Cheukting/mathqa huggingface dataset:
Question (geometry): a rectangular cube has sides measuring 15 inches long by 12 inches wide by 2 inches high . if the surface area of the rectangle is the same as a cube , what do the sides / walls of the cube measure ? round to the nearest whole number .
Options: a ) 7 , b ) 5 , c ) 9 , d ) 6 , e ) 4
Rationale: first calculate the surface area of the rectangle by multiplying the length and width of the rectangle together , then multiply by 2 to get both sides of the rectangle . this calculates to 360 inches . find the surface area of the sides of the rectangular cube . multiply the height by the length of the rectangle . multiply the answer by 2 ( for the 2 sides on the rectangular cube ) . this calculates to 60 inches . then multiply the width of the rectangle by the height . multiply the answer by 2 ( for the 2 sides on the rectangular cube ) . this calculates to 48 inches . add the totals together to get the rectangular cube surface area of 468 inches . since a square cube has 6 sides - divide the surface area by 6 . this calculates to 78 inches as the surface area of each side of the cube . the square root of 78 is 8.831 . rounding to the nearest whole number that makes each side of the cube measuring 9 inches . the correct answer is ( c ) .
Answer: c
Question (general): what is the units digit of the solution to 177 ^ 28 − 133 ^ 23 ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 6 , e ) 9
Rationale: "let ' s reduce the clutter and make it easy to solve so , 7 ^ 28 - 3 ^ 23 will have the same units digit as the big numbers above both 7 and 3 have a cyclicity of 4 , i . e . their powers repeat the units digit after every 4 th power so , 7 ^ 28 has the same units digit as 7 ^ 4 , which is 1 similarly , 3 ^ 23 has the same units digit as 3 ^ 3 , which is 7 now , we get xx . . . xx 1 - xx . . . . xx 7 = xx . . . xx 4 thus , the units digit of the solution to 177 ^ 28 - 133 ^ 23 is 4 correct option : c"
Answer: c
Question (gain): a watch was sold at a loss of 10 % . if it was sold for rs . 140 more , there would have been a gain of 3 % . what is the cost price ?
Options: a ) 1000 , b ) 2876 , c ) 1077 , d ) 2778 , e ) 2711
Rationale: "90 % 103 % - - - - - - - - 13 % - - - - 140 100 % - - - - ? = > rs . 1077 answer : c"
Answer: c
Question (general): if there is an equal probability of a child being born a boy or a girl , what is the probability that a couple who have 6 children have two children of the same sex and one of the opposite sex ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 1 / 4 , d ) 3 / 16 , e ) 3 / 5
Rationale: "no of ways of selecting a gender - 2 c 1 no of ways of selecting any 2 children out of 6 = 6 c 2 total possible outcomes - 2 ^ 6 ( each child can be either a girl or a boy ) probability = 2 c 1 * 6 c 2 / 2 ^ 6 = 2 * 6 / 2 * 2 * 2 * 2 * 2 * 2 = 12 / 64 = 3 / 16 ans = d"
Answer: d
Question (gain): what is 25 % of 25 % equal to
Options: a ) 0.625 , b ) 0.0625 , c ) 6.25 , d ) 0.00625 , e ) none
Rationale: "solution 25 % of 25 % = 25 / 100 x 25 / 100 = 1 / 16 = 0.0625 answer d"
Answer: d
Question (general): when positive integer x is divided by 12 , the quotient is y and the remainder is 3 . when 2 x is divided by 11 , the quotient is 3 y and the remainder is 6 . what is the value of 21 y – x ?
Options: a ) 3 , b ) 2 , c ) - 1 , d ) - 2 , e ) - 3
Rationale: "( 1 ) x = 12 y + 3 ( 2 ) 2 x = 33 y + 6 ( 2 ) - ( 1 ) : x = 21 y + 3 21 y - x = - 3 the answer is e ."
Answer: e
Question (geometry): the slant height of a cone is 18 cm and radius of the base is 8 cm , find the curved surface of the cone ?
Options: a ) 26 , b ) 452 , c ) 450 , d ) 440 , e ) 28
Rationale: "π * 18 * 8 = 452 answer : b"
Answer: b
Question (gain): a car has a 20 - gallon fuel to travel 500 miles . at this rate , how many gallons of fuel are needed for a 1000 mile car ?
Options: a ) 10 , b ) 30 , c ) 20 , d ) 40 , e ) 50
Rationale: number of gallons of fuel per mile = 500 / 20 = 25 gallons per mile number of gallons of fuel for a 1000 mile car = 1000 / 25 = 40 answer : d
Answer: d
Question (physics): nicky and cristina are running a 300 meter race . since cristina is faster than nicky , she gives him a 12 second head start . if cristina runs at a pace of 5 meters per second and nicky runs at a pace of only 3 meters per second , how many seconds will nicky have run before cristina catches up to him ?
Options: a ) 40 , b ) 50 , c ) 30 , d ) 60 , e ) 45
Rationale: "the distance traveled by both of them is the same at the time of overtaking . 3 ( t + 12 ) = 5 t t = 18 . cristina will catch up nicky in 18 seconds . so in 18 seconds cristina would cover = 18 * 5 = 90 meter . now time taken my nicky to cover 90 meter = 90 / 3 = 30 seconds . c"
Answer: c
Question (physics): nd the area of trapezium whose parallel sides are 20 cm and 18 cm long , and the distance between them is 13 cm ?
Options: a ) 216 cm 2 , b ) 238 cm 2 , c ) 240 cm 2 , d ) 247 cm 2 , e ) 250 cm 2
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 18 ) * ( 13 ) = 247 cm 2 answer : d"
Answer: d
Question (gain): after decreasing 24 % in the price of an article costs rs . 760 . find the actual cost of an article ?
Options: a ) 1218 , b ) 2777 , c ) 1000 , d ) 2688 , e ) 1991
Rationale: "cp * ( 76 / 100 ) = 760 cp = 10 * 100 = > cp = 1000 answer : c"
Answer: c
Question (gain): the salaries of a and b together amount to $ 7000 . a spends 95 % of his salary and b , 85 % of his . if now , their savings are the same , what is a ' s salary ?
Options: a ) $ 1000 , b ) $ 5250 , c ) $ 2500 , d ) $ 4500 , e ) $ 1200
Rationale: "let a ' s salary is x b ' s salary = 7000 - x ( 100 - 95 ) % of x = ( 100 - 85 ) % of ( 7000 - x ) x = $ 5250 answer is b"
Answer: b
Question (general): what is the least number should be added to 1056 , so the sum of the number is completely divisible by 28 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 8
Rationale: "( 1056 / 28 ) gives remainder 20 20 + 8 = 28 , so we need to add 8 e"
Answer: e
Question (gain): shopkeeper rise price by 34 % and gives successive discount of 10 % and 15 % . what is overall % gain or loss ?
Options: a ) 2.51 % , b ) 4.51 % , c ) 3.51 % , d ) 6.51 % , e ) 7.51 %
Rationale: let d initial price be 100 34 % rise now price = 134 / 100 * 100 = 134 10 % discount then price = 134 * 90 / 100 = 120.6 15 % discount then price = 120.6 * 85 / 100 = 102.51 so gain = 102.51 - 100 = 2.51 gain % = gain * 100 / cp = = > 2.51 * 100 / 100 = 2.51 % answer : a
Answer: a
Question (geometry): find the smallest number which should be multiplied with 1152 to make it a perfect square .
Options: a ) 2
b ) 1
c ) 3
d ) 5
e ) 6
Rationale: 1152 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 3 * 3 required smallest number = 2 2 is the smallest number which should be multiplied with 1152 to make it a perfect square . answer : a
Answer: a
Question (physics): the sector of a circle has radius of 21 cm and central angle 45 o . find its perimeter ?
Options: a ) 91.5 , b ) 92 , c ) 93 , d ) 94 , e ) 58.5
Rationale: "perimeter of the sector = length of the arc + 2 ( radius ) = ( 45 / 360 * 2 * 22 / 7 * 21 ) + 2 ( 21 ) = 58.5 cm answer : option e"
Answer: e
Question (physics): excluding stoppages , the speed of a train is 55 kmph and including stoppages it is 30 kmph . of how many minutes does the train stop per hour ?
Options: a ) 82 , b ) 27 , c ) 12 , d ) 82 , e ) 18
Rationale: "explanation : t = 25 / 55 * 60 = 27 answer : option b"
Answer: b
Question (general): find the average of all the numbers between 16 and 34 which are divisible by 5 ?
Options: a ) 10 , b ) 20 , c ) 28 , d ) 30 , e ) 15
Rationale: "average = ( 20 + 25 + 30 ) 3 = 85 / 3 = 28 answer is c"
Answer: c
Question (other): what is the square root of 261,121 ?
Options: a ) 476 , b ) 489 , c ) 497 , d ) 511 , e ) 524
Rationale: "1 ) checking the last digits in the answer options a , c , e are out since last digit of the square is known to be 1 . 2 ) b = 489 ^ 2 and d = 511 ^ 2 b = ( 500 - 11 ) ^ 2 and d = ( 500 + 11 ) ^ 2 since we need the answer less than 250000 = > b is out . thus we have d as the ans ."
Answer: d
Question (physics): a man can row 10 kmph in still water . when the river is running at 1.2 kmph , it takes him 1 hour to row to a place and back . what is the total distance traveled by the man ?
Options: a ) 6.24 km , b ) 6 km , c ) 9.86 km , d ) 5.66 km , e ) 10 km
Rationale: m = 10 s = 1.2 ds = 11.2 us = 8.8 x / 11.2 + x / 8.8 = 1 x = 4.93 d = 4.93 * 2 = 9.86 answer : c
Answer: c
Question (general): what is the tens digit of 36 ^ 10 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "36 ^ 10 = 6 ^ 20 if you type powers of six they end in 6 36 16 96 76 56 the pattern is 3 - - > 1 - - > 9 - - > 7 - - > 5 so for 36 we start with 3 - - > 9 - - > 5 - - > 1 - - > 7 and repeat . 36 ^ 10 will come at 7 . answer d ."
Answer: d
Question (general): the ratio between x and y is 8 / 5 ; x and y are decreased by 5 , what is the ratio between the new values of x and y ?
Options: a ) 8 / 5 , b ) 5 / 8 , c ) 4 , d ) 5 , e ) it can not be determined
Rationale: "ratio = 8 k / 5 k = 8 / 5 , 16 / 10 , etc . x and y are decreased by 5 - - > ( 8 k - 5 ) / ( 5 k - 5 ) new ratio can be 3 / 0 , 11 / 5 , etc . answer : e"
Answer: e
Question (general): # p is defined as 2 p + 20 for any number p . what is p , if # ( # ( # p ) ) = - 4 ?
Options: a ) – 108 , b ) – 44 , c ) 10 , d ) - 18 , e ) 18
Rationale: # p = 2 p + 20 - - - > # ( # p ) = 2 ( 2 p + 20 ) + 20 = 4 p + 60 and thus # ( 4 p + 60 ) = 2 ( 4 p + 60 ) + 20 = 8 p + 140 = - 4 - - - > 8 p = - 144 - - - > p = - 18 , d is the correct answer .
Answer: d
Question (general): the average student age of a certain class which has 30 students is 10 . if one student aged 11 go to another class and the age of the class teacher is included the average changes to 11 . what is the age of class teacher ?
Options: a ) 32 , b ) 41 , c ) 45 , d ) 48 , e ) 50
Rationale: "sum of ages of class before replacement = 30 x 10 = 300 sum of ages of class without teacher = 300 - 11 = 289 sum of ages of class after replacement = 30 x 11 = 330 age of teacher = 330 - 289 = 41 answer : b"
Answer: b
Question (general): find the number of divisors of 1728 . ?
Options: a ) 26 , b ) 27 , c ) 28 , d ) 29 , e ) 30
Rationale: "1728 = 2 ^ 6 * 3 ^ 3 hence the number of factors = ( 6 + 1 ) x ( 3 + 1 ) = 7 x 4 = 28 . we know that if a number represented in standard form ( a ^ m * b ^ n ) , then the number of factors is given by ( m + 1 ) ( n + 1 ) . answer is 28 answer : c"
Answer: c
Question (geometry): the diagonals of two squares are in the ratio of 2 : 5 then find the ratio of its areas ?
Options: a ) 2 : 12 , b ) 4 : 25 , c ) 5 : 31 , d ) 2 : 19 , e ) 3 : 17
Rationale: "let the diagonals of the squares be 2 x and 5 x ratio of their areas = 1 / 2 ( 2 x ) ^ 2 : 1 / 2 ( 5 x ) ^ 2 = 4 x ^ 2 : 25 x ^ 2 = 4 : 25 answer is b"
Answer: b
Question (general): ifaequals the sum of the even integers from 2 to 60 , inclusive , andbequals the sum of the odd integers from 1 to 59 , inclusive , what is the value of a - b ?
Options: a ) 1 , b ) 10 , c ) 30 , d ) 20 , e ) 21
Rationale: "this is a solution from beatthegmat : even numbers : ( 60 - 2 ) / 2 + 1 = 30 even integers . ( 60 + 2 ) / 2 = 31 is the average of the even set . sum = avg * ( # of elements ) = 31 * 30 = 930 = a odd numbers : ( 59 - 1 ) / 2 + 1 = 30 odd integers . ( 59 + 1 ) / 2 = 30 is the average of the odd set . sum = avg * ( # of elements ) = 30 * 30 = 900 = b a - b = 930 - 900 = 30 . answer : c"
Answer: c
Question (general): a , b and c have rs . 500 between them , a and c together have rs . 200 and b and c rs . 310 . how much does c have ?
Options: a ) 50 , b ) 78 , c ) 267 , d ) 29 , e ) 10
Rationale: "a + b + c = 500 a + c = 200 b + c = 310 - - - - - - - - - - - - - - a + b + 2 c = 510 a + b + c = 500 - - - - - - - - - - - - - - - - c = 10 answer : e"
Answer: e
Question (physics): a car takes 6 hours to cover a distance of 288 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 50 kmph , b ) 60 kmph , c ) 32 kmph , d ) 70 kmph , e ) none
Rationale: "time = 6 distence = 288 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 288 / 9 = 32 kmph c )"
Answer: c
Question (general): of the total amount that jill spent on a shopping trip , excluding taxes , she spent 50 percent on clothing , 20 percent on food , and 30 percent on other items . if jill paid a 4 percent tax on the clothing , no tax on the food , and an 8 percent tax on all other items , then the total tax that she paid was what percent of the total amount that she spent , excluding taxes ?
Options: a ) 2.8 % , b ) 3.6 % , c ) 4.4 % , d ) 5.2 % , e ) 6.0 %
Rationale: "let amount spent by jill = 100 clothing = 50 , food = 20 , others = 30 tax on clothing = 2 tax on others = 2.4 percentage = 4.4 / 100 4.4 % answer : c"
Answer: c
Question (gain): of the 200 employees in a certain company , 25 percent will be relocated to city x and the remaining 75 percent will be relocated to city y . however , 30 percent of the employees prefer city y and 70 percent prefer city x . what is the highest possible number of employees who will be relocated to the city they prefer ?
Options: a ) 65 , b ) 110 , c ) 115 , d ) 130 , e ) 135
Rationale: "140 prefer x ( group 1 ) ; 60 prefer y ( group 2 ) . city y needs 150 people : letall 60 who prefer y ( entire group 2 ) be relocated there , the rest 90 will be those who prefer x from group 1 ; city x needs 50 people : 140 - 90 = 50 from group 1 will be relocated to x , which they prefer . so , the highest possible number of employees who will be relocated to the city they prefer is 60 + 50 = 110 . answer : b ."
Answer: b
Question (general): united telephone charges a base rate of $ 8.00 for service , plus an additional charge of $ 0.25 per minute . atlantic call charges a base rate of $ 12.00 for service , plus an additional charge of $ 0.20 per minute . for what number of minutes would the bills for each telephone company be the same ?
Options: a ) 25 minutes , b ) 10 minutes , c ) 20 minutes , d ) 80 minutes , e ) 60 minutes
Rationale: "lets take number of minutesx . given that , 8 + 0.25 x = 12 + 0.2 x - > 0.05 x = 2 - > x = 80 minutes ans d"
Answer: d
Question (gain): by weight , liquid x makes up 0.8 percent of solution a and 1.8 percent of solution b . if 600 grams of solution a are mixed with 700 grams of solution b , then liquid x accounts for what percent of the weight of the resulting solution ?
Options: a ) 1.74 % , b ) 1.94 % , c ) 10 % , d ) 15 % , e ) 19 %
Rationale: "i think there is a typo in question . it should have been ` ` by weight liquid ' x ' makes up . . . . . ` ` weight of liquid x = 0.8 % of weight of a + 1.8 % of weight of b when 600 gms of a and 700 gms of b is mixed : weight of liquid x = ( 0.8 * 600 ) / 100 + ( 1.8 * 700 ) / 100 = 17.4 gms % of liquid x in resultant mixture = ( 17.4 / 1000 ) * 100 = 1.74 % a"
Answer: a
Question (gain): a , b and c invested rs . 6300 , rs . 4200 and rs . 10500 respectively , in a partnership business . find the share of a in profit of rs . 12200 after a year ?
Options: a ) 3660 , b ) 2881 , c ) 2887 , d ) 9977 , e ) 2212
Rationale: "6300 : 4200 : 10500 3 : 2 : 5 3 / 10 * 12200 = 3660 . answer : a"
Answer: a
Question (geometry): a right triangle with sides 3 cm , 4 cm and 5 cm is rotated about the side of 3 cm to form a cone . the volume of the cone so formed is
Options: a ) 12 π cm 3
b ) 15 π cm 3
c ) 16 π cm 3
d ) 20 π cm 3
e ) none
Rationale: solution clearly , we have r = 3 cm and h = 4 cm . ∴ volume = 1 / 3 π r 2 h = ( 1 / 3 x π x 32 x 4 ) cm 3 = 12 π cm 3 . answer a
Answer: a
Question (gain): on a certain transatlantic crossing , 20 percent of a ship ’ s passengers held round - trip tickets and also took their cars abroad the ship . if 80 percent of the passengers with round - trip tickets did not take their cars abroad the ship , what percent of the ship ’ s passengers held round - trip tickets ?
Options: a ) 20 % , b ) 40 % , c ) 60 % , d ) 80 % , e ) 100 %
Rationale: "let t be the total number of passengers . let x be the number of people with round trip tickets . 0.2 t had round trip tickets and took their cars . 0.2 x had round trip tickets and took their cars . 0.2 x = 0.2 t x = t the answer is e ."
Answer: e
Question (other): the ratio of money with ram and gopal is 7 : 17 and that with gopal and krishan is 7 : 17 . if ram has rs . 686 , krishan has ?
Options: a ) s . 2890 , b ) s . 4046 , c ) s . 1190 , d ) s . 1620 , e ) s . 2680
Rationale: "ram : gopal = 7 : 17 = 49 : 119 gopal : krishan = 7 : 17 = 119 : 289 ram : gopal : krishan = 49 : 119 : 289 ram : krishan = 49 : 289 thus , 49 : 289 = 686 : n & there n = 289 x 686 / 49 = rs . 4046 answer : b"
Answer: b
Question (general): a no . when divided by 220 gives a remainder 43 , what remainder will be obtainedby dividingthe same no . 17 ?
Options: a ) 5 , b ) 6 , c ) 9 , d ) 11 , e ) 15
Rationale: "221 + 43 = 264 / 17 = 9 ( remainder ) c"
Answer: c
Question (physics): two stations a and b are 110 km apart on a straight line . one train starts from a at 8 a . m . and travels towards b at 20 kmph . another train starts from b at 8 a . m . and travels towards a at a speed of 25 kmph . at what time will they meet ?
Options: a ) 11 , b ) 10 , c ) 8 , d ) 12 , e ) 15
Rationale: "suppose they meet x hours after 8 a . m . distance covered by a in x hours = 20 x km . distance covered by b in ( x - 1 ) hours = 25 ( x - 1 ) km . therefore 20 x + 25 ( x - 1 ) = 110 45 x = 135 x = 3 . so , they meet at 11 a . m . answer : a"
Answer: a
Question (physics): it takes joey the postman 1 hours to run a 2 mile long route every day . he delivers packages and then returns to the post office along the same path . if the average speed of the round trip is 5 mile / hour , what is the speed with which joey returns ?
Options: a ) 10 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "let his speed for one half of the journey be 2 miles an hour let the other half be x miles an hour now , avg speed = 5 mile an hour 2 * 2 * x / 2 + x = 5 4 x = 5 x + 10 = > x = 10 a"
Answer: a
Question (physics): a contractor undertakes to do a job within 100 days and hires 10 people to do it . after 20 days , he realizes that one fourth of the work is done so he fires 2 people . in how many more days w will the work get over ?
Options: a ) 60 , b ) w = 70 , c ) w = 75 , d ) w = 80 , e ) w = 100
Rationale: "we can also use the concept of man - days here 100 days - - > 10 men so the job includes 100 * 10 = 1000 man - days after 20 days 1 / 4 of job is completed so 1 / 4 x 1000 man - days = 250 man - days job is done now the balance job = 1000 - 250 = 750 man - days worth of job since 2 men are fired so b / l men = 8 therefore total no . of days of job = 750 man - day / 8 days = 375 / 4 = 94 days ( approx . ) now since this is total and ques . is asking for additional no . of days , so 94 - 20 = 74 days the nearest approx . to answer is 75 ans : c ( 75 days )"
Answer: c
Question (physics): ravi can do a piece of work in 24 days while prakash can do it in 40 days . in how many days will they finish it together ?
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 10
Rationale: "1 / 24 + 1 / 40 = 1 / 15 15 days answer : a"
Answer: a
Question (general): the tax on a commodity is diminished by 30 % but its consumption is increased by 20 % . find the decrease percent in the revenue derived from it ?
Options: a ) 18 % , b ) 72 % , c ) 32 % , d ) 16 % , e ) 52 %
Rationale: 100 * 100 = 10000 70 * 120 = 8400 10000 - - - - - - - 1600 100 - - - - - - - ? = 16 % answer : d
Answer: d
Question (general): when throwing 2 dices , and looking at the sum of numbers on the dices - what is the probability to have a sum which is smaller than 5 ?
Options: a ) 1 / 9 , b ) 1 / 6 , c ) 1 / 2 , d ) 1 / 3 , e ) 32 / 36
Rationale: a dice is composed of 6 numbers - 12 , 34 , 56 . when trowing 2 dices - there are 36 options ( 6 x 6 = 36 ) . if we want the sum of two dices to be < 5 there are those options : ( 11 ) , ( 12 ) , ( 21 ) , ( 13 ) , ( 31 ) , ( 22 ) - total of 6 options . therefore - the probability to have a sum which is smaller than 5 is 6 / 36 = 1 / 6 . answer : b
Answer: b
Question (general): a man is 24 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is :
Options: a ) 22 , b ) 28 , c ) 32 , d ) 48 , e ) 92
Rationale: "let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years . ( x + 24 ) + 2 = 2 ( x + 2 ) x + 26 = 2 x + 4 = > x = 22 . answer is a ."
Answer: a
Question (general): in a mixed college 160 students are there in one class . out of this 160 students 1 / 4 students are girls . how many boys are there ?
Options: a ) a ) 40 , b ) b ) 60 , c ) c ) 80 , d ) d ) 120 , e ) e ) 140
Rationale: total number of students : 160 total girls : 160 * 1 / 4 = 40 total boys : 160 - 40 = 120 answer is d
Answer: d
Question (gain): a and b put in rs . 300 and rs . 500 respectively into a business . a reinvests into the business his share of the first year ' s profit of rs . 200 where as b does not . in what ratio should they divide the second year ' s profit ?
Options: a ) 39 : 40 , b ) 39 : 49 , c ) 15 : 16 , d ) 14 : 18 , e ) 39 : 41
Rationale: explanation : 3 : 5 a = 3 / 8 * 200 = 75 375 : 400 39 : 40 answer : c
Answer: c
Question (general): if 42.18 = k ( 14 + m / 50 ) , where k and m are positive integers and m < 50 , then what is the value of k + m ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "42.18 = 14 k + km / 50 . . . we can rewrite the number as follows : 42 + 0.18 = 14 k + km / 50 . . . . . . . . since k is integer , then 42 = 14 k . . . . . . . . . . k = 3 0.18 = km / 50 . . . . . . 18 / 100 = 3 m / 50 . . . . . . m = 3 k + m = 3 + 3 = 6 answer : a"
Answer: a
Question (physics): it takes joey the postman 1 hours to run a 5 mile long route every day . he delivers packages and then returns to the post office along the same path . if the average speed of the round trip is 8 mile / hour , what is the speed with which joey returns ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 20
Rationale: let his speed for one half of the journey be 5 miles an hour let the other half be x miles an hour now , avg speed = 8 mile an hour 2 * 5 * x / 5 + x = 8 10 x = 8 x + 40 = > 2 x = 40 = > x = 20 e
Answer: e
Question (general): a ’ s speed is 20 / 16 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that the race ends in a dead heat ?
Options: a ) 1 / 17 , b ) 3 / 17 , c ) 1 / 10 , d ) 4 / 20 , e ) 3 / 10
Rationale: "we have the ratio of a ’ s speed and b ’ s speed . this means , we know how much distance a covers compared with b in the same time . this is what the beginning of the race will look like : ( start ) a _________ b ______________________________ if a covers 20 meters , b covers 16 meters in that time . so if the race is 20 meters long , when a reaches the finish line , b would be 4 meters behind him . if we want the race to end in a dead heat , we want b to be at the finish line too at the same time . this means b should get a head start of 4 meters so that he doesn ’ t need to cover that . in that case , the time required by a ( to cover 20 meters ) would be the same as the time required by b ( to cover 16 meters ) to reach the finish line . so b should get a head start of 4 / 20 th of the race . answer ( d )"
Answer: d