euclaise/mathqa_programs huggingface dataset:
Problem: a man took loan from a bank at the rate of 5 % p . a . s . i . after 13 years he had to pay rs . 1300 interest only for the period . the principal amount borrowed by him was ?
Options: a ) 1750 , b ) 4000 , c ) 3500 , d ) 2000 , e ) 1000
Rationale: "principal = ( 100 * 1300 ) / ( 5 * 13 ) = rs . 2000 answer : d"
Answer: d
Python program:
a = 1300 * 100
b = a / 13
c = b / 5
Problem: in a games hour 4 different types of players came to the ground ? cricket 15 , hokey 12 , football 13 , softball 15 . how many players are present in the ground ?
Options: a ) 70 , b ) 52 , c ) 55 , d ) 49 , e ) 50
Rationale: "total number of players = 15 + 12 + 13 + 15 = 55 answer is c"
Answer: c
Python program:
a = 15 + 12 
b = 13 + 15 
c = a + b
Problem: if 2 / z = 2 / ( z + 1 ) + 2 / ( z + 25 ) which of these integers could be the value of z ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5
Rationale: solving for z algebraically in this problem would not be easy . instead , we can follow the hint in the question ( “ which of these integers … ” ) and test each answer choice : a . 2 / 0 = 2 / 1 + 2 / 25 incorrect ( division by zero ) b . 2 / 1 = 2 / 2 + 2 / 26 incorrect c . 2 / 2 = 2 / 3 + 2 / 27 incorrect d . 2 / 3 = 2 / 4 + 2 / 28 incorrect e . 2 / 4 = 2 / 5 + 2 / 30 correct the correct answer is e , because it contains the only value that makes the equation work . notice how quickly this strategy worked in this case
Answer: e
Python program:
a = 2 + 2 
b = a + 1 
c = 25 / b
Problem: the average student age of a certain class which has 45 students is 14 . if one student aged 15 go to another class and the age of the class teacher is included the average changes to 14.66 . what is the age of class teacher ?
Options: a ) 30 , b ) 35 , c ) 38 , d ) 40 , e ) 45
Rationale: sum of ages of class before replacement = 45 x 14 = 630 sum of ages of class without teacher = 630 - 15 = 615 sum of ages of class after replacement = 45 x 14.66 = 660 age of teacher = 660 - 615 = 45 answer : e
Answer: e
Python program:
a = 45 * 14
b = 45 * 14
c = b - 15
d = a - c
Problem: 41 % of 801 – 150.17 = ? – 57 % of 910
Options: a ) 797 , b ) 697 , c ) 687 , d ) 699 , e ) 799
Rationale: "explanation : 328 – 150 = 178 x – 519 = 178 x = 697 answer : option b"
Answer: b
Python program:
a = 41 * 801
b = a / 150
Problem: the area of a square garden is q square feet and the perimeter is p feet . if q = 2 p + 33 , what is the perimeter of the garden in feet ?
Options: a ) 28 , b ) 32 , c ) 36 , d ) 40 , e ) 44
Rationale: "let x be the length of one side of the square garden . x ^ 2 = 8 x + 33 x ^ 2 - 8 x - 33 = 0 ( x - 11 ) ( x + 3 ) = 0 x = 11 , - 3 p = 4 ( 11 ) = 44 the answer is e ."
Answer: e
Python program:
a = 2 * 33
Problem: the mean of 50 observations was 41 . it was found later that an observation 48 was wrongly taken as 23 . the corrected new mean is
Options: a ) 35.2 , b ) 36.1 , c ) 36.5 , d ) 41.5 , e ) none
Rationale: "sol . therefore correct sum = ( 41 × 50 + 48 – 23 ) = 2075 . therefore correct mean = 2075 / 50 = 41.5 . answer d"
Answer: d
Python program:
a = 41 * 50
b = 50 - 2
c = b - 23
d = a + c 
e = d / 50
Problem: a batsman makes a score of 87 runs in the 17 th inning and thus increases his average by 3 . find his average after 17 th inning ?
Options: a ) 15 , b ) 88 , c ) 44 , d ) 54 , e ) 23
Rationale: "let the average after 7 th inning = x then average after 16 th inning = x - 3 16 ( x - 3 ) + 87 = 17 x x = 87 - 48 = 39 answer = b"
Answer: b
Python program:
a = 17 * 3
b = 87 - a
c = b + 3
Problem: in what time will a train 300 meters long cross an electric pole , if its speed is 90 km / hr
Options: a ) 5 seconds , b ) 12 seconds , c ) 3 seconds , d ) 2.5 seconds , e ) none of these
Rationale: "explanation : first convert speed into m / sec speed = 90 * ( 5 / 18 ) = 25 m / sec time = distance / speed = 300 / 25 = 12 seconds answer : b"
Answer: b
Python program:
a = 90 * const_0_2778
b = 300 / a
Problem: a present value of a machine is $ 1100 . its value depletion rate is 10 % per annum then find the machine value after 2 years ?
Options: a ) $ 900 , b ) $ 891 , c ) $ 915 , d ) $ 715 , e ) $ 795
Rationale: p = $ 1100 r = 10 % t = 2 years machine value after 2 years = p [ ( 1 - r / 100 ) ^ t ] = 1100 * 9 / 10 * 9 / 10 = $ 891 answer is b
Answer: b
Python program:
a = 10 / 100
b = 1 - a
c = b ** 2
d = 1100 * c
Problem: vanessa , mike and sarah have missed a total of 17 days of school this year . vanessa and mike have missed 14 days total , and mike and sarah have missed 12 days total . how many days of school did vanessa miss alone ?
Options: a ) 9 , b ) 4 , c ) 5 , d ) 2 , e ) 3
Rationale: vanessa + mike + sarah = 17 v + m = 14 m + s = 12 < < use this formula & plug into the original formula , to get vanessa ' s total v + ( m + s ) = 17 v + 12 = 17 subtract 12 from both sides v = 5 answer : c
Answer: c
Python program:
a = 17 - 12
Problem: sandy is younger than molly by 16 years . if the ratio of their ages is 7 : 9 , how old is sandy ?
Options: a ) 42 , b ) 49 , c ) 56 , d ) 63 , e ) 70
Rationale: "let sandy ' s age be 7 x and let molly ' s age be 9 x . 9 x - 7 x = 16 x = 8 sandy is 56 years old . the answer is c ."
Answer: c
Python program:
a = 9 - 7
b = 7 / a
c = b * 16
Problem: if both 7 ^ 2 and 3 ^ 3 are factors of the number a * 4 ^ 3 * 6 ^ 2 * 13 ^ 11 , then what is the smallest possible value of a ?
Options: a ) 99 , b ) 147 , c ) 363 , d ) 1200 , e ) 1625
Rationale: "the number a must include at least 3 * 7 ^ 2 = 147 the answer is b ."
Answer: b
Python program:
a = 7 * 2
b = a * 2
c = 7 * 2
d = c * 2
e = b + d 
f = 7 * 2
g = f * 2
h = e + g 
i = h + 2 
j = i + 4 
k = j + 4
Problem: in a village of 2,600 people , 800 people are over 70 years old and 850 people are female . it is known that 40 percent of the females are younger than 70 years old . if no one in the village is 70 years old , what is the probability that a person chosen at random is either a male or younger than 70 years old ?
Options: a ) 221 / 250 , b ) 199 / 250 , c ) 33 / 50 , d ) 8 / 25 , e ) 209 / 260
Rationale: the number of people younger than 70 years old is 2600 - 800 = 1800 the number of females older than 70 years old is 0.6 * 850 = 510 then the number of males older than 70 years old is 800 - 510 = 290 . the number of people who are either male or younger than 70 is 1800 + 290 = 2090 . p ( a person is younger than 70 or male ) = 2090 / 2600 = 209 / 260 the answer is e .
Answer: e
Python program:
a = 5 * 5
b = a / const_0_25
c = const_26 * b
d = 5 * 5
e = d / const_0_25
f = 40 / e
g = 1 - f
h = 850 * g
i = c - h
j = 5 * 5
k = j / const_0_25
l = const_26 * k
m = i / l
Problem: a circle graph shows how the budget of a certain company was spent : 60 percent for salaries , 9 percent for research and development , 5 percent for utilities , 4 percent for equipment , 2 percent for supplies , and the remainder for transportation . if the area of each sector of the graph is proportional to the percent of the budget it represents , how many degrees of the circle are used to represent transportation ?
Options: a ) 18 ° , b ) 36 ° , c ) 54 ° , d ) 72 ° , e ) 90 °
Rationale: "the percent of the budget for transportation is 100 - ( 60 + 9 + 5 + 4 + 2 ) = 20 % 100 % of the circle is 360 degrees . then ( 20 % / 100 % ) * 360 = 72 degrees the answer is d ."
Answer: d
Python program:
a = 60 + 9 
b = a + 5 
c = b + 4 
d = c + 2 
e = 100 - d
f = 360 * e
g = f / 100
Problem: two trains 140 m and 160 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?
Options: a ) 7 , b ) 8.2 , c ) 2 , d ) 10.8 , e ) 11.2
Rationale: "answer : option d relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 140 + 160 = 300 m . required time = 300 * 9 / 250 = 54 / 5 = 10.8 sec"
Answer: d
Python program:
a = 140 + 160 
b = 60 + 40 
c = b * const_0_2778
d = a / c
Problem: working alone , a can complete a certain kind of job in 6 hours . a and d , working together at their respective rates , can complete one of these jobs in 4 hours . in how many hours can d , working alone , complete one of these jobs ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "let total time taken by d to complete the job = d total time taken by a to complete the job = 6 work done by a in an hour 1 / a = 1 / 6 working together a and d can complete the job in 4 hours 1 / a + 1 / d = 1 / 4 = > 1 / d = 1 / 4 - 1 / a = 1 / 4 - 1 / 6 = 1 / 12 = > d = 12 hours answer c"
Answer: c
Python program:
a = 1/(4)
b = 1/(6)
c = a - b
d = 1/(c)
Problem: ashok secured average of 70 marks in 6 subjects . if the average of marks in 5 subjects is 74 , how many marks did he secure in the 6 th subject ?
Options: a ) 50 , b ) 74 , c ) 78 , d ) 80 , e ) none of these
Rationale: "explanation : number of subjects = 6 average of marks in 6 subjects = 70 therefore total marks in 6 subjects = 70 * 6 = 420 now , no . of subjects = 5 total marks in 5 subjects = 74 * 5 = 370 therefore marks in 6 th subject = 420 – 370 = 50 answer a"
Answer: a
Python program:
a = 70 * 6
b = 74 * 5
c = a - b
Problem: population is 23000 . population increases by 10 % every year , then the population after 3 years is ?
Options: a ) 26630 , b ) 26640 , c ) 36623 , d ) 30613 , e ) 26820
Rationale: "population after 1 st year = 23000 * 10 / 100 = 2300 = = = > 23000 + 2000 = 25300 population after 2 nd year = 25300 * 10 / 100 = 2530 = = = > 25300 + 2530 = 27830 population after 3 rd year = 27830 * 10 / 100 = 2783 = = = > 27830 + 2783 = 30613 answer : d"
Answer: d
Python program:
a = 3 * 10
b = a / 100
c = 1 + b 
d = 23000 * c
Problem: a train running at the speed of 72 km / hr crosses a pole in 9 seconds . find the length of the train ?
Options: a ) 150 meter , b ) 299 meter , c ) 666 meter , d ) 155 meter , e ) 180 meter
Rationale: "speed = 72 * ( 5 / 18 ) m / sec = 20 m / sec length of train ( distance ) = speed * time ( 20 ) * 9 = 180 meter answer : e"
Answer: e
Python program:
a = 72 * 1000
b = a / 3600
c = b * 9
Problem: two numbers are in the ratio of 5 : 7 . if 33 is subtracted from each number , they are in the ratio of 1 : 2 . what are the two numbers ?
Options: a ) 45 , 63 , b ) 50 , 70 , c ) 55 , 77 , d ) 60 , 84 , e ) 65 , 91
Rationale: "( 5 x - 33 ) : ( 7 x - 33 ) = 1 y : 2 y 5 x - 33 = y 7 x - 33 = 2 y 231 - 165 = 10 y - 7 y 66 = 3 y y = 22 5 x - 33 = 22 x = 11 the two numbers are 5 x and 7 x which are 55 and 77 . the answer is c ."
Answer: c
Python program:
a = 2 * 4
b = 1 * 33
c = a - b
d = c * 2
e = 7 / 5
f = d * e
g = 2 * 33
h = 1 * 33
i = g - h
j = i * 5
k = f - j
Problem: x and y are positive integers . when x is divided by 12 , the remainder is 5 , and when x is divided by 13 , the remainder is 3 . when y is divided by 14 , the remainder is 5 , and when y is divided by 7 , the remainder is 5 . what is the least possible value of x + y ?
Options: a ) 24 , b ) 12 , c ) 64 , d ) 48 , e ) 25
Rationale: "when x is divided by 12 , the remainder is 5 : so , the possible values of x are : 5 , 17 , 29 , 41 , etc . when x is divided by 13 , the remainder is 3 : so , the possible values of x are : 3 , 16,29 . . . stop . since both lists include 29 , the smallest possible value of x is 29 . when y is divided by 14 , the remainder is 5 : so , the possible values of y are : 5 , 19 , 33,47 etc . when y is divided by 7 , the remainder is 5 : so , the possible values of y are : 5 , 19 . . . stop . since both lists include 19 , the smallest possible value of y is 19 since the smallest possible values of x and y are 29 and 19 respectively , the smallest possible value of x + y is 48 . so , d is the correct answer to the original question ."
Answer: d
Python program:
a = 14 * 2
b = a + 5 
c = 5 + 12 
d = b - c
Problem: a train running at the speed of 180 km / hr crosses a pole in 7 seconds . what is the length of the train ?
Options: a ) 530 , b ) 305 , c ) 503 , d ) 430 , e ) 350
Rationale: "speed = ( 180 * 5 / 18 ) m / sec = ( 50 ) m / sec length of the train = ( speed x time ) = ( 50 * 7 ) m = 350 m . answer : e"
Answer: e
Python program:
a = 180 * 1000
b = a / 3600
c = b * 7
Problem: the length of a rectangular plot is thrice its breadth . if the area of the rectangular plot is 432 sq m , then what is the breadth of the rectangular plot ?
Options: a ) 12 , b ) 17 , c ) 18 , d ) 19 , e ) 14
Rationale: "let the breadth of the plot be b m . length of the plot = 3 b m ( 3 b ) ( b ) = 432 3 b 2 = 432 b 2 = 144 b = 12 m . answer : option a"
Answer: a
Python program:
a = 432 / 3
b = math.sqrt(a)
Problem: one side of a rectangle is 3 cm shorter than the other side . if we increase the length of each side by 1 cm , then the area of the rectangle will increase by 16 cm 2 . find the lengths of all sides .
Options: a ) 10 and 3 , b ) 9 and 6 , c ) 10 and 7 , d ) 3 and 10 , e ) 10 and 10
Rationale: "let x be the length of the longer side x > 3 , then the other side ' s length is x − 3 cm . then the area is s 1 = x ( x - 3 ) cm 2 . after we increase the lengths of the sides they will become ( x + 1 ) and ( x − 3 + 1 ) = ( x − 2 ) cm long . hence the area of the new rectangle will be a 2 = ( x + 1 ) ⋅ ( x − 2 ) cm 2 , which is 16 cm 2 more than the first area . therefore a 1 + 16 = a 2 x ( x − 3 ) + 16 = ( x + 1 ) ( x − 2 ) x 2 − 3 x + 16 = x 2 + x − 2 x − 2 2 x = 18 x = 9 . so , the sides of the rectangle are 9 cm and ( 9 − 3 ) = 6 cm long . so answer is b ."
Answer: b
Python program:
a = 16 / 2
b = a + 1 
c = b - 3
Problem: the difference between simple interest and compound interest on rs . 1200 for one year at 10 % per annum reckoned half - yearly is :
Options: a ) rs . 2.50 , b ) rs . 3 , c ) rs . 3.75 , d ) rs . 4 , e ) rs . 5
Rationale: s . i = ( 1000 * 10 * 4 ) / 100 = rs . 400 c . i = 1200 * 1 + 5 / 100 ) 2 – 1200 = 123 . difference = rs . ( 123 - 120 ) = rs . 3 answer : b
Answer: b
Python program:
a = 10 / 2
b = a / 100
c = b + 1 
d = c ** 2
e = d * 1200
f = e - 1200
g = 1200 * 10
h = g / 100
i = f - h
Problem: a rectangular tank needs to be coated with insulation . the tank has dimensions of 3 feet , 6 feet , and 2 feet . each square foot of insulation costs $ 20 . how much will it cost to cover the surface of the tank with insulation ?
Options: a ) $ 980
b ) $ 1060
c ) $ 1220
d ) $ 1440
e ) $ 1650
Rationale: the total surface area is 2 ( 2 * 3 + 3 * 6 + 2 * 6 ) = 72 square feet the total cost is 72 * $ 20 = $ 1440 the answer is d .
Answer: d
Python program:
a = surface_rectangular_prism * (
Problem: if a trader sold two cars each at rs . 325475 and gains 13 % on the first and loses 13 % on the second , then his profit or loss percent on the whole is ?
Options: a ) 1.69 % , b ) 1.74 % , c ) 1.84 % , d ) 1.47 % , e ) 1.24 %
Rationale: "sp of each car is rs . 325475 , he gains 13 % on first car and losses 13 % on second car . in this case , there will be loss and percentage of loss is given by = [ ( profit % ) ( loss % ) ] / 100 = ( 13 ) ( 13 ) / 100 % = 1.69 % answer : a"
Answer: a
Python program:
a = 13 * 13
b = a / 100
Problem: p , q and r have rs . 5000 among themselves . r has two - thirds of the total amount with p and q . find the amount with r ?
Options: a ) rs . 3000 , b ) rs . 3600 , c ) rs . 2000 , d ) rs . 4000 , e ) none of these
Rationale: "let the amount with r be rs . r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 5000 - r ) = > 3 r = 10000 - 2 r = > 5 r = 10000 = > r = 2000 . answer : c"
Answer: c
Python program:
a = 2 / 3
b = 1 + a 
c = 5000 / b
d = 2 / 3
e = c * d
Problem: a cab driver 5 days income was $ 250 , $ 400 , $ 750 , $ 400 , $ 500 . then his average income is ?
Options: a ) $ 440 , b ) $ 450 , c ) $ 460 , d ) $ 470 , e ) $ 480
Rationale: "avg = sum of observations / number of observations avg income = ( 250 + 400 + 750 + 400 + 500 ) / 5 = 460 answer is c"
Answer: c
Python program:
a = 250 + 400 
b = a + 750 
c = b + 400 
d = c + 500 
e = d / 5
Problem: 1903 x 1903 = ?
Options: a ) a ) 3623216 , b ) b ) 3624216 , c ) c ) 3624316 , d ) d ) 3621409 , e ) e ) 3625216
Rationale: "1903 x 1903 = ( 1903 ) 2 = ( 1900 + 3 ) 2 = ( 1900 ) 2 + ( 3 ) 2 + ( 2 x 1900 x 3 ) = 3610000 + 9 + 11400 . = 3621409 . d )"
Answer: d
Python program:
a = 1903 / 1903
b = a * 100
Problem: a man , a woman and a boy can together complete a piece of work in 3 days . if a man alone can do it in 6 days and a boy alone in 9 days , how long will a woman take to complete the work ?
Options: a ) 12 days , b ) 15 days , c ) 16 days , d ) 24 days , e ) 18 days
Rationale: explanation : ( 1 man + 1 woman + 1 boy ) ’ s 1 day ’ s work = 1 / 3 1 man ’ s 1 day work = 1 / 6 1 boy ’ s 1 day ’ s work = 1 / 9 ( 1 man + 1 boy ) ‘ s 1 day ’ s work = 1 / 6 + 1 / 9 = 5 / 18 therefore , 1 woman ’ s 1 day ’ s work = 1 / 3 – 5 / 18 = 1 / 18 therefore , the woman alone can finish the work in 18 days . answer : option e
Answer: e
Python program:
a = 1/(3)
b = 1/(6)
c = 1/(9)
d = b + c 
e = a - d
f = 1/(e)
Problem: a grocer has a sale of rs . 6435 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6700 ?
Options: a ) s . 4991 , b ) s . 5991 , c ) s . 6001 , d ) s . 6191 , e ) s . 7991
Rationale: "total fr 5 mnths = ( 6435 + 6927 + 6855 + 7230 + 6562 ) = rs 34009 . reqd . sale = rs . [ ( 6700 * 6 ) - 34009 ] = rs . ( 40200 - 34009 ) = rs . 6191 . answer : d"
Answer: d
Python program:
a = 5 + 1 
b = a * 6700
c = 6435 + 6927 
d = c + 6855 
e = d + 7230 
f = e + 6562 
g = b - f
Problem: if p and q are prime numbers , how many divisors does the product p ^ 3 * q ^ 7 have ?
Options: a ) 25 , b ) 30 , c ) 32 , d ) 35 , e ) 40
Rationale: "when a number n = a ^ x * b ^ y , where a and b are prime numbers , and x , y are positive integers , the number of divisors of n = ( x + 1 ) ( y + 1 ) therefore , the answer is c . 4 * 8 = 32"
Answer: c
Python program:
a = 3 + 1 
b = 7 + 1 
c = a * b
Problem: a person spends 40 % of his salary on food , 25 % on house rent , 15 % on entertainment and 15 % on conveyance . if his savings at the end of the month is rs . 1200 , then his salary per month in rupees is :
Options: a ) 4000 , b ) 24000 , c ) 8000 , d ) 10000 , e ) none of these
Rationale: "total expenditure = 40 + 25 + 15 + 15 = 95 % saving = ( 100 - 95 ) = 5 % 5 / 100 × salary = 1200 , salary = 24000 rs . answer : b"
Answer: b
Python program:
a = 1200 * 100
b = a / 15
Problem: a train , 135 meters long travels at a speed of 45 km / hr crosses a bridge in 30 seconds . the length of the bridge is
Options: a ) 270 m , b ) 245 m , c ) 235 m , d ) 220 m , e ) 240 m
Rationale: "explanation : assume the length of the bridge = x meter total distance covered = 135 + x meter total time taken = 30 s speed = total distance covered / total time taken = ( 135 + x ) / 30 m / s = > 45 ã — ( 10 / 36 ) = ( 135 + x ) / 30 = > 45 ã — 10 ã — 30 / 36 = 135 + x = > 45 ã — 10 ã — 10 / 12 = 135 + x = > 15 ã — 10 ã — 10 / 4 = 135 + x = > 15 ã — 25 = 135 + x = 375 = > x = 375 - 135 = 240 answer : option e"
Answer: e
Python program:
a = 45 * const_0_2778
b = a * 30
c = b - 135
Problem: find the ratio between 1 hr 30 minutes and 2 hrs 40 minutes .
Options: a ) 9 : 16 , b ) 5 : 9 , c ) 12 : 17 , d ) 13 : 24 , e ) none of these
Rationale: solution : the ratio = 1 hr 30 min : 2 hr 40 min . 90 min : 160 min = 9 : 16 . answer is a
Answer: a
Python program:
a = 1 * const_60
b = a + 30 
c = 2 * const_60
d = c + 40 
e = b / d
Problem: a batsman makes a score of 87 runs in the 17 th inning and thus increases his averages by 3 . what is his average after 17 th inning ?
Options: a ) 39 , b ) 35 , c ) 42 , d ) 40.5 , e ) 41
Rationale: "explanation : let the average after 17 innings = x total runs scored in 17 innings = 17 x average after 16 innings = ( x - 3 ) total runs scored in 16 innings = 16 ( x - 3 ) total runs scored in 16 innings + 87 = total runs scored in 17 innings = > 16 ( x - 3 ) + 87 = 17 x = > 16 x - 48 + 87 = 17 x = > x = 39 answer : option a"
Answer: a
Python program:
a = 17 * 3
b = 87 - a
c = b + 3
Problem: mrs . evans gave a test to her freshmen economics class , which has 40 students enrolled and 30 of them answered question 1 correctly . if 29 answered question 2 correctly and 10 did not take the test then how many answered both questions correctly ?
Options: a ) 24 , b ) 27 , c ) 29 , d ) 31 , e ) 33
Rationale: "total number of enrolled students = 40 number of students who did not take test = 10 hence , number of students who took test = 40 - 10 = 30 number of students who answered q 2 correctly = 29 , therefore , all students who took test answered q 2 correctly . so , number of students who answered q 1 correctly , also answered q 2 correctly = 29 . number of students who answered both q 1 & q 2 correctly = 29 . answer : c"
Answer: c
Python program:
a = 30 + 29 
b = a + 10 
c = b - 40
Problem: nina has exactly enough money to purchase 5 widgets . if the cost of each widget were reduced by $ 1.25 , then nina would have exactly enough money to purchase 8 widgets . how much money does nina have ?
Options: a ) $ 16.7 , b ) $ 24 , c ) $ 30 , d ) $ 36 , e ) $ 40
Rationale: "a its is . let price = x ( x - 1.25 ) 8 = 5 x x = 10 / 3 hence total money = 5 * 10 / 3 = 16.7"
Answer: a
Python program:
a = 1 * 25
b = 8 - 5
c = a / b
d = c * 5
Problem: if the sales tax reduced from 3 1 / 2 % to 3 1 / 3 % , then what difference does it make to a person who purchases an article with market price of rs . 9000 ?
Options: a ) 11 , b ) 13 , c ) 15 , d ) 18 , e ) 10
Rationale: "required difference = [ 3 ½ % of rs . 9000 ] – [ 3 1 / 3 % of rs . 9000 ] = [ ( 7 / 20 - ( 10 / 3 ) ] % of rs . 9000 = 1 / 6 % of rs . 9000 = rs . [ ( 1 / 6 ) 8 ( 1 / 100 ) * 9000 ] = rs . 15 . answer is c ."
Answer: c
Python program:
a = 1 / 2
b = a + 3 
c = 1 / 3
d = c + 3 
e = b - d
f = e * 9000
g = f / 100
Problem: in a kilometer race , a beats b by 40 meters or 15 seconds . what time does a take to complete the race ?
Options: a ) 277 sec , b ) 285 sec , c ) 267 sec , d ) 167 sec , e ) 276 sec
Rationale: "time taken by b run 1000 meters = ( 1000 * 15 ) / 50 = 300 sec . time taken by a = 300 - 15 = 285 sec . answer : b"
Answer: b
Python program:
a = 1 * 1000
b = 40 / 15
c = a / b
d = c - 15
Problem: a reduction of 40 % in the price of bananas would enable a man to obtain 67 more for rs . 40 , what is reduced price per dozen ?
Options: a ) 1.86 , b ) 2.86 , c ) 4.86 , d ) 3.86 , e ) 5.86
Rationale: "40 * ( 40 / 100 ) = 16 - - - 67 ? - - - 12 = > rs . 2.86 answer : b"
Answer: b
Python program:
a = 40 / 100
b = 40 * a
c = b / 67
d = 12 * c
Problem: a waitress ' s income consists of her salary and tips . during one week , her tips were 7 / 4 of her salary . what fraction of her income for the week came from tips ?
Options: a ) 1 / 9 , b ) 1 / 6 , c ) 2 / 3 , d ) 4 / 9 , e ) 7 / 11
Rationale: "her tips were 7 / 4 of her salary . let ' s say her salary = $ 4 this mean her tips = ( 7 / 4 ) ( $ 4 ) = $ 7 so , her total income = $ 4 + $ 7 = $ 11 what fraction of her income for the week came from tips $ 7 / $ 11 = 7 / 11 = e"
Answer: e
Python program:
a = 7 + 4 
b = 7 / a
Problem: if one cat eats 1.5 rats in 1.5 days , then in howmany days 3 cats will eat 3 rats ? ?
Options: a ) 1 day , b ) 2 days , c ) 3 days , d ) 4 days , e ) 5 days
Rationale: 1 cat - - - - - - 3 / 2 rat - - - - - - - - - 3 / 2 days 1 cat - - - - - - ( 3 / 2 ) * 2 rat - - - - - ( 3 / 2 ) * 2 days ( rat doubled , days doubled ) 1 * 3 cat - - - - - 3 rat - - - - - - - - - - - 3 / 3 = 1 day ( cat * 3 , same rat , days / 3 ) answer : a
Answer: a
Python program:
a = 1 / 5
b = a * 3
c = b / 3
Problem: the distance between two cities a and b is 465 km . a train starts from a at 8 a . m . and travel towards b at 60 km / hr . another train starts from b at 9 a . m and travels towards a at 75 km / hr . at what time do they meet ?
Options: a ) 09 , b ) 07 , c ) 12 , d ) 05 , e ) 03
Rationale: "explanation : suppose they meet x hrs after 8 a . m then , [ distance moved by first in x hrs ] + [ distance moved by second in ( x - 1 ) hrs ] = 465 therefore , 60 x + 75 ( x - 1 ) = 465 = > x = 3 . so , they meet at ( 8 + 4 ) i . e , 12 noon answer : c )"
Answer: c
Python program:
a = 465 + 75 
b = 60 + 75 
c = a / b
d = c + 8