euclaise/mathqa_programs huggingface dataset:
Problem: a river 2 m deep and 45 m wide is flowing at the rate of 4 kmph the amount of water that runs into the sea per minute is ?
Options: a ) 6000 m 3 , b ) 4580 m 3 , c ) 18500 m 3 , d ) 4900 m 3 , e ) 4700 m 3
Rationale: "explanation : ( 4000 * 2 * 45 ) / 60 = 6000 m 3 answer : option a"
Answer: a
Python program:
a = 2 * 45
b = 4 * 1000
c = a * b
d = 1 * const_60
e = c / d
Problem: the ratio of two quantities is 5 to 6 . if each of the quantities is increased by 15 , what is the ratio of these 2 new quantities ?
Options: a ) 5 : 6 , b ) 25 : 27 , c ) 15 : 16 , d ) 20 : 21 , e ) it can not be determined from the information given
Rationale: the ratio can not be straight way added any quantity . . . 5 : 6 means 5 x : 6 x . . . so when you add a quantity , it becomes 5 x + 15 : 6 x + 15 . . so value of x is must . . ans e
Answer: e
Python program:
a = 5 + 15 
b = 6 + 15 
c = a / b
Problem: a sum of $ 1000 amounts to $ 1500 in 5 years at simple interest . if the interest rate is increased by 5 % it would amount to how much ?
Options: a ) $ 1000 , b ) $ 750 , c ) $ 1541 , d ) $ 1478 , e ) $ 1750
Rationale: "s . i = 1500 - 1000 = 500 p = $ 1000 t = 5 years r = 100 * 500 / 1000 * 5 = 10 % new rate = 10 + 5 = 15 % new s . i . = 1000 * 15 * 5 / 100 = $ 750 new amount = 1000 + 750 = $ 1750 answer is e"
Answer: e
Python program:
a = 1500 - 1000
b = a / 5
c = b * 100
d = c / 1000
e = d + 5 
f = e / 100
g = 1000 * f
h = g * 5
i = 1000 + h
Problem: if f ( x ) = ax ^ 5 – 3 x ^ 2 + ax ^ 2 – x , then f ( b ) – f ( - b ) will equal :
Options: a ) 0 , b ) 2 ab , c ) 2 ab ^ 4 – 6 , d ) 2 ab ^ 5 - 2 b , e ) ab ^ 5
Rationale: "f ( x ) = ax ^ 5 – 3 x ^ 2 + ax ^ 2 – x f ( b ) = ab ^ 5 – 3 b ^ 2 + ab ^ 2 – b f ( - b ) = - ab ^ 5 – 3 b ^ 2 + ab ^ 2 + b f ( b ) - f ( - b ) = ab ^ 5 – 3 b ^ 2 + ab ^ 2 – b + ab ^ 5 + 3 b ^ 2 - ab ^ 2 – b = 2 ab ^ 5 - 2 b answer d"
Answer: d
Python program:
a = 2 * 10
Problem: the average age of students of a class is 15.8 years . the average age of boys in the class is 16.3 years and that of the girls is 15.4 years . the ration of the number of boys to the number of girls in the class is :
Options: a ) 2 : 5 , b ) 2 : 3 , c ) 2 : 4 , d ) 4 : 5 , e ) 2 : 9
Rationale: "let the ratio be k : 1 . then , k * 16.3 + 1 * 15.4 = ( k + 1 ) * 15.8 = ( 16.3 - 15.8 ) k = ( 15.8 - 15.4 ) = k = 0.4 / 0.5 = 4 / 5 required ratio = 4 / 5 : 1 = 4 : 5 . answer : d"
Answer: d
Python program:
a = 15 - 8
b = 16 - 3
c = a / b
Problem: a man whose bowling average is 12.4 , takes 8 wickets for 26 runs and there by decreases his average by 0.4 . the number of wickets taken by him before his last match is ?
Options: a ) 173 , b ) 174 , c ) 175 , d ) 176 , e ) 177
Rationale: "12.4 * x + 26 = ( 8 + x ) 12 solve equation x = 175 answer : c"
Answer: c
Python program:
a = math.floor(12, 4)
b = a * 8
c = b - 26
d = math.floor(12, 4)
e = 12 - 4
f = c / e
Problem: a train passes a station platform in 62 sec and a man standing on the platform in 20 sec . if the speed of the train is 54 km / hr . what is the length of the platform ?
Options: a ) 615 m , b ) 240 m , c ) 168 m , d ) 444 m , e ) 691 m
Rationale: "speed = 54 * 5 / 18 = 15 m / sec . length of the train = 15 * 20 = 300 m . let the length of the platform be x m . then , ( x + 300 ) / 62 = 15 = > x = 444 m answer : d"
Answer: d
Python program:
a = 54 * const_0_2778
b = 20 * a
Problem: a , b and c enter into a partnership by investing $ 7000 , $ 11000 and $ 18000 respectively . at the end of 8 months , b receives $ 2200 as his share . find the share of a .
Options: a ) $ 1200 , b ) $ 1300 , c ) $ 1400 , d ) $ 1500 , e ) $ 1600
Rationale: "the ratio of capital of a , b and c = 7000 : 11000 : 18000 = 7 : 11 : 18 a ' s share = ( 7 / 11 ) * 2200 = $ 1400 the answer is c ."
Answer: c
Python program:
a = 11000 * 8
b = a / 100
c = 2200 / b
d = 7000 * c
e = d * 8
f = e / 100
Problem: if 40 % of a certain number is 160 , then what is 10 % of that number ?
Options: a ) 100 , b ) 40 , c ) 80 , d ) 120 , e ) 110
Rationale: explanation : 40 % = 40 * 4 = 160 10 % = 10 * 4 = 40 answer : option b
Answer: b
Python program:
a = 40 / 100
b = 160 / a
c = 10 / 100
d = b * c
Problem: a man took loan from a bank at the rate of 12 % p . a . s . i . after 20 years he had to pay rs . 2100 interest only for the period . the principal amount borrowed by him was ?
Options: a ) 600 , b ) 715 , c ) 600 , d ) 875 , e ) 900
Rationale: "principal = ( 100 * 2100 ) / ( 12 * 20 ) = rs . 875 answer : d"
Answer: d
Python program:
a = 2100 * 100
b = a / 20
c = b / 12
Problem: the average ( arithmetic mean ) of 24 , 35 , and 58 is 6 more than the average of 19 , 51 , and x . what is x ?
Options: a ) 26 , b ) 27 , c ) 28 , d ) 29 , e ) 30
Rationale: "the average of 24 , 35 , and 58 is 39 . the average of 19 , 51 and x is 33 . then 19 + 51 + x = 99 . x = 29 . the answer is d ."
Answer: d
Python program:
a = 24 + 35 
b = a + 58 
c = 6 * 3
d = c + 19 
e = d + 51 
f = b - e
Problem: instead of multiplying a number by 5 , the number is divided by 5 . what is the percentage of error obtained ?
Options: a ) 98 % , b ) 97 % , c ) 96 % , d ) 99 % , e ) 95 %
Rationale: "let the number be x the right number is 5 x the wrong number is x / 5 error is ( 5 x - x / 5 ) = 24 x / 5 percentage of error is ( ( 24 x / 5 ) / 5 x ) * 100 = 96 % answer : c"
Answer: c
Python program:
a = 5 / 5
b = 5 * 5
c = a / b
d = c * 100
e = 100 - d
Problem: a person crosses a 600 m long street in 5 minutes , what is his speed in km per hour ?
Options: a ) 4.3 , b ) 7.2 , c ) 2.3 , d ) 3.2 , e ) 1.1
Rationale: "explanation : speed = { \ color { blue } \ left ( \ frac { 600 } { 5 \ times 60 } \ right ) m / sec = 2 m / sec = \ left ( 2 \ times \ frac { 18 } { 5 } \ right ) km / hr = 7.2 km / hr } answer : b"
Answer: b
Python program:
a = 600 / 1000
b = 5 * const_60
c = b / 3600
d = a / c
Problem: the length of a train and that of a platform are equal . if with a speed of 72 k / hr , the train crosses the platform in one minute , then the length of the train ( in meters ) is ?
Options: a ) 299 , b ) 266 , c ) 299 , d ) 750 , e ) 600
Rationale: "speed = [ 72 * 5 / 18 ] m / sec = 20 m / sec ; time = 1 min . = 60 sec . let the length of the train and that of the platform be x meters . then , 2 x / 60 = 20 = > x = 20 * 60 / 2 = 600 answer : e"
Answer: e
Python program:
a = 72 * 1000
b = const_60 / 1
c = a / b
d = c / 2
Problem: square a has an area of 81 square centimeters . square b has a perimeter of 32 centimeters . if square b is placed within square a and a random point is chosen within square a , what is the probability the point is not within square b ?
Options: a ) 17 / 64
b ) 17 / 81
c ) 16 / 25
d ) 3 / 5
e ) 6 / 25
Rationale: i guess it ' s mean that square b is placed within square aentirely . since , the perimeter of b is 32 , then its side is 32 / 4 = 8 and the area is 4 ^ 2 = 64 ; empty space between the squares is 81 - 64 = 17 square centimeters , so if a random point is in this area then it wo n ' t be within square b : p = favorable / total = 17 / 81 . answer : b
Answer: b
Python program:
a = 32 / 4
b = a ** 2
c = 81 - b
d = c / 81
Problem: one hour after yolanda started walking from x to y , a distance of 60 miles , bob started walking along the same road from y to x . if yolanda â s walking rate was 5 miles per hour and bob â s was 6 miles per hour , how many miles had bob walked when they met ?
Options: a ) 40 , b ) 25 , c ) 28 , d ) 30 , e ) 30.5
Rationale: "let t be the number of hours that bob had walked when he met yolanda . then , when they met , bob had walked 4 t miles and yolanda had walked 5 ( t + 1 ) miles . these distances must sum to 60 miles , so 6 t + 5 ( t + 1 ) = 60 , which may be solved for t as follows 6 t + 5 ( t + 1 ) = 60 6 t + 5 t + 5 = 60 11 t = 55 t = 5 ( hours ) therefore , bob had walked 6 t = 6 ( 5 ) = 30 miles when they met . the best answer is d ."
Answer: d
Python program:
a = 60 - 5
b = 5 + 6 
c = a / b
d = c * 6
Problem: in a class of 25 students , 15 play hockey and 16 play basketball . if there are 4 students who play neither sport , determine the number of students who play both hockey and basketball ?
Options: a ) 10 , b ) 11 , c ) 13 , d ) 14 , e ) 15
Rationale: let the number of who play both be x number of students who play sports 25 - 4 = 21 use venn diagram ( 15 - x ) + x + ( 16 - x ) = 21 which gives x = 10 answer is a 10 play both sport
Answer: a
Python program:
a = 15 + 16 
b = 25 - 4
c = a - b
Problem: what is the difference between 80 % of 170 and 35 % of 300 .
Options: a ) 30 , b ) 29 , c ) 37 , d ) 36 , e ) 31
Rationale: "( 80 / 100 ) * 170 â € “ ( 35 / 100 ) * 300 136 - 105 = 31 answer : e"
Answer: e
Python program:
a = 80 * 170
b = a / 100
c = 35 * 300
d = c / 100
e = b - d
Problem: a car travels first 160 km at 90 km / hr and the next 160 km at 80 km / hr . what is the average speed for the first 320 km of the tour ?
Options: a ) 71.11 , b ) 84.7 , c ) 71.1 , d ) 71.17 , e ) 71.13
Rationale: "car travels first 160 km at 90 km / hr time taken to travel first 160 km = distancespeed = 160 / 90 car travels next 160 km at 80 km / hr time taken to travel next 160 km = distancespeed = 160 / 80 total distance traveled = 160 + 160 = 2 × 160 total time taken = 160 / 90 + 160 / 80 average speed = total distance traveled / total time taken = 320 / ( 160 / 90 + 160 / 80 ) = 84.7 km / hr answer : b"
Answer: b
Python program:
a = 160 / 90
b = 160 / 80
c = a + b 
d = 1 / c
e = 320 * d
Problem: two trains are moving in the same direction at 72 kmph and 36 kmph . the faster train crosses a man in the slower train in 37 seconds . find the length of the faster train ?
Options: a ) 270 , b ) 370 , c ) 266 , d ) 299 , e ) 126
Rationale: "relative speed = ( 72 - 36 ) * 5 / 18 = 2 * 5 = 10 mps . distance covered in 37 sec = 37 * 10 = 370 m . the length of the faster train = 370 m . answer : b"
Answer: b
Python program:
a = 72 - 36
b = a / const_3_6
c = b * 37
Problem: a water tank which could be filled in 5 hours takes one more hour to be filled as a result of a leak in its bottom . if the tank is full calculate the time it will take for the leak empty it ?
Options: a ) 32 hours , b ) 30 hours , c ) 34 hours , d ) 31 hours , e ) 33 hours
Rationale: part filled without leak in 1 hour = 1 / 5 part filled with leak in 1 hour = 1 / 6 work done by leak in 1 hour = 1 / 5 â ˆ ’ 1 / 6 = 30 hours answer : b
Answer: b
Python program:
a = 5 + 1 
b = 1 / a
c = 5 / b
Problem: country x taxes each of its citizens an amount equal to 10 percent of the first $ 40,000 of income , plus 20 percent of all income in excess of $ 40,000 . if a citizen of country x is taxed a total of $ 8,000 , what is her income ?
Options: a ) $ 40,000 , b ) $ 56,000 , c ) $ 60,000 , d ) $ 66,667 , e ) $ 80,000
Rationale: "equation is correct , so math must be a problem . 0.10 * 40,000 + 0.2 * ( x - 40,000 ) = 8,000 - - > 4,000 + 0.2 x - 8,000 = 8,000 - - > 0.2 x = 12,000 - - > x = 60,000 . answer : c ."
Answer: c
Python program:
a = 4 * 10
b = a * 1000
c = 4 * 2
d = c * 1000
e = 10 / 100
f = 4 * 10
g = f * 1000
h = e * g
i = d - h
j = 20 / 100
k = i / j
l = b + k
Problem: two trains of length 100 m and 200 m are 70 m apart . they start moving towards each other on parallel tracks , at speeds 54 kmph and 72 kmph . after how much time will the trains meet ?
Options: a ) 2 sec , b ) 32 / 3 sec , c ) 20 / 7 sec , d ) 32 / 3 sec , e ) 53 / 2 sec
Rationale: "they are moving in opposite directions , relative speed is equal to the sum of their speeds . relative speed = ( 54 + 72 ) * 5 / 18 = 7 * 5 = 35 mps . the time required = d / s = 70 / 35 = 2 sec . answer : a"
Answer: a
Python program:
a = 54 + 72 
b = a * const_0_2778
c = 70 / b
Problem: the area of a rectangular plot is 24 times its breadth . if the difference between the length and the breadth is 10 metres , what is its breadth ?
Options: a ) 14 metres
b ) 5 metres
c ) 7.5 metres
d ) data inadequate
e ) none of these
Rationale: l × b = 24 × b ∴ l = 24 m and l – b = 10 ∴ b = 24 – 10 = 14 m answer a
Answer: a
Python program:
a = 24 - 10
Problem: peter ' s average ( arithmetic mean ) test score on 4 tests is 78 . what must be the student ' s score on a 5 th test for the peter ' s average score on the 5 tests to be 80 ?
Options: a ) 80 , b ) 82 , c ) 84 , d ) 86 , e ) 88
Rationale: e . 88 peter must score at least an 80 for sure . if he scores an 8 , then he will need to score 2 pots for each of the 4 other tests tomake upthe difference . they each were at 78 ( at least the average is , but this is a small point and does n ' t matter to the answer ) . so 4 tests that were each 2 points short of the 80 average that is desired means the next test must be 8 points higher than the desired average , so 80 + 8 = 88 .
Answer: e
Python program:
a = 5 * 80
b = 4 * 78
c = a - b
Problem: a 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 14 sec . what is the length of the platform ?
Options: a ) 287 m , b ) 350 m , c ) 267 m , d ) 535.71 m , e ) 656 m
Rationale: "speed = 300 / 14 = 150 / 7 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 39 = 150 / 7 = > x = 535.71 m . answer : d"
Answer: d
Python program:
a = speed * (
b = a - 39
Problem: a type of extra - large suv averages 12.2 miles per gallon ( mpg ) on the highway , but only 7.6 mpg in the city . what is the maximum distance , in miles , that this suv could be driven on 21 gallons of gasoline ?
Options: a ) 190 , b ) 284.6 , c ) 300 , d ) 256 , e ) 312
Rationale: "so 12.2 * 21 = 256 . . imo option d is correct answer . ."
Answer: d
Python program:
a = 12 * 2
Problem: find the 15 th term of an arithmetic progression whose first term is 2 and the common difference is 3 .
Options: a ) 45 , b ) 38 , c ) 44 , d ) 40 , e ) 46
Rationale: "n th term of a . p = a + ( n - 1 ) * d = 2 + ( 15 - 1 ) * 3 , = 2 + 42 = 44 . answer : c"
Answer: c
Python program:
a = 15 - 1
b = a * 3
c = b + 2
Problem: a fill pipe can fill 1 / 2 of cistern in 15 minutes . in how many minutes , it can fill 1 / 2 of the cistern ?
Options: a ) 1 min , b ) 5 min , c ) 10 min , d ) 15 min , e ) 20 min
Rationale: "required time = 15 * 2 * 1 / 2 = 15 minutes answer is d"
Answer: d
Python program:
a = 15 / 1
Problem: a train passes a platform in 30 seconds . the same train passes a man standing on the platform in 20 seconds . if the speed of the train is 54 km / hr , the length of the platform is
Options: a ) 150 meter , b ) 240 meter , c ) 200 meter , d ) 260 meter , e ) none of these
Rationale: "explanation : speed of the train = 54 km / hr = ( 54 × 10 ) / 30 m / s = 15 m / s length of the train = speed × time taken to cross the man = 15 × 20 = 300 m let the length of the platform = l time taken to cross the platform = ( 300 + l ) / 15 = > ( 300 + l ) / 15 = 30 = > 300 + l = 15 × 30 = 450 = > l = 450 - 300 = 150 meter answer : option a"
Answer: a
Python program:
a = const_0_2778 * 54
b = 30 - 20
c = a * b
Problem: kiran has 85 currency notes in all , some of which were of rs . 100 denomination and the remaining of rs . 50 denomination . the total amount of all these currency notes was rs . 5000 . how much amount did she have in the denomination of rs . 50 ?
Options: a ) 1900 , b ) 3500 , c ) 4000 , d ) 4200 , e ) 4450
Rationale: "let the number of 50 – rupee notes be x . then , the number of 100 - rupee notes = ( 85 – x ) 50 x + 100 ( 85 – x ) = 5000 = x + 2 ( 85 – x ) = 100 = x = 70 so , required amount = rs . ( 50 x 70 ) = rs . 3500 answer : option b"
Answer: b
Python program:
a = 50 * 85
b = 5000 - a
c = b / 50
d = 85 - c
e = d * 50
Problem: a 250 meter long train crosses a platform in 40 seconds while it crosses a signal pole in 20 seconds . what is the length of the platform ?
Options: a ) 500 , b ) 1000 , c ) 350 , d ) 250 , e ) 20
Rationale: "speed = [ 250 / 20 ] m / sec = 25 / 2 m / sec . let the length of the platform be x meters . then , x + 250 / 40 = 25 / 2 2 ( x + 250 ) = 1000 è x = 250 m . answer : d"
Answer: d
Python program:
a = 250 / 20
b = a * 40
c = b - 250
Problem: in a 4 person race , medals are awarded to the fastest 3 runners . the first - place runner receives a gold medal , the second - place runner receives a silver medal , and the third - place runner receives a bronze medal . in the event of a tie , the tied runners receive the same color medal . ( for example , if there is a two - way tie for first - place , the top two runners receive gold medals , the next - fastest runner receives a silver medal , and no bronze medal is awarded ) . assuming that exactly 3 medals are awarded , and that the 3 medal winners stand together with their medals to form a victory circle , how many different victory circles are possible ?
Options: a ) 24 , b ) 52 , c ) 96 , d ) 144 , e ) 648
Rationale: gold can be awarded in 4 ways , then silver can be awarded in 3 ways and bronze in 2 ways . therefore the total number of ways are : 4 * 3 * 2 = 24 ways of awarding the medals and the same number of ways of forming the circle . this is when there is no tie . and if there is tie , for example all three receive the gold or the silver or the bronze , then there are 4 more cases . which implies 24 * 4 = 96 . ans : c
Answer: c
Python program:
a = math.factorial(4)
b = a * 4
Problem: a goods train runs at the speed of 72 kmph and crosses a 350 m long platform in 26 seconds . what is the length of the goods train ?
Options: a ) 230 m , b ) 140 m , c ) 160 m , d ) 170 m , e ) none of these
Rationale: explanation : speed = [ 72 x ( 5 / 18 ) ] m / sec = 20 m / sec . time = 26 sec . let the length of the train be x metres . then , [ ( x + 350 ) / 26 ] = 20 = > x + 350 = 520 = > x = 170 . answer : d
Answer: d
Python program:
a = const_0_2778 * 72
b = 350 / a
c = 26 - b
d = const_0_2778 * 72
e = c * d
Problem: the population of a town increased from 1 , 62,500 to 2 , 62,500 in a decade . the average percent increase of population per year is :
Options: a ) 4.37 % , b ) 5 % , c ) 6.154 % , d ) 8.75 % , e ) none of these
Rationale: "solution increase in 10 year = ( 262500 - 162500 ) = 100000 . increase % = ( 100000 / 162500 x 100 ) % = 61.54 % â ˆ ´ required average = ( 61.54 / 10 ) % = 6.154 % answer c"
Answer: c
Python program:
a = 10 * 1000
b = a * 10
c = b - 1000
d = c - 1000
e = 2 + 3 
f = e * 100
g = d - f
h = 3 + 4 
i = h * 10
j = 2 + 3 
k = i + j 
l = k * 1000
m = g / l
n = m - 1
o = n / 10
p = o * 100
q = p + 4
Problem: find the probability that a number selected from numbers 1 , 2 , 3 , . . . , 45 is a prime number , when each of the given numbers is equally likely to be selected ?
Options: a ) 10 / 45 , b ) 14 / 45 , c ) 8 / 45 , d ) 3 / 45 , e ) 7 / 45
Rationale: "let x be the event of selecting a prime number . x = { 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41,43 } n ( x ) = 14 , n ( s ) = 45 hence , the required probability is 14 / 45 . answer : b"
Answer: b
Python program:
a = 3 * 5
b = a / 45
Problem: on increasing the price of t . v . sets by 80 % , their sale decreases by 20 % . what is the effect on the revenue receipts of the shop ?
Options: a ) 44 , b ) 5 , c ) 56 , d ) 2 , e ) 7
Rationale: "explanation : let the price be = rs . 100 , and number of units sold = 100 then , sale value = rs . ( 100 × 100 ) = rs . 10000 new sale value = rs . ( 180 × 80 ) = rs . 14400 increase % = 4400 / 10000 × 100 = 44 % answer : a"
Answer: a
Python program:
a = 100 + 80 
b = 100 + 80 
c = b * 20
d = c / 100
e = d + 100 
f = a - e
Problem: in a hostel , the number of students decreased by 15 % and the price of food increased by 20 % over the previous year . if each student consumes the same amount of food then by how much should the consumption of food be cut short by every student , so that the total cost of the food remains the same as that of the previous year ?
Options: a ) 19 % , b ) 15 % , c ) 25 % , d ) 40 % , e ) 1.96 %
Rationale: "cost of food ( c ) = food consumed per student ( f ) * number of students ( n ) * price of food ( p ) originally , c = fnp when number of students decrease by 15 % , and the price of food increases by 20 % , c = f ( new ) * ( 0.85 n ) * ( 1.2 p ) = > f ( new ) = f / ( 0.85 * 1.2 ) = > f ( new ) = 0.9804 f therefore the new cost of food must be 98.04 % of the old cost , or the cost of food must decrease by 1.96 % ( option e )"
Answer: e
Python program:
a = 100 * 100
b = 100 - 15
c = 100 + 20 
d = b * c
e = a / d
f = 1 - e
g = f * 100
Problem: a family pays $ 800 per year for an insurance plan that pays 70 percent of the first $ 1,000 in expenses and 100 percent of all medical expenses thereafter . in any given year , the total amount paid by the family will equal the amount paid by the plan when the family ' s medical expenses total .
Options: a ) $ 1,000 , b ) $ 1,200 , c ) $ 1,400 , d ) $ 1,800 , e ) $ 2,200
Rationale: "upfront payment for insurance plan = 800 $ family needs to pay 30 % of first 1000 $ in expense = 300 $ total amount paid by family when medical expenses are equal to or greater than 1000 $ = 800 + 300 = 1100 $ total amount paid by insurance plan for first 1000 $ = 800 $ total amount paid by family will equal amount paid by plan when medical expense = 1400 $ ( since insurance plan will pay 100 % of amount that exceeds 1100 $ ) answer c"
Answer: c
Python program:
a = 1 - 0
Problem: a bag contains 5 red , 6 blue and 4 green balls . if 2 ballsare picked at random , what is the probability that both are red ?
Options: a ) 2 / 15 , b ) 2 / 21 , c ) 5 / 26 , d ) 3 / 29 , e ) 4 / 27
Rationale: p ( both are red ) , = 5 c 215 c 2 = 5 c 215 c 2 = 10 / 105 = 2 / 21 b
Answer: b
Python program:
a = math.comb(5, 2)
b = 5 + 6 
c = b + 4 
d = math.comb(c, 2)
e = a / d
Problem: seed mixture x is 40 percent ryegrass and 60 percent bluegrass by weight ; seed mixture y is 25 percent ryegrass and 75 percent fescue . if a mixture of x and y contains 27 percent ryegrass , what percent of the weight of this mixture is x ?
Options: a ) 10 % , b ) 13.33 % , c ) 40 % , d ) 50 % , e ) 66.66 %
Rationale: "- - - - - - - - - - - - - - - - > ryegrass x - - - - - - - - - - - - - - > 40 % y - - - - - - - - - - - - - - > 25 % m ( mixture ) - - - - > 27 % 0.4 x + ( m - x ) 0.25 = 0.27 m 0.15 x = 0.02 m x = 0.1333 m x = 13.33 % of m b"
Answer: b
Python program:
a = 27 - 25
b = 40 / 100
c = 25 / 100
d = b - c
e = a / d
Problem: a , b , c , d , e , f are the only 6 families in indira nagar . a , b , c , d , e and f has 7 , 8 , 10 , 13 , 6 , and 10 member in their families respectively . if 1 member from all the 6 families left their respective families to accommodate themselves in the hostel of iim lucknow , then the average number of member now in each family of indira nagar is
Options: a ) 8 , b ) 9 , c ) 10 , d ) 13 , e ) 15
Rationale: answer required average = ( ( 7 - 1 ) + ( 8 - 1 ) + ( 10 - 1 ) + ( 13 - 1 ) + ( 6 - 1 ) + ( 10 - 1 ) ) / 6 = ( 7 + 8 + 10 + 13 + 6 + 10 ) / 6 - ( 6 x 1 ) / 6 = 9 - 1 = 8 correct option : a
Answer: a
Python program:
a = 10 - 2
Problem: a rectangular grass field is 75 m * 40 m , it has a path of 2.5 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 2 per sq m ?
Options: a ) s . 1350
b ) s . 1327
c ) s . 1200
d ) s . 1397
e ) s . 1927
Rationale: area = ( l + b + 2 d ) 2 d = ( 75 + 40 + 2.5 * 2 ) 2 * 2.5 = > 600 600 * 2 = rs . 1200 answer : c
Answer: c
Python program:
a = 2 * 5
b = 75 + a 
c = 2 * 5
d = 40 + c 
e = rectangle_area - (
f = e * rectangle_area
Problem: if - 2 x + 3 y = 8 and 4 x - 3 y = 20 , what is the sum of x and y ?
Options: a ) 24 , b ) 28 , c ) 18 , d ) 26 , e ) 32
Rationale: "given - 2 x + 3 y = 8 - - - eq 1 4 x - 3 y = 20 - - eq 2 sum both eqns we get 2 x = 28 = > x = 14 sub 2 x in eq 1 = > - 28 + 3 y = 8 . = > y = 12 now x + y = 12 + 14 = 26 option d is correct answer ."
Answer: d
Python program:
a = 8 + 20 
b = a / 3
c = b * 3
d = 20 + c 
e = d / 2
f = 8 + 20 
g = f / 3
h = e * g