Cheukting/mathqa huggingface dataset:
Question (general): ( x + 7 ) is a factor in x ^ 2 - mx - 35 . what is the value of m ?
Options: a ) - 3 , b ) - 2 , c ) - 4 , d ) - 5 , e ) - 6
Rationale: "i solved the second degree equation and found it like this : x ^ 2 - mx - 35 ( x - 5 ) ( x + 7 ) x = 5 or x = - 7 substituting both values for x in the equation we find : x ^ 2 - mx - 35 = > ( - 7 ) ^ 2 - m ( - 7 ) = 35 = > 49 + 7 m = 35 = > 7 m = 35 - 49 = - 14 = > m = - 2 and with 5 , using a similar process we end up with : ( 5 ) ^ 2 - m ( 5 ) = 35 - 10 = 5 m m = - 2 ao , ans b"
Answer: b
Question (general): the product of two positive integers is 575 and their difference is 2 . what is the bigger number ?
Options: a ) 21 , b ) 23 , c ) 25 , d ) 27 , e ) 29
Rationale: "let ' s use trial and error to find the two numbers . 27 * 25 = 675 ( too high ) 25 * 23 = 575 the answer is c ."
Answer: c
Question (general): at a certain pizza parlor , the diameter of a large pizza is 40 % larger than the diameter of a small pizza . what is the percent increase in total amount of pizza , from a small to a large ?
Options: a ) 20 % , b ) 40 % , c ) 64 % , d ) 80 % , e ) 96 %
Rationale: a real world problem — - yum ! — - but again , the specifics of the shape don ’ t matter . diameter increases 40 % , so k = 1.4 in this case . “ amount of pizza ” just means the area of the circle , so k ^ 2 = ( 1.4 ) ^ 2 = 1.96 , which is the multiplier for a 96 % increase . that ’ s the percent increase in area . answer = e
Answer: e
Question (physics): on a map , 2.5 inches represent 40 miles . how many miles approximately is the distance if you measured 155 centimeters assuming that 1 - inch is 2.54 centimeters ?
Options: a ) 990.4 , b ) 970 , c ) 972 , d ) 976.4 , e ) 975
Rationale: "1 inch = 2.54 cm 2.5 inch = 2.54 * 2.5 cm 6.35 cm = 40 miles 155 cms = 40 / 6.35 * 155 = 976.4 miles answer : d"
Answer: d
Question (general): the average weight of 20 persons sitting in a boat had some value . a new person added to them whose weight was 48 kg only . due to his arrival , the average weight of all the persons decreased by 5 kg . find the average weight of first 20 persons ?
Options: a ) 55 , b ) 56 , c ) 57 , d ) 58 , e ) 59
Rationale: 20 x + 48 = 21 ( x – 5 ) x = 57 answer : c
Answer: c
Question (general): if two integers x , y ( x > y ) are selected from - 4 to 4 ( inclusive ) , how many cases are there ?
Options: a ) 27 , b ) 30 , c ) 33 , d ) 36 , e ) 39
Rationale: "there are 9 integers from - 4 to 4 inclusive . 9 c 2 = 36 . the answer is d ."
Answer: d
Question (general): a man is 24 years older than his son . in four years , his age will be twice the age of his son . the present age of the son is
Options: a ) 14 years , b ) 18 years , c ) 20 years , d ) 22 years , e ) none
Rationale: "solution let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years . then â € ¹ = â € º ( x + 24 ) + 4 = 2 ( x + 4 ) â € ¹ = â € º x + 28 = 2 x + 8 x = 20 . answer c"
Answer: c
Question (gain): a car is purchased on hire - purchase . the cash price is $ 23 000 and the terms are a deposit of 10 % of the price , then the balance to be paid off over 60 equal monthly instalments . interest is charged at 12 % p . a . what is the monthly instalment ?
Options: a ) $ 503 , b ) $ 504 , c ) $ 515 , d ) $ 543 , e ) $ 552
Rationale: "explanation : cash price = $ 23 000 deposit = 10 % ã — $ 23 000 = $ 2300 loan amount = $ 23000 â ˆ ’ $ 2300 number of payments = 60 = $ 20700 i = p * r * t / 100 i = 12420 total amount = 20700 + 12420 = $ 33120 regular payment = total amount / number of payments = 552 answer : e"
Answer: e
Question (general): on the number line , if x is halfway between - 8 and 4 , and if y is halfway between - 2 and 6 , what number is halfway between x and y ?
Options: a ) - 2 , b ) - 1 , c ) 0 , d ) 1 , e ) 2
Rationale: x = - 2 and y = 2 . the answer is c .
Answer: c
Question (gain): a survey was sent to 90 customers , 15 of whom responded . then the survey was redesigned and sent to another 50 customers , 9 of whom responded . by approximately what percent did the response rate increase from the original survey to the redesigned survey ?
Options: a ) 2 % , b ) 5 % , c ) 8 % , d ) 28 % , e ) 63 %
Rationale: "rate of first survey = 15 / 90 rate of second survey = 9 / 50 % response rate increase ( 9 / 50 - 15 / 90 ) / ( 15 / 90 ) = 8 % answer is c = 8 %"
Answer: c
Question (gain): company kw is being sold , and both company a and company b were considering the purchase . the price of company kw is 50 % more than company a has in assets , and this same price is also 100 % more than company b has in assets . if companies a and b were to merge and combine their assets , the price of company kw would be approximately what percent of these combined assets ?
Options: a ) 66 % , b ) 75 % , c ) 86 % , d ) 116 % , e ) 150 %
Rationale: "let the price of company a ' s assets be 100 price of assets of kw is 50 % more than company a ' s assets which is 150 price of assets of kw is 100 % more than company b ' s assets which means price of company b ' s assets is half the price of kw = 75 a + b = 175 kw = 150 kw / ( a + b ) * 100 = 150 / 175 * 100 = 85.7 % or 86 % answer : c"
Answer: c
Question (geometry): a rectangular field is to be fenced on three sides leaving a side of 80 feet uncovered . if the area of the field is 680 sq . ft , how many feet of fencing will be required ?
Options: a ) 44 ft , b ) 97 ft , c ) 22 ft , d ) 11 ft , e ) 66 ft
Rationale: "given that length and area , so we can find the breadth . length x breadth = area 80 x breadth = 680 breadth = 8.5 feet area to be fenced = 2 b + l = 2 ( 8.5 ) + 80 = 97 feet answer : b ) 97 ft"
Answer: b
Question (general): rs . 120 are divided among a , b , c such that a ' s share is rs . 20 more than b ' s and rs . 20 less than c ' s . what is b ' s share
Options: a ) rs 10 , b ) rs 20 , c ) rs 24 , d ) rs 28 , e ) none of these
Rationale: explanation : let c = x . then a = ( x � 20 ) and b = ( x � 40 ) . x + x - 20 + x - 40 = 120 or x = 60 . a : b : c = 40 : 20 : 60 = 2 : 1 : 3 . b ' s share = rs . 120 * ( 1 / 6 ) = rs . 20 answer : b
Answer: b
Question (general): a certain meter records voltage between 0 and 10 volts inclusive . if the average value of 3 recordings on the meter was 5 volts , what was the smallest possible recording in volts ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "if average of 3 is 5 so sum of 3 should be 15 3 recording can be from 0 - 10 inclusive to find one smallest other two should be highest so , lets assume three var are a , b , c say a is smallest and give b and c greatest readings say 6 and 6 so a has to be 3 b"
Answer: b
Question (gain): the ratio of investments of two partners p and q is 7 : 5 and the ratio of their profits is 7 : 10 . if p invested the money for 10 months , find for how much time did q invest the money ?
Options: a ) 11 , b ) 10 , c ) 20 , d ) 16 , e ) 12
Rationale: "7 * 5 : 10 * x = 7 : 10 x = 20 answer : c"
Answer: c
Question (gain): a jar full of whisky contains 40 % alcohol . a part of this whisky is replaced by another containg 19 % alcohol and now the percentage of alcohol was found to be 25 % . what quantity of whisky is replaced ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 2 / 5 , d ) 3 / 5 , e ) 4 / 5
Rationale: "let us assume the total original amount of whiskey = 10 ml - - - > 4 ml alcohol and 6 ml non - alcohol . let x ml be the amount removed - - - > total alcohol left = 4 - 0.4 x new quantity of whiskey added = x ml out of which 0.19 is the alcohol . thus , the final quantity of alcohol = 4 - 0.4 x + 0.19 x - - - - > ( 4 - 0.21 x ) / 10 = 0.26 - - - > x = 20 / 3 ml . per the question , you need to find the x ml removed as a ratio of the initial volume - - - > ( 20 / 3 ) / 10 = 2 / 5 . hence , c is the correct answer ."
Answer: c
Question (general): if x is an integer such that 0 < x < 12 , 1 < x < 15 , 10 > x > 5 , 11 > x > 8 , and x + 2 < 12 , then x is
Options: a ) 3 , b ) 5 , c ) 7 , d ) 9 , e ) 11
Rationale: "0 < x < 12 , 1 < x < 15 , - 5 < x < 10 8 < x < 11 x < 10 from above : 8 < x < 10 - - > x = 9 . answer : d ."
Answer: d
Question (general): a sum of money lent out at s . i . amounts to rs . 660 after 2 years and to rs . 1020 after a further period of 5 years . the sum is ?
Options: a ) s . 440 , b ) s . 500 , c ) s . 540 , d ) s . 740 , e ) s . 516
Rationale: "s . i for 5 years = ( 1020 - 660 ) = rs . 360 . s . i . for 2 years = 360 / 5 * 2 = rs . 144 . principal = ( 660 - 144 ) = rs . 516 . answer : e"
Answer: e
Question (other): what number has a 5 : 1 ratio to the number 8 ?
Options: a ) 22 , b ) 40 , c ) 88 , d ) 52 , e ) 12
Rationale: 5 : 1 = x : 8 x = 40 answer : b
Answer: b
Question (general): for an agricultural experiment , 500 seeds were planted in one plot and 200 were planted in a second plot . if exactly 30 percent of the seeds in the first plot germinated and exactly 50 percent of the seeds in the second plot germinated , what percent of the total number of seeds germinated ?
Options: a ) 35.7 % , b ) 25 % , c ) 32 % , d ) 30.8 % , e ) 60 %
Rationale: "from the first plot 0.30 * 500 = 150 ; from the second plot 0.50 * 200 = 100 ; total percent = ( 150 + 100 ) / ( 500 + 200 ) = 0.357 . answer : a ."
Answer: a
Question (general): what is the total number of prime numbers less than 70 ?
Options: a ) 17 , b ) 18 , c ) 19 , d ) 20 , e ) 21
Rationale: solution prime numbers less than 70 are = 12 . 2,3 , 5,7 , 11,13 , 17,19 , 23,29 , 31,37 , 41,43 , 47,53 , 59,61 , and 67 their number is 19 . answer c
Answer: c
Question (general): 3 / 5 of all married couples have more than one child . 1 / 2 of all married couples have more than 3 children . what fraction of all married couples have 2 or 3 children ?
Options: a ) 1 / 5 , b ) 1 / 10 , c ) 7 / 20 , d ) 3 / 5 , e ) it can not be determined from the given information .
Rationale: "plug in simple numbers . take 100 couples for example . 3 / 5 of 100 couples have more than one child = 60 couples . 1 / 2 of 100 couples have more than 3 kids = 50 couples . this implies that 50 couples are a subset of 60 couples and the complement of 60 couples within those 100 couples , which equals 40 couples have either one or no kids at all . we need to find couples that have 2 or 3 kids , so essentially , it is 60 - 50 = 10 . fraction will be 10 / 100 = 1 / 10 . option b"
Answer: b
Question (gain): at a special sale , 6 tickets can be purchased for the price of 3 tickets . if 6 tickets are purchased at the sale , the amount saved will be what percent of the original price of the 6 tickets ?
Options: a ) 20 % , b ) 33.3 % , c ) 40 % , d ) 50 % , e ) 66.6 %
Rationale: let the price of a ticket be rs . 100 , so 3 tickets cost 300 & 6 tickets cost 600 6 tickets purchased at price of 3 tickets ie . , for 300 , so amount saved s rs . 300 , % of 6 tickets = ( 300 / 600 ) * 100 = 50 % answer : d
Answer: d
Question (general): a 4 - digit code can consist of the digits 0 ~ 9 except that it does not contain the digits 1 , 2 , 4 , and 6 at all . if repeated digits are allowed , what is the probability that it has at least one even digit ?
Options: a ) 23 / 24 , b ) 31 / 36 , c ) 55 / 64 , d ) 65 / 81 , e ) 75 / 121
Rationale: p ( no even digits ) = 2 / 3 * 2 / 3 * 2 / 3 * 2 / 3 = 16 / 81 p ( at least one even digit ) = 1 - 16 / 81 = 65 / 81 the answer is d .
Answer: d
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 15 % ?
Options: a ) 228 , b ) 480 , c ) 267 , d ) 288 , e ) 544
Rationale: "sp = 800 profit = 25 % cp = ( sp ) * [ 100 / ( 100 + p ) ] = 800 * [ 100 / 125 ] = 640 loss = 25 % = 25 % of 640 = rs . 96 sp = cp - loss = 640 - 96 = rs . 544 answer : e"
Answer: e
Question (physics): the speed of a train is 120 kmph . what is the distance covered by it in 10 minutes ?
Options: a ) 26 kmph , b ) 20 kmph , c ) 28 kmph , d ) 30 kmph , e ) 40 kmph
Rationale: "120 * 10 / 60 = 20 kmph answer : b"
Answer: b
Question (general): from a total of 4 boys and 4 girls , how many 4 - person committees can be selected if the committee must have exactly 2 boys and 2 girls ?
Options: a ) 16 , b ) 36 , c ) 60 , d ) 120 , e ) 240
Rationale: "answer = b = 36 no of 4 person committees that can be formed = 4 c 2 * 4 c 2 = 36 answer b"
Answer: b
Question (gain): if an article is sold at 20 % profit instead of 14 % profit , then the profit would be rs . 180 more . what is the cost price ?
Options: a ) rs . 1000 , b ) rs . 2000 , c ) rs . 3000 , d ) rs . 4000 , e ) rs . 5200
Rationale: "explanation : let the cost price of an article be rs . x . ( 20 % of x ) - ( 14 % of x ) = 180 20 x / 100 - 14 x / 100 = 105 = > 6 x = 180 * 100 = > x = 3000 cost price = rs . 3000 answer : c"
Answer: c
Question (general): find the greatest number that exactly divides 35 , 91 and 840 ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "the greatest number that exactly divides 35 , 91 and 840 is the hcf of the three numbers . so , calculating hcf we get the answer 7 . answer : c"
Answer: c
Question (physics): joe needs to paint all the airplane hangars at the airport , so he buys 360 gallons of paint to do the job . during the first week , he uses 1 / 3 of all the paint . during the second week , he uses 1 / 5 of the remaining paint . how many gallons of paint has joe used ?
Options: a ) 168 , b ) 144 , c ) 175 , d ) 216 , e ) 250
Rationale: "total paint initially = 360 gallons paint used in the first week = ( 1 / 3 ) * 360 = 120 gallons . remaning paint = 240 gallons paint used in the second week = ( 1 / 5 ) * 240 = 48 gallons total paint used = 168 gallons . option a"
Answer: a
Question (probability): find the probability that a non leap year selected at random will have 53 sundays
Options: a ) 6 / 7 , b ) 5 / 7 , c ) 4 / 7 , d ) 3 / 7 , e ) 1 / 7
Rationale: "there are 365 days in a leap year : 52 weeks and 1 more days . so , 52 sundays and 1 days . this 1 days can be { mon , tue , wed , thu , fri , sat , sun } ( 7 cases ) . in order to have 53 sundays we should have sun case . the probability of that is 1 / 7 . answer : e ."
Answer: e
Question (general): when a number is divided by 6 & then multiply by 12 the answer is 11 what is the no . ?
Options: a ) 4.5 , b ) 5 , c ) 5.5 , d ) 5.8 , e ) 6
Rationale: "if $ x $ is the number , x / 6 * 12 = 11 = > 2 x = 11 = > x = 5.5 c"
Answer: c
Question (physics): sides of a rectangular park are in the ratio 3 : 2 and its area is 2400 sq m , the cost of fencing it at 50 ps per meter is ?
Options: a ) 287 , b ) 100 , c ) 125 , d ) 988 , e ) 271
Rationale: "3 x * 2 x = 2400 = > x = 20 2 ( 60 + 40 ) = 200 m 200 * 1 / 2 = rs . 100 answer : b"
Answer: b
Question (general): if 3 x + 4 y = 60 and 6 x - 4 y = 12 , what is the product of x and y ?
Options: a ) 80 , b ) 54 , c ) 54 , d ) 72 , e ) 12
Rationale: given 3 x + 4 y = 60 - - - eq 1 6 x - 4 y = 12 - - eq 2 sum both eqns we get 9 x = 72 = > x = 8 sum 6 x in eq 2 = > 48 - 4 y = 12 . = > y = 9 now xy = 8 * 9 = 72 option d is correct answer .
Answer: d
Question (geometry): a rope can make 70 rounds of the circumference of a cylinder whose radius of the base is 14 cm . how many times can it go round a cylinder having radius 20 cm ?
Options: a ) 49 rounds
b ) 42 rounds
c ) 54 rounds
d ) 52 rounds
e ) none of these
Rationale: explanation : let the required number of rounds be x more radius , less rounds ( indirect proportion ) hence we can write as radius 14 : 20 } : : x : 70 ⇒ 14 × 70 = 20 x ⇒ 14 × 7 = 2 x ⇒ x = 7 × 7 = 49 . answer : option a
Answer: a
Question (general): a seller of used cars has 18 cars to sell and each of his clients selected 3 cars that he liked most . if each car was selected exactly thrice , how many clients visited the garage ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 18 , e ) 16
Rationale: "ifno caris selected more than once then the number of clients = 18 / 3 = 6 but since every car is being selected three times so no . of clients must be thrice as well = 6 * 3 = 18 answer : option d"
Answer: d
Question (gain): what percent of 120 are 90 ?
Options: a ) 25 % , b ) 50 % , c ) 75 % , d ) 33 % , e ) 30 %
Rationale: "explanation : ( ? % / 100 ) * 120 = 90 ? = 75 % answer is c"
Answer: c
Question (gain): vijay sells a cupboard at 12 % below cost price . had he got rs . 1650 more , he would have made a profit of 12 % . what is the cost price of the cupboard ?
Options: a ) 7450 , b ) 14900 , c ) 7400 , d ) 6875 , e ) none of these
Rationale: "explanation : cost price = 1650 / ( 0.12 + 0.12 ) = 2086 / 0.24 = rs . 6875 answer d"
Answer: d
Question (gain): a hostel had provisions for 250 men for 48 days . if 50 men left the hostel , how long will the food last at the same rate ?
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 65
Rationale: "a hostel had provisions for 250 men for 48 days if 50 men leaves the hostel , remaining men = 250 - 50 = 200 we need to find out how long the food will last for these 200 men . let the required number of days = x days more men , less days ( indirect proportion ) ( men ) 250 : 200 : : x : 48 250 × 48 = 200 x 5 × 48 = 4 x x = 5 × 12 = 60 answer d"
Answer: d
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 12 such machines to perform the same job ?
Options: a ) 6 hours , b ) 8.75 hours , c ) 12 hours , d ) 4 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 3 machines 12 units of work ( 12 machines ) - - - > 1 hour for 48 units of work 12 * 4 - - - > 1 * 4 hours d 4 hours"
Answer: d
Question (physics): if a motorist had driven 1 hour longer on a certain day and at an average rate of 5 miles per hour faster , he would have covered 70 more miles than he actually did . how many more miles would he have covered than he actually did if he had driven 1 hours longer and at an average rate of 10 miles per hour faster on that day ?
Options: a ) 100 , b ) 120 , c ) 130 , d ) 150 , e ) 160
Rationale: "case 1 : let rate = r , time = t , and distance = d so d = rt case 2 : ( d + 70 ) = ( r + 5 ) ( t + 1 ) case 3 : ( d + x ) = ( r + 10 ) ( t + 1 ) x = 130 ans c"
Answer: c
Question (general): if a 5 percent deposit that has been paid toward the purchase of a certain product is $ 50 , how much more remains to be paid ?
Options: a ) $ 550 , b ) $ 650 , c ) $ 750 , d ) $ 850 , e ) $ 950
Rationale: "95 % remains to be paid so the remaining amount is 19 * 50 = $ 950 . the answer is e ."
Answer: e
Question (gain): john buys good worth rs . 6650 . he gets a rebate of 6 % on it . after getting the rebate , he pays sales tax @ 10 % . find the amount he will have to pay for the goods .
Options: a ) rs . 6876.10 , b ) rs . 4500 , c ) rs . 4600 , d ) rs . 3400 , e ) rs . 7500
Rationale: rebate = 6 % of rs . 6650 = rs . 6 x 6650 = rs . 399 . 100 sales tax = 10 % of rs . ( 6650 - 399 ) = rs . 10 x 6251 = rs . 625.10 100 final amount = rs . ( 6251 + 625.10 ) = rs . 6876.10 correct answer - a
Answer: a
Question (other): the ratio of the adjacent angles of a parallelogram is 4 : 11 . also , the ratio of the angles of quadrilateral is 5 : 6 : 7 : 12 . what is the sum of the smaller angle of the parallelogram and the second largest angle of the quadrilateral ?
Options: a ) 132 ° , b ) 228 ° , c ) 156 ° , d ) 224 ° , e ) none of these
Rationale: the measures of the adjacent angles of a parallelogram add up to be 180 ° given so , 4 x + 11 x = 180 ° or , 15 x = 180 ° or , x = 12 ° hence the angles of the parallelogram are 48 ° and 132 ° further it is given we know sum of all the four angles of a quadrilateral is 360 ° so , 5 y + 6 y + 7 y + 12 y = 360 ° or , 5 y + 6 y + 7 y + 12 y = 360 ° or , 30 y = 360 ° or , y = 12 ° hence the angles of the quadrilateral are 60 ° , 72 , 84 ° and 144 ° will be 48 ° + 84 ° = 132 ° answer : a
Answer: a
Question (gain): a and b start a business , with a investing the total capital of rs . 25000 , on the condition that b pays a interest @ 10 % per annum on his half of the capital . a is a working partner and receives rs . 250 per month from the total profit and any profit remaining is equally shared by both of them . at the end of the year , it was found that the income of a is twice that of b . find the total profit for the year ?
Options: a ) a ) 22500 , b ) b ) 33500 , c ) c ) 22510 , d ) d ) 33510 , e ) e ) 11500
Rationale: "interest received by a from b = 10 % of half of rs . 25000 = 10 % * 12500 = 1250 . amount received by a per annum for being a working partner = 250 * 12 = rs . 3000 . let ' p ' be the part of the remaining profit that a receives as his share . total income of a = ( 1250 + 3000 + p ) total income of b = only his share from the remaining profit = ' p ' , as a and b share the remaining profit equally . income of a = twice the income of b ( 1250 + 3000 + p ) = 2 ( p ) p = 4250 total profit = 2 p + 3000 = 2 * 4250 + 3000 = 11500 answer : e"
Answer: e
Question (physics): one pipe can fill a tank three times as fast as another pipe . if together the two pipes can fill tank in 38 min , then the slower pipe alone will be able to fill the tank in ?
Options: a ) 229 , b ) 787 , c ) 152 , d ) 128 , e ) 121
Rationale: "let the slower pipe alone fill the tank in x min . then , faster pipe will fill it in x / 3 min . 1 / x + 3 / x = 1 / 38 4 / x = 1 / 38 = > x = 152 min . answer : c"
Answer: c
Question (probability): a circular dartboard of radius 1 foot is at a distance of 20 feet from you . you throw a dart at it and it hits the dartboard at some point q in the circle . what is the probability that q is closer to the center of the circle than the periphery ?
Options: a ) 0.75 , b ) 1 , c ) 0.25 , d ) 0.5 , e ) 0.58
Rationale: radius of inner dartboard / overall radius of dartboard ( ( r / 2 ) ^ 2 ) / ( r ^ 2 ) = 1 / 4 = 0.25 answer : c
Answer: c
Question (general): a factory producing tennis balls stores them in either big boxes , 25 balls per box , or small boxes , 20 balls per box . if 76 freshly manufactured balls are to be stored , what is the least number of balls that can be left unboxed ?
Options: a ) 2 , b ) 1 , c ) 4 , d ) 6 , e ) 8
Rationale: "we have to work with multiples of 20 and 25 . first , we must know the limits of this multiples , so : 76 / 25 = 3 . . . . so the max is 3 76 / 20 = 3 . . . so the max is 3 76 - 75 = 1 answer : b"
Answer: b
Question (general): a , b and c have rs . 700 between them , a and c together have rs . 300 and b and c rs . 600 . how much does c have ?
Options: a ) 200 , b ) 250 , c ) 300 , d ) 350 , e ) 400
Rationale: "a + b + c = 700 a + c = 300 b + c = 600 - - - - - - - - - - - - - - a + b + 2 c = 900 a + b + c = 700 - - - - - - - - - - - - - - - - c = 200 answer : a"
Answer: a
Question (physics): a and b together can do a work in 7 days . if a alone can do it in 14 days . in how many days can b alone do it ?
Options: a ) 14 , b ) 10 , c ) 21 , d ) 20 , e ) 25
Rationale: "a 14 1 / 7 â € “ 1 / 14 = 1 / 14 = > 14"
Answer: a
Question (physics): a and b start walking towards each other at 7 am at speed of 12 kmph and 13 kmph . they were initially 25 km apart . at what time do they meet ?
Options: a ) 8 pm , b ) 6 am , c ) 7 am , d ) 10 am , e ) 8 am
Rationale: "time of meeting = distance / relative speed = 25 / 13 + 12 = 25 / 25 = 1 hr after 7 pm = 8 am answer is e"
Answer: e
Question (general): find the lowest common multiple of 24 , 36 and 42 .
Options: a ) 360 , b ) 504 , c ) 510 , d ) 320 , e ) 280
Rationale: "lcm = 2 * 2 * 2 * 3 * 3 * 7 = 504 . answer is b"
Answer: b
Question (general): if a / b = 1 / 7 , b / c = 3 , c / d = 2 / 3 , d / e = 2 and e / f = 1 / 2 , then what is the value of abc / def ?
Options: a ) 72 / 21 , b ) 27 / 85 , c ) 34 / 47 , d ) 13 / 81 , e ) 16 / 21
Rationale: "say a = 1 . then : a / b = 1 / 7 - - > b = 7 ; b / c = 3 - - > c = 7 / 3 ; c / d = 2 / 3 - - > d = 7 / 2 ; d / e = 2 - - > e = 7 / 4 ; e / f = 1 / 2 - - > f = 7 / 2 . abc / def = ( 1 * 7 * 7 / 3 ) / ( 7 / 2 * 7 / 4 * 7 / 2 ) = 16 / 21 . answer : e ."
Answer: e