although usually i have no problems with sets questions like this . i believe it must be a 700 + question . yes , you are right . i read the question incorrectly ! i glazed overnotfor some reason . if 20 % of the workers who do not have a retirement plan are women , 80 % who do not have retirement plan are men . also 40 % who do have retirement plan are men . since 1 / 3 do not have retirement plan and 2 / 3 do have , it becomes a simple weighted average question . cavg = ( 90 * 1 + 40 * 2 ) / 3 = 170 / 3 % are men total = 120 * 300 / 170 = 211 no . of women = 211 - 120 = 91 e
Answer: e
Question (physics): the distance from city a to city b is 120 miles . while driving from city a to city b , cara drives at a constant speed of 30 miles per hour . dan leaves city a 60 minutes after cara . what is the minimum constant speed in miles per hour that dan must exceed in order to arrive in city b before cara ?
Options: a ) 42 , b ) 44 , c ) 46 , d ) 48 , e ) 40
Rationale: the time it takes cara to drive to city b is 120 / 30 = 4 hours . dan needs to take less than 3 hours for the trip . dan needs to exceed a constant speed of 120 / 3 = 40 miles per hour . the answer is e .
Answer: e
Question (physics): jack and christina are standing 150 feet apart on a level surface . their dog , lindy , is standing next to christina . at the same time , they all begin moving toward each other . jack walks in a straight line toward christina at a constant speed of 7 feet per second and christina walks in a straight line toward jack at a constant speed of 8 feet per second . lindy runs at a constant speed of 10 feet per second from christina to jack , back to christina , back to jack , and so forth . what is the total distance , in feet , that lindy has traveled when the three meet at one place ?
Options: a ) 40 , b ) 60 , c ) 80 , d ) 100 , e ) 120
Rationale: "the relative speed of jack and christina is 7 + 8 = 15 feet per second . the distance between them is 210 feet , hence they will meet in ( time ) = ( distance ) / ( relative speed ) = 150 / 15 = 10 seconds . for all this time lindy was running back and forth , so it covered ( distance ) = ( speed ) * ( time ) = 10 * 10 = 100 feet . answer : d ."
Answer: d
Question (general): how many different positive integers exist between 10 ^ 4 and 10 ^ 5 , the sum of whose digits is equal to 2 ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "10001 10010 10100 11000 20000 total no . = 5 c"
Answer: c
Question (physics): a man by motorcycle goes from delhi to bharatpur , a distance of 192 km , at an average speed of 32 kmph . another man starts from delhi by car 2.5 h after the motorcyclist starts and reaches bharatpur half an hour late . what is the ratio of person on the motorcycle to the person going by car ?
Options: a ) 1 : 2 , b ) 2 : 3 , c ) 10 : 27 , d ) 5 : 4 , e ) 4 : 5
Rationale: a man by motorcycle goes from delhi to bharatpur the time take by the motorcyclist = 192 / 32 = 6 hours another man start from delhi be car after 2.5 hour the man starts = 6 - 2.5 = 3.5 and the man on can reaches half and hour late which is = 3.5 + . 5 = 4 thus , the ratio between motorcycle to car is 4 : 6 or , 2 : 3 . answer : b
Answer: b
Question (general): if p / q = 4 / 5 , then the value of 18 / 7 + { ( 2 q - p ) / ( 2 q + p ) } is ?
Options: a ) 3 / 7 , b ) 34 , c ) 1 , d ) 2 , e ) 3
Rationale: "answer given exp . = 18 / 7 + { ( 2 q - p ) / ( 2 q + p ) } dividing numerator as well as denominator by q , exp = 18 / 7 + { 2 - p / q ) / ( 2 + p / q ) } = 18 / 7 + { ( 2 - 4 / 5 ) / ( 2 + 4 / 5 ) } = 18 / 7 + 6 / 14 = 18 / 7 + 3 / 7 = 21 / 7 = 3 correct option : e"
Answer: e
Question (gain): a scuba diver descends at a rate of 30 feet per minute . a diver dive from a ship to search for a lost ship at the depth of 2400 feet below the sea level . . how long will he take to reach the ship ?
Options: a ) 70 minutes , b ) 72 minutes , c ) 80 minutes , d ) 76 minutes , e ) 77 minutes
Rationale: "time taken to reach = 2400 / 30 = 80 minutes answer : c"
Answer: c
Question (general): how many zeroes are there at the end of the number n , if n = 150 ! + 300 ! ?
Options: a ) 28 , b ) 31 , c ) 34 , d ) 37 , e ) 40
Rationale: "the number of zeroes at the end of 150 ! will be less than the number of zeroes at the end of 300 ! hence it is sufficient to calculate the number of zeroes at the end of 150 ! the number of zeroes = [ 150 / 5 ] + [ 150 / 25 ] + [ 150 / 125 ] = 30 + 6 + 1 = 37 the answer is d ."
Answer: d
Question (general): how many prime numbers are between 26 / 3 and 85 / 6 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "26 / 3 = 8 . xxx 85 / 6 = 14 . xxx so we need to find prime numbers between 8 ( exclusive ) - 13 ( inclusive ) there are 2 prime numbers 1113 hence answer will be ( b ) 2 b"
Answer: b
Question (general): average of 10 matches is 32 , how many runs one should should score to increase his average by 5 runs .
Options: a ) a ) 70 , b ) b ) 76 , c ) c ) 78 , d ) d ) 80 , e ) e ) 87
Rationale: "explanation : average after 11 innings should be 37 so , required score = ( 11 * 37 ) - ( 10 * 32 ) = 407 - 320 = 87 answer : option e"
Answer: e
Question (general): if there are 4 peanuts in a box and mary puts 2 more peanuts inside , how many peanuts are in the box ?
Options: a ) 8 , b ) 9 , c ) 6 , d ) 11 , e ) 12
Rationale: "2 + 4 = 6 correct answer is c ) 6"
Answer: c
Question (physics): speed of a boat in standing water is 16 kmph and the speed of the stream is 2 kmph . a man rows to a place at a distance of 6840 km and comes back to the starting point . the total time taken by him is :
Options: a ) 914.2 hours , b ) 900 hours , c ) 915 hours , d ) 868.6 hours , e ) 915 hours
Rationale: "explanation : speed downstream = ( 16 + 2 ) = 18 kmph speed upstream = ( 16 - 2 ) = 14 kmph total time taken = 6840 / 18 + 6840 / 14 = 380 + 488.6 = 868.6 hours answer : option d"
Answer: d
Question (general): in august , a cricket team that played 120 matches won 22 % of the games it played . after a continuous winning streak , this team raised its average to 52 % . how many matches did the team win to attain this average ?
Options: a ) 40 , b ) 52 , c ) 68 , d ) 75 , e ) 98
Rationale: "let the no of matches played more = x so , ( 120 + x ) * 52 / 100 = 26.4 + x by solving we get x = 75 answer : d"
Answer: d
Question (general): jane started baby - sitting when she was 16 years old . whenever she baby - sat for a child , that child was no more than half her age at the time . jane is currently 32 years old , and she stopped baby - sitting 10 years ago . what is the current age of the oldest person for whom jane could have baby - sat ?
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: "check two extreme cases : jane = 16 , child = 8 , years ago = 32 - 16 = 16 - - > child ' s age now = 8 + 16 = 24 ; jane = 22 , child = 11 , years ago = 32 - 22 = 10 - - > child ' s age now = 11 + 10 = 21 . answer : e ."
Answer: e
Question (geometry): a cylindrical container of radius 6 cm and height 15 cm is filled with ice - cream . the whole icecream has to be distributed to 10 children in equal cones with hemispherical tops . if the height of the conical portion is four times the radius of its base , find the radius of the ice - cream cone .
Options: a ) 1
b ) 2
c ) 3
d ) 4
e ) 5
Rationale: volume of given ice cream = ( pie ) * 6 ² * 15 = 540 ( pie ) dividing to 10 children volume given to a child = 54 ( pie ) let r be radius and h be the height of the cone , then ( pie ) r ² h / 3 + 2 ( pie ) r ³ / 3 = 54 ( pie ) also given h = 4 r 4 r ³ / 3 + 2 r ³ / 3 = 54 2 r ³ = 54 r ³ = 27 r = 3 answer : c
Answer: c
Question (other): if 1 = 3 2 = 6 3 = 9 4 = 12 5 = 15 then 9 = ? hint : its a logic riddle not a mathematical riddle
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: c 3 as stated 3 = 9 = > 9 = 3 answer is c
Answer: c
Question (physics): find the area of trapezium whose parallel sides are 20 cm and 18 cm long , and the distance between them is 25 cm ?
Options: a ) 827 cm 2 , b ) 216 cm 2 , c ) 285 cm 2 , d ) 178 cm 2 , e ) 475 cm 2
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 18 ) * ( 25 ) = 475 cm 2 answer : e"
Answer: e
Question (general): in a forest 170 deer were caught , tagged with electronic markers , then released . a week later , 50 deer were captured in the same forest . of these 50 deer , it was found that 5 had been tagged with the electronic markers . if the percentage of tagged deer in the second sample approximates the percentage of tagged deer in the forest , and if no deer had either left or entered the forest over the preceding week , what is the approximate number of deer in the forest ?
Options: a ) 150 , b ) 750 , c ) 1,250 , d ) 1,700 , e ) 2,500
Rationale: "the percentage of tagged deer in the second sample = 5 / 50 * 100 = 10 % . so , 170 tagged deers comprise 10 % of total # of deers - - > total # of deers = 170 * 10 = 1,700 . answer : d ."
Answer: d
Question (physics): in an examination , a student scores 5 marks for every correct answer and loses 2 marks for every wrong answer . if he attempts all 100 questions and secures 290 marks , the number of questions he attempts correctly , is :
Options: a ) 60 , b ) 80 , c ) 70 , d ) 45 , e ) 50
Rationale: "let the number of correct answers be x . number of incorrect answers = ( 100 â € “ x ) . 5 x â € “ 2 ( 100 â € “ x ) = 290 or 7 x = 490 or x = 70 . answer : c"
Answer: c
Question (general): there are 3 boats b 1 , b 2 and b 3 working together they carry 60 people in each trip . one day an early morning b 1 carried 50 people in few trips alone . when it stopped carrying the passengers b 2 and b 3 started carrying the people together . it took a total of 10 trips to carry 300 people by b 1 , b 2 and b 3 . it is known that each day on an average 300 people cross the river using only one of the 3 boats b 1 , b 2 and b 3 . how many trips it would take to b 1 , to carry 150 passengers alone ?
Options: a ) 15 , b ) 30 , c ) 25 , d ) 10 , e ) 15
Rationale: explanation : combined efficiency of all the three boats = 60 passenger / trip now , consider option ( a ) 15 trips and 150 passengers means efficiency of b 1 = 10 p / t which means in carrying 50 passengers b 1 must has taken 5 trips . so the rest trips equal to 5 ( 10 - 5 = 5 ) in which b 2 and b 3 together carried remaining 250 ( 300 - 50 = 250 ) passengers . therefore the efficiency of b 2 and b 3 = 250 / 5 = 50 p / t since , the combined efficiency of b 1 , b 2 and b 3 is 60 . which is same as given in the first statement hence option ( a ) is correct answer : a
Answer: a
Question (general): the average age of 12 men is increased by years when two of them whose ages are 21 years and 23 years are replaced by two new men . the average age of the two new men is
Options: a ) 22 , b ) 30 , c ) 34 , d ) 38 , e ) 27
Rationale: "total age increased = ( 12 * 2 ) years = 24 years . sum of ages of two new men = ( 21 + 23 + 24 ) years = 68 years average age of two new men = ( 68 / 2 ) years = 34 years . answer : c"
Answer: c
Question (physics): a boat can travel with a speed of 24 km / hr in still water . if the speed of the stream is 4 km / hr , find the time taken by the boat to go 112 km downstream
Options: a ) 3 hours , b ) 4 hours , c ) 5 hours , d ) 6 hours , e ) 7 hours
Rationale: "explanation : speed of the boat in still water = 24 km / hr speed of the stream = 4 km / hr speed downstream = ( 22 + 5 ) = 28 km / hr distance travelled downstream = 112 km time taken = distance / speed = 112 / 28 = 4 hours answer : option b"
Answer: b
Question (physics): find the l . c . m . of 72 , 108 and 2100 .
Options: a ) 37800 , b ) 37600 , c ) 37200 , d ) 37500 , e ) none of them
Rationale: 72 = 2 ^ 3 x 3 ^ 2 , 108 = 3 ^ 3 x 2 ^ 2 , 2100 = 2 ^ 2 x 5 ^ 2 x 3 x 7 . l . c . m . = 2 ^ 3 x 3 ^ 3 x 5 ^ 2 x 7 = 37800 . answer is a .
Answer: a
Question (general): the average of 10 numbers is calculated as 16 . it is discovered later on that while calculating the average , the number 55 was incorrectly read as 25 , and this incorrect number was used in the calculation . what is the correct average ?
Options: a ) 17 , b ) 19 , c ) 25 , d ) 31 , e ) 46
Rationale: "the total sum of the numbers should be increased by 30 . then the average will increase by 30 / 10 = 3 . the correct average is 19 . the answer is b ."
Answer: b
Question (general): the average of 1 st 3 of 4 numbers is 16 and of the last 3 are 15 . if the sum of the first and the last number is 21 . what is the last numbers ?
Options: a ) 2 , b ) 4 , c ) 9 , d ) 5 , e ) 7
Rationale: "a + b + c = 48 b + c + d = 45 a + d = 21 a – d = 3 a + d = 21 2 d = 18 d = 9 answer c"
Answer: c
Question (physics): how many inches are in 2000 millimeters ? ( round your answer to the nearest hundredth of of an inch ) .
Options: a ) 48.74 inches , b ) 58.74 inches , c ) 78.74 inches , d ) 28.74 inches , e ) 88.74 inches
Rationale: one inch is the same as 25.4 mm . let x inches be the same as 1000 mm x = 1 inch * 2000 mm / 25.4 mm = 78.74 inches correct answer c
Answer: c
Question (general): the average of 6 no . ' s is 6.40 . the average of 2 of them is 6.2 , while the average of the other 2 is 6.1 . what is the average of the remaining 2 no ' s ?
Options: a ) 2.3 , b ) 2.6 , c ) 6.9 , d ) 4.5 , e ) 4.6
Rationale: "sum of the remaining two numbers = ( 6.4 * 6 ) - [ ( 6.2 * 2 ) + ( 6.1 * 2 ) ] = 38.40 - ( 12.4 + 12.2 ) = 38.40 - 24.6 = 13.80 required average = ( 13.8 / 2 ) = 6.9 answer : c"
Answer: c
Question (physics): the current in a river is 6 mph . a boat can travel 20 mph in still water . how far up the river can the boat travel if the round trip is to take 10 hours ?
Options: a ) 69 miles , b ) 88 miles , c ) 96 miles , d ) 91 miles , e ) 112 miles
Rationale: "upstream speed = 20 - 6 = 14 mph downstream speed = 20 + 6 = 26 mph d / 14 + d / 26 = 10 hours solving for d we get d = 91 answer : d"
Answer: d
Question (general): a school has 6 maths 5 physics and 5 chemistry teachers each teacher can teach 4 subjects max what is he minimum number of teachers required
Options: a ) 2 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "total subjects = 6 + 5 + 5 = 16 max subjects by 1 teacher = 4 so , min of teachers required = 16 / 4 = 4 answer : b"
Answer: b
Question (physics): if a monkey can climb 6 meter & slip down 3 meter in alternate minutes , than how much time can be taken by the monkey to climb up to a height of 60 meter .
Options: a ) 36 min , b ) 37 min , c ) 38 min , d ) 39 min , e ) 32 min
Rationale: in 1 st min it climb 6 m and in 2 nd min it slips 3 m , so it final displacement is 3 m in 2 min . now for 51 m it has taken 34 min . in 35 min it goes to 57 m . in 36 min come down to 54 m . in 37 min it goes to 60 answer : b
Answer: b
Question (physics): on a map , 1.5 inches represent 24 miles . how many miles approximately is the distance if you measured 46 centimeters assuming that 1 - inch is 2.54 centimeters ?
Options: a ) 174.2 , b ) 212 , c ) 288.1 , d ) 290 , e ) 282.4
Rationale: "1.5 inch = 2.54 * 1.5 cm . so , 2.54 * 1.5 represents 24 miles . so for 46 cm . : 46 / ( 2.54 * 1.5 ) = x / 24 - - - > x = 24 * 46 / ( 3.81 ) = 290 answer will be d ."
Answer: d
Question (general): the cash realised on selling a 14 % stock is rs . 104.25 , brokerage being 1 / 4 % is ?
Options: a ) 104 , b ) 106 , c ) 102 , d ) 192 , e ) 122
Rationale: "cash realised = rs . ( 104.25 - 0.25 ) = rs . 104 . answer : a"
Answer: a
Question (other): how many numbers up to 200 are divisible by 2 and 3 both ?
Options: a ) 22 , b ) 33 , c ) 77 , d ) 28 , e ) 22
Rationale: explanation : 200 / 6 = 33 2 / 6 = > 33 numbers answer : b
Answer: b
Question (general): a dog has 15 bones , then he finds 8 more bones . now how many bones does he have .
Options: a ) a ) 7 , b ) b ) 27 , c ) c ) 23 , d ) d ) 19 , e ) e ) 21
Rationale: 15 + 8 = 23 . answer is c .
Answer: c
Question (general): last year manfred received 26 paychecks . each of his first 6 paychecks was $ 750 ; each of his remaining paychecks was $ 20 more than each of his first 6 paychecks . to the nearest dollar , what was the average ( arithmetic mean ) amount of his pay checks for the year ?
Options: a ) $ 752 , b ) $ 755 , c ) $ 765 , d ) $ 773 , e ) $ 775
Rationale: = ( 750 * 6 + 770 * 20 ) / 26 = 765 answer is c . posted from my mobile device
Answer: c
Question (gain): what is the rate percent when the simple interest on rs . 800 amount to rs . 200 in 4 years ?
Options: a ) 5 % , b ) 7 % , c ) 6.25 % , d ) 2 % , e ) 4 %
Rationale: "200 = ( 800 * 4 * r ) / 100 r = 6.25 % answer : c"
Answer: c
Question (geometry): the sides of a cube are in the ratio 1 : 2 the ratio of their volume is ?
Options: a ) 1 : 6
b ) 1 : 4
c ) 1 : 0
d ) 1 : 2
e ) 1 : 1
Rationale: 1 : 4 answer : b
Answer: b
Question (physics): a can do a piece of work in 12 days . he worked for 15 days and then b completed the remaining work in 10 days . both of them together will finish it in .
Options: a ) 12 1 / 2 days , b ) 10 1 / 2 days , c ) 12 1 / 3 days , d ) 10 1 / 3 days , e ) 11 1 / 2 days
Rationale: explanation : 15 / 25 + 10 / x = 1 = > x = 25 1 / 25 + 1 / 25 = 2 / 25 25 / 2 = 12 1 / 2 days answer a
Answer: a
Question (physics): a train running at the speed of 6 km / hr crosses a pole in 2 seconds . find the length of the train ?
Options: a ) 150 , b ) 872 , c ) 3.33 , d ) 3.21 , e ) 30.1
Rationale: "speed = 6 * ( 5 / 18 ) m / sec = 5 / 3 m / sec length of train ( distance ) = speed * time 5 / 3 ) * 2 = 3.33 meter answer : c"
Answer: c
Question (general): the denominator of a fraction is 5 greater than the numerator . if the numerator and the denominator are increased by 1 , the resulting fraction is equal to 7 â  „ 12 . what is the value of the original fraction ?
Options: a ) 6 / 11 , b ) 8 / 13 , c ) 11 / 16 , d ) 12 / 17 , e ) 14 / 19
Rationale: let the numerator be x . then the denominator is x + 5 . x + 1 / x + 6 = 7 / 12 . 12 x + 12 = 7 x + 42 . 5 x = 30 . x = 6 . the original fraction is 6 / 11 . the answer is a .
Answer: a
Question (general): if the sum of two positive integers is 22 and the difference of their squares is 44 , what is the product of the two integers ?
Options: a ) 108 , b ) 119 , c ) 120 , d ) 135 , e ) 143
Rationale: "let the 2 positive numbers x and y x + y = 22 - - 1 x ^ 2 - y ^ 2 = 44 = > ( x + y ) ( x - y ) = 44 - - 2 using equation 1 in 2 , we get = > x - y = 2 - - 3 solving equation 1 and 3 , we get x = 12 y = 10 product = 12 * 10 = 120 answer c"
Answer: c
Question (physics): suppose you work for a manufacturing plant that pays you $ 12.50 an hour plus $ 0.16 for each widget you make . how many widgets must you produce in a 40 hour week to earn $ 660 ( before payroll deductions ) ?
Options: a ) 800 , b ) 900 , c ) 1000 , d ) 1100 , e ) 1200
Rationale: "total pay = 40 * $ 12.50 + $ 0.16 * x = 660 x = 160 / 0.16 = 1000 the answer is c ."
Answer: c
Question (physics): in a stream running at 3 kmph , a motor boat goes 10 km upstream and back again to the starting point in 57 minutes . find the speed of motor boat in still water ?
Options: a ) 18 kmph , b ) 22 kmph , c ) 16 kmph , d ) 20 kmph , e ) none of these
Rationale: "explanation : let the speed of motor boat instill water be x kmph then , speed in downstream = ( x + 3 ) km and . speed in upstream = ( x - 3 ) kmph time taken to row 10 km & back = ( 10 / x + 3,10 / x - 3 ) 10 / x + 3 + 10 / x - 3 = 57 / 60 11 x 2 - 240 x - 44 = 0 ( x - 22 ) ( 11 x + 2 ) = 0 x = 22 or x = - 2 / 11 then x = 22 kmph answer : option b"
Answer: b
Question (general): in a can , there is a mixture of milk and water in the ratio 4 : 5 . if it is filled with an additional 4 litres of milk the can would be full and ratio of milk and water would become 6 : 5 . find the capacity of the can ?
Options: a ) 40 , b ) 44 , c ) 48 , d ) 22 , e ) none of these
Rationale: "let the capacity of the can be t litres . quantity of milk in the mixture before adding milk = 4 / 9 ( t - 4 ) after adding milk , quantity of milk in the mixture = 6 / 11 t . 6 t / 11 - 4 = 4 / 9 ( t - 4 ) 10 t = 396 - 176 = > t = 22 . answer : d"
Answer: d
Question (geometry): people were sitting in a circle . 7 th one is direct opposite to 18 th one . . then how many were there in that group ?
Options: a ) 21
b ) 22
c ) 23
d ) 24
e ) 20
Rationale: 7 th one is exactly opposite represents half of circle . with 7 and 18 total members are 12 for remaing half = 12 * 2 - 2 ( 7 th and 18 th ( already taken ) ) = 22 answer : b
Answer: b
Question (general): a no . when divided by 221 gives a remainder 43 , what remainder will be obtainedby dividingthe same no . 17 ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 11 , e ) 14
Rationale: "221 + 43 = 264 / 17 = 9 ( remainder ) c"
Answer: c
Question (geometry): a certain cube floating in a bucket of water has between 80 and 90 percent of its volume below the surface of the water . if between 6 and 13 cubic centimeters of the cube ' s volume is above the surface of the water , then the length of a side of the cube is approximately
Options: a ) 4 , b ) 5 , c ) 7 , d ) 8 , e ) 9
Rationale: "if sides are 7 , vol = 7 ^ 3 = 343 80 % = 274.4 , 90 % = 308.7 so vol above water , between 68.6 and 34.3 - - > too big if side are 4 , vol = 64 80 % = 51.2 , 90 % = 57.6 vol above water between 12.8 and 6.4 so 4 should be the answer . check option c , if sides are 5 , vol = 125 80 % = 100 , . 90 % = 112.5 vol above water between 12.5 - 25 ( sides are 4 cubic centimeters ) a"
Answer: a
Question (general): there are 25 balls which are red , blue or green . if 8 balls are blue and the sum of green balls and blue balls is less than 17 , at most how many green balls are there ?
Options: a ) 8 , b ) 5 , c ) 6 , d ) 7 , e ) 10
Rationale: "r + g + b = 25 b = 8 b + g < 17 = > 8 + g < 17 = > g < 9 = > at most 8 green balls answer : a"
Answer: a