Cheukting/mathqa huggingface dataset:
Question (general): in an election between two candidates a and b , the number of valid votes received by a exceeds those received by b by 15 % of the total number of votes polled . if 20 % of the votes polled were invalid and a total of 5720 votes were polled , then how many valid votes did b get ?
Options: a ) 1859 , b ) 2999 , c ) 2834 , d ) 2777 , e ) 2991
Rationale: "let the total number of votes polled in the election be 100 k . number of valid votes = 100 k - 20 % ( 100 k ) = 80 k let the number of votes polled in favour of a and b be a and b respectively . a - b = 15 % ( 100 k ) = > a = b + 15 k = > a + b = b + 15 k + b now , 2 b + 15 k = 80 k and hence b = 32.5 k it is given that 100 k = 5720 32.5 k = 32.5 k / 100 k * 85720 = 1859 the number of valid votes polled in favour of b is 1859 . answer : a"
Answer: a
Question (general): 10 x 1.8 - 2 x 1.5 / 0.3 = ?
Options: a ) 30 , b ) 20 , c ) 15 , d ) 44 , e ) 50
Rationale: given expression = ( 18 - 3.0 ) / 0.3 = 15 / 0.3 = 150 / 3 = 50 answer is e .
Answer: e
Question (gain): there are 1000 students in a school and among them 20 % of them attends chess class . 10 % of the students who are in the chess class are also enrolled for swimming . no other students are interested in swimming so how many will attend the swimming class if all enrolled attends ?
Options: a ) 1 , b ) 10 , c ) 100 , d ) 50 , e ) 20
Rationale: "20 % of 1000 gives 200 . so 200 attends chess and 10 % of 200 gives 20 . so 20 enrolled for swimming answer : e"
Answer: e
Question (general): an object thrown directly upward is at a height of h feet after t seconds , where h = - 15 ( t - 2 ) ^ 2 + 150 . at what height , in feet , is the object 2 seconds after it reaches its maximum height ?
Options: a ) 72 , b ) 90 , c ) 124 , d ) 132 , e ) 140
Rationale: "we see that h will be a maximum h = 150 when t - 2 = 0 , that is when t = 2 . at t = 4 , h = - 15 ( 4 - 2 ) ^ 2 + 150 = - 15 ( 4 ) + 150 = 90 the answer is b ."
Answer: b
Question (physics): a trader sells 66 meters of cloth for rs . 660 at the profit of rs . 5 per metre of cloth . what is the cost price of one metre of cloth ?
Options: a ) 26 , b ) 88 , c ) 90 , d ) 42 , e ) 5
Rationale: "sp of 1 m of cloth = 660 / 66 = rs . 10 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 10 - rs . 5 = rs . 5 answer : e"
Answer: e
Question (general): what is the sum of the first 15 terms of an a . p whose 11 th and 7 th terms are 5.25 and 3.25 respectively
Options: a ) 56.25 , b ) 60 , c ) 52.5 , d ) 5.25 , e ) none of these
Rationale: a + 10 d = 5.25 , a + 6 d = 3.25 , 4 d = 2 , d = ½ a + 5 = 5.25 , a = 0.25 = ¼ , s 15 = 15 / 2 ( 2 * ¼ + 14 * ½ ) = 15 / 2 ( 1 / 2 + 14 / 2 ) = 15 / 2 * 15 / 2 = 225 / 4 = 56.25 answer : a
Answer: a
Question (general): the average marks of a class of 30 students is 40 and that of another class of 50 students is 70 . find the average marks of all the students ?
Options: a ) 52.5 , b ) 52.9 , c ) 52.1 , d ) 58.75 , e ) 42.5
Rationale: "sum of the marks for the class of 30 students = 30 * 40 = 1200 sum of the marks for the class of 50 students = 50 * 70 = 3500 sum of the marks for the class of 80 students = 1200 + 3500 = 4700 average marks of all the students = 4700 / 80 = 58.75 answer : d"
Answer: d
Question (geometry): the ratio of the length and the width of a rectangle is 4 : 3 and the area of the rectangle is 6348 sq cm . what is the ratio of the width and the area of the rectangle ?
Options: a ) 1 : 96 , b ) 1 : 99 , c ) 1 : 94 , d ) 1 : 92 , e ) 1 : 91
Rationale: "let the length and the width be 4 x and 3 x respectively . area = ( 4 x ) ( 3 x ) = 6348 12 x ^ 2 = 6348 x ^ 2 = 529 x = 23 the ratio of the width and the area is 3 x : 12 x ^ 2 = 1 : 4 x = 1 : 92 the answer is d ."
Answer: d
Question (general): rates for having a manuscript typed at a certain typing service are $ 5 per page for the first time a page is typed and $ 3 per page each time a page is revised . if a certain manuscript has 100 pages , of which 30 were revised only once , 20 were revised twice , and the rest required no revisions , what was the total cost of having the manuscript typed ?
Options: a ) $ 430 , b ) $ 620 , c ) $ 650 , d ) $ 680 , e ) $ 710
Rationale: "for 100 - 30 - 20 = 50 pages only cost is 5 $ per page for the first time page is typed - 50 * 5 = 250 $ ; for 30 pages the cost is : first time 5 $ + 3 $ of the first revision - 30 * ( 5 + 3 ) = 240 $ ; for 20 pages the cost is : first time 5 $ + 3 $ of the first revision + 3 $ of the second revision - 20 ( 5 + 3 + 3 ) = 220 $ ; total : 250 + 240 + 220 = 710 $ . answer : e ."
Answer: e
Question (probability): three unbiased coins are tossed . what is the probability of getting at least 2 heads ?
Options: a ) 1 / 4 , b ) 1 / 2 , c ) 1 / 3 , d ) 1 / 8 , e ) 1 / 6
Rationale: "here s = { ttt , tth , tht , htt , thh , hth , hht , hhh } let e = event of getting at least two heads = { thh , hth , hht , hhh } p ( e ) = n ( e ) / n ( s ) = 4 / 8 = 1 / 2 answer b ."
Answer: b
Question (general): the captain of a cricket team of 11 members is 26 years old and the wicket keeper is 2 years older . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . what is the average age of the team ?
Options: a ) 23 years , b ) 22 years , c ) 25 years , d ) 26 years , e ) 27 years
Rationale: "explanation let the average age of the whole team by x years . 11 x â € “ ( 26 + 28 ) = 9 ( x - 1 ) 11 x â € “ 9 x = 45 2 x = 45 x = 22 . so , average age of the team is 22 years . answer b"
Answer: b
Question (general): if josh , doug , and brad have a total of $ 68 between them , and josh has two times as much money as brad but only 3 - fourths as much as doug , how much money does brad have ?
Options: a ) $ 10 , b ) $ 24 , c ) $ 26 , d ) $ 12 , e ) $ 36
Rationale: josh + doug + brad = 68 ; josh = 2 brad , josh = 3 / 4 doug josh + 1 / 2 josh + 4 / 3 josh = 68 ( substituted the given values ) josh = 24 . 24 = 3 / 4 doug = > doug = 32 josh + doug + brad = 68 24 + 32 + brad = 68 brad = 12 answer is d .
Answer: d
Question (physics): mahesh can do a piece of work in 45 days . he works at it for 20 days and then rajesh finished it in 30 days . how long will y take to complete the work ?
Options: a ) 54 , b ) 25 , c ) 37 , d ) 41 , e ) 30
Rationale: work done by mahesh in 45 days = 20 * 1 / 45 = 4 / 9 remaining work = 1 - 4 / 9 = 5 / 9 5 / 9 work is done by rajesh in 30 days whole work will be done by rajesh is 30 * 9 / 5 = 54 days answer is a
Answer: a
Question (physics): the speed of a car is 100 km in the first hour and 30 km in the second hour . what is the average speed of the car ?
Options: a ) 50 kmph , b ) 65 kmph , c ) 75 kmph , d ) 85 kmph , e ) 65 kmph
Rationale: "explanation : s = ( 100 + 30 ) / 2 = 65 kmph e )"
Answer: e
Question (physics): the hour hand of a watch rotates 30 degrees every hour . how many complete rotations does the hour hand make in 6 days ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: explanation : there are 360 degrees in a complete circle , so 360 / 30 = 12 hours to make one full circle . in 6 days there are 24 hours x 6 = 144 hours total . the total number of rotations will be 144 / 12 = 12 . answer : ( c )
Answer: c
Question (general): find the remainder when 6 ^ 23 is divided by 5 ?
Options: a ) 3 , b ) 2 , c ) 1 , d ) 0 , e ) 4
Rationale: "6 ^ 23 = 6 ^ ( 4 * 5 + 3 ) = 6 ^ ( 20 ) * 6 ^ 3 last 3 digits = 216 216 / 5 remainder = 1 answer : c"
Answer: c
Question (physics): a vessel of capacity 75 litres is fully filled with pure milk . nine litres of milk is removed from the vessel and replaced with water . nine litres of the solution thus formed is removed and replaced with water . find the quantity of pure milk in the final milk solution ?
Options: a ) 23.89 , b ) 72.9 , c ) 58.08 , d ) 78.3 , e ) 79.3
Rationale: "explanation : let the initial quantity of milk in vessel be t litres . let us say y litres of the mixture is taken out and replaced by water for n times , alternatively . quantity of milk finally in the vessel is then given by [ ( t - y ) / t ] n * t for the given problem , t = 75 , y = 9 and n = 2 . hence , quantity of milk finally in the vessel = [ ( 75 - 9 ) / 75 ] ^ 2 ( 75 ) = 58.08 litres . answer : option c"
Answer: c
Question (physics): riya and priya set on a journey . riya moves eastward at a speed of 25 kmph and priya moves westward at a speed of 40 kmph . how far will be priya from riya after 15 minutes
Options: a ) 18 kms , b ) 16 kms , c ) 50 kms , d ) 30 kms , e ) 40 kms
Rationale: "total eastward distance = 25 kmph * 1 / 4 hr = 6.25 km total westward distance = 40 kmph * 1 / 4 hr = 10 km total distn betn them = 6.25 + 10 = 16.25 km ans 16 km answer : b"
Answer: b
Question (general): the product of two successive numbers is 9506 . which is the smaller of the two numbers ?
Options: a ) 78 , b ) 68 , c ) 88 , d ) 97 , e ) 37
Rationale: "d 97 from the given alternatives , 97 × 98 = 9506 ∴ smaller number = 97"
Answer: d
Question (general): if 2 ^ 4 , 3 ^ 3 , and 10 ^ 3 are factors of the product of 1,452 and w , where w is a positive integer , what is the smallest possible value of w ?
Options: a ) 198 , b ) 288 , c ) 363 , d ) 360 , e ) 484
Rationale: i will go with d ( pending elements to match is 2 ^ 2 * 3 ^ 2 * 10 ^ 1 = 360
Answer: d
Question (other): the l . c . m . of 2 numbers is 100 . the numbers are in the ratio 4 : 1 . find their product ?
Options: a ) 1200 , b ) 2000 , c ) 2500 , d ) 3200 , e ) 1250
Rationale: "let the numbers be 4 x and x l . c . m . = 4 x 4 x = 100 x = 25 the numbers are = 100 and 25 required product = 100 * 25 = 2500 answer is c"
Answer: c
Question (general): a , b , c subscribe rs . 50,000 for a business . a subscribes rs . 4000 more than b and b rs . 5000 more than c . out of a total profit of rs . 30,000 , b receives :
Options: a ) s . 10,000 , b ) s . 10,200 , c ) s . 10,400 , d ) s . 10,700 , e ) s . 10,800
Rationale: "let c = x . then , b = x + 5000 and a = x + 5000 + 4000 = x + 9000 . so , x + x + 5000 + x + 9000 = 50000 3 x = 36000 x = 12000 a : b : c = 21000 : 17000 : 12000 = 21 : 17 : 12 . b ' s share = rs . ( 30000 x 17 / 50 ) = rs . 10,200 . b"
Answer: b
Question (general): the difference between a positive proper fraction and its reciprocal is 9 / 20 . the fraction is :
Options: a ) 4 / 5 , b ) 5 / 4 , c ) 3 / 5 , d ) 2 / 5 , e ) 3 / 4
Rationale: "let the required fraction be x . then 1 / x - x = 9 / 20 ( 1 - x ^ 2 ) / x = 9 / 20 = = > 20 - 20 x ^ 2 = 9 x 20 x ^ 2 + 9 x - 20 = 0 20 x ^ 2 + 25 x - 16 x - 20 = 0 5 x ( 4 x + 5 ) - 4 ( 4 x + 5 ) = 0 ( 4 x + 5 ) ( 5 x - 4 ) = 0 x = 4 / 5 ( neglecting - ve value ) answer a ) 4 / 5"
Answer: a
Question (general): a man is 20 years older than his son . in two years , his age will be twice the age of his son . the present age of his son is :
Options: a ) 14 years , b ) 18 years , c ) 20 years , d ) 22 years , e ) 16 years
Rationale: "let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years . ( x + 20 ) + 2 = 2 ( x + 2 ) x + 22 = 2 x + 4 x = 18 . answer : b"
Answer: b
Question (general): a mixture contains milk and water in the ratio 5 : 4 . on adding 30 litters of water , the ratio of milk to water becomes 5 : 7 . total quantity of milk & water before adding water to it ?
Options: a ) 90 , b ) 120 , c ) 80 , d ) 70 , e ) 60
Rationale: "explanation : milk : water = 5 : 4 5 x : 4 x + 30 = 5 : 7 7 [ 5 x ] = 5 [ 4 x + 30 ] 35 x = 20 x + 150 35 x - 20 x = 150 15 x = 150 x = 10 the quantity of milk in the original mixture is = 5 : 4 = 5 + 4 = 9 9 x = 90 short cut method : milk : water = 5 : 4 after adding 30 liters of water milk : water = 5 : 7 milk is same but water increse 30 liters then the water ratio is increse 3 parts 3 part - - - - - > 30 liters the quantity of milk in the original mixture is = 5 : 4 = 5 + 4 = 9 9 parts - - - - - > 9 liters ( answer is = 90 ) short cut method - 2 : for only milk problems milk : water 5 : 4 5 : 7 milk ratio same but water ratio 3 parts incress per 30 liters 3 part of ratio - - - - - - - > 30 liters 1 part of ratio - - - - - - - > 10 liters 9 part of ratio - - - - - - > 90 liters answer : option a"
Answer: a
Question (other): in a class , 30 students pass in english and 20 students in math , while some students among these pass in both . how many more students do only english as compared to those doing only maths ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) indeterminate
Rationale: let us consider tht x student are tohse who passed in both english and maths . . . so first we remove x student from both of them therefore , english = 30 - x maths = 20 - x now , number of students more in english = ( 30 - x ) - ( 20 - x ) = 30 - x - 20 + x = 10 answer : a
Answer: a
Question (physics): a metal company ' s old machine makes bolts at a constant rate of 100 bolts per hour . the company ' s new machine makes bolts at a constant rate of 150 bolts per hour . if both machines start at the same time and continue making bolts simultaneously , how many minutes will it take the two machines to make a total of 550 bolts ?
Options: a ) 36 , b ) 72 , c ) 120 , d ) 132 , e ) 180
Rationale: "old machine 100 bolts in 60 mins so , 5 / 3 bolts in 1 min new machine 150 bolts in 60 mins so , 5 / 2 bolts in 1 min together , 5 / 3 + 5 / 2 = 25 / 6 bolts in 1 min so , for 550 bolts 550 * 6 / 25 = 132 mins ans d"
Answer: d
Question (gain): in a village of 2,700 people , 900 people are over 70 years old and 1200 people are female . it is known that 40 percent of the females are younger than 70 years old . if no one in the village is 70 years old , what is the probability that a person chosen at random is either a female or younger than 70 years old ?
Options: a ) 7 / 8 , b ) 14 / 15 , c ) 29 / 30 , d ) 44 / 45 , e ) 131 / 135
Rationale: "the number of people younger than 70 years old is 2700 - 900 = 1800 the number of females older than 70 years old is 0.6 * 1200 = 720 the number of people who are either female or younger than 70 is 1800 + 720 = 2520 . p ( a person is younger than 70 or male ) = 2520 / 2700 = 14 / 15 the answer is b ."
Answer: b
Question (general): how many integers between 362855 and 852755 have tens digit 1 and units digit 3 ?
Options: a ) 4,888 , b ) 4,898 , c ) 4,889 , d ) 4,869 , e ) 4,896
Rationale: there is one number in hundred with 1 in the tens digit and 3 in the units digit : 13 , 113 , 213 , 313 , . . . the difference between 362,855 and 852,755 is 852,755 - 362,855 = 489,900 - one number per each hundred gives 133,900 / 100 = 4,889 numbers . answer : c .
Answer: c
Question (geometry): the length of each side of square a is increased by 100 percent to make square b . if the length of the side of square b is increased by 80 percent to make square c , by what percent is the area of square c greater than the sum of the areas of squares a and b ?
Options: a ) 75 % , b ) 80 % , c ) 100 % , d ) 150 % , e ) 159.2 %
Rationale: "let length of each side of square a be 10 area of a = 10 ^ 2 = 100 since , length of each side of square a is increased by 100 percent to make square b length of each side of square b = 2 * 10 = 20 area of b = 20 ^ 2 = 400 since , length of the side of square b is increased by 80 percent to make square c length of each side of square c = 1.8 * 20 = 36 area of c = 36 ^ 2 = 1296 difference in areas of c and cummulative areas of a and b = 1296 - ( 400 + 100 ) = 796 percent is the area of square c greater than the sum of the areas of squares a and b = ( 796 / 500 ) * 100 % = 159.2 % answer e"
Answer: e
Question (general): what are the last two digits of ( 301 * 401 * 503 * 604 * 646 * 547 * 448 * 349 ) ^ 2
Options: a ) 96 , b ) 76 , c ) 56 , d ) 44 , e ) 16
Rationale: "( ( 301 * 401 * 503 * 604 * 646 ) * ( 547 * 448 * 349 ) ) ^ 2 if you observe above digits , last digit are : 1,1 , 3,4 , 6,7 , 8,9 ; 1 & 5 are missing ; so i have rearranged them so that multiplication will be easy for me as initial 4 digits have last two digits as 01 , 01,03 , 04,46 and final three as 47 * 48 * 49 . solving for only last two digits and multiplying them we get : ( ( 03 * 04 * 46 ) ( 56 * 49 ) ) ^ 2 = ( 52 * 44 ) ^ 2 = 88 ^ 2 = 44 hence answer is d"
Answer: d
Question (general): a corporation that had $ 10 billion in profits for the year paid out $ 200 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 = [ ( 200 million ) / ( 10 billion ) ] * 100 = [ ( 200 * 10 ^ 6 ) / ( 10 * 10 ^ 9 ) ] * 100 = ( 20 / 1000 ) * 100 = 2 % so answer is ( d )"
Answer: d
Question (general): the 15 homes in a new development are each to be sold for one of 3 different prices so that the developer receives an average ( arithmetic mean ) of $ 200000 per home . if 4 of the homes are to be sold for $ 170000 each and 5 are to be sold for $ 200000 each , what will be the selling price of each of the remaining 8 homes ?
Options: a ) $ 200,000 , b ) $ 210,000 , c ) $ 215,000 , d ) $ 220,000 , e ) $ 230,000
Rationale: imo the answer has to be d . 5 houses are being sold for 200,000 . 4 houses are being sold for $ 30,000 less , resulting in a loss of $ 120,000 . to make the average selling price intact i . e . $ 200,000 , the remaining 8 houses must be sold at such a profit that it compensates for the loss of 120,000 . hence 8 x = 120,000 . x = 15,000 . the 8 houses are sold at $ 15,000 profit or at $ 215,000 . ( answer c )
Answer: c
Question (gain): a reduction in the price of petrol by 10 % enables a motorist to buy 5 gallons more for $ 200 . find the original price of petrol ?
Options: a ) $ 11 , b ) $ 5 , c ) $ 45 , d ) $ 400 , e ) $ 4.4
Rationale: "price decreased by 10 % , so 9 / 10 times , which means that original gallons bought increased 10 / 9 times . since this increase equals to 5 gallons then 45 gallons were bought originally ( 45 * 10 / 9 = 50 - - > increase 5 gallons ) . hence original price was 200 / 45 = $ 4.4 answer : e ."
Answer: e
Question (gain): if each side of a square is increased by 25 % , find the percentage change in its area .
Options: a ) 46.25 % , b ) 56.25 % , c ) 56 % , d ) 50.25 % , e ) 36.25 %
Rationale: "let each side of the square be a . then , area = a 2 . new side = ( 125 a / 100 ) = ( 5 a / 4 ) . new area = ( 5 a / 4 ) 2 = ( 25 a 2 ) / 16 . increase in area = ( ( 25 a 2 ) / 16 ) - a 2 = ( 9 a 2 ) / 16 . increase % = [ ( ( 9 a 2 ) / 16 ) * ( 1 / a 2 ) * 100 ] % = 56.25 % . answer b 56.25 %"
Answer: b
Question (general): at a summer camp with 1,500 participants , 1 / 2 of the campers are aged 10 to 12 . next year , the number of campers aged 10 to 12 will increase by 1 / 3 . after this change , what percentage of the total 1,500 campers will the 10 to 12 - year - olds represent ?
Options: a ) 62 , b ) 64 , c ) 65 , d ) 66 2 / 3 % , e ) 67
Rationale: "total - 1,500 participants campers are aged 10 to 12 = ( 1 / 2 ) * 1500 = 750 next year , campers are aged 10 to 12 = ( 4 / 3 ) * 750 = 1000 percentage = ( 1000 / 1500 ) * 100 = 66 2 / 3 % answer : option d"
Answer: d
Question (general): a big container is 50 % full with water . if 20 liters of water is added , the container becomes 3 / 4 full . what is the capacity of the big container in liters ?
Options: a ) 80 , b ) 90 , c ) 100 , d ) 110 , e ) 120
Rationale: "20 liters is 25 % of the capacity c . 20 = 0.25 c c = 80 liters . the answer is a ."
Answer: a
Question (general): 0.0007 ? = 0.01
Options: a ) 70 , b ) 7 , c ) 0.7 , d ) 0.07 , e ) none of these
Rationale: "explanation : required answer = 0.0007 / 0.01 = 0.07 / 1 = 0.07 . answer : option d"
Answer: d
Question (physics): a goods train runs at a speed of 72 kmph and crosses a 260 m long platform in 26 seconds . what is the length of the goods train ?
Options: a ) 230 m , b ) 240 m , c ) 260 m , d ) 270 m , e ) 250 m
Rationale: s = 260 + x / t 72 * 5 / 18 = 260 + x / 26 x = 260 answer : c
Answer: c
Question (physics): the area of a sector of a circle of radius 5 cm formed by an arc of length 4 cm is ?
Options: a ) 8.78 , b ) 8.67 , c ) 8.75 , d ) 10 , e ) 8.28
Rationale: "( 5 * 4 ) / 2 = 10 answer : d"
Answer: d
Question (physics): if an object travels 200 feet in 2 seconds , what is the object ' s approximate speed in miles per hour ? ( note : 1 mile = 5280 feet )
Options: a ) 68 , b ) 54 , c ) 21 , d ) 48 , e ) 22
Rationale: "1 mile = 5280 feet = > 1 feet = 1 / 5280 miles if the object travels 200 feet in 2 sec then it travels 200 / 2 * 60 * 60 feet in 1 hour ( 1 hr = 60 min * 60 sec ) = 3600 * 100 feet in 1 hour = 360000 feet in 1 hr = 360000 / 5280 miles in 1 hour = 36000 / 528 miles / hr ~ 68 miles / hr answer - a"
Answer: a
Question (general): a certain lab experiments with white and brown mice only . in one experiment , 2 / 3 of the mice are white . if there are 14 white mice in the experiment , how many brown mice are in the experiment ?
Options: a ) 12 , b ) 8 , c ) 28 , d ) 7 , e ) 27
Rationale: let total number of mice = m number of white mice = 2 / 3 m = 14 m = 21 number of brown mice = 1 / 3 m = 1 / 3 * 21 = > brown mice = 7 answer d
Answer: d
Question (general): if an integer n is to be chosen at random from the integers 1 to 96 , inclusive , what is the probability that n ( n + 1 ) ( n + 2 ) will be divisible by 12 ?
Options: a ) 1 / 48 , b ) 234 / 8 , c ) 1 / 24 , d ) 5 / 8 , e ) 3 / 4
Rationale: "i get 5 / 8 as well 1 to 96 inclusive means we have 48 odd and 48 even integers e o e / 12 = integer , therefore we have 48 / 96 numbers divisible by 8 o e o / 12 = not integer we can not forget multiples of 12 from 1 to 96 we have 8 numbers that are multiple of 12 therefore , 48 / 96 + 8 / 96 = 23 / 48 answer : b"
Answer: b
Question (general): a theater box office sold an average ( arithmetic mean ) of 68 tickets per staff member to a particular movie . among the daytime staff , the average number sold per member was 80 , and among the evening staff , the average number sold was 60 . if there are no other employees , what was the ratio of the number of daytime staff members to the number of evening staff members ?
Options: a ) 2 : 3 , b ) 1 : 4 , c ) 5 : 6 , d ) 7 : 11 , e ) 3 : 7
Rationale: "deviation from the mean for the daytime staff = 80 - 68 = 12 . deviation from the mean for the evening staff = 68 - 60 = 8 . thus , the ratio of the number of daytime staff members to the number of evening staff members is 8 : 12 = 2 : 3 . the answer is a ."
Answer: a
Question (general): if 7 log ( 4 * 5 ^ 2 ) = x , find x
Options: a ) 12 , b ) 11 , c ) 10 , d ) 14 , e ) 13
Rationale: "7 ( log 2 ^ 2 * 5 ^ 2 ) = x 7 log ( 5 * 2 ) ^ 2 = x 7 * 2 log ( 5 * 2 ) = x 14 log 10 = x log 10 base 10 = 1 so 14 * 1 = x x = 14 answer : d"
Answer: d
Question (probability): a bag contains 6 black and 8 white balls . one ball is drawn at random . what is the probability that the ball drawn is white ?
Options: a ) 3 / 4 , b ) 4 / 7 , c ) 1 / 7 , d ) 1 / 8 , e ) 4 / 3
Rationale: "let number of balls = ( 6 + 8 ) = 14 . number of white balls = 8 . p ( drawing a white ball ) = 8 / 14 = 4 / 7 . option b ."
Answer: b
Question (gain): we had $ 2800 left after spending 30 % of the money that we took for shopping . how much money did we start with ?
Options: a ) $ 3700 , b ) $ 4000 , c ) $ 4300 , d ) $ 4600 , e ) $ 4900
Rationale: "let x be the amount of money we started with . 0.7 x = 2800 x = 4000 the answer is b ."
Answer: b
Question (general): ? x 48 = 173 x 240
Options: a ) 545 , b ) 685 , c ) 865 , d ) 495 , e ) 534
Rationale: "let y x 48 = 173 x 240 then y = ( 173 x 240 ) / 48 = 173 x 5 = 865 . answer : c"
Answer: c
Question (geometry): the ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm . find the ratio of the breadth and the area of the rectangle ?
Options: a ) 1 : 96
b ) 1 : 99
c ) 1 : 95
d ) 1 : 12
e ) 1 : 11
Rationale: let the length and the breadth of the rectangle be 4 x cm and 3 x respectively . ( 4 x ) ( 3 x ) = 6912 12 x 2 = 6912 x 2 = 576 = 4 * 144 = 22 * 122 ( x > 0 ) = > x = 2 * 12 = 24 ratio of the breadth and the areas = 3 x : 12 x 2 = 1 : 4 x = 1 : 96 . answer : a
Answer: a