euclaise/mathqa_programs huggingface dataset:
Problem: the average weight of 8 people increases by 2.5 kg when a new person comes in place of one of them weighing 35 kg . what is the weight of the new person ?
Options: a ) 75 kg , b ) 85 kg , c ) 95 kg , d ) 65 kg , e ) 55 kg
Rationale: "the total weight increase = ( 8 x 2.5 ) kg = 20 kg weight of new person = ( 35 + 20 ) kg = 55 kg the answer is e ."
Answer: e
Python program:
a = 2 * 5
b = a + 35
Problem: from an island , it is possible to reach the mainland by either ferry p or ferry q . ferry p travels for 2 hours at 8 kilometers per hour , while ferry q takes a route that is three times longer . if ferry p is slower than ferry q by 4 kilometers per hour , how many hours longer is the journey of ferry q compared with the journey of ferry p ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: the distance traveled by ferry p is 16 km . then the distance traveled by ferry q is 48 km . ferry q travels at a speed of 12 kph . the time of the journey for ferry q is 48 / 12 = 4 hours , which is 2 hours more than ferry p . the answer is b .
Answer: b
Python program:
a = 8 * 2
b = 3 * a
c = 8 + 4 
d = b / c
e = d - 2
Problem: a car takes 6 hours to cover a distance of 324 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 ) 65 kmph , d ) 36 kmph , e ) none
Rationale: "time = 6 distence = 324 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 324 / 9 = 36 kmph d )"
Answer: d
Python program:
a = 6 * 3
b = a / 2
c = 324 / b
Problem: in a renowned city , the average birth rate is 4 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 ) 86,400 , b ) 172,800 , c ) 468,830 , d ) 338,200 , e ) 259,200
Rationale: "every 2 seconds , 2 persons are added ( 4 - 2 ) . every second 1 person are added . in a day 24 hrs = 24 * 60 minutes = 24 * 60 * 60 = 86400 seconds . 86400 * 1 = 86400 option a"
Answer: a
Python program:
a = 4 - 2
b = a * 3600
c = b * 12
Problem: steve traveled the first 5 hours of his journey at 40 mph and the last 3 hours of his journey at 80 mph . what is his average speed of travel for the entire journey ?
Options: a ) 53.33 mph , b ) 88 mph , c ) 60 mph , d ) 64 mph , e ) 66.67 mph
Rationale: average speed = total distance / total time = ( 40 * 5 + 80 * 3 ) / ( 5 + 3 ) = 440 / 5 = 88 answer : b
Answer: b
Python program:
a = 80 * 3
b = 40 * 5
c = a + b 
d = 3 + 5 
e = c / d
f = 100 / 3
g = f - const_0_33
h = e + g
Problem: if circles x and y have the same area and circle x has a circumference of 20 π , half of the radius of circle y is :
Options: a ) 16 , b ) 5 , c ) 4 , d ) 2 , e ) 1
Rationale: "x b é radius of circle x ý b é radius of circle y given : pi * x ^ 2 = pi * ý ^ 2 also , 2 * pi * x = 20 * pi x = 10 thus ý = 10 y / 2 = 5 ans : b"
Answer: b
Python program:
a = 20 / 2
b = a / 2
Problem: ravi and sunil are partners in a business . ravi invests rs . 20,000 for 8 months and sunil invested rs . 16000 for 10 months then after one year ratio of their profits will be
Options: a ) 1 : 1 , b ) 2 : 3 , c ) 3 : 2 , d ) 3 : 1 , e ) 3 : 4
Rationale: "= ( 15000 * 8 ) : ( 8000 * 10 ) = 160000 : 160000 = 1 : 1 answer : a"
Answer: a
Python program:
a = 4 * 3
b = 10 * 2
c = a * b
d = c * 100
e = d * 8
f = 16000 * 10
g = e / f
Problem: tanks c and b are each in the shape of a right circular cylinder . the interior of tank c has a height of 10 meters and a circumference of 8 meters , and the interior of tank b has a height of 8 meters and a circumference of 10 meters . the capacity of tank c is what percent of the capacity of tank b ?
Options: a ) 75 %
b ) 80 %
c ) 100 %
d ) 120 %
e ) 125 %
Rationale: b . for c , r = 8 / 2 pi . its capacity = ( 4 pi ) ^ 2 * 10 = 160 pi for b , r = 10 / pi . its capacity = ( 5 pi ) ^ 2 * 8 = 200 pi c / b = 160 pi / 200 pi = 0.8
Answer: b
Python program:
a = 8 / 2
b = volume_cylinder / (
c = 10 / 2
d = b * volume_cylinder
Problem: a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 22 , the how old is b ?
Options: a ) 7 , b ) 9 , c ) 8 , d ) 11 , e ) 10
Rationale: "explanation : let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 22 ⇒ 5 x = 20 ⇒ x = 4 . hence , b ' s age = 2 x = 8 years . answer : c"
Answer: c
Python program:
a = 22 - 2
b = a * 2
c = 4 + 1 
d = b / c
Problem: in the fifth grade at parkway elementary school there are 420 students . 312 students are boys and 250 students are playing soccer . 78 % of the students that play soccer are boys . how many girl student are in parkway that is not playing soccer ?
Options: a ) 69 . , b ) 73 . , c ) 53 , d ) 91 , e ) 108
Rationale: "total students = 420 boys = 312 , girls = 108 total playing soccer = 250 78 % of 250 = 195 are boys who play soccer . girls who play soccer = 55 . total girls who do not play soccer = 108 - 55 = 53 . correct option : c"
Answer: c
Python program:
a = 420 - 312
b = 250 * 78
c = b / 100
d = 250 - c
e = a - d
Problem: the price of 3 pants and 6 t - shirts is rs . 1500 . with the same money one can buy 1 pant and 12 t - shirts . if one wants to buy 8 t - shirts , how much shall she have to pay ?
Options: a ) 700 , b ) 300 , c ) 250 , d ) 550 , e ) 800
Rationale: let the price of a pant and a t - shirt be rs . x and rs . y respectively . then , 3 x + 6 y = 1500 . . . . ( i ) and x + 12 y = 1500 . . . . ( ii ) divide equation ( i ) by 3 , we get the below equation . = x + 2 y = 500 . - - - ( iii ) now subtract ( iii ) from ( ii ) x + 12 y = 1500 ( - ) x + 2 y = 500 - - - - - - - - - - - - - - - - 10 y = 1000 - - - - - - - - - - - - - - - - cost of 8 t - shirts = 8 * 100 = 800 answer : e
Answer: e
Python program:
a = 12 - 6
b = 3 - 1
c = a / b
d = c * 3
e = d + 6 
f = 1500 / e
g = f * 8
Problem: rs . 770 were divided among a , b , c in such a way that a had rs . 40 more than b and c had rs 30 more than a . how much was b â € ™ s share ?
Options: a ) rs . 260 , b ) rs . 270 , c ) rs . 280 , d ) rs . 290 , e ) rs . 300
Rationale: let b gets rs x . then we can say a gets rs ( x + 40 ) and c gets rs ( x + 70 ) . x + 40 + x + x + 70 = 770 3 x = 660 x = 220 . b â € ™ s share = rs ( 220 + 70 ) = rs . 290 d
Answer: d
Python program:
a = 40 + 40 
b = a + 30 
c = 770 - b
d = c / 3
e = d + 30 
f = e + 40
Problem: what is the greatest of 3 consecutive integers whose sum is 39 ?
Options: a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: "39 / 3 = 13 the three numbers are 12 , 13 , and 14 . the answer is a ."
Answer: a
Python program:
a = 39 - 3
b = a / 3
c = b + 2
Problem: john and jacob set out together on bicycle traveling at 15 and 9 miles per hour , respectively . after 40 minutes , john stops to fix a flat tire . if it takes john one hour to fix the flat tire and jacob continues to ride during this time , how many hours will it take john to catch up to jacob assuming he resumes his ride at 15 miles per hour ? ( consider john ' s deceleration / acceleration before / after the flat to be negligible )
Options: a ) 3 , b ) 3 1 / 3 , c ) 3 1 / 2 , d ) 4 , e ) 1 1 / 4
Rationale: john ' s speed - 15 miles / hr jacob ' s speed - 9 miles / hr after 40 min ( i . e 2 / 3 hr ) , distance covered by john = 15 x 2 / 3 = 10 miles . jacob continues to ride for a total of 1 hour and 40 min ( until john ' s bike is repaired ) . distance covered in 1 hour 40 min ( i . e 5 / 3 hr ) = 9 x 5 / 3 = 15 miles . now , when john starts riding back , the distance between them is 7.5 miles . jacob and john are moving in the same direction . for john to catch jacob , the effective relative speed will be 15 - 9 = 6 miles / hr . thus , to cover 7.5 miles at 6 miles / hr , john will take 7.5 / 6 = 1.25 hours answer e
Answer: e
Python program:
a = 15 - 9
b = 40 / const_60
c = b * 15
d = 40 / const_60
e = d * 9
f = c - e
g = 9 - f
h = a + g 
i = 40 / const_60
j = i * 15
k = 40 / const_60
l = k * 9
m = j - l
n = h / m
Problem: 23 × 19 × ? ÷ 19 ÷ 17 = 115
Options: a ) 65 , b ) 75 , c ) 85 , d ) 95 , e ) 45
Rationale: "explanation : 23 × 19 × ? ÷ 19 ÷ 17 = 115 = > ( 23 × 19 × ? ) / ( 19 × 17 ) = 115 = > ? = ( 115 × 19 × 17 ) / ( 23 × 19 ) = 85 answer : option c"
Answer: c
Python program:
a = 23 * 19
Problem: a city with a population of 97500 is to be divided into 6 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district . what is the minimum possible population that the least populated district could have ?
Options: a ) 15,000 , b ) 15,500 , c ) 16,000 , d ) 16,500 , e ) 17,000
Rationale: the minimum possible population occurs when all the other districts have a population that is 10 % greater than the least populated district . let p be the population of the least populated district . then 97,500 = p + 5 ( 1.1 ) p 6.5 p = 97,5000 p = 15,000 the answer is a .
Answer: a
Python program:
a = 100 + 10 
b = a / 100
c = 6 - 1
d = b * c
e = d + 1 
f = 97500 / e
g = f / 1000
Problem: pipe a can fill a tank in 10 hr , pipe b in 20 hr and pipe c in 40 hr . if all the pipes are open in how many hours will tank be filled ?
Options: a ) 1 hr , b ) 30 min , c ) 15 min , d ) 17 min , e ) 10 min
Rationale: part filled by ( a + b + c ) in 1 hour = 1 / 10 + 1 / 20 + 1 / 40 = 7 / 40 all the 3 pipes together will fill the tank in 17 min approximately answer is d
Answer: d
Python program:
a = 10 / 10
b = 10 / 20
c = a + b 
d = 10 / 40
e = c + d 
f = e * 10
Problem: a 40 kg metal bar made of alloy of tin and silver lost 4 kg of its weight in the water . 10 kg of tin loses 1.375 kg in the water ; 5 kg of silver loses 0.375 kg . what is the ratio of tin to silver in the bar ?
Options: a ) 1 / 4 , b ) 2 / 5 , c ) 1 / 2 , d ) 3 / 5 , e ) 2 / 3
Rationale: you can simply use this formula to avoid confusion : w 1 / w 2 = ( a 2 - aavg ) / ( avg - a 1 ) here is how you will find the values of a 1 an a 2 . we have an overall loss ( average loss ) . the average loss is 4 kg when 40 kg alloy is immersed . this is a loss of ( 4 / 40 ) * 100 = 10 % . this is aavg the loss of tin is 1.375 kg for every 10 kg . this means it loses ( 1.375 / 10 ) * 100 = 13.75 % of its weight in water . this is a 1 . the loss of silver is . 375 kg for every 5 kg . this means it loses ( . 375 / 5 ) * 100 = 7.5 % of its weight in water . this is a 2 . weight of tin / weight of silver = ( silver ' s loss - avg loss ) / ( avg loss - tin ' s loss ) x / y = ( 7.5 - 10 ) / ( 10 - 13.75 ) = 2 / 3 e
Answer: e
Python program:
a = 0 / 375
b = a * 40
c = 4 - b
d = 1 / 375
e = 0 / 375
f = d - e
g = c / f
h = 0 / 375
i = h * 40
j = 4 - i
k = 1 / 375
l = 0 / 375
m = k - l
n = j / m
o = 40 - n
p = g / o
Problem: in a sports club with 28 members , 17 play badminton and 19 play tennis and 2 do not play either . how many members play both badminton and tennis ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "let x play both badminton and tennis so 17 - x play only badminton and 19 - x play only tennis . 2 play none and there are total 30 students . hence , ( 17 - x ) + ( 19 - x ) + x + 2 = 28 38 - 2 x + x = 28 38 - x = 28 x = 10 so 8 members play both badminton and tennis . d"
Answer: d
Python program:
a = 17 + 19 
b = a + 2 
c = b - 28
Problem: village x has a population of 74000 , which is decreasing at the rate of 1200 per year . village y has a population of 42000 , which is increasing at the rate of 800 per year . in how many years will the population of the two villages be equal ?
Options: a ) 15 , b ) 16 , c ) 11 , d ) 18 , e ) 13
Rationale: "let the population of two villages be equal after p years then , 74000 - 1200 p = 42000 + 800 p 2000 p = 32000 p = 16 answer is b ."
Answer: b
Python program:
a = 74000 - 42000
b = 800 + 1200 
c = a / b
Problem: the radius of a semi circle is 6.5 cm then its perimeter is ?
Options: a ) 32.7 , b ) 32.4 , c ) 33.4 , d ) 32.8 , e ) 32.1
Rationale: "36 / 7 r = 6.5 = 33.4 answer : c"
Answer: c
Python program:
a = circumface / (
b = a + 2
Problem: a number x is 3 times another number y . the percentage that y is less than x is
Options: a ) 12.5 % , b ) 66.6 % , c ) 80 % , d ) 11 % , e ) 1 %
Rationale: "say y = 1 and x = 3 . then y = 1 is less than x = 3 by ( 3 - 1 ) / 3 * 100 = 2 / 3 * 100 = 66.6 % . answer : b ."
Answer: b
Python program:
a = 3 - 1
b = a / 3
c = b * 100
Problem: two trains of length 100 m and 200 m are 100 m apart . they start moving towards each other on parallel tracks , at speeds 54 kmph and 36 kmph . in how much time will the trains cross each other ?
Options: a ) 12 sec , b ) 13 sec , c ) 15 sec , d ) 16 sec , e ) 17 sec
Rationale: "d relative speed = ( 54 + 36 ) * 5 / 18 = 5 * 5 = 25 mps . the time required = d / s = ( 100 + 100 + 200 ) / 25 = 400 / 25 = 16 sec ."
Answer: d
Python program:
a = 54 + 36 
b = a * const_0_2778
c = 100 / b
Problem: if a car had traveled 20 kmh faster than it actually did , the trip would have lasted 30 minutes less . if the car went exactly 60 km , at what speed did it travel ?
Options: a ) 35 kmh , b ) 40 kmh , c ) 50 kmh , d ) 60 kmh , e ) 65 kmh
Rationale: "time = distance / speed difference in time = 1 / 2 hrs 60 / x - 60 / ( x + 20 ) = 1 / 2 substitute the value of x from the options . - - > x = 40 - - > 60 / 40 - 60 / 60 = 3 / 2 - 1 = 1 / 2 answer : b"
Answer: b
Python program:
a = 60 * 20
b = 2 * a
c = b * 4
d = 20 ** 2
e = c + d 
f = math.sqrt(e)
g = f - 20
h = g / 2
Problem: a student has to obtain 33 % of the total marks to pass . he got 59 marks and failed by 40 marks . the maximum marks are ?
Options: a ) 450 , b ) 300 , c ) 500 , d ) 610 , e ) 175
Rationale: "let the maximum marks be x then , 33 % of x = 59 + 40 33 x / 100 = 99 x = 300 answer is b"
Answer: b
Python program:
a = 59 + 40 
b = 33 / 100
c = a / b
Problem: the ratio of the volumes of two cubes is 1728 : 1331 . what is the ratio of their total surface areas ?
Options: a ) 144 : 121 , b ) 141 : 127 , c ) 144 : 191 , d ) 181 : 161 , e ) 81 : 182
Rationale: "explanation : ratio of the sides = ³ √ 1728 : ³ √ 1331 = 12 : 11 ratio of surface areas = 12 ^ 2 : 11 ^ 2 = 144 : 121 answer : option a"
Answer: a
Python program:
a = 1728 / 1331
b = 1 / 3
c = a ** b
Problem: the amount of principal rs . 8000 at compound interest at the ratio of 5 % p . a . for 4 years is
Options: a ) s . 9621 , b ) s . 6921 , c ) s . 9724 , d ) s . 6261 , e ) s . 6361
Rationale: "c . i = p ( 1 + r / 100 ) ^ n = 8000 ( 1 + 5 / 100 ) ^ 4 = rs 9724 answer : c"
Answer: c
Python program:
a = 5 / 100
b = 1 + a 
c = b ** 4
d = 8000 * c
Problem: there are 6 working days in a regular week and for each day , the working hours are 10 . a man earns rs . 2.10 per hour for regular work and rs . 4.20 per hour for overtime . if he earns rs . 525 in 4 weeks , how many hours did he work ?
Options: a ) 225 , b ) 235 , c ) 215 , d ) 255 , e ) 245
Rationale: egular working hours in 4 weeks = ( 4 × 6 × 10 ) = 240 hours amount earned by working in these regular working hours = 240 × 2.10 = rs . 504 additional amount he earned = 525 - 504 = rs . 21 hours he worked overtime = 21 / 4.2 = 210 / 42 = 5 hours total hours he worked = 240 + 5 = 245 hours answer is e .
Answer: e
Python program:
a = 4 * 6
b = a * 10
c = 4 * 6
d = c * 10
e = d * 2
f = 525 - e
g = f / 4
h = b + g
Problem: due to construction , the speed limit along an 7 - mile section of highway is reduced from 55 miles per hour to 35 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "7 / 35 - 7 / 55 = 7 / 5 * ( 11 - 7 ) / 77 = 7 / 5 * 4 / 77 * 60 min = 7 * 12 * 4 / 77 = 336 / 77 ~ 4.3 answer - c"
Answer: c
Python program:
a = 55 + 7 
b = a - 1
c = 7 / 35
d = 7 / 55
e = c - d
f = b * e
g = max(f)
Problem: if the price of gasoline increases by 25 % and a driver intends to spend only 5 % more on gasoline , by how much percent should the driver reduce the quantity of gasoline that he buys ?
Options: a ) 20 % , b ) 16 % , c ) 15 % , d ) 12 % , e ) 10 %
Rationale: "let x be the amount of gasoline the driver buys originally . let y be the new amount of gasoline the driver should buy . let p be the original price per liter . ( 1.25 * p ) y = 1.05 ( p * x ) y = ( 1.05 / 1.25 ) x = 0.84 x which is a reduction of 16 % . the answer is b ."
Answer: b
Python program:
a = 25 + 100 
b = 5 + 100 
c = a - b
d = 25 + 100 
e = c / d
f = e * 100
Problem: the dimensions of a room are 25 feet * 15 feet * 12 feet . what is the cost of white washing the four walls of the room at rs . 9 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each ?
Options: a ) 4000 , b ) 345 , c ) 5673 , d ) 6530 , e ) 8154
Rationale: "area of the four walls = 2 h ( l + b ) since there are doors and windows , area of the walls = 2 * 12 ( 15 + 25 ) - ( 6 * 3 ) - 3 ( 4 * 3 ) = 906 sq . ft . total cost = 906 * 9 = rs . 8154 answer : option e"
Answer: e
Python program:
a = 2 * 12
b = 15 + 25 
c = a * b
d = 6 * 3
e = c - d
f = 4 * 3
g = 3 * f
h = e - g
i = h * 9
Problem: d and e are two points respectively on sides ab and ac of triangle abc such that de is parallel to bc . if the ratio of area of triangle ade to that of the trapezium decb is 25 : 144 and bc = 13 cm , then find the length of de .
Options: a ) 12 , b ) 5 , c ) 14 , d ) 11 , e ) 15
Rationale: "abc and ade are similar triangles . so ( side of abc / side of ade ) ^ 2 = 169 / 25 side of abc / side of ade = 13 / 5 so the length of de = 5 answer - b"
Answer: b
Python program:
a = 144 + 25 
b = 144 / a
c = math.sqrt(b)
d = c * 13
Problem: there are 24 stations between ernakulam and chennai . how many second class tickets have to be printed , so that a passenger can travel from one station to any other station ?
Options: a ) 800 , b ) 820 , c ) 650 , d ) 870 , e ) 900
Rationale: "the total number of stations = 26 from 26 stations we have to choose any two stations and the direction of travel ( ernakulam to chennai is different from chennai to ernakulam ) in 26 p 2 ways . 26 p 2 = 26 * 25 = 650 answer : c"
Answer: c
Python program:
a = 24 + 2 
b = 24 + 2 
c = b - 1
d = a * c
Problem: jaclyn buys $ 50 000 worth of debentures in a company . she earns 9.5 % p . a . simple interest , paid to her quarterly ( that is , every 3 months ) . if the agreed period of the debenture was 18 months : calculate the amount of interest jaclyn will earn for each quarter
Options: a ) 1187.5 , b ) 1234 , c ) 1289 , d ) 1345 , e ) none of these
Rationale: "explanation : i = ( p x r x t ) / 100 answer : a"
Answer: a
Python program:
a = 100 * 100
b = a * 9
c = b / 100
d = c / 4
Problem: x does a work in 30 days . y does the same work in 45 days . in how many days they together will do the same work ?
Options: a ) 18 , b ) 12 , c ) 20 , d ) 30 , e ) 15
Rationale: "x ' s 1 day ' s work = 1 / 30 y ' s 1 day ' s work = 1 / 45 ( x + y ) ' s 1 day ' s work = ( 1 / 30 + 1 / 45 ) = 1 / 18 both together will finish the work in 18 days . correct option is a"
Answer: a
Python program:
a = 1 / 30
b = 1 / 45
c = a + b 
d = 1/(c)
Problem: how many positive integer solutions does the equation 2 x + 3 y = 100 have ?
Options: a ) 50 , b ) 33 , c ) 16 , d ) 35 , e ) 14
Rationale: "formula : ( constant ) / ( lcm of two nos ) = 100 / ( 2 * 3 ) = 15.5 answer : c"
Answer: c
Python program:
a = 3 / 2
Problem: if 3 : 7 : : x : 21 , then find the value of x
Options: a ) 7 , b ) 8 , c ) 11 , d ) 6 , e ) 9
Rationale: explanation : treat 3 : 7 as 3 / 7 and x : 21 as x / 21 , treat : : as = so we get 3 / 7 = x / 21 = > 7 x = 63 = > x = 9 option e
Answer: e
Python program:
a = 7 * 3
b = a + 7 
c = b / 21
Problem: how many pieces of 0.42 meteres can be cut from a rod 36.5 meteres long
Options: a ) 30 , b ) 40 , c ) 86 , d ) 89 , e ) 95
Rationale: "explanation : we need so simple divide 36.5 / 0.42 , = ( 3650 / 42 ) = 86 option c"
Answer: c
Python program:
a = 36 / 5
Problem: if the cost price is 94 % of sp then what is the profit %
Options: a ) 5.07 % , b ) 6 % , c ) 5.7 % , d ) 6.50 % , e ) 6.25 %
Rationale: "sol . sp = rs 100 : then cp = rs 94 : profit = rs 6 . profit = { ( 6 / 94 ) * 100 } % = 6.25 % answer is e ."
Answer: e
Python program:
a = 100 - 94
b = a / 94
c = b * 100
Problem: if a is a positive integer , and if the units digit of a ^ 2 is 1 and the units digit of ( a + 1 ) ^ 2 is 0 , what is the units digit of ( a + 2 ) ^ 2 ?
Options: a ) 1 . , b ) 3 . , c ) 5 . , d ) 7 . , e ) 9 .
Rationale: "if the units digit of a ^ 2 is 1 , then the units digit of a is either 1 or 9 . if the units digit of ( a + 1 ) ^ 2 is 0 , then the units digit of a + 1 is 0 . to satisfy both conditions , the units digit of a must be 9 . then a + 2 has the units digit of 1 , thus the units digit of ( a + 2 ) ^ 2 will be 1 . the answer is a ."
Answer: a
Python program:
a = 1 * 2
b = a + 2 
c = b ** 2
Problem: a full stationary oil tank that is a right circular cylinder has a radius of 100 feet and a height of 25 feet . oil is pumped from the stationary tank to an oil truck that has a tank that is a right circular cylinder until the truck ' s tank is completely filled . if the truck ' s tank has a radius of 5 feet and a height of 10 feet , how far did the oil level drop in the stationary tank ?
Options: a ) 2.5 ft
b ) 1 ft
c ) 0.5 ft
d ) 0.25 ft
e ) 0.025 ft
Rationale: in order to fill up the tank , same volume is shifted from one tank to the other . pi r 1 ^ 2 h 1 = pi r 2 ^ 2 h 2 5 * 5 * 10 = 100 * 100 * h 2 h 2 = . 025 ft e is the answer
Answer: e
Python program:
a = volume_cylinder / (
Problem: a person saved $ 10 in buying an item on sale . if he spent $ 100 for the item , approximately how much percent he saved in the transaction ?
Options: a ) 8 % , b ) 10 % , c ) 2 % , d ) 5 % , e ) 6 %
Rationale: actual price = 100 + 10 = $ 110 saving = 10 / 110 * 100 = 100 / 11 = 10 % approximately answer is b
Answer: b
Python program:
a = 10 + 100 
b = 10 / a
c = b * 100
d = math.floor(c)
e = d + 1
Problem: two family reunions are happening at the same hotel , the oates reunion and the yellow reunion . all 100 guests at the hotel attend at least one of the reunions . if 42 people attend the oates reunion and 65 people attend the yellow reunion , how many people attend both reunions ?
Options: a ) 2 , b ) 7 , c ) 10 , d ) 16 , e ) 22
Rationale: no of people in oates reunion = 42 no of people in yellow reunion = 65 attending both = x all guests attend at least one . therefore , 100 = 42 + 65 - ( both ) both = 7 answer b
Answer: b
Python program:
a = 42 + 65 
b = a - 100
Problem: in a certain animal population , for each of the first 3 months of life , the probability that an animal will die during that month is 1 / 10 . for a group of 200 newborn members of the population , approximately how many would be expected to survive the first 3 months of life ?
Options: a ) 140 , b ) 146 , c ) 152 , d ) 162 , e ) 170
Rationale: "number of newborns that can die in first month = 1 / 10 * 200 = 20 survived = 180 number of newborns that can die in second month = 1 / 10 * 180 = 18 survived = 162 number of newborns that can die in third month = 1 / 10 * 162 = 16 survived = 146 answer : b"
Answer: b
Python program:
a = 1 / 10
b = 1 - a
c = 200 * b
d = 1 / 10
e = 1 - d
f = c * e
g = 1 / 10
h = 1 - g
i = f * h
Problem: two numbers are in the ratio of 5 : 7 . if 7 is subtracted from each number , they are in the ratio of 2 : 3 . what are the two numbers ?
Options: a ) 35 , 49 , b ) 40 , 56 , c ) 45 , 63 , d ) 50 , 70 , e ) 55 , 77
Rationale: "( 5 x - 7 ) : ( 7 x - 7 ) = 2 y : 3 y 5 x - 7 = 2 y 7 x - 7 = 3 y 49 - 35 = 15 y - 14 y 14 = y 5 x - 7 = 28 x = 7 the two numbers are 5 x and 7 x which are 35 and 49 . the answer is a ."
Answer: a
Python program:
a = 3 * 7
b = 2 * 7
c = a - b
d = c * 5
e = 7 / 5
f = d * e
g = 3 * 7
h = 2 * 7
i = g - h
j = i * 5
k = f - j