Cheukting/mathqa huggingface dataset:
Question (general): a man purchased 4 blankets @ rs . 100 each , 5 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 150 . find the unknown rate of two blankets ?
Options: a ) a ) 300 , b ) b ) 350 , c ) c ) 450 , d ) d ) 470 , e ) e ) 500
Rationale: "explanation : 10 * 150 = 1500 4 * 100 + 5 * 150 = 1150 1500 – 1150 = 350 b"
Answer: b
Question (general): of 70 players on a football team , 31 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?
Options: a ) 57 , b ) 59 , c ) 63 , d ) 71 , e ) 92
Rationale: "total = 70 thrower = 31 rest = 70 - 31 = 39 left handed = 39 / 3 = 13 right handed = 26 if all thrower are right handed then total right handed is 31 + 26 = 57 so a . 57 is the right answer"
Answer: a
Question (general): each week , harry is paid x dollars per hour for the first 30 hours and 1.5 x dollars for each additional hour worked that week . each week , james is paid x dollars per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week james worked a total of 53 hours . if harry and james were paid the same amount last week , how many hours did harry work last week ?
Options: a ) 35 , b ) 36 , c ) 37 , d ) 38 , e ) 54
Rationale: "amount earned by james = 40 * x + 13 * 2 x = 66 x therefore , amount earned by harry = 66 x but we know the amount harry earned assuming working y hours ( y > 30 ) is 30 * x + ( y - 30 ) * 1.5 x [ [ we know y > 30 because in 30 h the most harry could earn is 30 x , but he has earned 66 x ] ] so x * ( 1.5 y - 45 + 30 ) = 66 x or x * ( 1.5 y - 15 ) = 66 x so 1.5 y - 15 = 66 so 1.5 y = 81 so y = 54 answer is e"
Answer: e
Question (geometry): triangle xyz is an isosceles right triangle . if side xy is longer than side yz , and the area of the triangle is 9 , what is the measure of side xy ?
Options: a ) 4 , b ) 4 √ 2 , c ) 8 , d ) 6 , e ) can not be determined from the information provided
Rationale: "ans d . . 6 . . xy being larger means it is the hyp . . area = ( 1 / 2 ) * ( yz ) ^ 2 = 9 or yz = 3 * \ sqrt { 2 } . . therefore hyp = xy = 6"
Answer: d
Question (gain): yesterday ' s closing prices of 1980 different stocks listed on a certain stock exchange were all different from today ' s closing prices . the number of stocks that closed at a higher price today than yesterday was 20 percent greater than the number that closed at a lower price . how many of the stocks closed at a higher price today than yesterday ?
Options: a ) 484 , b ) 1080 , c ) 1,100 , d ) 1,320 , e ) 1,694
Rationale: lets consider the below - the number of stocks that closed at a higher price = h the number of stocks that closed at a lower price = l we understand from first statement - > h + l = 1980 - - - - ( 1 ) we understand from second statement - > h = ( 120 / 100 ) l = > h = 1.2 l - - - - ( 2 ) solve eq ( 1 ) ( 2 ) to get h = 1080 . b is my answer .
Answer: b
Question (physics): a man walking at the rate of 5 km / hr crosses a bridge in 15 minutes . the length of the bridge ( in metres ) is ?
Options: a ) 2267 , b ) 1162 , c ) 2276 , d ) 1250 , e ) 1262
Rationale: "explanation : speed = ( 5 x 5 / 18 ) m / sec = 25 / 18 m / sec . distance covered in 15 minutes = ( 25 / 18 x 15 x 60 ) m = 1250 m . answer : d"
Answer: d
Question (general): a 75 m long train is running at 54 km / hr . in how much time will it cross an electric pole ?
Options: a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25
Rationale: speed of the train = ( 54 * 5 / 18 ) m / sec = 15 m / sec . length of the train = ( speed x time ) time = ( length of the train / speed ) = ( 75 / 15 ) = 5 sec answer : a
Answer: a
Question (gain): a reduction of 24 % in the price of salt enables a lady to obtain 10 kgs more for rs . 100 , find the original price per kg ?
Options: a ) s . 2.8 , b ) s . 2.4 , c ) s . 2.5 , d ) s . 2.2 , e ) s . 3.16
Rationale: "100 * ( 24 / 100 ) = 24 - - - 10 ? - - - 1 = > rs . 2.4 100 - - - 76 ? - - - 2.4 = > rs . 3.16 answer : e"
Answer: e
Question (general): what is the least number that should be added to 1077 , so the sum of the number is divisible by 23 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "( 1077 / 23 ) gives a remainder 19 so we need to add 4 . the answer is d ."
Answer: d
Question (physics): how many pieces of 0.63 meteres can be cut from a rod 32.5 meteres long
Options: a ) 30 , b ) 40 , c ) 51 , d ) 60 , e ) 70
Rationale: "explanation : we need so simple divide 32.5 / 0.63 , = ( 3250 / 63 ) = 51 option c"
Answer: c
Question (other): how many terminating zeroes q does 200 ! have ?
Options: a ) 40 , b ) 48 , c ) 49 , d ) 55 , e ) 64
Rationale: you have 40 multiples of 5 , 8 of 25 and 1 of 125 . this will give 49 zeros . c
Answer: c
Question (general): gold is 19 times as heavy as water and copper is 9 times as heavy as water . in what ratio should these be mixed to get an alloy 17 times as heavy as water ?
Options: a ) 1 : 2 , b ) 3 : 2 , c ) 4 : 1 , d ) 5 : 2 , e ) 6 : 5
Rationale: "g = 19 w c = 9 w let 1 gm of gold mixed with x gm of copper to get 1 + x gm of the alloy 1 gm gold + x gm copper = x + 1 gm of alloy 19 w + 9 wx = x + 1 * 17 w 19 + 9 x = 17 ( x + 1 ) x = 1 / 4 ratio of gold with copper = 1 : 1 / 4 = 4 : 1 answer is c"
Answer: c
Question (gain): a man bought an article and sold it at a gain of 5 % . if he had bought it at 5 % less and sold it for re 2 less , he would have made a profit of 10 % . the c . p . of the article was
Options: a ) 344 , b ) 218 , c ) 400 , d ) 388 , e ) 211
Rationale: "explanation : let original cost price is x its selling price = ( 105 / 100 ) * x = 21 x / 20 new cost price = ( 95 / 100 ) * x = 19 x / 20 new selling price = ( 110 / 100 ) * ( 19 x / 20 ) = 209 x / 200 [ ( 21 x / 20 ) - ( 209 x / 200 ) ] = 2 = > x = 400 answer : c ) rs 400"
Answer: c
Question (general): a city with a population of 218,000 is to be divided into 10 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district . what is the minimum possible population that the least populated district could have ?
Options: a ) 19,920 , b ) 19,940 , c ) 19,960 , d ) 19,980 , e ) 20,000
Rationale: "the minimum possible population occurs when all the other districts have a population that is 10 % greater than the least populated district . let p be the population of the least populated district . then 218,000 = p + 9 ( 1.1 ) p 10.9 p = 218,000 p = 20,000 the answer is e ."
Answer: e
Question (general): two trains of equal are running on parallel lines in the same direction at 47 km / hr and 36 km / hr . the faster train passes the slower train in 36 sec . the length of each train is ?
Options: a ) 50 , b ) 88 , c ) 66 , d ) 55 , e ) 22
Rationale: "let the length of each train be x m . then , distance covered = 2 x m . relative speed = 47 - 36 = 11 km / hr . = 11 * 5 / 18 = 55 / 18 m / sec . 2 x / 36 = 55 / 18 = > x = 55 . answer : d"
Answer: d
Question (general): a confectioner decides to sell all of his pastry due to the coming holiday . his pastry goods are equally divided among a group of 30 regular customers . if only 49 customers come to the bakery , each one will receive 6 less pastry goods . how much pastry does the confectioner needs to sell ?
Options: a ) 450 . , b ) 412 . , c ) 432 . , d ) 502 . , e ) 522 .
Rationale: pastry is divided in 30 customers equally . so , total number of pastry must be a multiple of 30 only option a satisfies the condition , and hence is the answer
Answer: a
Question (general): if x and y are positive integers and x = 5 y + 7 , what is the remainder when x is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "this question asks what is . . . ( the answer ) , so we know that the answer will be consistent . as such , we can test values to quickly get the solution . we ' re told that x and y are positive integers and x = 5 y + 7 . we ' re asked for the remainder when x is divided by 5 . if . . . . y = 1 x = 12 12 / 5 = 2 remainder 2 final answer : c"
Answer: c
Question (gain): on a certain road 14 % of the motorists exceed the posted speed limit and receive speeding tickets , but 20 % of the motorists who exceed the posted speed limit do not receive speeding tickets . what percent of the motorists on the road exceed the posted speed limit ?
Options: a ) 10.5 % , b ) 12.5 % , c ) 17.5 % , d ) 22 % , e ) 30 %
Rationale: "answer is c . this question is in the og and thus well explained by ets . those who exceed : x so x = 14 % + 0,2 x id est x = 17,5 %"
Answer: c
Question (general): the average weight of 8 person ' s increases by 6 kg when a new person comes in place of one of them weighing 45 kg . what is the weight of the new person ?
Options: a ) 90 , b ) 93 , c ) 56 , d ) 80.5 , e ) 78
Rationale: "total increase in weight = 8 × 6 = 48 if x is the weight of the new person , total increase in weight = x − 45 = > 48 = x - 45 = > x = 48 + 45 = 93 answer : b"
Answer: b
Question (general): how many digits 2 ^ 300 has ?
Options: a ) 31 , b ) 35 , c ) 50 , d ) 91 , e ) 101
Rationale: 2 ^ 10 = 1.024 * 10 ^ 3 = > 2 ^ 100 = ( 1.024 ) ^ 10 * 10 ^ 90 therefore 91 digits would be my best guess d
Answer: d
Question (general): after distributing the sweets equally among 25 children , 8 sweets remain . had the number of children been 28 , 22 sweets would have been left after equal distribution . what was the total number of sweets ?
Options: a ) 328 , b ) 348 , c ) 358 , d ) 362 , e ) data inadequate
Rationale: explanation : let the total number of sweets be ( 25 x + 8 ) . then , ( 25 x + 8 ) - 22 is divisible by 28 ( 25 x - 14 ) is divisible by 28 28 x - ( 3 x + 14 ) is divisible by 28 ( 3 x + 14 ) is divisible by 28 x = 14 . therefore total number of sweets = ( 25 x 14 + 8 ) = 358 . answer : c
Answer: c
Question (general): a batsman scored 150 runs which included 3 boundaries and 8 sixes . what percent of his total score did he make by running between the wickets ?
Options: a ) 45 ( 4 / 11 ) % , b ) 60 % , c ) 45 ( 5 / 11 ) % , d ) 44 ( 5 / 11 ) % , e ) none of these
Rationale: "explanation : total runs scored = 150 total runs scored from boundaries and sixes = 3 x 4 + 8 x 6 = 60 total runs scored by running between the wickets = 150 - 60 = 90 required % = ( 90 / 150 ) × 100 = 60 % answer : option b"
Answer: b
Question (gain): rs . 2500 is divided into two parts such that if one part be put out at 5 % simple interest and the other at 6 % , the yearly annual income may be rs . 120 . how much was lent at 5 % ?
Options: a ) 2333 , b ) 2777 , c ) 3000 , d ) 1000 , e ) 2871
Rationale: ( x * 5 * 1 ) / 100 + [ ( 2500 - x ) * 6 * 1 ] / 100 = 120 x = 3000 answer : c
Answer: c
Question (general): when 52416 is divided by 312 , the quotient is 168 . what will be the quotient when 52.416 is divided by 0.000168 ?
Options: a ) 5 , b ) 6 , c ) 4 , d ) 3 , e ) 8
Rationale: for the 1 st no . there are 2 digits after decimal for the 2 nd no . there are 7 digits after decimal total no . of decimals = 9 req . no . of digits = ( n - 1 ) = ( 9 - 1 ) = 8 answer : e
Answer: e
Question (general): the average age of a class of 23 students is 22 years . the average increased by 1 when the teacher ' s age also included . what is the age of the teacher ?
Options: a ) 40 , b ) 41 , c ) 46 , d ) 42 , e ) 49
Rationale: "total age of all students = 23 ã — 22 total age of all students + age of the teacher = 24 ã — 23 age of the teacher = 24 ã — 23 â ˆ ’ 23 ã — 22 = 23 ( 24 â ˆ ’ 22 ) = 23 ã — 2 = 46 answer is c ."
Answer: c
Question (general): x is a positive integer less than 600 . when x is divided by 7 , the remainder is 1 ; when x is divided by 3 , the remainder is 2 . how many x are there ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: "the nubmer which when divided by 7 leaves remainder 1 should be of the form 7 k + 1 this number when divided by 3 leaves remainder 2 . so , ( 7 k + 1 ) - 2 should be divisible by 3 or 7 k - 1 should be divisible by 3 . we now put the values of k starting from 0 to find first number divisible by 3 we find 1 st number at k = 1 thus smallest number will be 7 ( 1 ) + 1 = 8 now , next number will be = 8 + lcm of 37 i . e 29 now we will find number of all such values less than 500 by using the formula for last term of an a . p 8 + ( n - 1 ) 21 = 600 n = 25.42 or n = 25 answer : - e"
Answer: e
Question (geometry): if the radius of a circle is increased by 30 % then the area is increased by :
Options: a ) 44 % , b ) 69 % , c ) 144 % , d ) 40 % , e ) none of the above
Rationale: "initially a = pi * r 2 now r 2 = 130 / 100 r then area = pi * ( 130 r / 100 ) 2 area = 169 r / 100 that is area increases from 100 to 169 = increase in area = 69 % answer : b"
Answer: b
Question (geometry): the length of a rectangle hall is 5 m more than its breadth . the area of the hall is 750 m 2 . the length of the hall is :
Options: a ) 15 m
b ) 22.5 m
c ) 25 m
d ) 30 m
e ) none of these
Rationale: solution let breadth = x metres . then , length = ( x + 5 ) metres . then x ( x + 5 ) = 750 ⇔ x 2 + 5 x − 750 = 0 ⇔ ( x + 30 ) ( x + 25 ) = 0 ⇔ x = 25 . ∴ length = ( x + 5 ) = 30 m . answer d
Answer: d
Question (geometry): what is the perimeter of a square with area p ^ 2 / 16 ?
Options: a ) 3 p / 4
b ) 3 p ^ 2 / 4
c ) p
d ) 3 p ^ 2
e ) 4 p / 3
Rationale: area of square , ( side ) ^ 2 = ( p / 4 ) ^ 2 therefore side of the square = p / 4 perimeter of square = 4 * side = 4 * ( p / 4 ) = p answer is c .
Answer: c
Question (geometry): 65 small identical cubes are used to form a large cube . how many more cubes are needed to add one top layer of small cube all over the surface of the large cube ?
Options: a ) 64
b ) 128
c ) 151
d ) 216
e ) 256
Rationale: 65 small cube will make a large cube with 4 cubes in each line i . e . adding one layer will require one cube at each end and hence new cube will have 6 cubes in each line . total number of small cubes in new cube = 6 ^ 3 = 216 extra cube required = 216 - 65 = 151 hence , c is the answer .
Answer: c
Question (physics): how long does a train 100 m long traveling at 60 kmph takes to cross another train of 170 m in length has a speed of 40 kmph ?
Options: a ) 1.42 sec , b ) 16.8 sec , c ) 5 sec , d ) 1.68 sec , e ) 3.6 sec
Rationale: "d = 100 m s = ( 60 + 40 ) * 5 / 18 = 250 / 3 t = 100 * 9 / 250 = 3.6 sec answer : e"
Answer: e
Question (other): a student committee on academic integrity has 90 ways to select a president and vice president from a group of candidates . the same person can not be both president and vice president . how many candidates are there ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "let the number of people to choose from = n no of people to be chosen = 2 the number of ways 2 people can be chosen from n people = nc 2 now , the two people selected can be arranged in 2 ! ways hence nc 2 * 2 ! = 90 which gives n = 10 answer : d"
Answer: d
Question (general): in the coordinate plane , line a has a slope of - 1 and an x - intercept of 2 . line b has a slope of 5 and a y - intercept of - 10 . if the two lines intersect at the point ( a , b ) , what is the sum a + b ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: the equation of line a is y = - x + 2 the equation of line b is y = 5 x - 10 5 x - 10 = - x + 2 x = 2 y = 0 the point of intersection is ( 2,0 ) and then a + b = 2 . the answer is c .
Answer: c
Question (general): if 9 is added to thrice a number and this sum is multiplied by 6 , the result is the same as if the number is multiplied by 7 and 10 is added to the product . what is the number ?
Options: a ) - 7 , b ) - 8 , c ) - 9 , d ) - 10 , e ) - 11
Rationale: let the number be x ; 6 ( 9 + 3 x ) = 7 x + 10 ; x = - 11 answer : e
Answer: e
Question (gain): a circle graph shows how the megatech corporation allocates its research and development budget : 14 % microphotonics ; 24 % home electronics ; 20 % food additives ; 29 % genetically modified microorganisms ; 8 % industrial lubricants ; and the remainder for basic astrophysics . if the arc of each sector of the graph is proportional to the percentage of the budget it represents , how many degrees of the circle are used to represent basic astrophysics research ?
Options: a ) 8 ° , b ) 10 ° , c ) 18 ° , d ) 36 ° , e ) 52 °
Rationale: "14 % microphotonics ; 24 % home electronics ; 20 % food additives ; 29 % genetically modified microorganisms ; 8 % industrial lubricants ; 100 - ( 14 + 24 + 20 + 29 + 8 ) = 5 % basic astrophysics . 5 % of 360 ° is 18 ° . answer : c ."
Answer: c
Question (general): by how much does the larger root of the equation 2 q ^ 2 + 5 q = 12 exceed the smaller root ?
Options: a ) 5 / 2 , b ) 10 / 3 , c ) 7 / 2 , d ) 14 / 3 , e ) 11 / 2
Rationale: "for 2 q ^ 2 + 5 q = 12 roots are [ - 5 + sqrt ( 25 + 96 ) ] / 4 or [ - 5 - sqrt ( 25 + 96 ) ] / 4 = 1.5 or - 4 hence larger root 1.5 is 1.5 - ( - 4 ) = 5.5 = 11 / 2 greater than smaller root ( - 4 ) . hence option ( e ) ."
Answer: e
Question (geometry): a perfect square is defined as the square of an integer and a perfect cube is defined as the cube of an integer . how many positive integers n are there such that n is less than 30,000 and at the same time n is a perfect square and a perfect cube ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "if n is a perfect square and a perfect cube , then n = a ^ 6 for some integer a . the numbers are 1 ^ 6 = 1 , 2 ^ 6 = 64 , 3 ^ 6 = 729 , 4 ^ 6 = 4096 , 5 ^ 6 = 15,625 . the answer is b ."
Answer: b
Question (general): for the positive integers x , x + 2 , x + 4 , x + 7 , and x + 27 , the mean is how much greater than the median ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 4 , e ) 7
Rationale: "mean = ( x + x + 2 + x + 4 + x + 7 + x + 27 ) / 5 = ( 5 x + 40 ) / 5 = x + 8 median = x + 4 thus mean - median = x + 8 - ( x + 4 ) = 4 answer = d"
Answer: d
Question (general): a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 68 % of the distribution lies one standard deviation g of the mean , what percent of the distribution is less than m + g ?
Options: a ) 16 % , b ) 32 % , c ) 48 % , d ) 84 % , e ) 92 %
Rationale: "16 % ________________________________________________ m + g 34 % ________________________________________________ m 34 % ________________________________________________ m - g 16 % since 68 % lies one standard deviation from mean m , = > 50 % of 68 % lies on either side as it is symmetric about m . thus 16 % lie below m - g and 16 % lie above m + g now below m + g = 16 + 34 + 34 = 84 % hence d"
Answer: d
Question (general): pradeep has to obtain 35 % of the total marks to pass . he got 185 marks and failed by 25 marks . the maximum marks are
Options: a ) 300 , b ) 600 , c ) 800 , d ) 1000 , e ) 900
Rationale: explanation : let their maximum marks be x . then , 35 % of x = 185 + 25 = > 35 / 100 x = 210 x = ( 210100 / 35 ) x = 600 . answer : b
Answer: b
Question (gain): in a sample of 800 high school students in which all students are either freshmen , sophomores , juniors , or seniors , 22 percent are juniors and 75 percent are not sophomores . if there are 160 seniors , how many more freshmen than sophomores are there among the sample of students ?
Options: a ) 42 , b ) 48 , c ) 64 , d ) 76 , e ) 88
Rationale: "200 are sophomores . the number of freshmen is 600 - 160 - 0.22 ( 800 ) = 264 the answer is c ."
Answer: c
Question (geometry): a tailor trims 6 feet from opposite edges of a square piece of cloth , and 5 feet from the other two edges . if 120 square feet of cloth remain , what was the length of a side of the original piece of cloth ?
Options: a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 28
Rationale: "let the original side of the square be x . ( x - 12 ) * ( x - 10 ) = 120 = 10 * 12 x = 22 the answer is b ."
Answer: b
Question (geometry): find the area of a parallelogram with base 14 cm and height 24 cm .
Options: a ) 336 , b ) 384 , c ) 345 , d ) 244 , e ) 242
Rationale: "area of a parallelogram = base * height = 14 * 24 = 336 cm 2 answer : option a"
Answer: a
Question (general): a man saves a certain portion of his income during a year and spends the remaining portion on his personal expenses . next year his income increases by 35 % but his savings increase by 100 % . if his total expenditure in 2 years is double his expenditure in 1 st year , what % age of his income in the first year did he save ?
Options: a ) 25 % , b ) 28 % , c ) 30 % , d ) 32.5 % , e ) 35 %
Rationale: "1 st year income = i 1 st year savings = s 1 st year expense = e 1 2 nd year income = 1.35 i 2 nd year savings = 2 s ( 100 % increase ) 2 nd year expense = e 2 e 1 + e 2 = 2 e 1 e 2 = e 1 that means expenses are same during both years . with increase of 35 % income the savings increased by 100 % . or s = . 35 i or s = 35 % of income e is the answer"
Answer: e
Question (gain): how is 5 % expressed as a decimal fraction ?
Options: a ) 0.5 , b ) 0.05 , c ) 0.005 , d ) 0.0005 , e ) 5
Rationale: "5 / 100 = 0.05 answer : b"
Answer: b
Question (geometry): 34 . the side surface of a cylinder is rolled with a rectangular plate . if the perimeter of the circular base is 6 feet , and the diagonal of the rectangular plate was 10 ft . what is height of the of the cylinder ?
Options: a ) 7 , b ) 10 , c ) 8 , d ) 12 , e ) 15
Rationale: think of a pringles can . if you took off the bottom and top and cut a slit down the length , it would flatten to a rectangle . the dimensions of the rectangle are the height of the can and the circumference of the circle . since you know both , one side and thehypothenuse use pythagoreans theorem or properties of 3 - 4 - 5 triangles to solve for the other side , 8 . correct answer c .
Answer: c
Question (physics): a train traveling at 100 kmph overtakes a motorbike traveling at 64 kmph in 85 seconds . what is the length of the train in meters ?
Options: a ) 400 meters , b ) 1111 meters , c ) 160 meters , d ) 850 meters , e ) none of these
Rationale: train overtakes a bike means that we are talking about total length of the train . ( train ' s head is close to bike when it started and its tail crosses the bike when it overtakes the bike ) relative speed = 100 - 64 = 36 km / h = 36000 m / h time = 85 seconds distance = speed * time 36000 * 85 / 3600 = 850 meters . d is the answer .
Answer: d
Question (general): how many three digit numbers q are divisible by 78 or 91 ?
Options: a ) 17 , b ) 19 , c ) 20 , d ) 21 , e ) 22
Rationale: "the answer will be 19 . explanation : 78 = 2 * 3 * 13 now multiples of 78 , 156 . . . . 780 , now 1000 - 780 = 220 only two more muktiples of 78 can exists . so total number of 3 digit multiples of 78 are 9 + 2 = 11 91 = 13 * 7 - - total number of three digit multiples - - 9 no remember we have a common multiples as well - - 13 * 7 * 6 = 91 * 6 = 546 so total number of multiples q - - 11 + 9 - 1 = 19 . hence answer is 19 . b"
Answer: b
Question (general): how many numbers from 2 to 9 are exactly divisible by 2 ?
Options: a ) a ) 2 , b ) b ) 3 , c ) c ) 5 , d ) d ) 4 , e ) e ) 8
Rationale: "2 / 2 = 1 and 9 / 2 = 4 4 - 1 = 3 3 + 1 = 4 numbers . answer : d"
Answer: d
Question (general): p , q , r enter into a partnership & their share are in the ratio 1 / 2 : 1 / 3 : 1 / 4 , after two months , p withdraws half of the capitals & after 10 months , a profit of rs 378 is divided among them . what is q ' s share ?
Options: a ) 114 , b ) 120 , c ) 134 , d ) 144 , e ) none of these
Rationale: explanation : the ratio of their initial investment = 1 / 2 : 1 / 3 : 1 / 4 = 6 : 4 : 3 let ' s take the initial investment of p , q and r as 6 x , 4 x and 3 x respectively a : b : c = ( 6 x * 2 + 3 x * 10 ) : 4 x * 12 : 3 x * 12 = ( 12 + 30 ) : 4 * 12 : 3 * 12 = ( 4 + 10 ) : 4 * 4 : 12 = 14 : 16 : 12 = 7 : 8 : 6 b ' s share = 378 * ( 8 / 21 ) = 18 * 8 = 144 . answer : option d
Answer: d
Question (general): if a ( a + 5 ) = 36 and b ( b + 5 ) = 36 , where a ≠ b , then a + b =
Options: a ) − 48 , b ) − 5 , c ) 2 , d ) 46 , e ) 48
Rationale: "i . e . if a = 4 then b = - 9 or if a = - 9 then b = 4 but in each case a + b = - 9 + 4 = - 5 answer : option b"
Answer: b