euclaise/mathqa_programs huggingface dataset:
Problem: pipe p can fill a tank in 8 hours , pipe q in 12 hours and pipe r in 20 hours . if all the pipes are open , in how many hours will the tank be filled ?
Options: a ) 2 hours , b ) 2.4 hours , c ) 3.8 hours , d ) 3.5 hours , e ) 4.5 hours
Rationale: explanation : part filled by ( p + q + r ) in 1 hour = ( 1 / 8 + 1 / 12 + 1 / 20 ) = 31 / 120 all the three pipes together will fill the tank = 120 / 31 = 3.8 hours answer c
Answer: c
Python program:
a = 1 / 20
b = 1 / 8
c = 1 / 12
d = b + c 
e = a + d 
f = 1/(e)
Problem: a worker ' s take - home pay last year was the same each month , and she saved the same fraction of her take - home pay each month . the total amount of money that she had saved at the end of the year was 5 times the amount of that portion of her monthly take - home pay that she did not save . if all the money that she saved last year was from her take - home pay , what fraction of her take - home pay did she save each month ?
Options: a ) 2 / 11 , b ) 3 / 14 , c ) 5 / 17 , d ) 7 / 20 , e ) 11 / 30
Rationale: "let x be the fraction of her take - home pay that the worker saved . let p be the monthly pay . 12 xp = 5 ( 1 - x ) p 12 xp = 5 p - 5 xp 17 xp = 5 p x = 5 / 17 the answer is c ."
Answer: c
Python program:
a = 12 / 5
b = a + 1 
c = 1/(b)
Problem: a trader mixes 80 kg of tea at 15 per kg with 20 kg of tea at cost price of 20 per kg . in order to earn a profit of 35 % , what should be the sale price of the mixed tea ?
Options: a ) 23.75 , b ) 21.6 , c ) 20 , d ) 19.2 , e ) none of these
Rationale: "c . p . of mixture = 80 × 15 + 20 × 20 / 80 + 20 = 16 ∴ s . p . = ( 100 + 35 ) / 100 × 16 = 21.6 answer b"
Answer: b
Python program:
a = 80 * 15
b = 20 * 20
c = a + b 
d = 80 + 20 
e = c / d
f = e * 35
g = f / 100
h = 80 * 15
i = 20 * 20
j = h + i 
k = 80 + 20 
l = j / k
m = g + l
Problem: if the sum of two numbers is 55 and the h . c . f and l . c . m of these numbers are 5 and 120 respectively , then the sum of the reciprocal of the numbers is equal to :
Options: a ) 55 / 601 , b ) 601 / 55 , c ) 11 / 120 , d ) 120 / 11 , e ) 120 / 13
Rationale: "let the numbers be a and b . then , a + b = 55 and ab = 5 * 120 = 600 . required sum = 1 / a + 1 / b = ( a + b ) / ab = 55 / 600 = 11 / 120 . answer : c"
Answer: c
Python program:
a = 5 + 120 
b = 5 * 120
c = a / b
Problem: a person bought 129 glass bowls at a rate of rs . 11 per bowl . he sold 118 of them at rs . 15 and the remaining broke . what is the percentage gain for a ?
Options: a ) 40 , b ) 2900 / 129 , c ) 2430 / 70 , d ) 2791 / 11 , e ) 2719 / 8
Rationale: "cp = 129 * 11 = 1419 and sp = 118 * 15 = 1770 gain % = 100 * ( 1770 - 1419 ) / 1419 = 2900 / 129 answer : b"
Answer: b
Python program:
a = 118 * 15
b = 129 * 11
c = a - b
d = 129 * 11
e = c / d
f = e * 100
Problem: a cube of edge 12 cm is immersed completely in a rectangular vessel containing water . if the dimensions of the base of vessel are 20 cm * 15 cm , find the rise in water level ?
Options: a ) 5.76 cm , b ) 8.25 cm , c ) 11.25 cm , d ) 15.12 cm , e ) 20.62 cm
Rationale: "increase in volume = volume of the cube = 12 * 12 * 12 cm ^ 3 rise in water level = volume / area = 12 * 12 * 12 / 20 * 15 = 5.76 cm answer is a"
Answer: a
Python program:
a = volume_cube / (
Problem: two cars are driving toward each other . the first car is traveling at a speed of 100 km / h , which is 20 % slower than the second car ' s speed . if the distance between the cars is 1125 km , how many hours will it take until the two cars meet ?
Options: a ) 4 , b ) 4.5 , c ) 4.8 , d ) 5 , e ) 5.5
Rationale: "the speed of the first car is 100 km / h . the speed of the second car is 100 / 0.8 = 125 km / h . the two cars complete a total of 225 km each hour . the time it takes the cars to meet is 1125 / 225 = 5 hours . the answer is d ."
Answer: d
Python program:
a = 100 * 4
b = 4 * 100
c = 1 + 4 
d = b / c
e = d * 4
f = a + e 
g = 4 * 100
h = 1 + 4 
i = g / h
j = 100 + i 
k = f / j
Problem: a train 140 m long running at 84 kmph crosses a platform in 16 sec . what is the length of the platform ?
Options: a ) 287 , b ) 298 , c ) 233 , d ) 726 , e ) 267
Rationale: "d = 84 * 5 / 18 = 16 = 373 â € “ 140 = 233 answer : c"
Answer: c
Python program:
a = 84 * const_0_2778
b = 16 * a
c = b - 140
Problem: by travelling at 70 kmph , a person reaches his destination on time . he covered two - third the total distance in one - third of the total time . what speed should he maintain for the remaining distance to reach his destination on time ?
Options: a ) 25 kmph , b ) 20 kmph , c ) 28 kmph , d ) 35 kmph , e ) 32 kmph
Rationale: let the time taken to reach the destination be 3 x hours . total distance = 70 * 3 x = 210 x km he covered 2 / 3 * 210 x = 140 x km in 1 / 3 * 3 x = x hours so , the remaining 70 x km , he has to cover in 2 x hours . required speed = 70 x / 2 x = 35 kmph . answer : d
Answer: d
Python program:
a = 70 * 3
b = 70 * 3
c = b * 2
d = c / 3
e = a - d
f = 3 - 1
g = e / f
Problem: the cost of registration at a professional association meeting was $ 50 per person ; a lunch for registrants only was available for an additional $ 22 per person . if the number of registrants who paid for lunch was 50 more than the number who did not , and if receipts for registration and lunch totaled $ 82,900 , how many people paid just for registration at the meeting ?
Options: a ) 700 , b ) 650 , c ) 1,300 , d ) 1,500 , e ) 1,800
Rationale: "hope this might be useful to you . let the number of people who have opted only to register = x now since the registration cost is 50 $ per person , the total amount sums to = 50 x $ as per the information given in the question , the number of registrants who paid for lunch was 50 more than the number who did not . that means , total number of people who registered and paid for lunch = 50 + x . for the people who registered for lunch the cost is 50 $ ( for the event registration ) + 22 $ ( for lunch ) = 72 $ . total amount in this case sums to = 72 ( 50 + x ) = 3600 + 72 x now , total amount received was 82900 . thus , from the above data , 50 x + 3600 + 72 x = 82900 122 x = 82900 - 3600 122 x = 79300 x = 650 hence the correct ans is b"
Answer: b
Python program:
a = 1 * 1
Problem: the unit digit in the product ( 594 * 897 * 929 * 462 ) is :
Options: a ) 2 , b ) 5 , c ) 6 , d ) 4 , e ) 10
Rationale: "explanation : unit digit in the given product = unit digit in ( 4 * 7 * 9 * 2 ) = 4 answer : d"
Answer: d
Python program:
a = 594 * 897
b = a * 929
c = b * 462
d = 594 * 897
e = d * 929
f = e * 462
g = 4 + 4 
h = f - g
i = c - h
Problem: how many times will the digit 8 be written when listing the integers from 1 to 1000 ?
Options: a ) 164 , b ) 297 , c ) 300 , d ) 345 , e ) 482
Rationale: "many approaches are possible . for example : consider numbers from 0 to 999 written as follows : 1 . 000 2 . 001 3 . 002 4 . 003 . . . . . . . . . 1000 . 999 we have 1000 numbers . we used 3 digits per number , hence used total of 3 * 1000 = 3000 digits . now , why should any digit have preferences over another ? we used each of 10 digits equal # of times , thus we used each digit ( including 8 ) 3000 / 10 = 300 times . answer : c ."
Answer: c
Python program:
a = 1 * 10
b = a * 10
c = b * 3
Problem: a train passes a station platform in 36 sec and a man standing on the platform in 20 sec . if the speed of the train is 63 km / hr . what is the length of the platform ?
Options: a ) 240 , b ) 288 , c ) 277 , d ) 226 , e ) 280
Rationale: "speed = 63 * 5 / 18 = 17.5 m / sec . length of the train = 17.5 * 20 = 350 m . let the length of the platform be x m . then , ( x + 350 ) / 36 = 17.5 = > x = 280 m . answer : e"
Answer: e
Python program:
a = 63 * const_0_2778
b = 20 * a
Problem: machine a and machine b are each used to manufacture 330 sprockets . it takes machine a 10 hours longer to produce 330 sprockets than machine b . machine b produces 10 percent more sprockets per hour than machine a . how many sprockets per hour does machine a produces ?
Options: a ) 5 , b ) 4 , c ) 6 , d ) 8 , e ) 3
Rationale: "machine b : takes x hours to produce 330 sprockets machine a : takes ( x + 10 ) hours to produce 330 sprockets machine b : in 1 hour , b makes 330 / x sprockets machine a : in 1 hour , a makes 330 / ( x + 10 ) sprockets equating : 1.1 ( 330 / ( x + 10 ) ) = 330 / x 484 / ( x + 10 ) = 330 / x 363 x = 330 x + 3300 33 x = 3300 x = 100 a makes 330 / ( 110 ) = 3 sprockets per hour answer : e"
Answer: e
Python program:
a = 10 * 330
b = 100 + 10 
c = b / 100
d = a * c
e = 100 + 10 
f = e / 100
g = 330 * f
h = g - 330
i = d / h
j = 330 / i
Problem: if the ratio of the sum of the first 6 terms of a g . p . to the sum of the first 3 terms of the g . p . is 217 , what is the common ratio of the g . p ?
Options: a ) 3 , b ) 1 / 3 , c ) 2 , d ) 6 , e ) 1 / 6
Rationale: "217 = ( a 1 + a 2 + a 3 + a 4 + a 5 + a 6 ) / ( a 1 + a 2 + a 3 ) factorize the same terms 217 = 1 + ( a 4 + a 5 + a 6 ) / ( a 1 + a 2 + a 3 ) write every term with respect to r a 1 = a 1 a 2 = a 1 * r ^ 1 a 3 = a 1 * r ^ 2 . . . . . . . . . 217 = 1 + ( a 1 ( r ^ 3 + r ^ 4 + r ^ 5 ) ) / ( a 1 ( 1 + r ^ 1 + r ^ 2 ) ) 216 = ( r ^ 3 ( 1 + r ^ 1 + r ^ 2 ) ) / ( ( 1 + r ^ 1 + r ^ 2 ) ) 216 = r ^ 3 r = 6 d"
Answer: d
Python program:
a = 217 - 1
b = 1 / 3
c = a ** b
Problem: on dividing 136 by a number , the quotient is 9 and the remainder is 1 . find the divisor ?
Options: a ) a ) 12 , b ) b ) 15 , c ) c ) 16 , d ) d ) 17 , e ) e ) 18
Rationale: "d = ( d - r ) / q = ( 136 - 1 ) / 9 = 135 / 9 = 15 b )"
Answer: b
Python program:
a = 136 / 9
b = math.floor(a)
Problem: a 72 gallon solution of salt and water is 10 % salt . how many gallons of water must be added to the solution in order to decrease the salt to 8 % of the volume ?
Options: a ) 8 , b ) 12 , c ) 18 , d ) 14 , e ) 16
Rationale: "amount of salt = 7.2 assume x gallons of water are added . 7.2 / 72 + x = 8 / 100 720 = 8 x + 576 8 x = 144 x = 18 correct option : c"
Answer: c
Python program:
a = 10 - 8
b = 72 * a
c = b / 8
Problem: the simple interest on a sum of money will be rs . 600 after 10 years . if the principal is trebled after 5 years what will be the total interest at the end of the tenth year ?
Options: a ) 8981 , b ) 3799 , c ) 1200 , d ) 2693 , e ) 1732
Rationale: "p - - - 10 - - - - 600 p - - - 5 - - - - - 300 3 p - - - 5 - - - - - 900 - - - - - - = > 1200 answer : c"
Answer: c
Python program:
a = 600 / 10
b = a * 5
c = b * 3
d = 600 / 10
e = d * 5
f = c + e
Problem: a rectangular floor that measures 24 meters by 64 meters is to be covered with carpet squares that each measure 8 meters by 8 meters . if the carpet squares cost $ 24 apiece , what is the total cost for the number of carpet squares needed to cover the floor ?
Options: a ) $ 200
b ) $ 576
c ) $ 480
d ) $ 960
e ) $ 1,920
Rationale: the width of the rectangular floor ( 24 m ) is a multiple of one side of the square ( 8 m ) , and the length of the floor ( 64 m ) is also a multiple of the side of the square . so the number of carpets to cover the floor is ( 24 / 8 ) * ( 64 / 8 ) = 24 . the total cost is 24 * 24 = $ 576 . the answer is , therefore , b .
Answer: b
Python program:
a = 24 * 24
Problem: what least number must be subtracted from 427751 so that remaining no . is divisible by 10
Options: a ) 3 , b ) 1 , c ) 6 , d ) 8 , e ) 9
Rationale: "explanation : on dividing 427751 by 10 we get the remainder 1 , so 1 should be subtracted option b"
Answer: b
Python program:
a = 427751 / 10
b = math.floor(a)
c = b * 10
d = 427751 - c
Problem: jim is able to sell a hand - carved statue for $ 660 which was a 20 % profit over his cost . how much did the statue originally cost him ?
Options: a ) $ 496.30 , b ) $ 512.40 , c ) $ 550 , d ) $ 574.90 , e ) $ 588.20
Rationale: "cost price = 660 / 120 * 100 = 550 answer : c"
Answer: c
Python program:
a = 20 / 100
b = a + 1 
c = 660 / b
Problem: the minute hand of a clock overtakes the hour hand at intervals of 65 minutes of correct time . how much does the clock gain or lose in 12 hours ?
Options: a ) 27.273 seconds , b ) 29.273 seconds , c ) 37.273 seconds , d ) 47.273 seconds , e ) 17.273 seconds
Rationale: after 60 minute rotation the minute hand will make an angle of 30 degree with hour hand . after that let the time required to make an overtake is t minute in this time angle covered by minute hand = ( 360 / 60 ) t = 6 t similarly angle covered by hour hand = ( 30 / 60 ) t = t / 2 so for overtake 6 t = 30 + t / 2 or t = 60 / 11 min = 5 min and 5 / 11 min = 5 min and 300 / 11 sec = 5 min and 27.273 sec so clock loses 27.273 seconds answer : a
Answer: a
Python program:
a = 2 * 3
b = a * const_60
c = 2 * 3
d = c * const_60
e = 2 * 3
f = e * const_60
g = 3 * 4
h = f / g
i = d - h
j = i / const_60
k = b / j
l = k - 65
m = l * const_60
Problem: students at a school were on average 180 cm tall . the average female height was 170 cm , and the average male height was 184 cms . what was the ratio f of men to women ?
Options: a ) 5 : 2 , b ) 5 : 1 , c ) 4 : 3 , d ) 4 : 1 , e ) 3 : 1
Rationale: ( a ) f = 184 x 5 + 170 x 2 = 1260 . a
Answer: a
Python program:
a = 180 - 170
b = 184 - 180
c = a / b
Problem: average monthly income of a family of 3 earning members was rs . 735 . one of the earning members died and therefore , the average income came down to rs 650 . the income of the deceased was ?
Options: a ) rs . 692.80 , b ) rs . 905 , c ) rs . 990 , d ) rs . 1385 , e ) none
Rationale: "answer income of the deceased = total income of 4 members - total income of remaining 3 members . = 735 x 3 - 650 x 2 rs . = 905 rs . correct option : b"
Answer: b
Python program:
a = 735 * 3
b = 3 - 1
c = 650 * b
d = a - c
Problem: a started a business with an investment of rs . 70000 and after 6 months b joined him investing rs . 120000 . if the profit at the end of a year is rs . 52000 , then the share of b is ?
Options: a ) 2888 , b ) 24000 , c ) 27777 , d ) 29997 , e ) 27712
Rationale: "ratio of investments of a and b is ( 70000 * 12 ) : ( 120000 * 6 ) = 7 : 6 total profit = rs . 52000 share of b = 6 / 13 ( 52000 ) = rs . 24000 answer : b"
Answer: b
Python program:
a = const_60 * 100
b = 52000 - a
Problem: a tank can supply water to a village for 20 days . if a leak at the bottom of the tank drains out 10 liters per day , the supply lasts for 15 days only . for how many days will the supply last if the leak drains out 20 liters per day ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 14
Rationale: "losing 10 liters per day results in a loss of 150 liters in 15 days . so , those 150 liters were for 5 days , making daily consumption of the village 30 liters per day . thus the capacity of the tank is 30 * 20 = 600 liters . losing 20 liters plus 30 liters gives 50 liters per day . at this rate the supply will last 600 / 50 = 12 days . the answer is d ."
Answer: d
Python program:
a = 10 * 15
b = 20 - 15
c = a / b
d = c * 20
e = 10 * 15
f = 20 - 15
g = e / f
h = 20 + g 
i = d / h
Problem: 31 of the scientists that attended a certain workshop were wolf prize laureates , and 14 of these 31 were also nobel prize laureates . of the scientists that attended that workshop and had not received the wolf prize , the number of scientists that had received the nobel prize was 3 greater than the number of scientists that had not received the nobel prize . if 50 of the scientists attended that workshop , how many of them were nobel prize laureates ?
Options: a ) a ) 11 , b ) b ) 18 , c ) c ) 25 , d ) d ) 29 , e ) d ) 36
Rationale: "lets solve by creating equation . . w = 31 . . total = 50 . . not w = 50 - 31 = 19 . . now let people who were neither be x , so out of 19 who won nobel = x + 3 . . so x + x + 3 = 19 or x = 8 . . so who won nobel but not wolf = x + 3 = 11 . . but people who won both w and n = 13 . . so total who won n = 11 + 14 = 25 . . c"
Answer: c
Python program:
a = 50 - 31
b = a - 3
c = b / 2
d = 3 + c 
e = d + 14
Problem: a committee is reviewing a total of 20 x black - and - white films and 6 y color films for a festival . if the committee selects y / x % of the black - and - white films and all of the color films , what fraction x of the selected films are in color ?
Options: a ) 1 / 130 , b ) 1 / 5 , c ) 3 / 13 , d ) 10 / 13 , e ) 30 / 31
Rationale: "it ' s y / xpercentnot y / x . if x = 20 and y = 10 . then : 20 x = 400 black - and - white films ; 6 y = 60 color films . y / x % = 10 / 20 % = 0.5 % of the black - and - white films , so 2 black - and - white films and all 60 color films , thus total of 62 films were selected . color films thus compose x = 60 / 62 = 30 / 31 of the selected films . answer : e ."
Answer: e
Python program:
a = 20 / 100
b = a + 6 
c = 6 / b
Problem: if the average ( arithmetic mean ) of x + 1 , x + 4 , and x + 7 is 0 , then x =
Options: a ) – 4 , b ) – 3 , c ) – 2 , d ) – 1 , e ) 0
Rationale: "( x + 1 + x + 4 + x + 7 ) / 3 = 0 = > 3 x + 12 = 0 = > x = - 4 answer a"
Answer: a
Python program:
a = 4 * 2
b = 1 * 2
c = a - b
Problem: for how many integers pair ( x , y ) satisfies the result ( 1 / x ) + ( ( 1 / y ) = 1 / 16
Options: a ) a ) 12 , b ) b ) 6 , c ) c ) 10 , d ) d ) 16 , e ) e ) 19
Rationale: it seems that the accepted answer is wrong , according to wolframalpha . the answer should be 31 , which is n ' t even listed as a selectable answer . e
Answer: e
Python program:
a = 16 + 1 
b = a + 1 
c = b + 1
Problem: of the female students at barkely university , 3 / 5 are on the honor roll . of the male students , 2 / 5 are on the honor roll . if 5 / 9 of the students are female , what fraction of all the students are on the honor roll ?
Options: a ) 5 / 9 , b ) 3 / 15 , c ) 23 / 45 , d ) 43 / 60 , e ) 53 / 90
Rationale: "let the total students be 45 given 5 / 9 of the students are females = 25 then males = 4 / 9 = 20 3 / 5 of the females are on honor roll = 15 males on the honor roll = 2 / 5 = 8 total students on honor roll = 15 + 8 = 23 fraction = 23 / 45 c"
Answer: c
Python program:
a = 3 * 2
b = a * 2
c = b + 2 
d = 5 * 3
e = 2 * d
f = c / e
Problem: abcd is a square . e and f are the midpoints of sides cd and bc , respectively . what is the ratio of the shaded region area to the unshaded region ?
Options: a ) 1 : 1
b ) 2 : 1
c ) 3 : 1
d ) 5 : 3
e ) 8 : 3
Rationale: let ' s join the midpoints as shown in the figure then we ' ll get four small squares . . . aodx be 1 and similarly all squares . . and we can split the unit 1 into half and half as per the mid points . . . then shaded will be 1 + 1 / 2 + 1 / 2 + 1 / 2 = 5 / 2 and unshaded is 1 / 2 + 1 / 2 + 1 / 2 = 3 / 2 . . shaded : unshaded is 5 : 3 . . ans option d .
Answer: d
Python program:
a = 1 / 2
b = 1 + a 
c = 1 / 2
d = b + c 
e = 1 / 2
f = d + e 
g = 1 / 2
h = 1 / 2
i = g + h 
j = 1 / 2
k = i + j 
l = f / k
Problem: a certain clock marks every hour by striking a number of times equal to the hour , and the time require for a stroke is exactly equal to the time interval between strokes . at 6 : 00 the time lapse between the beginning of the first stoke and the end of the last stroke is 22 seconds . at 7 : 00 , how many seconds elapse between the beginning of the first stroke and the end of the last stroke ?
Options: a ) 26 , b ) 29 , c ) 19 , d ) 30 , e ) 40
Rationale: "at 6 ' o clock , there would be 6 strikes . first strike , then a short interval , the second strike , then a short interval and so on till the 6 th strike . so there would be in all 5 intervals between 6 strikes . similarly , between 7 strikes , there would be 6 intervals . according to the question , the time spent in the strike and the interval is same . at 6 ' o clock , the 6 strikes and the 5 intervals together take 22 sec so each strike and each interval takes 2 secs . at 7 ' o clock , the 7 strikes and 6 intervals will take 2 * ( 7 + 6 ) = 26 secs a"
Answer: a
Python program:
a = 7 - 1
b = a + 7 
c = 6 - 1
d = c + 6 
e = 22 / d
f = b * e
Problem: a dishonest dealer professes to sell goods at the cost price but uses a weight of 600 grams per kg , what is his percent ?
Options: a ) 28 % , b ) 66.7 % , c ) 55 % , d ) 28 % , e ) 55 %
Rationale: "600 - - - 400 100 - - - ? = > 66.7 % answer : b"
Answer: b
Python program:
a = 100 / 600
b = 3 + 2 
c = b * 2
d = 100 * c
e = a * d
f = e - 100
Problem: 15 men can complete a piece of work in 25 days . in how many days can 20 men complete that piece of work ?
Options: a ) 55 days , b ) 18.75 days , c ) 20 days , d ) 88 days , e ) 44 days
Rationale: "15 * 25 = 20 * x = > x = 18.75 days answer : b"
Answer: b
Python program:
a = 25 * 15
b = a / 20
Problem: if n is a prime number greater than 5 , what is the remainder when n ^ 2 is divided by 23 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5
Rationale: "there are several algebraic ways to solve this question including the one under the spoiler . but the easiest way is as follows : since we can not have two correct answersjust pick a prime greater than 5 , square it and see what would be the remainder upon division of it by 23 . n = 5 - - > n ^ 2 = 49 - - > remainder upon division 49 by 23 is 3 . answer : d ."
Answer: d
Python program:
a = 5 + 2 
b = a ** 2
c = 23 * 4
d = b - c
Problem: the sum of all solutions for x in the equation x ^ 2 – 8 x + 21 = | x – 2 | + 5 is equal to :
Options: a ) – 7 , b ) 7 , c ) 10 , d ) 12 , e ) 18
Rationale: "x ^ 2 - 8 x + 16 = | x - 2 | rhs can be - ve or + ve x ^ 2 - 9 x + 18 = 0 x ^ 2 - 7 x + 14 = 0 x = 7,6 , 3,2 we test all 3 values in original equation , all ok . thus , sum = 7 + 6 + 3 + 2 = 18 ans ( e )"
Answer: e
Python program:
a = 5 * 2
Problem: 80 is what percent of 160 ?
Options: a ) 35 % , b ) 40 % , c ) 45 % , d ) 50 % , e ) 55 %
Rationale: 80 / 160 × 100 = 50 % answer : d
Answer: d
Python program:
a = 80 / 160
b = a * 100
Problem: the price of commodity x increases by 30 cents every year , while the price of commodity y increases by 20 cents every year . if in 2001 , the price of commodity x was $ 4.20 and the price of commodity y was $ 4.40 , in which year will commodity x cost 40 cents more than the commodity y ?
Options: a ) 2007 , b ) 2008 , c ) 2009 , d ) 2010 , e ) 2011
Rationale: "the cost of commodity x increases by 10 cents per year relative to commodity y . the price of x must gain 20 + 40 = 60 cents on commodity y , which will take 6 years . the answer is a ."
Answer: a
Python program:
a = 40 / 100
b = 4 - 40
c = a + b 
d = 30 / 100
e = 4 - 40
f = d - e
g = c / f
h = 2001 + g
Problem: a 300 metre long train crosses a platform in 39 seconds while it crosses a post in 18 seconds . what is the length of the platform ?
Options: a ) 150 m , b ) 350 m , c ) 420 m , d ) 600 m , e ) 700 m
Rationale: explanation : length of the train = distance covered in crossing the post = speed × time = speed × 18 speed of the train = 300 / 18 m / s = 50 / 3 m / s time taken to cross the platform = 39 s ( 300 + x ) / ( 50 / 3 ) = 39 s where x is the length of the platform 300 + x = ( 39 × 50 ) / 3 = 650 meter x = 650 - 300 = 350 meter answer : option b
Answer: b
Python program:
a = 18 / 3
b = 300 / a
c = b * 39
d = 3 * 300
e = c - d
f = e / 3
Problem: 39 persons can repair a road in 24 days , working 5 hours a day . in how many days will 30 persons , working 6 hours a day , complete the work ?
Options: a ) 10 , b ) 13 , c ) 14 , d ) 15 , e ) 26
Rationale: "let the required number of days be x . less persons , more days ( indirect proportion ) more working hours per day , less days ( indirect proportion ) persons 30 : 39 : : 12 : x working hours / day 6 : 5 30 x 6 x x = 39 x 5 x 24 x = ( 39 x 5 x 24 ) / ( 30 x 6 ) x = 26 . answer : e"
Answer: e
Python program:
a = 39 * 24
b = a * 5
c = 30 * 6
d = b / c
Problem: two boats are heading towards each other at constant speeds of 4 miles / hr and 20 miles / hr respectively . they begin at a distance 20 miles from each other . how far are they ( in miles ) one minute before they collide ?
Options: a ) 1 / 12 , b ) 6 / 15 , c ) 1 / 6 , d ) 1 / 3 , e ) 1 / 5
Rationale: "the question asks : how far apart will they be 1 minute = 1 / 60 hours before they collide ? since the combined rate of the boats is 4 + 20 = 25 mph then 1 / 60 hours before they collide they ' ll be rate * time = distance - - > 24 * 1 / 60 = 6 / 15 miles apart . answer : b ."
Answer: b
Python program:
a = 20 + 4 
b = a / const_60
Problem: 1 / 0.04 is equal to
Options: a ) 25.5 , b ) 2.5 , c ) 25 , d ) . 25 , e ) none of these
Rationale: "explanation : 1 / 0.04 = ( 1 * 100 ) / 4 = 100 / 4 = 25 option c"
Answer: c
Python program:
a = 1 / 0