euclaise/mathqa_programs huggingface dataset:
Problem: a company that ships boxes to a total of 13 distribution centers uses color coding to identify each center . if either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors , what is the minimum number of colors needed for the coding ? ( assume that the order of the colors in a pair does not matter )
Options: a ) 6 , b ) 5 , c ) 8 , d ) 9 , e ) 10
Rationale: "back - solving is the best way to solve this problem . you basically need 13 combinations ( including single colors ) if we start from option 1 - > 1 = > 4 c 2 + 4 = 10 ( not enough ) 2 = > 5 c 2 + 5 = 15 ( enough ) since the minimum number is asked . it should be 5 . answer - b"
Answer: b
Python program:
a = 13 / 2
b = a - 1
c = math.factorial(b)
d = math.factorial(3)
e = math.factorial(2)
f = d * e
g = c / f
h = 13 / 2
i = h - 1
j = g - i
Problem: a and b start from house at 10 am . they travel on the mg road at 20 kmph and 40 kmph . there is a junction t on their path . a turns left at t junction at 12 : 00 noon , b reaches t earlier , and turns right . both of them continue to travel till 2 pm . what is the distance between a and b at 2 pm
Options: a ) 160 km , b ) 170 km , c ) 180 km , d ) 190 km , e ) 150 km
Rationale: at 12 a will travel = 20 * 2 = 40 km b will travel this 40 km in 40 / 40 = 1 hr i . e . by 11 am . after t junction for a - distance travelled = 2 * 20 = 40 km for b distance travelled = 40 * 3 = 120 so distance between a & b is = 120 + 40 = 160 km answer : a
Answer: a
Python program:
a = 12 - 10
b = 20 * a
c = 40 * 3
d = b + c
Problem: the circulation for magazine p in 1971 was 4 times the average ( arithmetic mean ) yearly circulation for magazine p for the years 1972 - 1980 . what is the ratio of the circulation in 1971 to the total circulation during 1971 - 1980 for magazine p ?
Options: a ) 4 / 7 , b ) 5 / 7 , c ) 3 / 7 , d ) 2 / 7 , e ) 1 / 7
Rationale: there are 9 years from 1972 - 1980 , inclusive . let ' s say the average circulation every year between 1972 - 1980 inclusive is x . so the total circulation is 9 x from 1972 - 1980 , inclusive . in 1971 , the circulation is 4 x . so total circulation for 1971 - 1980 is 4 x + 9 x = 13 x . ratio of circulation in 1971 to total circulation during 1971 - 1980 is 4 x to 14 x or 4 / 14 = 2 / 7 answer : d
Answer: d
Python program:
a = 1980 - 1972
b = a + 1 
c = b + 4 
d = c + 1 
e = 4 / d
Problem: the regular price per can of a certain brand of soda is $ 0.30 . if the regular price per can is discounted 15 percent when the soda is purchased in 24 - can cases , what is the price of 72 cans of this brand of soda purchased in 24 - can cases ?
Options: a ) $ 16.32 , b ) $ 18.36 , c ) $ 21.60 , d ) $ 24.48 , e ) $ 28.80
Rationale: "the discounted price of one can of soda is ( 0.85 ) ( $ 0.30 ) , or $ 0.255 . therefore , the price of 72 cans of soda at the discounted price would be ( 72 ) ( $ 0.255 ) = 18.36 answer : b ."
Answer: b
Python program:
a = 100 - 15
b = a / 100
c = 0 * 30
d = b * c
Problem: a bag contains 12 red marbles . if someone were to remove 2 marbles from the bag , one at a time , and replace the first marble after it was removed , the probability that neither marble would be red is 9 / 16 . how many marbles are in the bag ?
Options: a ) 48 , b ) 24 , c ) 60 , d ) 72 , e ) 84
Rationale: "ok let me see if i can explain what went on in the previous post lets say i have x marbles in the bag in total - - > out of them 12 are red so the probability of pulling a non - red marble is ( x - 12 ) / x now the marble is placed back in the bag and we have x marbles again , of which again 12 are red . so the probability of pulling a non - red marble out is ( x - 12 ) / x probability theorm states that if the probability of event a occuring is m and the probability of event b occuring is n then the probability of both a and b occuring is m * n so therefore the probability of 2 non - red marbles getting pulled out is [ ( x - 12 ) / x ] * [ ( x - 12 ) / x ] this is given as 9 / 16 - - > ( x - 12 ) ^ 2 = 16 / 25 x ^ 2 a square rooting u have x - 12 / x = 3 / 4 or 4 x - 48 = 3 x or x = 48"
Answer: a
Python program:
a = 9 / 16
b = math.sqrt(a)
c = 1 - b
d = 12 / c
Problem: the average marks of a class of 26 students is 40 and that of another class of 50 students is 60 . find the average marks of all the students ?
Options: a ) 52.2 , b ) 59.5 , c ) 52.8 , d ) 52.5 , e ) 53.1
Rationale: sum of the marks for the class of 26 students = 26 * 40 = 1040 sum of the marks for the class of 50 students = 50 * 60 = 3000 sum of the marks for the class of 76 students = 1040 + 3000 = 4040 average marks of all the students = 4040 / 76 = 53.15 answer : e
Answer: e
Python program:
a = 26 * 40
b = 50 * 60
c = a + b 
d = 26 + 50 
e = c / d
Problem: a train 125 m long passes a man , running at 6 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is ?
Options: a ) 51 , b ) 50 , c ) 88 , d ) 65 , e ) 22
Rationale: "speed of the train relative to man = ( 125 / 10 ) m / sec = ( 25 / 2 ) m / sec . [ ( 25 / 2 ) * ( 18 / 5 ) ] km / hr = 45 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 6 ) km / hr . x - 6 = 45 = = > x = 51 km / hr . answer : a"
Answer: a
Python program:
a = 6 * const_0_2778
b = a * 6
c = 125 - b
d = c / 6
e = d / const_0_2778
Problem: tom and john traveled in the same direction along the equal route at their constant speed rates of 15 km per hour and 10 km per hour , respectively . after 15 minutes tom passed john , tom reaches a certain gas station , how many l minutes it takes john to reach the station ?
Options: a ) 5 min , b ) 6 min , c ) 7 and 1 / 2 min , d ) 8 min , e ) 10 min
Rationale: since the question states “ after 15 minutes ” , we can say tom traveled 15 / 4 km for 15 minutes as he can travel 15 km per hour . hence , using the same logic , we can say john traveled 10 / 4 km as he travels 10 km per hour . so , john has to travel ( 15 / 4 ) - ( 10 / 4 ) km = 5 / 4 km more . since john ’ s speed is 10 km / hour , which means 1 km / 6 minutes . as he has to travel 5 / 4 km more , it is going to take him 6 ( 5 / 4 ) minutes . hence , l 6 ( 5 / 4 ) = 15 / 2 minutes . the correct answer is c .
Answer: c
Python program:
a = 15 - 10
b = 15 / const_60
c = a * b
d = c * const_60
e = d / 10
f = e / 2
g = f - const_0_25
h = g * 10
Problem: pipe a can fill a tank in 8 hours . due to a leak at the bottom , it takes 12 hours for the pipe a to fill the tank . in what time can the leak alone empty the full tank ?
Options: a ) 5 , b ) 24 , c ) 78 , d ) 90 , e ) 54
Rationale: "let the leak can empty the full tank in x hours 1 / 8 - 1 / x = 1 / 12 = > 1 / x = 1 / 8 - 1 / 12 = ( 3 - 2 ) / 24 = 1 / 24 = > x = 24 . answer : b"
Answer: b
Python program:
a = 12 * 8
b = 12 - 8
c = a / b
Problem: three 8 faced dice are thrown together . the probability that all the three show the same number on them is ?
Options: a ) 1 / 38 , b ) 1 / 48 , c ) 1 / 56 , d ) 1 / 64 , e ) 1 / 68
Rationale: "it all 3 numbers have to be same basically we want triplets . 111 , 222 , 333 , 444 , 555 , 666 , 777 and 888 . those are eight in number . further the three dice can fall in 8 * 8 * 8 = 512 ways . hence the probability is 8 / 512 = 1 / 64 answer : d"
Answer: d
Python program:
a = 1 / 8
b = 1 / 8
c = a * b
d = 1 / 8
e = c * d
f = 1 / 8
g = e * f
Problem: an escalator is descending at constant speed . a walks down and takes 50 steps to reach the bottom . b runs down and takes 90 steps in the same time as a takes 10 steps . how many steps are visible when the escalator is not operating ?
Options: a ) 80 , b ) 90 , c ) 100 , d ) 110 , e ) 120
Rationale: lets suppose that a walks down 1 step / min and escalator moves n steps / min it is given that a takes 50 steps to reach the bottom in the same time escalator would have covered 50 n steps so total steps on escalator is 50 + 50 n . again it is given that b takes 90 steps to reach the bottom and time taken by him for this is equal to time taken by a to cover 10 steps i . e 10 minutes . so in this 10 min escalator would have covered 10 n steps . so total steps on escalatro is 90 + 10 n again equating 50 + 50 n = 90 + 10 n we get n = 1 hence total no . of steps on escalator is 100 . answer : c
Answer: c
Python program:
a = 90 - 50
b = 90 - 50
c = a / b
d = 50 * c
e = 50 + d
Problem: how many kg of sugar must be added to 30 kg of 2 % solution of sugar and water to increase it to a 10 % solution ?
Options: a ) 2.6 kg , b ) 4 kg , c ) 3.4 kg , d ) 1.8 kg , e ) none of these
Rationale: explanation : solution : amount of sugar in 30 kg solution = ( 2 / 100 * 30 ) kg = 0.6 kg . let x kg of sugar be added . then , ( 0.6 + x ) / ( 30 + x ) = 10 / 100 60 + 100 x = 300 + 10 x x = 240 / 90 = 8 / 3 = 2.6 answer : a
Answer: a
Python program:
a = 30 * 10
b = 2 / 100
c = b * 30
d = c * 100
e = a - d
f = 30 * 3
g = e / f
Problem: each of the integers from 1 to 18 is written on the a seperate index card and placed in a box . if the cards are drawn from the box at random without replecement , how many cards must be drawn to ensure that the product of all the integers drawn is even
Options: a ) 19 , b ) 12 , c ) 11 , d ) 10 , e ) 3
Rationale: out of the 18 integers : 9 are odd and 9 are even . if we need to make sure that the product of all the integers withdrawn is even then we need to make sure that we have at least one even number . in the worst case : 1 . we will end up picking odd numbers one by one , so we will pick all 9 odd numbers first 2 . 10 th number will be the first even number so we need to withdraw at least 10 numbers to make sure that we get one even number and the product of all the integers picked is even . so , answer will be 10 . ( d )
Answer: d
Python program:
a = 18 / 2
b = a + 1
Problem: suppose f ( x ) is an odd function for which f ( x + 2 ) = f ( x ) for all x , and f ( x ) = x 2 for x 2 ( 0 , 1 ) . compute f ( - 3 / 2 ) + f ( 1 ) .
Options: a ) - 1 , b ) - 1 / 2 , c ) - 1 / 4 , d ) 1 / 4 , e ) 1 / 2
Rationale: because f is periodic , we know that f ( - 3 / 2 ) = f ( 1 / 2 ) = ( 1 / 2 ) 2 = 1 = 4 . because f is odd , we know that f ( 1 ) = - f ( / 1 ) , but because f is periodic , f ( 1 ) = f ( - 1 ) . therefore , f ( 1 ) = 0 and the answer is 1 = 4 . correct answer d
Answer: d
Python program:
a = 2 + 2 
b = 1 / a
Problem: a lent rs . 5000 to b for 2 years and rs . 3000 to c for 4 years on simple interest at the same rate of interest and received rs . 1980 in all from both of them as interest . the rate of interest per annum is ?
Options: a ) 16 % , b ) 12 % , c ) 9 % , d ) 10 % , e ) 45 %
Rationale: "let the rate be r % p . a . then , ( 5000 * r * 2 ) / 100 + ( 3000 * r * 4 ) / 100 = 1980 100 r + 120 r = 1980 r = 9 % answer : c"
Answer: c
Python program:
a = 5000 * 2
b = 3000 * 4
c = a + b 
d = 1980 / c
e = d * 100
Problem: sari and ken climb up a mountain . at night , they camp together . on the day they are supposed to reach the summit , sari wakes up at 06 : 00 and starts climbing at a constant pace . ken starts climbing only at 08 : 00 , when sari is already 600 meters ahead of him . nevertheless , ken climbs at a constant pace of 500 meters per hour , and reaches the summit before sari . if sari is 50 meters behind ken when he reaches the summit , at what time did ken reach the summit ?
Options: a ) 13 : 00 , b ) 11 : 15 , c ) 14 : 00 , d ) 15 : 00 , e ) 15 : 30
Rationale: "both sari and ken climb in the same direction . speed of sari = 600 / 2 = 300 meters / hr ( since she covers 700 meters in 2 hrs ) speed of ken = 500 meters / hr at 8 : 00 , distance between ken and sari is 600 meters . ken needs to cover this and another 50 meters . time he will take = total distance to be covered / relative speed = ( 600 + 50 ) / ( 500 - 300 ) = 3.25 hrs starting from 8 : 00 , in 5 hrs , the time will be 11 : 15 answer ( b )"
Answer: b
Python program:
a = 600 + 50 
b = 600 / 2
c = 500 - b
d = a / c
e = d + 8
Problem: if x > 0 , x / 50 + x / 5 is what percent of x ?
Options: a ) 6 % , b ) 25 % , c ) 37 1 / 2 % , d ) 60 % , e ) 75 %
Rationale: "just plug and chug . since the question asks for percents , pick 100 . ( but any number will do . ) 100 / 50 + 100 / 5 = 2 + 20 = 25 25 is 25 % of 100 = b"
Answer: b
Python program:
a = 1 / 50
b = 1 / 5
c = a + b 
d = c * 100
Problem: in what time will a railway train 60 m long moving at the rate of 72 kmph pass a telegraph post on its way ?
Options: a ) 8 sec , b ) 3 sec , c ) 2 sec , d ) 6 sec , e ) 9 sec
Rationale: "t = 60 / 72 * 18 / 5 = 3 sec answer : b"
Answer: b
Python program:
a = 72 * const_0_2778
b = 60 / a
Problem: a can do a piece of work in 18 days and b alone can do it in 10 days . b works at it for 5 days and then leaves . a alone can finish the remaining work in
Options: a ) 5 days , b ) 6 days , c ) 7.5 days , d ) 8.5 days , e ) 9 days
Rationale: "explanation : b ' s 5 days work = 1 / 10 ∗ 5 = 1 / 2 remaining work = 1 − 1 / 2 = 1 / 2 a can finish work = 18 ∗ 1 / 2 = 9 days option e"
Answer: e
Python program:
a = 1 / 18
b = 1 / 10
c = a + b 
d = 1 / c
Problem: x starts a business with rs . 45000 . y joins in the business after 3 months with rs . 36000 . what will be the ratio in which they should share the profit at the end of the year ?
Options: a ) 20 : 9 , b ) 2 : 1 , c ) 3 : 2 , d ) 2 : 3 , e ) 5 : 3
Rationale: "ratio in which they should share the profit = ratio of the investments multiplied by the time period = 45000 × 12 : 36000 × 9 = 45 × 12 : 36 × 9 = 15 × 12 : 9 × 9 = 20 : 9 answer is a ."
Answer: a
Python program:
a = 45000 * 12
b = 4 + 3 
c = 36000 * b
d = a / c
Problem: a car travels first 160 km at 75 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 ) 71.12 , c ) 71.1 , d ) 71.17 , e ) 77.42
Rationale: car travels first 160 km at 75 km / hr time taken to travel first 160 km = distancespeed = 160 / 75 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 / 75 + 160 / 80 average speed = total distance traveled / total time taken = 320 / ( 160 / 75 + 160 / 80 ) = 77.42 km / hr answer : e
Answer: e
Python program:
a = 160 / 75
b = 160 / 80
c = a + b 
d = 1 / c
e = 320 * d
Problem: if a – 8 = b , then determine the value of | a - b | - | b - a | .
Options: a ) 16 , b ) 0 , c ) 4 , d ) 2 , e ) 1
Rationale: sol . ( b ) | a - b | = | 8 | = 8 = > | b - a | = | - 8 | = 8 = > | a - b | - | b - a | = 8 - 8 = 0 . answer b
Answer: b
Python program:
a = 1 - 1
b = a + 8 
c = 1 - 1
d = c + 8 
e = b - d
f = e + 1
Problem: the difference between compound interest and simple interest on a certain amount of money at 5 % per annum for 2 years is 18 . find the sum :
Options: a ) 4500 , b ) 7500 , c ) 5000 , d ) 7200 , e ) none of these
Rationale: "sol . ( d ) let the sum be 100 . therefore , si = 100 × 5 × 2100 = 10100 × 5 × 2100 = 10 and ci = 100 ( 1 + 5100 ) 2 − 100100 ( 1 + 5100 ) 2 − 100 ∴ = 100 × 21 × 2120 × 20 − 100 = 414 = 100 × 21 × 2120 × 20 − 100 = 414 difference of ci and si = 41 ⁄ 4 - 10 = 1 ⁄ 4 if the difference is 1 ⁄ 4 , the sum = 100 = > if the difference is 18 , the sum = 400 × 18 = 7200 answer d"
Answer: d
Python program:
a = 5 / 100
b = 1 + a 
c = b ** 2
d = 5 / 100
e = 2 * d
f = 1 + e 
g = c - f
h = 18 / g
Problem: a can contains a mixture of liquids a and b is the ratio 7 : 5 . when 9 litres of mixture are drawn off and the can is filled with b , the ratio of a and b becomes 7 : 9 . how many liter w of liquid a was contained by the can initially ?
Options: a ) 10 , b ) 20 , c ) 21 , d ) 25 , e ) 27
Rationale: "as a : b : : 7 : 5 - - - > only option c is a multiple of 7 and hence it is a good place to start . also a : b : : 7 : 5 means that , a = ( 712 ) * total and b = ( 5 / 12 ) * total if a = 21 , b = 15 - - - > remove 9 litres - - - > you remove ( 7 / 12 ) * 9 of a - - - > a remaining = 21 - ( 7 / 12 ) * 9 = 63 / 4 similarly , for b , you remove ( 5 / 12 ) * 9 - - - > b remaining = 15 - ( 5 / 12 ) * 9 = 45 / 4 and then add 9 more litres of b - - - > 9 + 45 / 4 = 81 / 4 thus a / b ( final ratio ) = ( 45 / 4 ) / ( 81 / 4 ) = 7 : 9 , the same as the final ratio mentioned in the question . hence c is the correct answer . a / b = 7 / 9 = ( 7 x - ( 7 / 12 ) * 9 ) / ( 5 x - ( 5 / 12 ) * 9 + 9 ) , where 7 x and 5 x are initial quantities of a and b respectively . thus , 7 / 9 = ( 7 x - ( 7 / 12 ) * 9 ) / ( 5 x - ( 5 / 12 ) * 9 + 9 ) - - - > giving you x = 3 . thus a ( original ) w = 7 * 3 = 21 . c"
Answer: c
Python program:
a = 7 + 9 
b = 7 + 5 
c = 5 / b
d = c * 9
e = 9 - d
f = a * e
g = 9 * 7
h = 7 * 5
i = g - h
j = f / i
k = 7 * j
Problem: a train 360 m long runs with a speed of 45 km / hr . what time will it take to pass a platform of 180 m long ?
Options: a ) 38 sec , b ) 35 sec , c ) 43.2 sec , d ) 40 sec , e ) none of these
Rationale: "speed = 45 km / hr = 45 ã — ( 5 / 18 ) m / s = 150 / 12 = 50 / 4 = 25 / 2 m / s total distance = length of the train + length of the platform = 360 + 180 = 540 meter time taken to cross the platform = 540 / ( 25 / 2 ) = 540 ã — 2 / 25 = 43.2 seconds answer : c"
Answer: c
Python program:
a = 180 / 1000
b = 360 / 1000
c = a + b 
d = c / 45
e = d * 3600
Problem: if the length of the longest chord of a certain circle is 22 , what is the radius of that certain circle ?
Options: a ) 11 , b ) 5 , c ) 10 , d ) 15 , e ) 20
Rationale: "longest chord of a circle is the diameter of the circle diameter = 2 * radius if diameter of the circle is given as 22 = 2 * 11 so radius of the circle = 11 correct answer - a"
Answer: a
Python program:
a = 22 / 2
Problem: company c produces toy trucks at a cost of $ 5.00 each for the first 100 trucks and $ 3.50 for each additional truck . if 500 toy trucks were produced by company c and sold for $ 20.00 each , what was company c ’ s gross profit ?
Options: a ) $ 7,250 , b ) $ 8,500 , c ) $ 8,100 , d ) $ 8,250 , e ) $ 8,600
Rationale: "cost of 500 trucks : ( 100 * 5 ) + ( 400 * 3.5 ) = 500 + 1400 = $ 1900 revenue : 500 * 20 = $ 10000 profit : 10000 - 1900 = $ 8100 option c is correct"
Answer: c
Python program:
a = 500 * 20
b = 5 * 0
c = a - b
d = 500 - 100
e = d * 3
f = c - e
g = f / 1000
h = math.floor(g)
Problem: if y is 70 % greater than x , than x is what % less than y ?
Options: a ) 18.7 , b ) 25.5 , c ) 33.3 , d ) 41.2 , e ) 54.4
Rationale: y = 1.7 x x = y / 1.7 = 10 y / 17 x is 7 / 17 less which is about 41.2 % less than y . the answer is d .
Answer: d
Python program:
a = 70 + 100 
b = 70 / a
c = b * 100
Problem: in a room filled with 7 people , 3 people have exactly 1 sibling in the room and 4 people have exactly 2 siblings in the room . if two individuals are selected from the room at random , what is the probability that those two individuals are not siblings ?
Options: a ) 5 / 21 , b ) 3 / 7 , c ) 4 / 7 , d ) 5 / 7 , e ) 13 / 21
Rationale: there are suppose a b c d e f g members in the room 4 people who have exactly one sibling . . . . a b c d . . . . ( a is bs ∘ sssibl ∈ g ∘ ssand ∘ ssviceversa ) ∘ ss ( c ∘ ssis ∘ ssds ∘ sssibl ∈ g ∘ ssand ∘ ssviceversa ) ∘ ss ( c ∘ ssis ∘ ssdssibl ∈ gandviceversa ) ( cisds sibling and viceversa ) ( c is ds sibling and viceversa ) . . . now remaning efg are 4 people who have exactly 2 siblings . . . . ( e has f and g as his / her sibling and so on . . ) there are now 3 different set of siblings ( a and b ) ( c and d ) ; ( efg ) now first selecting 2 people out of 7 is 7 c 2 = 21 first sibling pair - - - - ( a and b ) - - selecting 2 people - - 2 c 2 = 1 second sibling pair ( c and d ) - - selecting 2 people - - 2 c 2 = 1 third sibling pair ( e f g ) - - selecting 2 out of 4 - - 4 c 2 = 6 total = 1 + 1 + 6 = 8 but , a / c to formula p ( success ) - 1 - p ( fail ) here , p ( failure ) is selecting 2 people who are siblings = 8 / 21 ( 21 is 7 c 2 ) = 1 - 8 / 21 = 13 / 21 ans e
Answer: e
Python program:
a = 3 / 7
b = 7 - 2
c = 7 - 1
d = b / c
e = a * d
f = 3 / 7
g = 7 - 3
h = 7 - 1
i = g / h
j = f * i
k = e + j
Problem: mohit sold an article for $ 27000 . had he offered a discount of 10 % on the selling price , he would have earned a profit of 8 % . what is the cost price of the article ?
Options: a ) 16000 , b ) 22500 , c ) 15000 , d ) 18000 , e ) 17000
Rationale: "let the cp be $ x . had he offered 10 % discount , profit = 8 % profit = 8 / 100 x and hence his sp = x + 8 / 100 x = $ 1.08 x = 27000 - 10 / 100 ( 27000 ) = 27000 - 2700 = $ 22500 = > 1.08 x = 22500 = > x = 22500 b"
Answer: b
Python program:
a = 27000 * 10
b = a / 100
c = 27000 - b
d = 100 + 8 
e = c / d
f = e * 100
Problem: if a farmer wants to plough a farm field on time , he must plough 260 hectares a day . for technical reasons he ploughed only 85 hectares a day , hence he had to plough 2 more days than he planned and he still has 40 hectares left . what is the area of the farm field and how many days the farmer planned to work initially ?
Options: a ) 312 , b ) 490 , c ) 720 , d ) 435 , e ) 679
Rationale: "let x be the number of days in the initial plan . therefore , the whole field is 260 â ‹ … x hectares . the farmer had to work for x + 2 days , and he ploughed 85 ( x + 2 ) hectares , leaving 40 hectares unploughed . then we have the equation : 260 x = 85 ( x + 2 ) + 40 175 x = 210 x = 1.2 so the farmer planned to have the work done in 6 days , and the area of the farm field is 260 ( 1.2 ) = 312 hectares correct answer a"
Answer: a
Python program:
a = 2 * 85
b = 40 + a 
c = 260 - 85
d = b / c
e = d * 260
Problem: on my sister ' s 15 th birthday , she was 159 cm in height , having grown 6 % since the year before . how tall was she the previous year ?
Options: a ) 150 cm , b ) 160 cm , c ) 170 cm , d ) 140 cm , e ) 150 cm
Rationale: explanation : given that height on 15 th birthday = 159 cm and growth = 6 % let the previous year height = x then height on 15 th birthday = x × ( 100 + 6 ) / 100 = x × 106 / 100 ⇒ 159 = x × 106 / 100 ⇒ x = 159 × 100 / 106 = 1.5 × 100 = 150 cm answer : option a
Answer: a
Python program:
a = 6 / 100
b = 1 + a 
c = 159 / b
Problem: jim â € ™ s taxi service charges an initial fee of $ 2.35 at the beginning of a trip and an additional charge of $ 0.35 for each 2 / 5 of a mile traveled . what is the total charge for a trip of 3.6 miles ?
Options: a ) $ 3.15 , b ) $ 4.45 , c ) $ 4.80 , d ) $ 5.50 , e ) $ 5.40
Rationale: "let the fixed charge of jim â € ™ s taxi service = 2.35 $ and charge per 2 / 5 mile ( . 4 mile ) = . 35 $ total charge for a trip of 3.6 miles = 2.35 + ( 3.6 / . 4 ) * . 35 = 2.35 + 9 * . 35 = 5.5 $ answer d"
Answer: d
Python program:
a = 2 / 5
b = 3 / 6
c = b * 0
d = c + 2
Problem: a special municipal payroll tax charges not tax on a payroll less than $ 200,000 and only 0.2 % on a company ’ s payroll above $ 200,000 . if belfried industries paid $ 400 in this special municipal payroll tax , then they must have had a payroll of
Options: a ) $ 180,000 , b ) $ 400,000 , c ) $ 220,000 , d ) $ 402,000 , e ) $ 2 , 200,000
Rationale: "answer : b , ( with different approach ) : the 400 paid is 0.2 % of the additional amount above 200,000 . let it be x now 0.2 % of x = 400 therefore x = 200,000 total = 200,000 + x = 400,000"
Answer: b
Python program:
a = 400 * 100
b = a * 10
Problem: the speed of a boat in still water in 20 km / hr and the rate of current is 3 km / hr . the distance travelled downstream in 24 minutes is :
Options: a ) 9.6 , b ) 10.2 , c ) 9.2 , d ) 10.4 , e ) 9.0
Rationale: "speed downstream = ( 20 + 3 ) = 23 kmph time = 24 minutes = 24 / 60 hour = 2 / 5 hour distance travelled = time × speed = 2 / 5 × 23 = 9.20 km answer is c ."
Answer: c
Python program:
a = 20 + 3 
b = 24 / const_60
c = a * b
Problem: what is the sum of all possible solutions to | x - 3 | ^ 2 + | x - 3 | = 42 ?
Options: a ) 4 , b ) 3 , c ) 5 , d ) 6 , e ) 2
Rationale: "denote | x - 3 | as y : y ^ 2 + y = 42 - - > y = - 7 or y = 6 . discard the first solution since y = | x - 3 | , so it ' s an absolute value and thus can not be negative . y = | x - 3 | = 6 - - > x = 9 or x = - 4 . the sum = 5 . answer : c ."
Answer: c
Python program:
a = 4 + 3 
b = 3 - 4
c = a + b