Cheukting/mathqa huggingface dataset:
Question (general): two digits in john ' s age are the same as the digit in the wilson ' s age , but in reverse order . in 21 years john will be twice as old as wilson will be then . what is the difference in their current age ?
Options: a ) 25 , b ) 43 , c ) 14 , d ) 36 , e ) 12
Rationale: john ' s age = 10 x + y so wilson ' s age = 10 y + x . . after 21 years , 10 x + y + 21 = 2 * ( 10 y + x + 21 ) . . . . so 21 + 19 y = 8 x . . . check for odd values of y , y = 1 satisfies the eqn with x = 5 . . . so ages are 51 and 15 and ans as found correctly by u is d . . 36
Answer: d
Question (general): a cab driver 5 days income was $ 45 , $ 50 , $ 60 , $ 65 , $ 70 . then his average income is ?
Options: a ) $ 58 , b ) $ 42 , c ) $ 65 , d ) $ 48 , e ) $ 62
Rationale: avg = sum of observations / number of observations avg income = ( 45 + 50 + 60 + 65 + 70 ) / 5 = 58 answer is a
Answer: a
Question (general): if a : b is 3 : 4 and b : c is 4 : 5 then a : c is equal to
Options: a ) 1 : 3 , b ) 3 : 5 , c ) 3 : 4 , d ) 3 : 7 , e ) 1 : 5
Rationale: the two ratios given are having the same number 4 for b in both the ratios . hence - a : b = 3 : 4 b : c = 4 : 5 = > a : c = 3 : 5 answer b
Answer: b
Question (general): in a box of 9 pencils , a total of 2 are defective . if a customer buys 3 pencils selected at random from the box , what is the probability that neither pencils will be defective ?
Options: a ) 5 / 12 , b ) 1 / 15 , c ) 2 / 13 , d ) 2 / 15 , e ) 1 / 17
Rationale: first , there are 7 c 3 ways you can select 3 good pencils from 4 good ones . second , there are 9 c 3 ways you select 3 pencils from 6 ones in the box . then , the probability that neither pen will be defective is : 7 c 3 / 9 c 3 = 35 / 84 = 5 / 12 answer is a
Answer: a
Question (gain): what profit percent is made by selling an article at a certain price , if by selling at 2 / 3 rd of that price , there would be a loss of 18 % ?
Options: a ) 20 % , b ) 26 % , c ) 42 % , d ) 27 % , e ) 23 %
Rationale: sp 2 = 2 / 3 sp 1 cp = 100 sp 2 = 82 2 / 3 sp 1 = 82 sp 1 = 123 100 - - - 23 = > 23 % answer : e
Answer: e
Question (physics): 8 identical machines , working alone and at their constant rates , take 6 hours to complete a job lot . how long would it take for 6 such machines to perform the same job ?
Options: a ) 2.25 hours , b ) 8 hours , c ) 12 hours , d ) 14.25 hours , e ) 16 hours
Rationale: "let each machine do 1 unit of work for 1 hour 8 machines - - > 8 units of work in 1 hour for 6 hours = 8 * 6 = 48 units of total work is done . now this 48 units of total work must be done by 6 machines 6 units of work ( 6 machines ) - - - > 1 hour for 48 units of work 6 * 8 - - - > 1 * 8 hours b 8 hours"
Answer: b
Question (gain): by selling an article at rs . 800 , a shopkeeper makes a profit of 25 % . at what price should he sell the article so as to make a loss of 40 % ?
Options: a ) s . 429 , b ) s . 480 , c ) s . 429 , d ) s . 128 , e ) s . 384
Rationale: "sp = 800 profit = 25 % cp = ( sp ) * [ 100 / ( 100 + p ) ] = 800 * [ 100 / 125 ] = 640 loss = 40 % = 40 % of 640 = rs . 256 sp = cp - loss = 640 - 256 = rs . 384 answer : e"
Answer: e
Question (gain): milk contains 10 % water . what content of pure milk should be added to 20 liters of milk to reduce this to 5 % ?
Options: a ) 20 liters , b ) 25 liters , c ) 30 liters , d ) 15 liters , e ) 18 liters
Rationale: quantity of water in 20 liters = 10 % of 20 liters = 2 liters let x liters of pure milk be added . then , 2 / ( 20 + x ) = 5 / 100 5 x = 100 x = 20 liters answer is a
Answer: a
Question (physics): it takes avery 3 hours to build a brick wall while tom can do it in 2 hours . if the two start working together and after an hour avery leaves , how much time will it take tom to complete the wall on his own ?
Options: a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 60
Rationale: "avery takes 3 hours tom takes 2 hours efficiency of avery is 1 / 3 units / hr efficiency of tom is 1 / 2 units / hr combined efficiency of tom and avery is 1 / 3 + 1 / 2 = 5 / 6 units / hr since they worked for 1 hour they completed 5 / 6 units of work and 1 / 6 units of work is left which is to be completed by tom ( since avery left ) so time taken by tom to complete the remaining work will be 1 / 6 / 1 / 2 hours = > 1 / 3 * 60 = 20 minutes . . . answer will be ( a )"
Answer: a
Question (general): salesperson a ' s compensation for any week is $ 360 plus 6 percent of the portion of a ' s total sales above $ 2,000 for that week . salesperson b ' s compensation for any week is 8 percent of a ' s total sales for that week . for what amount of total weekly sales would both salepeople earn the same compensation ?
Options: a ) $ 12,000 , b ) $ 18,000 , c ) $ 15,000 , d ) $ 4,500 , e ) $ 4,000
Rationale: "sometime , setting up an equation is an easy way to go with : 360 + 0.06 ( x - 2000 ) = 0.08 x x = 12000 ans : a"
Answer: a
Question (physics): a car gets 40 kilometers per gallon of gasoline . how many gallons of gasoline would the car need to travel 200 kilometers ?
Options: a ) 4.5 , b ) 5 , c ) 6.5 , d ) 7.5 , e ) 8.5
Rationale: "each 40 kilometers , 1 gallon is needed . we need to know how many 40 kilometers are there in 180 kilometers ? 200 ÷ 40 = 5 × 1 gallon = 5 gallons correct answer b"
Answer: b
Question (general): at a monthly meeting , 3 / 5 of the attendees were males and 7 / 8 of the male attendees arrived on time . if 9 / 10 of the female attendees arrived on time , what fraction of the attendees at the monthly meeting did not arrive on time ?
Options: a ) 23 / 200 , b ) 11 / 100 , c ) 7 / 50 , d ) 3 / 20 , e ) 4 / 25
Rationale: males who did not arrive on time are 1 / 8 * 3 / 5 = 3 / 40 of the attendees . females who did not arrive on time are 1 / 10 * 2 / 5 = 2 / 50 of the attendees . the fraction of all attendees who did not arrive on time is 3 / 40 + 2 / 50 = 23 / 200 the answer is a .
Answer: a
Question (probability): there are 15 boys and 10 girls in a class . if three students are selected at random , in how many ways that 1 girl and 2 boys are selected ?
Options: a ) 950 , b ) 1050 , c ) 2150 , d ) 2050 , e ) 1000
Rationale: "n ( s ) = sample space = 25 c 3 = 2300 e = event that 1 girl and 2 boys are selected n ( e ) = we have to select 2 boys from 15 and 1 girl from 10 = 15 c 2 * 10 c 1 = 1050 ans - b"
Answer: b
Question (physics): 12 men can complete a piece of work in 25 days . in how many days can 20 men complete that piece of work ?
Options: a ) 55 days , b ) 77 days , c ) 20 days , d ) 88 days , e ) 15 days
Rationale: "12 * 25 = 20 * x = > x = 15 days answer : e"
Answer: e
Question (gain): consider a lady took a loan from a bank at the rate of 12 % p . a . simple interest . after 3 years she had to pay rs . 7200 interest only for the period . the principal amount borrowed by her was
Options: a ) rs . 2000 , b ) rs . 10000 , c ) rs . 15000 , d ) rs . 20000 , e ) none of these
Rationale: explanation : principal = rs . ( 100 × 7200 / 12 × 3 ) = > rs . 20,000 . answer : d
Answer: d
Question (general): how many pages do you need if you have to write 150 lines of information into pages that each hold 30 lines ?
Options: a ) a ) 7 , b ) b ) 5 , c ) c ) 9 , d ) d ) 8 , e ) e ) none of the above
Rationale: sol . 30 lines per page total 150 lines = 150 / 30 = 5 answer : b
Answer: b
Question (other): a dog takes 10 leaps for every 2 leaps of a hare . if one leap of the dog is equal to 2 leaps of the hare , the ratio of the speed of the dog to that of the hare is :
Options: a ) 5 : 1 , b ) 10 : 1 , c ) 15 : 1 , d ) 20 : 1 , e ) 25 : 1
Rationale: "explanation : dog : hare = ( 10 * 2 ) leaps of hare : 2 leaps of hare = 20 : 2 . answer : b ) 10 : 1"
Answer: b
Question (physics): a train running at the speed of 60 km / hr crosses a pole in 9 seconds . what is the length of the train ?
Options: a ) 100 , b ) 120 , c ) 130 , d ) 150 , e ) 160
Rationale: "speed = ( 60 * 5 / 18 ) m / sec = ( 50 / 3 ) m / sec length of the train = ( speed x time ) = ( 50 / 3 * 9 ) m = 150 m . answer : option d"
Answer: d
Question (geometry): triangle xyz is an isosceles right triangle . if side xy is longer than side yz , and the area of the triangle is 64 , what is the measure of side xy ?
Options: a ) 4 , b ) 16 , c ) 8 , d ) 8 √ 2 , e ) can not be determined from the information provided
Rationale: "ans b . . 16 . xy being larger means it is the hyp . . area = ( 1 / 2 ) * ( yz ) ^ 2 = 64 or yz = 8 * \ sqrt { 2 } . . therefore hyp = xy = 16"
Answer: b
Question (general): a sum of money lent out at s . i . amounts to rs . 780 after 2 years and to rs . 1020 after a further period of 5 years . the sum is ?
Options: a ) s . 684 , b ) s . 500 , c ) s . 540 , d ) s . 740 , e ) s . 840
Rationale: "s . i for 5 years = ( 1020 - 780 ) = rs . 240 . s . i . for 2 years = 240 / 5 * 2 = rs . 96 . principal = ( 780 - 96 ) = rs . 684 answer : a"
Answer: a
Question (general): there are 40 balls which are red , blue or green . if 15 balls are green and the sum of red balls and green balls is less than 25 , at most how many red balls are there ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 9
Rationale: "r + g + b = 40 g = 15 r + g < 25 = > r + 15 < 25 = > r < 10 = > at most 6 red balls answer : e"
Answer: e
Question (gain): the sale price of an article including the sales tax is rs . 616 . the rate of sales tax is 10 % . if the shopkeeper has made a profit of 13 % , then the cost price of the article is :
Options: a ) 545 , b ) 334 , c ) 555 , d ) 664 , e ) 5598
Rationale: "110 % of s . p . = 616 s . p . = ( 616 * 100 ) / 110 = rs . 560 c . p = ( 110 * 560 ) / 113 = rs . 545 answer : option a"
Answer: a
Question (gain): in order to obtain an income of rs . 580 from 15 % stock at rs . 100 , one must make an investment of
Options: a ) 5363 , b ) 6240 , c ) 8700 , d ) 5600 , e ) 2732
Rationale: "to obtain rs . 10 , investment = rs . 100 . to obtain rs . 580 , investment = = rs . 8700 . answer : c"
Answer: c
Question (gain): a shopkeeper sold an article offering a discount of 4 % and earned a profit of 20 % . what would have been the percentage of profit earned if no discount was offered ?
Options: a ) 25 , b ) 28 , c ) 30 , d ) 32 , e ) 34
Rationale: "let c . p . be rs . 100 . then , s . p . = rs . 120 let marked price be rs . x . then , 96 / 100 x = 120 x = 12000 / 96 = rs . 125 now , s . p . = rs . 125 , c . p . = rs . 100 profit % = 25 % . answer : a"
Answer: a
Question (geometry): the surface area of a cube is 1734 sq . cm . find its volume
Options: a ) 2334 cubic . cm
b ) 3356 cubic . cm
c ) 4913 cubic . cm
d ) 3478 cubic . cm
e ) none of these
Rationale: explanation : let the edge of the cube bea . then , 6 a 2 = 1734 = > a = 17 cm . volume = a 3 = 173 = 4193 cm 3 answer : c
Answer: c
Question (physics): apple street begins at peach street and runs directly east for 3.2 kilometers until it ends when it meets cherry street . apple street is intersected every 200 meters by a perpendicular street , and each of those streets other than peach street and cherry street is given a number beginning at 1 st street ( one block east of peach street ) and continuing consecutively ( 2 nd street , 3 rd street , etc . . . ) until the highest - numbered street one block west of cherry street . what is the highest - numbered street that intersects apple street ?
Options: a ) 14 th , b ) 15 th , c ) 16 th , d ) 17 th , e ) 18 th
Rationale: 3.2 km / 200 m = 16 . however , the street at the 3.2 - km mark is not 16 th street ; it is cherry street . therefore , the highest numbered street is 15 th street . the answer is b .
Answer: b
Question (other): a bag contains 8 red , 6 blue and 4 green balls . if 2 ballsare picked at random , what is the probability that both are red ?
Options: a ) 1 / 13 , b ) 2 / 23 , c ) 5 / 26 , d ) 7 / 30 , e ) 3 / 23
Rationale: "p ( both are red ) , = 8 c 216 c 2 = 8 c 216 c 2 = 28 / 120 = 7 / 30 d"
Answer: d
Question (physics): a , b and c completed a piece of work , a worked for 6 days , b for 9 days and c for 4 days . their daily wages were in the ratio of 3 : 4 : 5 . find the daily wages of c , if their total earning was $ 1480 ?
Options: a ) $ 100 , b ) $ 150 , c ) $ 125 , d ) $ 134 , e ) $ 243
Rationale: a $ 100 3 x 4 x 5 x 6 9 4 18 x + 36 x + 20 x = 1480 74 x = 1480 = > x = 20 5 x = 100 rs .
Answer: a
Question (general): the average salary of the employees in a office is rs . 120 / month . the avg salary of officers is rs . 440 and of non officers is rs 110 . if the no . of officers is 15 , then find the no of nonofficers in the office .
Options: a ) 400 , b ) 420 , c ) 480 , d ) 450 , e ) 510
Rationale: "let no . of non - officers be x 15 * 440 + x * 110 = ( x + 15 ) 120 x = 480 c"
Answer: c
Question (general): what is the sum of the multiples of 5 from 80 to 140 , inclusive ?
Options: a ) 560 , b ) 780 , c ) 990 , d ) 1008 , e ) 1200
Rationale: "the formula we want to use in this type of problem is this : average * total numbers = sum first , find the average by taking the sum of the f + l number and divide it by 2 : a = ( f + l ) / 2 second , find the total numbers in our range by dividing our f and l numbers by 5 and add 1 . ( 140 / 5 ) - ( 80 / 5 ) + 1 multiply these together so what we show average * total numbers = sum ( 80 + 140 ) / 2 * ( 140 / 5 ) - ( 80 / 5 ) + 1 = sum 110 * 9 = 990 c"
Answer: c
Question (geometry): a rectangular field is to be fenced on three sides leaving a side of 30 feet uncovered . if the area of the field is 720 sq . feet , how many feet of fencing will be required ?
Options: a ) 78 , b ) 40 , c ) 68 , d ) 88 , e ) none
Rationale: "explanation we have : l = 30 ft and lb = 720 sq . ft . so , b = 24 ft . length of fencing = ( l + 2 b ) = ( 30 + 48 ) ft = 78 ft . answer a"
Answer: a
Question (physics): jack and jill are marathon runners . jack can finish a marathon ( 42 km ) in 5 hours and jill can run a marathon in 4.2 hours . what is the ratio of their average running speed ? ( jack : jill )
Options: a ) 14 / 15 , b ) 15 / 14 , c ) 4 / 5 , d ) 21 / 25 , e ) can not be determined
Rationale: "average speed of jack = distance / time = 42 / 5 average speed of jill = 42 / ( 4.2 ) = 10 ratio of average speed of jack to jill = ( 42 / 5 ) / 10 = 42 / 50 = 21 / 25 answer d"
Answer: d
Question (other): a bottle contains a certain solution . in the bottled solution , the ratio of water to soap is 3 : 2 , and the ratio of soap to salt is three times this ratio . the solution is poured into an open container , and after some time , the ratio of water to soap in the open container is halved by water evaporation . at that time , what is the ratio of water to salt in the solution ?
Options: a ) 1 : 1 , b ) 2 : 3 , c ) 3 : 2 , d ) 9 : 4 , e ) 27 : 8
Rationale: "water : soap = 3 : 2 soap : salt = 9 : 2 = > for 9 soap , salt = 2 = > for 2 soap , salt = ( 2 / 9 ) * 2 = 4 / 9 so , water : soap : salt = 3 : 2 : 4 / 9 = 27 : 18 : 4 after open container , water : soap : salt = 13.5 : 18 : 4 so , water : salt = 13.5 : 4 = 27 : 8 answer : e"
Answer: e
Question (other): at a party , 13 guests brought wine and 14 guests brought beer . if exactly 11 guests brought only one of the two types of drinks , how many guests brought both types of drinks ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 14
Rationale: say x guests brought both drinks . ( 13 - x ) + ( 14 - x ) = 11 - - > x = 8 . answer : d .
Answer: d
Question (general): a sum of money is put out at compound interest for 2 years at 20 % . it would earn rs . 482 more if the interest were paid half - yearly . calculate the sum .
Options: a ) 2878 , b ) 279 , c ) 279 , d ) 482 , e ) 661
Rationale: p ( 11 / 10 ) 4 - p ( 6 / 5 ) 2 = 482 p = 2000 answer : d
Answer: d
Question (gain): a broker invested her own money in the stock market . during the first year , she increased her stock market wealth by 75 percent . in the second year , largely as a result of a slump in the stock market , she suffered a 30 percent decrease in the value of her stock investments . what was the net increase or decrease on her overall stock investment wealth by the end of the second year ?
Options: a ) − 5 % , b ) 5 % , c ) 15 % , d ) 20 % , e ) 22.5 %
Rationale: "the actual answer is obtained by multiplying 175 % by 70 % and subtracting 100 % from this total . that is : 175 % × 70 % = 122.5 % ; 122.5 % − 100 % = 122.5 % . answer : e"
Answer: e
Question (general): farm tax is levied on the 50 % of the cultivated land . the tax department collected total $ 3840 through the farm tax from the village of mr . william . mr . william paid only $ 480 as farm tax . the percentage of total land of mr . willam over the total taxable land of the village is :
Options: a ) 15 % , b ) 25 % , c ) 0.125 % , d ) 0.2083 % , e ) none
Rationale: "this will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village . that leads to ( 480 / 3840 ) x 100 = 12.5 % in percentage terms . but the question asks ratio between his total land to total cultivated land . hence the answer is 12.5 % x ( 100 / 50 ) = 25 % the correct answer is ( b ) ."
Answer: b
Question (general): the total number of digits used in numbering the pages of a book having 266 pages is
Options: a ) 732 , b ) 990 , c ) 109 , d ) 130 , e ) 690
Rationale: "total number of digits = ( no . of digits in 1 - digit page nos . + no . of digits in 2 - digit page nos . + no . of digits in 3 - digit page nos . ) = ( 1 x 9 + 2 x 90 + 3 x 167 ) = ( 9 + 180 + 501 ) = 690 . answer : e"
Answer: e
Question (other): the ratio of incomes of two person p 1 and p 2 is 5 : 4 and the ratio of their expenditures is 3 : 2 . if at the end of the year , each saves rs . 1400 , then what is the income of p 1 ?
Options: a ) s . 800 , b ) s . 2400 , c ) s . 4000 , d ) s . 3500 , e ) s . 4200
Rationale: "let the income of p 1 and p 2 be rs . 5 x and rs . 4 x respectively and let their expenditures be rs . 3 y and 2 y respectively . then , 5 x – 3 y = 1400 … ( i ) and 4 x – 2 y = 1400 … … . . ( ii ) on multiplying ( i ) by 2 , ( ii ) by 3 and subtracting , we get : 2 x = 1400 - > x = 700 p 1 ’ s income = rs 5 * 700 = rs . 3500 answer : d"
Answer: d
Question (gain): the value of a machine depreciates at the rate of 10 % every year . it was purchased 3 years ago . if its present value is rs 8,748 , its purchase price was ?
Options: a ) rs 16,000 , b ) rs 18,000 , c ) rs 12,000 , d ) rs 14,000 , e ) none of these
Rationale: "we have p = 8748 , r = - 10 and n = 3 therefore , the purchase price of the machine = p / ( 1 + ( r / 100 ) ) n = 8748 / ( 1 - ( 10 / 100 ) ) 3 = 8748 x ( 100 / 90 ) x ( 100 / 90 ) x ( 100 / 90 ) = 12,000 . answer : c"
Answer: c
Question (general): a new home buyer pays 4 % annual interest on her first mortgage and 9 % annual interest on her second mortgage . if she borrowed a total of $ 340,000 , 80 % of which was in the first mortgage , what is her approximate monthly interest payment ?
Options: a ) $ 1,416 , b ) $ 1,733 , c ) $ 3,466 , d ) $ 13,333 , e ) $ 20,796
Rationale: "0.04 x + 0.09 y = 340000 [ 1 ] 0.04 x = 0.80 * 340000 = 272000 [ 2 ] 272000 + 0.09 y = 340000 - - > 0.09 y = 64000 [ 3 ] 272000 / 12 = 22666.67 [ 4 ] 64000 / 12 = 5666.67 [ 5 ] adding [ 4,5 ] we get : 28333.33 [ 6 ] dividing [ 6 ] / 2 to get an average we get 1.416 , ans a"
Answer: a
Question (general): a mixture of 150 liters of wine and water contains 10 % water . how much more water should be added so that water becomes 25 % of the new mixture ?
Options: a ) 10 , b ) 30 , c ) 20 , d ) 15 , e ) 16
Rationale: "number of liters of water in 150 liters of the mixture = 10 % of 150 = 10 / 100 * 150 = 15 liters . p liters of water added to the mixture to make water 25 % of the new mixture . total amount of water becomes ( 15 + p ) and total volume of mixture is ( 150 + p ) . ( 15 + p ) = 25 / 100 * ( 150 + p ) 60 + 4 p = 150 + p p = 30 liters . answer : b"
Answer: b
Question (general): what is the difference between the local values of 8 in the number 58408 ?
Options: a ) 2992 , b ) 7992 , c ) 2877 , d ) 2077 , e ) 6229
Rationale: explanation : 8000 â € “ 8 = 7992 answer : b
Answer: b
Question (general): three numbers are in the ratio of 2 : 3 : 4 . if the sum of the squares of the extremes is 180 , then the middle number is :
Options: a ) 6 , b ) 12 , c ) 15 , d ) 9 , e ) 7
Rationale: "number be = 2 x , 3 x , 4 x , ( 2 x ) 2 + ( 4 x ) 2 = 180 20 x = 180 ⇒ x = 9 ⇒ x = 3 , midline number = 3 × 3 = 9 answer : d"
Answer: d
Question (geometry): the area of a parallelogram is 147 sq m and its base is thrice the corresponding height . then the length of the base is ?
Options: a ) 14 m , b ) 29 m , c ) 49 m , d ) 7 , e ) none
Rationale: b * h = 147 b * h = 147 = > b ^ 2 = 49 m . b = 7 answer : ( d )
Answer: d
Question (physics): a contractor undertakes to complete the construction of a tunnel 720 meters long in 240 days and employs 60 men for the purpose . after 120 days , he finds that only 240 meters of the tunnel is complete . how many more men should be employ in order to complete the work in time ?
Options: a ) 22 , b ) 27 , c ) 60 , d ) 88 , e ) 12
Rationale: in 120 days , only 240 m of the tunnel is constructed by 60 men . the remaining 120 days , 480 m of the tunnel can be constructed by 120 men . additional number of men required = 120 - 60 = 60 men . answer : b
Answer: b
Question (physics): a certain automobile company ’ s best - selling model is the speedster . the speedster , like all of their other models , comes in coupe and convertible styles . 2 / 3 of the current inventory is speedsters , of which 4 / 5 are convertibles . if there are 50 vehicles that are not speedsters , how many speedster convertibles are there ?
Options: a ) 30 , b ) 48 , c ) 60 , d ) 80 , e ) 90
Rationale: "total vehicle = 2 / 3 of speedster + 1 / 3 of others . speedster convertibles = 2 / 3 total vehicle * 4 / 5 given : 1 / 3 constitutes 50 vehicles . hence 2 / 3 constitutes 100 speedster convertibls = 100 * 4 / 5 = 80 d"
Answer: d
Question (general): if there are 4 peanuts in a box and mary puts 12 more peanuts inside , how many peanuts are in the box ?
Options: a ) 8 , b ) 16 , c ) 10 , d ) 11 , e ) 12
Rationale: "12 + 4 = 16 correct answer is b ) 16"
Answer: b
Question (other): 4 dice are thrown and the sum of the numbers noted is 10 . find the probability that all the numbers lie between 2 and 5 ( both inclusive ) ?
Options: a ) 11 / 79 , b ) 10 / 79 , c ) 12 / 79 , d ) 13 / 79 , e ) 14 / 79
Rationale: sum of numbers noted on 4 dice ( with six faces ) to be 10 will include combinations : ( 1,1 , 2,6 ) ( 1,1 , 3,5 ) ( 1,1 , 4,4 ) ( 1,1 , 5,3 ) ( 1,1 , 6,2 ) ( 1,2 , 1,6 ) ( 1,2 , 2,5 ) ( 1,2 , 3,4 ) ( 1,2 , 4,3 ) ( 1,2 , 5,2 ) ( 1,2 , 6,1 ) ( 1,3 , 1,5 ) ( 1,3 , 2,4 ) ( 1,3 , 3,3 ) ( 1,3 , 4,2 ) ( 1,3 , 5,1 ) ( 1,4 , 1,4 ) ( 1,4 , 2,3 ) ( 1,4 , 3,2 ) ( 1,4 , 4,1 ) ( 1,5 , 1,3 ) ( 1,5 , 2,2 ) ( 1,5 , 3,1 ) ( 1,6 , 1,2 ) ( 1,6 , 2,1 ) ( 2,1 , 1,6 ) ( 2,1 , 2,5 ) ( 2,1 , 3,4 ) ( 2,1 , 4,3 ) ( 2,1 , 5,2 ) ( 2,1 , 6,1 ) ( 2,2 , 1,5 ) ( 2,2 , 2,4 ) ( 2,2 , 3,3 ) ( 2,2 , 4,2 ) ( 2,2 , 5,1 ) ( 2,3 , 1,4 ) ( 2,3 , 2,3 ) ( 2,3 , 3,2 ) ( 2,3 , 4,1 ) ( 2,4 , 1,3 ) ( 2,4 , 2,2 ) ( 2,4 , 3,1 ) ( 2,5 , 1,2 ) ( 2,5 , 2,1 ) ( 2,6 , 1,1 ) ( 3,1 , 1,5 ) ( 3,1 , 2,4 ) ( 3,1 , 3,3 ) ( 3,1 , 4,2 ) ( 3,1 , 5,1 ) ( 3,2 , 1,4 ) ( 3,2 , 2,3 ) ( 3,2 , 3,2 ) ( 3,2 , 4,1 ) ( 3,3 , 1,3 ) ( 3,3 , 2,2 ) ( 3,3 , 3,1 ) ( 3,4 , 1,2 ) ( 3,4 , 2,1 ) ( 3,5 , 1,1 ) ( 4,1 , 1,4 ) ( 4,1 , 2,3 ) ( 4,1 , 3,2 ) ( 4,1 , 4,1 ) ( 4,2 , 1,3 ) ( 4,2 , 2,2 ) ( 4,2 , 3,1 ) ( 4,3 , 1,2 ) ( 4,3 , 2,1 ) ( 4,4 , 1,1 ) ( 5,1 , 1,3 ) ( 5,1 , 2,2 ) ( 5,1 , 3,1 ) ( 5,2 , 1,2 ) ( 5,2 , 2,1 ) ( 5,3 , 1,1 ) ( 6,1 , 1,2 ) ( 6,1 , 2,1 ) - - - - - - - total 79 combinations with all the numbers lie between 2 and 5 are ( 2,2 , 2,4 ) ( 2,2 , 3,3 ) ( 2,2 , 4,2 ) ( 2,3 , 2,3 ) ( 2,3 , 3,2 ) ( 2,4 , 2,2 ) ( 3,2 , 2,3 ) ( 3,2 , 3,2 ) ( 3,3 , 2,2 ) ( 4,2 , 2,2 ) - - - - - - total 10 so probability = 10 / 79 answer : b
Answer: b
Question (physics): a truck covers a distance of 200 metres in 1 minute whereas a bus covers a distance of 100 kms in 50 minutes . the ratio of their speeds is ?
Options: a ) 2 : 3 , b ) ratio 1 : 5 , c ) ratio 1 : 10 , d ) ratio 9 : 13 , e ) ratio 7 : 15
Rationale: "ratio of speeds = ( 200 / 60 ) 18 / 5 : 60 * 100 / 50 = 12 : 120 = 1 : 10 answer is c"
Answer: c