euclaise/mathqa_programs huggingface dataset:
Problem: the average monthly income of p and q is rs . 5050 . the average monthly income of q and r is rs . 6250 and the average monthly income of p and r is rs . 5200 . the monthly income of p is ?
Options: a ) rs . 3000 , b ) rs . 4000 , c ) rs . 5000 , d ) rs . 6000 , e ) rs . 7000
Rationale: "let p , q and r represent their respective monthly incomes . then , we have : p + q = ( 5050 x 2 ) = 10100 . . . . ( i ) q + r = ( 6250 x 2 ) = 12500 . . . . ( ii ) p + r = ( 5200 x 2 ) = 10400 . . . . ( iii ) adding ( i ) , ( ii ) and ( iii ) , we get : 2 ( p + q + r ) = 33000 or p + q + r = 16500 . . . . ( iv ) subtracting ( ii ) from ( iv ) , we get p = 4000 . p ' s monthly income = rs . 4000 . b )"
Answer: b
Python program:
a = 5050 + 5200 
b = a - 6250
Problem: a rectangular wall is covered entirely with two kinds of decorative tiles : regular and jumbo . 1 / 3 of the tiles are jumbo tiles , which have a length three times that of regular tiles and have the same ratio of length to width as the regular tiles . if regular tiles cover 60 square feet of the wall , and no tiles overlap , what is the area of the entire wall ?
Options: a ) 160
b ) 240
c ) 330
d ) 440
e ) 560
Rationale: the number of jumbo tiles = x . the number of regular tiles = 2 x . assume the ratio of the dimensions of a regular tile is a : a - - > area = a ^ 2 . the dimensions of a jumbo tile is 3 a : 3 a - - > area = 9 a ^ 2 . the area of regular tiles = 2 x * a ^ 2 = 60 . the area of jumbo tiles = x * 9 a ^ 2 = 4.5 ( 2 x * a ^ 2 ) = 4.5 * 60 = 270 . total area = 60 + 270 = 330 . answer : c .
Answer: c
Python program:
a = 60 * 3
b = a / 2
c = b * 3
d = 60 + c
Problem: in a group of 26 junior high school students , 7 take french , 10 take spanish , and 4 take both languages . the students taking both french and spanish are not counted with the 7 taking french or the 10 taking spanish . how many students are not taking either french or spanish ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 8
Rationale: "c 5 add 7 + 10 + 4 to get 21 . then subtract 21 from the total students ⇒ 26 – 21 = 5 . answer is c"
Answer: c
Python program:
a = 7 + 10 
b = 26 - a
Problem: a mixture contains alcohol and water in the ratio 4 : 3 . if 8 litres of water is added to the mixture , the ratio becomes 4 : 5 . find the quantity of alcohol in the given mixture
Options: a ) 15 litres , b ) 10 litres , c ) 30 litres , d ) 22 litres , e ) 16 litres
Rationale: "let the quantity of alcohol and water be 4 x litres and 3 x litres respectively 4 x / ( 3 x + 8 ) = 4 / 5 20 x = 4 ( 3 x + 8 ) 8 x = 32 x = 4 quantity of alcohol = ( 4 x 4 ) litres = 16 litres . answer is e ."
Answer: e
Python program:
a = 8 * 1
Problem: what is the sum of the multiples of 4 between 19 and 130 inclusive ?
Options: a ) 2012 , b ) 2044 , c ) 2060 , d ) 2072 , e ) 2080
Rationale: "the fastest way in an ap is to find the average and multiply with total integers . . between 19 and 130 , the smallest multiple of 4 is 20 and largest = 128 . . average = ( 20 + 128 ) / 2 = 148 / 2 = 74 . total numbers = ( 128 - 20 ) / 4 + 1 = 27 + 1 = 28 . . sum = 28 * 74 = 2072 ans d"
Answer: d
Python program:
a = 130 - 3
b = 19 + 2 
c = a + b 
d = c / 2
e = 130 - 3
f = 19 + 2 
g = e - f
h = g / 4
i = h + 1 
j = d * i
Problem: a certain article of clothing was discounted during a special sale to 3 / 4 of its original retail price . when the clothing did n ' t sell , it was discounted even further to 2 / 5 of its original retail price during a second sale . by what percent did the price of this article of clothing decrease from the first sale to the second sale ?
Options: a ) 50 % , b ) 33.33 % , c ) 25 % , d ) 46.66 % , e ) 12.5 %
Rationale: say the original retail price of the item was $ 200 . the price after the first sale = 3 / 4 * $ 200 = $ 150 . the price after the second sale = 2 / 5 * $ 200 = $ 80 . the percent change from the first sale to the second = ( 150 - 80 ) / 150 = 1 / 3 = 46.66 % . answer : d .
Answer: d
Python program:
a = 3 / 4
b = 3 / 4
c = 2 / 5
d = b * c
e = a - d
f = e * 100
Problem: bruce and anne can clean their house in 4 hours working together at their respective constant rates . if anne ’ s speed were doubled , they could clean their house in 3 hours working at their respective rates . how many hours does it currently take anne to clean the house on her own ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 12 , e ) 14
Rationale: "lets suppose anne and bruce take a and b hrs working separately so in 1 hour they can together finish 1 / a + 1 / b portion of the work which equals 1 / 4 ( as the work is completed in 4 hours ) after anne doubles her rate of work the portion completed by the both is 1 / a + 2 / b which is equal to 1 / 3 ( as the work is completed in 3 hours ) solving these 2 equations we can find b as 12 answer : d"
Answer: d
Python program:
a = 1 / 3
b = 1 / 4
c = a - b
d = 1/(c)
Problem: if p and q are prime numbers , how many divisors does the product p ^ 3 * q ^ 6 have ?
Options: a ) 9 , b ) 12 , c ) 18 , d ) 28 , e ) 363
Rationale: ", p ^ 2 , p ^ 3 and q , q ^ 1 , q ^ 2 . . . . q ^ 6 together essentially there are 18 different combinations you can make ( 3 x 6 ) also you have to include the different combinations the p and q exponents can be a divisor . there are 3 different p exponents and 6 different q exponents : p , p ^ 2 , p ^ 3 , q , q ^ 2 , q ^ 3 . . . q ^ 6 also add 1 since ` ` 1 ' ' can also be a divisor . 18 + 3 + 6 + 1 = 28 , answer : d"
Answer: d
Python program:
a = 3 + 1 
b = 6 + 1 
c = a * b
Problem: two men started from the same place walk at the rate of 10 kmph and 12 kmph respectively . what time will they take to be 10 km apart , if they walk in the same direction ?
Options: a ) 5 hours , b ) 6 hours , c ) 8 hours , d ) 10 hours , e ) 12 hours
Rationale: "to be 2 km apart they take 1 hour to be 10 km apart they take = 1 / 2 * 10 = 5 hours answer is a"
Answer: a
Python program:
a = 12 - 10
b = a / 10
Problem: the rate of interest on a sum of money is 3 % p . a . for the first 3 years , 4 % p . a . for the next 4 years , and 5 % for the period beyond 7 years . if the s . i , occurred on the sum for the total period of 8 years is rs . 540 / - , the sum is
Options: a ) 1,200 , b ) 1,800 , c ) 2,100 , d ) 2,250 , e ) 2,540
Rationale: "explanation : i 1 = ( p x 3 x 3 ) / 100 = p / 11 i 2 = ( p x 4 x 4 ) / 100 = 4 p / 25 i 3 = ( p x 1 x 5 ) / 100 = p / 20 p / 11 + 4 p / 25 + p / 20 = 540 30 p / 100 = 540 p = 1800 answer : option b"
Answer: b
Python program:
a = 540 / 540
Problem: in a renowned city , the average birth rate is 6 people every two seconds and the death rate is 2 people every two seconds . estimate the size of the population net increase that occurs in one day .
Options: a ) 32,300 , b ) 172,800 , c ) 468,830 , d ) 338,200 , e ) 259,200
Rationale: "every 2 seconds , 4 persons are added ( 6 - 2 ) . every second 2 persons are added . in a day 24 hrs = 24 * 60 minutes = 24 * 60 * 60 = 86400 seconds . 86400 * 2 = 172800 option b is the answer ."
Answer: b
Python program:
a = 6 - 2
b = a * 3600
c = b * 12
Problem: for every x , the action [ x ] is defined : [ x ] is the greatest integer less than or equal to x . what is the value of [ 6.5 ] x [ 2 / 3 ] + [ 2 ] x 7.2 + [ 8.3 ] - 6.6 ?
Options: a ) 12.6 . , b ) 15.8 . , c ) 14.4 . , d ) 16.2 . , e ) 16.4 .
Rationale: "[ 6.5 ] x [ 2 / 3 ] + [ 2 ] x 7.2 + [ 8.3 ] - 6.6 = 6 * 0 + 2 * 7.2 + 8 - 6.6 = 0 + 14.4 + 1.4 15.8 answer b"
Answer: b
Python program:
a = 2 * 7
b = 4 / 10
c = 8 - 3
d = a + c 
e = d - 6
Problem: a car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 300 kilometers per hour . at what speed , in kilometers per hour , is the car traveling ?
Options: a ) 300 , b ) 320 , c ) 330 , d ) 340 , e ) 290
Rationale: "answer a 300 * t = 1 km = > t = 1 / 360 km / h v * ( t + 2 / 3600 ) = 1 v ( 1 / 360 + 2 / 3600 ) = 1 = > v = 300 km / h"
Answer: a
Python program:
a = 1 / 300
b = 3600 * a
c = b + 2 
d = c / 3600
e = 1 / d
Problem: in a group of 25 , 13 can speak latin , 15 can speak french , and 6 do n ' t speak either . how many of these speak both latin and french ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 8
Rationale: let no . of persons who speeks booth latin and french = x so , no . of persons who speeks only latin = 13 - x no . of persons who speeks only french = 15 - x no . of persons who speeks dont speek any lag = 6 therefore ( 13 - x ) + ( 15 - x ) + x + 6 = 25 34 - x = 25 x = 9 answer : a
Answer: a
Python program:
a = 13 + 15 
b = a + 6 
c = b - 25
Problem: a train of length 250 m crosses a bridge of length 120 m in 20 seconds . what is the speed of train ?
Options: a ) 33 , b ) 27 , c ) 66.6 , d ) 22 , e ) 72
Rationale: "sol : ( length of train + length of bridge ) = speed of train x time ( 250 + 120 ) = 20 x speed speed = 370 / 20 = 18.5 m / s = 66.6 km / h answer = c"
Answer: c
Python program:
a = 250 + 120 
b = a / 20
c = const_3_6 * b
Problem: a survey of n people in the town of eros found that 50 % of them preferred brand a . another survey of 150 people in the town of angie found that 60 % preferred brand a . in total , 55 % of all the people surveyed together preferred brand a . what is the total number of people surveyed ?
Options: a ) 50 , b ) 100 , c ) 150 , d ) 300 , e ) 250
Rationale: "it is simply a weighted average question . since the given average of 50 % and 60 % is 55 % ( right in the middle ) , it means the number of people surveyed in eros ( n ) is same as the number of people surveyed in angie . so n = 150 total = 150 + 150 = 300 answer ( d )"
Answer: d
Python program:
a = 60 / 100
b = 150 * a
c = 55 / 100
d = 150 * c
e = b - d
f = 55 / 100
g = 50 / 100
h = f - g
i = e / h
Problem: in what ratio should a 20 % methyl alcohol solution be mixed with a 50 % methyl alcohol solution so that the resultant solution has 40 % methyl alcohol in it ?
Options: a ) 1 : 3 , b ) 1 : 2 , c ) 2 : 3 , d ) 2 : 1 , e ) 3 : 1
Rationale: two things to remember : - 1 ) the ratio of quantity mixed to get an average is related to the ratio of each qty ' s distance from average . 2 ) more the qty of x from that of y , more closer will be average to x . . qty of 20 % / qty of 50 % = ( 50 − 40 ) / ( 40 − 20 ) = 1 / 2 = 1 : 2 answer : b
Answer: b
Python program:
a = 50 - 40
b = 40 - 20
c = a / b
Problem: each of the 42 points is placed either inside or on the surface of a perfect sphere . if 65 % or fewer of the points touch the surface , what is the maximum number of segments which , if connected from those points to form chords , could be the diameter of the sphere ?
Options: a ) 7 , b ) 11 , c ) 13 , d ) 23 , e ) 38
Rationale: "maximum number of points on the surface is 65 % * 42 = 27.3 . . . or 27 since it has to be an integer now note that if two points form a diameter , they can not be part of any other diameter . so in the best case we can pair up the points we have 27 points , so at best we can form 13 pairs ( 26 ) . so , answer is ( c )"
Answer: c
Python program:
a = 65 / 100
b = 42 * a
c = b / 2
Problem: rs . 800 becomes rs . 956 in 3 years at a certain rate of simple interest . if the rate of interest is increased by 4 % , what amount will rs . 800 become in 3 years .
Options: a ) rupees 1052 , b ) rs 1152 , c ) rs 1252 , d ) rs 1352 , e ) none of these
Rationale: explanation : s . i . = 956 - 800 = rs 156 r = 156 ∗ 100 / 800 ∗ 3 r = 6 1 / 2 % new rate = 6 1 / 2 + 4 = 21 / 2 % new s . i . = 800 × 21 / 2 × 3100 = 252 now amount will be 800 + 252 = 1052 option a
Answer: a
Python program:
a = 956 - 800
b = a * 100
c = 800 * 3
d = b / c
e = d + 4 
f = 800 * e
g = f * 3
h = g / 100
i = 800 + h
Problem: in the rectangular coordinate system , if the line x = 8 y + 5 passes through points ( m , n ) and ( m + 2 , n + p ) , what is the value of p ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 5 , e ) 1 / 6
Rationale: "x = 8 y + 5 , and thus y = x / 8 - 5 / 8 the slope is 1 / 8 . the slope of a line through points ( m , n ) and ( m + 2 , n + p ) is ( n + p - n ) / ( m + 2 - m ) = p / 2 p / 2 = 1 / 8 and thus p = 1 / 4 the answer is c ."
Answer: c
Python program:
a = 2 / 8
Problem: a taxi leaves point a 5 hours after a bus left the same spot . the bus is traveling 10 mph slower than the taxi . find the speed of the taxi , if it overtakes the bus in three hours .
Options: a ) 20 , b ) 24 , c ) 32 , d ) 16 , e ) 40
Rationale: "let the speed of bus be v - 10 , speed of taxi be v the bus travelled a total of 8 hrs and taxi a total of 3 hrs . hence 8 * ( v - 10 ) = 3 v 8 v - 80 = 3 v 5 v = 80 d"
Answer: d
Python program:
a = 5 * 10
b = 5 * 10
c = a + b 
d = 5 + 5 
e = d - 5
f = c / e
Problem: the length of a rectangular landscape is 12 times its breadth . there is a playground in it whose area is 1200 square mtr & which is 1 / 4 rd of the total landscape . what is the length of the landscape ?
Options: a ) 90 , b ) 120 , c ) 240 , d ) 180 , e ) 110
Rationale: "sol . x * 12 x = 4 * 1200 x = 20 length = 12 * 20 = 240 c"
Answer: c
Python program:
a = 4 * 0
b = a * 10
Problem: if x , y , and z are positive real numbers such that x + y - z = 62 , y - z + x = 82 , and z - x + y = 100 , then find the x + y + z value ?
Options: a ) 80 , b ) 91 , c ) 62 , d ) 74 , e ) 82
Rationale: "x + y - z = 62 , - - - - - - 1 ) y - z + x = 82 , - - - - - - 2 ) z - x + y = 100 - - - - - - 3 ) from ( 1 ) & ( 2 ) 2 z = 20 z = 10 from ( 2 ) & ( 3 ) 2 y = 182 y = 91 then x = 62 - 81 = - 19 x + y + z = 82 correct option is e"
Answer: e
Python program:
a = 82 - 62
b = 100 - a
Problem: how many seconds will a 400 metre long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?
Options: a ) 24 , b ) 30 , c ) 40 , d ) 45 , e ) 50
Rationale: "relative speed of the train = 63 - 3 = 60 kmph = 60 * 5 / 18 = 50 / 3 m / sec t = 400 * 3 / 50 = 24 sec answer : a"
Answer: a
Python program:
a = 63 - 3
b = const_0_2778 * a
c = 400 / b
Problem: a 240 meter long train crosses a man standing on the platform in 4 sec . what is the speed of the train ?
Options: a ) 176 kmph , b ) 108 kmph , c ) 216 kmph , d ) 134 kmph , e ) 161 kmph
Rationale: "s = 240 / 4 * 18 / 5 = 216 kmph answer : c"
Answer: c
Python program:
a = 240 / 4
b = a * const_3_6
Problem: the population of a town is 10000 . it decreases annually at the rate of 10 % p . a . what will be its population after 2 years ?
Options: a ) 4300 , b ) 4500 , c ) 8100 , d ) 5230 , e ) 5366
Rationale: "10000 × 90 / 100 × 90 / 100 = 8100 answer : c"
Answer: c
Python program:
a = 10 / 100
b = 10000 * a
c = 10000 - b
d = 10 / 100
e = 10000 * d
f = 10000 - e
g = 10 / 100
h = f * g
i = c - h
Problem: a boat running downstream covers a distance of 10 km in 3 hr while for covering the same distance upstream , it takes 6 hr . what is the speed of the boat ?
Options: a ) 2.5 kmph , b ) 3.5 kmph , c ) 4.5 kmph , d ) 1.5 kmph , e ) 9.5 kmph
Rationale: speed upstream = 10 / 3 speed of boat down stream = 10 / 6 speed of boat = 1 / 2 ( 10 / 3 + 10 / 6 ) = 2.5 kmph answer : a
Answer: a
Python program:
a = 10 / 3
b = 10 / 6
c = a + b 
d = c / 2
Problem: a fort had provision of food for 150 men for 45 days . after 15 days , 25 men left the fort . the number of days for which the remaining food will last , is :
Options: a ) 36 , b ) 37 1 / 4 , c ) 42 , d ) 54 , e ) 48
Rationale: "after 15 days : 150 men had food for 30 days . suppose 125 men had food for x days . now , less men , more days ( indirect proportion ) therefore 125 : 150 : : 30 : x < = > 125 x x = 150 x 30 = > x = 150 x 30 / 125 = > x = 36 . correct answer is a"
Answer: a
Python program:
a = 25 + 15 
b = 150 * a
c = 150 - 25
d = b / c
Problem: the length of a room is 8 m and width is 4.75 m . what is the cost of paying the floor by slabs at the rate of rs . 900 per sq . metre .
Options: a ) 25650 , b ) 25750 , c ) 26550 , d ) 26750 , e ) 34200
Rationale: "area = 8 × 4.75 sq . metre . cost for 1 sq . metre . = rs . 900 hence total cost = 8 × 4.75 × 900 = 8 × 4275 = rs . 34200 answer is e ."
Answer: e
Python program:
a = 8 * 4
b = 900 * a
Problem: a person distributed 15 % of his income to his 3 children each . he deposited 30 % of his income to his wife ' s account . he donated 5 % of remaining amount to an orphan house . finally he has $ 40000 . find his total income ?
Options: a ) a ) 452000 , b ) b ) 200000 , c ) c ) 800000 , d ) d ) 500000 , e ) e ) 652000
Rationale: "3 children got = 3 * 15 % = 45 % wife got = 30 % orphan house = 5 % total = 45 + 30 + 5 = 80 % remaining = 100 - 80 = 20 % 20 % = 40000 100 % = 40000 * 100 / 20 = $ 200000 answer is b"
Answer: b
Python program:
a = 15 * 3
b = a + 30 
c = b + 5 
d = 100 - c
e = 40000 / d
f = e * 100
Problem: the difference between a two - digit number and the number obtained by interchanging the positions of its digits is 81 . what is the difference between the two digits of that number ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: "sol . let the ten ’ s digit be x and unit ’ s digit be y , then , ( 10 x + y ) - ( 10 y + x ) = 81 ⇔ 9 ( x - y ) = 81 ⇔ x - y = 9 answer e"
Answer: e
Python program:
a = 10 - 1
b = 81 / a
Problem: a and b runs around a circular track . a beats b by one round or 10 minutes . in this race , they had completed 4 rounds . if the race was only of one round , find the a ' s time over the course :
Options: a ) 8.5 min
b ) 7.5 min
c ) 1.5 min
d ) 9.5 min
e ) 4.5 min
Rationale: explanation : b runs around the track in 10 min . i . e , speed of b = 10 min per round a beats b by 1 round time taken by a to complete 4 rounds = time taken by b to complete 3 rounds = 30 min a ' s speed = 30 / 4 min per round = 7.5 min per round hence , if the race is only of one round a ' s time over the course = 7 min 30 sec answer : b
Answer: b
Python program:
a = 4 - 1
b = a * 10
c = b / 4
Problem: a certain industrial loom weaves 0.127 meters of cloth every second . approximately how many seconds will it take for the loom to weave 15 meters of cloth ?
Options: a ) 114 , b ) 115 , c ) 116 , d ) 117 , e ) 118
Rationale: "let the required number of seconds be x more cloth , more time , ( direct proportion ) hence we can write as ( cloth ) 0.127 : 15 : : 1 : x = > 0.127 * x = 15 = > x = 15 / 0.127 = > x = 118 answer : e"
Answer: e
Python program:
a = 15 / 0
Problem: the average marks of a class of 35 students is 45 and that of another class of 55 students is 65 . find the average marks of all the students ?
Options: a ) 52.6 , b ) 52.4 , c ) 52.1 , d ) 57 , e ) 52.9
Rationale: "sum of the marks for the class of 35 students = 35 * 45 = 1575 sum of the marks for the class of 55 students = 55 * 65 = 3575 sum of the marks for the class of 90 students = 1575 + 3575 = 5150 average marks of all the students = 5150 / 90 = 57 . answer : d"
Answer: d
Python program:
a = 35 * 45
b = 55 * 65
c = a + b 
d = 35 + 55 
e = c / d
Problem: a and b together have $ 100 . if 3 / 10 of a ' s amount is equal to 1 / 5 of b ' s amount , how much amount does b have ?
Options: a ) $ 60 , b ) $ 55 , c ) $ 42 , d ) $ 31 , e ) $ 100
Rationale: "3 / 10 a = 1 / 5 b a = 1 / 5 * 10 / 3 b a = 2 / 3 b a / b = 2 / 3 a : b = 2 : 3 b ' s share = 100 * 3 / 5 = $ 60 answer is a"
Answer: a
Python program:
a = 1 / 5
b = 3 / 10
c = a / b
d = c + 1 
e = 100 / d
Problem: two cars start from the opposite places of a main road , 150 km apart . first car runs for 30 km and takes a right turn and then runs 15 km . it then turns left and then runs for another 25 km and then takes the direction back to reach the main road . in the mean time , due to minor break down the other car has run only 35 km along the main road . what would be the distance between two cars at this point ?
Options: a ) 65 , b ) 38 , c ) 60 , d ) 28 , e ) 21
Rationale: answer : c ) 60 km
Answer: c
Python program:
a = 150 - 35
b = 30 + 30 
c = a - b
Problem: if the given two numbers are respectively 6 % and 30 % of a third number , then what percentage is the first of the second ?
Options: a ) 20 % , b ) 25 % , c ) 18 % , d ) 30 % , e ) none of these
Rationale: here , l = 6 and m = 30 therefore , first number = l / m x 100 % of second number = 6 / 30 x 100 % of second number = 20 % of second number answer : a
Answer: a
Python program:
a = 6 / 100
b = 30 / 100
c = a / b
d = c * 100
Problem: mary can do a piece of work in 11 days . rosy is 10 % more efficient than mary . the number of days taken by rosy to do the same piece of work is ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30
Rationale: "ratio of times taken by mary and rosy = 110 : 100 = 11 : 10 suppose rosy takes x days to do the work . 11 : 10 : : 11 : x = > x = 10 days . hence , rosy takes 10 days to complete the work . answer : a"
Answer: a
Python program:
a = 10 / 100
b = 1 + a 
c = 11 / b
Problem: in a certain game of dice , the player ’ s score is determined as a sum of three throws of a single die . the player with the highest score wins the round . if more than one player has the highest score , the winnings of the round are divided equally among these players . if jim plays this game against 24 other players , what is the probability of the minimum score that will guarantee jim some monetary payoff ?
Options: a ) 1 / 216 , b ) 1 / 221 , c ) 1 / 212 , d ) 1 / 84 , e ) 1 / 42
Rationale: "toguaranteethat jim will get some monetary payoff he must score the maximum score of 6 + 6 + 6 = 18 , because if he gets even one less than that so 17 , someone can get 18 and jim will get nothing . p ( 18 ) = 1 / 6 ^ 3 = 1 / 216 . answer : a ."
Answer: a
Python program:
a = 24 / 3
b = a - 1
c = b ** 2
d = 1 / c
Problem: 24 oz of juice p and 25 oz of juice v are mixed to make smothies m and y . the ratio of p to v in smothie m is 4 is to 1 and that in y is 1 is to 5 . how many ounces of juice p are contained in the smothie m ?
Options: a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25
Rationale: the ratio of p to v in smothie m is 4 is to 1 and that in y is 1 is to 5 . p 1 + p 2 = 24 v 1 + v 2 = 25 p 1 = 4 v 1 p 2 = v 2 / 5 4 v 1 + v 2 / 5 = 24 v 1 + v 2 = 25 4 v 2 - v 2 / 5 = 76 19 v 2 / 5 = 76 = > v 2 = 20 = > v 1 = 5 = > p 1 = 20 answer - d
Answer: d
Python program:
a = 24 * 5
b = a - 25
c = 4 * 5
d = c - 1
e = b / d
f = e * 4
Problem: a volume of 10940 l water is in a container of sphere . how many hemisphere of volume 4 l each will be required to transfer all the water into the small hemispheres ?
Options: a ) 2812 , b ) 8231 , c ) 2734 , d ) 2735 , e ) 4254
Rationale: "a volume of 4 l can be kept in 1 hemisphere therefore , a volume of 10940 l can be kept in ( 10940 / 4 ) hemispheres ans . 2735 answer : d"
Answer: d
Python program:
a = 10940 / 4
Problem: a train leaves mumabai at 9 am at a speed of 40 kmph . after one hour , another train leaves mumbai in the same direction as that of the first train at a speed of 80 kmph . when and at what distance from mumbai do the two trains meet ?
Options: a ) 87 , b ) 279 , c ) 80 , d ) 278 , e ) 379
Rationale: "when the second train leaves mumbai the first train covers 40 * 1 = 40 km so , the distance between first train and second train is 40 km at 10.00 am time taken by the trains to meet = distance / relative speed = 40 / ( 80 - 40 ) = 1 hours so , the two trains meet at 11 a . m . the two trains meet 1 * 80 = 80 km away from mumbai . answer : c"
Answer: c
Python program:
a = 40 * 1
b = 80 - 40
c = a / b
d = c * 80
Problem: 0 , 1 , 4 , 15 , 64 , ____
Options: a ) 225 , b ) 325 , c ) 125 , d ) 145 , e ) none
Rationale: "0 , 1,4 , 15,64 . . . . . 0 * 1 + 1 = 1 1 * 2 + 2 = 4 4 * 3 + 3 = 15 15 * 4 + 4 = 64 64 * 5 + 5 = 325 answer : b"
Answer: b
Python program:
a = negate - (
Problem: virginia , adrienne , and dennis have taught history for a combined total of 93 years . if virginia has taught for 9 more years than adrienne and for 9 fewer years than dennis , for how many years has dennis taught ?
Options: a ) 23 , b ) 32 , c ) 40 , d ) 41 , e ) 44
Rationale: "let number of years taught by virginia = v number of years taught by adrienne = a number of years taught by dennis = d v + a + d = 96 v = a + 9 = > a = v - 9 v = d - 9 = > a = ( d - 9 ) - 9 = d - 18 d - 9 + d - 18 + d = 93 = > 3 d = 93 + 27 = 120 = > d = 40 answer c"
Answer: c
Python program:
a = 9 + 9 
b = a + 9 
c = 93 - b
d = c / 3
e = 9 + 9 
f = d + e