euclaise/mathqa_programs huggingface dataset:
Problem: a shopkeeper sold an article offering a discount of 5 % and earned a profit of 21.6 % . what would have been the percentage of profit earned if no discount was offered ?
Options: a ) 60 % , b ) 28 % , c ) 30 % , d ) 56 % , e ) 73 %
Rationale: "let c . p . be rs . 100 . then , s . p . = rs . 121.60 let marked price be rs . x . then , 95 / 100 x = 121.60 x = 12160 / 95 = rs . 128 now , s . p . = rs . 128 , c . p . = rs . 100 profit % = 28 % . answer : b"
Answer: b
Python program:
a = 100 + 21 
b = a * 100
c = 100 - 5
d = b / c
e = d - 100
Problem: the average salary of all the workers in a workshop is rs . 8000 . the average salary of 10 technicians is rs . 12000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is :
Options: a ) 22 , b ) 21 , c ) 88 , d ) 30 , e ) 29
Rationale: "explanation : lot the total number of workers be v then , 8 ooov = ( 12000 * 10 ) + 6000 ( v - 10 ) < = > 2000 v = 60000 < = > v = 30 answer : d ) 30"
Answer: d
Python program:
a = 12000 - 8000
b = 10 * a
c = 8000 - 6000
d = b / c
e = 10 + d
Problem: in a kilometer race , a beats b by 100 meters or 10 seconds . what time does a take to complete the race ?
Options: a ) 90 sec , b ) 190 sec , c ) 290 sec , d ) 490 sec , e ) 390 sec
Rationale: "time taken by b run 1000 meters = ( 1000 * 10 ) / 100 = 100 sec . time taken by a = 100 - 10 = 90 sec . answer : a"
Answer: a
Python program:
a = 1 * 1000
b = 100 / 10
c = a / b
d = c - 10
Problem: a space shuttle orbits the earth at about 4 kilometers per second . this speed is equal to how many kilometers per hour ?
Options: a ) 480 , b ) 14,400 , c ) 24,200 , d ) 28,800 , e ) 48,000
Rationale: "seconds in 1 hours : 60 s in 1 min 60 min in 1 hr 60 * 60 = 3600 sec in 1 hr 4 * 3600 = 14,400 answer : b"
Answer: b
Python program:
a = 4 * 3600
Problem: a jar contains only red , yellow , and orange marbles . if there are 3 red , 3 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ?
Options: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22
Rationale: "i started by finding the 2 probabilities , without calculation , like this : p ( yyr ) p ( yry ) p ( ryy ) i calculated the first one and ended in 1 / 22 . i looked at the answer choices at this point and saw answer d : 3 / 22 . this helped me realise that for the 3 possible orderings the probabbility is the same . so , it should be ( 1 / 45 ) * ( 2 ) , which indeed is 2 / 45 . c"
Answer: c
Python program:
a = math.comb(3, 2)
b = math.comb(3, 1)
c = a * b
d = 3 + 4 
e = d + 3 
f = math.comb(e, 3)
g = c / f
Problem: there are 2 friends peter and paul . peter age is twice as old as paul when peter was as old as paul is now . sum of the present ages of peter and paul is 35 . what is the present age of peter ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30
Rationale: let pauls age be ' a ' and peters be ' e ' e + a = 35 ( given ) e = 35 - a - - - - - - eq 1 when peter was as old as paul that is when peter ' s age was ' a ' pauls age was a - ( e - a ) = 2 a - e now peters age is e = 2 ( 2 a - e ) e = 4 a - 2 e 3 e = 4 a 3 ( 35 - a ) = 4 a 105 - 3 a = 4 a a = 15 hence e = 20 answer : c
Answer: c
Python program:
a = 4 + 3 
b = 35 / a
c = b * 4
Problem: the area of a parallelogram is 162 sq m and its altitude is twice the corresponding base . then the length of the base is ?
Options: a ) 8 , b ) 9 , c ) 7 , d ) 62 , e ) 2
Rationale: "2 x * x = 162 = > x = 9 answer : b"
Answer: b
Python program:
a = 162 / 2
b = math.sqrt(a)
Problem: 34 . the side surface of a cylinder is rolled with a rectangular plate . if the height of a cylinder tank is 10 feet and the perimeter of the circular base is 4 feet , what is the area of the rectangular plate ?
Options: a ) 24 , b ) 34 , c ) 28 , d ) 40 , e ) 14
Rationale: think of a pringles can . if you took off the bottom and top and cut a slit down the length , it would flatten to a rectangle . the dimensions of the rectangle are the height of the can and the circumference of the circle . since you know both you can multiply them together to find the area , 40 . ( correct answer d )
Answer: d
Python program:
a = 4 ** 2
b = 10 ** 2
c = a - b
d = math.sqrt(c)
Problem: 8 % people of a village in sri lanka died by bombardment , 15 % of the remainder left the village on account of fear . if now the population is reduced to 3553 , how much was it in the beginning ?
Options: a ) 2988 , b ) 4543 , c ) 4400 , d ) 2871 , e ) 881
Rationale: "x * ( 92 / 100 ) * ( 85 / 100 ) = 3553 x = 4543 answer : b"
Answer: b
Python program:
a = 100 - 8
b = a / 100
c = 100 - 15
d = c / 100
e = b * d
f = 3553 / e
g = math.floor(f)
Problem: 57 persons can repair a road in 12 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 ) 19
Rationale: "according to the chain rule , m 1 x t 1 = m 2 x t 2 therefore , 57 x 12 x 5 = 30 x 6 x x x = 19 hence , the number of days = 19 . answer : e"
Answer: e
Python program:
a = 57 * 12
b = a * 5
c = 30 * 6
d = b / c
Problem: how many plants will be there in a circular bed whose outer edge measure 30 cms , allowing 4 cm 2 for each plant ?
Options: a ) 18 , b ) 750 , c ) 24 , d ) 120 , e ) none of these
Rationale: "circumference of circular bed = 30 cm area of circular bed = ( 30 ) 2 ⁄ 4 π space for each plant = 4 cm 2 ∴ required number of plants = ( 30 ) 2 ⁄ 4 π ÷ 4 = 17.89 = 18 ( approx ) answer a"
Answer: a
Python program:
a = 2 * math.pi
b = 30 / a
c = circle_area / (
Problem: the product z of two prime numbers is between 20 and 60 . if one of the prime numbers is greater than 2 but less than 6 and the other is greater than 18 but less than 36 then what is z ?
Options: a ) 21 , b ) 35 , c ) 39 , d ) 51 , e ) 57
Rationale: "the smallest possible product is 57 which is 3 * 19 . all other products are too big . the answer is e ."
Answer: e
Python program:
a = 20 - 4
b = a * 3
Problem: a boat goes 100 km downstream in 10 hours , and 60 m upstream in 15 hours . the speed of the stream is ?
Options: a ) 3 , b ) 22 1 / 4 , c ) 22 1 / 2 , d ) 22 1 / 1 , e ) 22 1 / 3
Rationale: "100 - - - 10 ds = 10 ? - - - - 1 60 - - - - 15 us = 4 ? - - - - - 1 s = ( 10 - 4 ) / 2 = 3 kmp answer : a"
Answer: a
Python program:
a = 100 / 10
b = 60 / 15
c = a - b
d = c / 2
Problem: in how many ways can 16 different gifts be divided among 4 children such that each child receives exactly two gifts ?
Options: a ) 16 ^ 4 , b ) ( 4 ! ) ^ 4 , c ) 16 ! / ( 2 ! ) ^ 4 , d ) 16 ! / 2 ! , e ) 4 ^ 16
Rationale: total 16 different gifts , and 4 children . thus any one child gets 16 c 2 gifts , then the other child gets 14 c 2 gifts ( 16 total - 2 already given ) , then the third one gets 12 c 2 gifts , and the last child gets 10 c 2 gifts . since order in which each child gets the gift is not imp , thus , ans : 16 c 2 * 14 c 2 * 12 c 2 * 10 c 2 = 16 ! / ( 2 ! ) ^ 4 c
Answer: c
Python program:
a = math.factorial(16)
b = 2 ** 4
c = a / b
d = math.factorial(16)
e = 2 ** 4
f = d / e
g = c / f
Problem: how many different values of positive integer x , for which | x + 4 | < x , are there ?
Options: a ) 0 , b ) 2 , c ) 3 , d ) 8 , e ) 16
Rationale: answer d i opted to put the random value option . i used 0 , 4 , - 4 and the the extreme of 60 and - 60 . . i was able to solve it in 1 : 09 d
Answer: d
Python program:
a = 4 + 4
Problem: at a certain resort , each of the 39 food service employees is trained to work in a minimum of 1 restaurant and a maximum of 3 restaurants . the 3 restaurants are the family buffet , the dining room , and the snack bar . exactly 15 employees are trained to work in the family buffet , 18 are trained to work in the dining room , and 12 are trained to work in the snack bar . if 4 employees are trained to work in exactly 2 restaurants , how many employees are trained to work in all 3 restaurants ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 1
Rationale: "39 = 15 + 18 + 12 - 4 - 2 x 2 x = 15 + 18 + 12 - 4 - 39 = 41 - 39 = 2 x = 1 e"
Answer: e
Python program:
a = 15 + 18 
b = a + 12 
c = b - 4
d = c - 39
e = d / 2
Problem: a computer manufacturer produces a certain electronic component at a cost of $ 60 per component . shipping costs for delivering the components are $ 2 per unit . further , the manufacturer has costs of $ 16,500 a month related to the electronic component regardless of how many it produces . if the manufacturer produces and sells 150 components a month , what is the lowest price it can sell them for such that the costs do n ' t exceed the revenues ?
Options: a ) $ 28 , b ) $ 82 , c ) $ 172 , d ) $ 138 , e ) $ 192
Rationale: "this question can be solved easily using a equation model . 150 * p = 16500 ( fixed cost ) + 150 * 60 + 150 * 2 . = 16500 + 9000 + 300 = p = $ 172 . c"
Answer: c
Python program:
a = 4 * 4
b = a * 1000
c = 2 * 100
d = b + c 
e = 60 + 2 
f = e * 150
g = d + f 
h = g / 150
Problem: a beaker contains 180 liters of alcohol . on 1 st day , 60 l of alcohol is taken out and replaced by water . 2 nd day , 60 l of mixture iss taken out and replaced by water and the process continues day after day . what will be the quantity of alcohol in beaker after 3 days
Options: a ) 53.3 , b ) 53.8 , c ) 53.7 , d ) 53.5 , e ) 353.3
Rationale: use the formula , final alcohol = initial alcohol × ( 1 − replacementquantityfinalvolume ) n × ( 1 − replacementquantityfinalvolume ) n final alcohol = 180 ( 1 − 60180 ) 3180 ( 1 − 60180 ) 3 = 180 × ( 23 ) 3 = 53.3 ans : a
Answer: a
Python program:
a = 60 / 180
b = 1 - a
c = b ** 3
d = 180 * c
Problem: how many two - digit whole numbers yield a remainder of 1 when divided by 10 and also yield a remainder of 1 when divided by 6 ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: the possible number n can be written as follow : n = multiple of lcm ( 6,10 ) + 1 st such number n = 30 x + 1 possible values = 1 , 31 , 61 , 91 answer : 3 such 2 digit number . answer : d
Answer: d
Python program:
a = 1 + 1 
b = a + 1
Problem: how long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 150 m in length ?
Options: a ) sec , b ) sec , c ) sec , d ) sec , e ) sec
Rationale: "d = 110 + 150 = 260 m s = 60 * 5 / 18 = 50 / 3 t = 260 * 3 / 50 = 15.6 sec answer : d"
Answer: d
Python program:
a = 110 + 150 
b = 60 * const_0_2778
c = a / b
Problem: a car travels uphill at 30 km / hr and downhill at 70 km / hr . it goes 100 km uphill and 50 km downhill . find the average speed of the car ?
Options: a ) 32 kmph , b ) 33 kmph , c ) 34 kmph , d ) 35 kmph , e ) 37 kmph
Rationale: avg speed = total distance / total time . total distance traveled = 100 + 50 = 150 km ; time taken for uphill journey = 100 / 30 = 10 / 3 ; time taken for down hill journey = 50 / 60 = 5 / 7 ; avg speed = 150 / ( 10 / 3 + 5 / 7 ) = 37 kmph answer : e
Answer: e
Python program:
a = 100 + 50 
b = 100 / 30
c = 50 / 70
d = b + c 
e = a / d
Problem: in the faculty of reverse - engineering , 226 second year students study numeric methods , 423 second year students study automatic control of airborne vehicles and 134 second year students study them both . how many students are there in the faculty if the second year students are approximately 75 % of the total ?
Options: a ) 515 . , b ) 545 . , c ) 618 . , d ) 687 . , e ) 666 .
Rationale: "answer is d : 687 solution : total number of students studying both are 423 + 226 - 134 = 515 ( subtracting the 134 since they were included in the both the other numbers already ) . so 75 % of total is 515 , so 100 % is approx . 687 ."
Answer: d
Python program:
a = 226 + 423
Problem: in a certain boys camp , 20 % of the total boys are from school a and 30 % of those study science . if there are 77 boys in the camp that are from school a but do not study science then what is the total number of boys in the camp ?
Options: a ) 550 , b ) 245 , c ) 150 , d ) 35 , e ) 350
Rationale: "since 30 % of the boys from school a study science , then 70 % of the boys from school a do not study science and since 20 % of the total number of boys are from school a , then 0.2 * 0.7 = 0.14 , or 14 % of the boys in the camp are from school a and do not study science . we are told that this number equals to 77 , so 0.14 * { total } = 77 - - > { total } = 550 . answer : a ."
Answer: a
Python program:
a = 100 - 30
b = a / 100
c = 20 / 100
d = b * c
e = 77 / d
Problem: if x = 1 + √ 2 , then what is the value of x 4 - 4 x 3 + 4 x 2 + 1 ?
Options: a ) - 1 , b ) 0 , c ) 1 , d ) 2 , e ) 3
Rationale: "answer x = 1 + √ 2 ∴ x 4 - 4 x 3 + 4 x 2 + 5 = x 2 ( x 2 - 4 x + 4 ) + 1 = x 2 ( x - 2 ) 2 + 1 = ( 1 + √ 2 ) 2 ( 1 + √ 2 - 2 ) 2 + 1 = ( √ 2 + 1 ) 2 ( √ 2 - 1 ) 2 + 1 = [ ( √ 2 ) 2 - ( 1 ) 2 ] 2 + 1 = ( 2 - 1 ) 2 = 1 + 1 = 2 correct option : d"
Answer: d
Python program:
a = math.sqrt(2)
b = 1 + a 
c = b ** 2
d = math.sqrt(2)
e = 1 + d 
f = e - 2
g = f ** 2
h = c * g
i = h + 4
Problem: vlaudia can choose any two of 4 different candles and any 8 of 9 different flowers for a centerpiece arrangement . given these choices , how many candle + flower groupings can she select ?
Options: a ) 54 , b ) 72 , c ) 96 , d ) 144 , e ) 432
Rationale: vlaudia can choose any two of four different candles and any 8 of 9 different flowers for a centerpiece arrangement . 2 candles from 4 candles : 4 c 2 : 6 8 flowers from 9 flowers : 9 c 8 : 9 so total grouping 9 * 6 = 54 . answer is a .
Answer: a
Python program:
a = math.factorial(9)
b = math.factorial(8)
c = a / b
d = math.factorial(4)
e = 2 * 2
f = d / e
g = c * f
Problem: how many odd integers from 1 to 100 ( both inclusive ) have odd number of factors ?
Options: a ) 13 , b ) 14 , c ) 5 , d ) 6 , e ) 7
Rationale: integers having odd number of factors will be perfect squares . odd numbers will have odd perfect squares . thus , the possible values for the perfect squares are : 1 , 9,25 , 49,81 and the corresponding integers are 1 , 3,5 , 7,9 ( more than 4 ) . thus c is the correct answer .
Answer: c
Python program:
a = 100 / 2
b = a / 2
c = b - 10
d = c - 10
Problem: how many litres of pure acid are there in 10 litres of a 25 % solution
Options: a ) 1.5 , b ) 1.6 , c ) 2.5 , d ) 1.8 , e ) 1.9
Rationale: explanation : question of this type looks a bit typical , but it is too simple , as below . . . it will be 10 * 25 / 100 = 2.5 answer : option c
Answer: c
Python program:
a = 25 / 100
b = a * 10
Problem: there are 15 teams in a soccer league and each team plays each of the other teams once . how many games will be played in total ?
Options: a ) 105 , b ) 110 , c ) 115 , d ) 120 , e ) 125
Rationale: "15 c 2 = 105 the answer is a ."
Answer: a
Python program:
a = math.factorial(15)
b = 15 - 2
c = math.factorial(b)
d = math.factorial(2)
e = c * d
f = a / e
Problem: rahim bought 65 books for rs . 6500 from one shop and 35 books for rs . 2000 from another . what is the average price he paid per book ?
Options: a ) 80 , b ) 138 , c ) 100 , d ) 129 , e ) 85
Rationale: "average price per book = ( 6500 + 2000 ) / ( 65 + 35 ) = 8500 / 100 = rs . 85 answer : e"
Answer: e
Python program:
a = 6500 + 2000 
b = 65 + 35 
c = a / b
Problem: at a certain restaurant , the ratio of the number of cooks to the number of waiters is 3 to 10 . when 12 more waiters are hired , the ratio of the number of cooks to the number of waiters changes to 3 to 13 . how many cooks does the restaurant have ?
Options: a ) 4 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: "originally there were 3 k cooks and 10 k waiters . 13 k = 10 k + 12 k = 4 there are 12 cooks . the answer is d ."
Answer: d
Python program:
a = 12 / 13
b = 12 / 13
c = a * b
Problem: a man engaged a servant on the condition that he would pay him rs . 800 and a uniform after one year service . he served only for 9 months and received uniform and rs . 400 , find the price of the uniform ?
Options: a ) s . 800 , b ) s . 85 , c ) s . 90 , d ) s . 100 , e ) s . 120
Rationale: "9 / 12 = 3 / 4 * 800 = 600 400 - - - - - - - - - - - - - 200 1 / 4 - - - - - - - - 200 1 - - - - - - - - - ? = > rs . 800 answer : a"
Answer: a
Python program:
a = 9 * 800
b = 3 * 4
c = b * 400
d = a - c
e = 3 * 4
f = e * 1
g = d / f
h = g * 4
Problem: a customer purchased a package of ground beef at a cost of $ 1.96 per pound . for the same amount of money , the customer could have purchased a piece of steak that weighed 30 percent less than the package of ground beef . what was the cost per pound of the steak ?
Options: a ) $ 4.65 , b ) $ 4.10 , c ) $ 3.60 , d ) $ 3.20 , e ) $ 2.80
Rationale: "for simplicity , let ' s assume the customer bought 1 pound of ground beef for $ 1.96 . let x be the price per pound for the steak . then 0.7 x = 196 x = 196 / 0.7 = $ 2.80 the answer is e ."
Answer: e
Python program:
a = const_0_25 * 2
b = const_0_33 * 1
c = a + b 
d = 1 / 96
Problem: a computer manufacturer produces a certain electronic component at a cost of $ 80 per component . shipping costs for delivering the components are $ 7 per unit . further , the manufacturer has costs of $ 16,500 a month related to the electronic component regardless of how many it produces . if the manufacturer produces and sells 150 components a month , what is the lowest price it can sell them for such that the costs do n ' t exceed the revenues ?
Options: a ) $ 28 , b ) $ 82 , c ) $ 110 , d ) $ 138 , e ) $ 197
Rationale: "by the question , the equation would be 150 p - 87 * 150 - 16500 = 0 p being the price we want to find and equation resulting zero means revenue and costs are equal so we can get the minimum price of the component . solving the equation , we get p = $ 197 . answer e for me ."
Answer: e
Python program:
a = 4 * 4
b = a * 1000
c = 7 * 100
d = b + c 
e = 80 + 7 
f = e * 150
g = d + f 
h = g / 150
Problem: what is the sum of the greatest common factor and the lowest common multiple of 24 and 36 ?
Options: a ) 92 , b ) 84 , c ) 24 , d ) 60 , e ) 184
Rationale: "prime factorization of 24 = 2 x 2 x 2 x 3 prime factorization of 36 = 2 x 2 x 3 x 3 gcf = 12 lcm = 72 sum = 84 answer b ."
Answer: b
Python program:
a = 24 * 36
b = a / 4
Problem: a car travels at a speed of 65 miles per hour . how far will it travel in 5 hours ?
Options: a ) 125 miles , b ) 225 miles , c ) 325 miles , d ) 425 miles , e ) 525 miles
Rationale: "during each hour , the car travels 65 miles . for 5 hours it will travel 65 + 65 + 65 + 65 + 65 = 5 × 65 = 325 miles correct answer is c ) 325 miles"
Answer: c
Python program:
a = 65 * 5
Problem: in a race where 12 cars are running , the chance that car x will win is 1 / 6 , that y will win is 1 / 10 and that z will win is 1 / 8 . assuming that a dead heat is impossible , find the chance that one of them will win .
Options: a ) 1 / 140 , b ) 1 / 180 , c ) 27 / 410 , d ) 47 / 120 , e ) 57 / 120
Rationale: "required probability = p ( x ) + p ( y ) + p ( z ) ( all the events are mutually exclusive ) . = 1 / 6 + 1 / 10 + 1 / 8 = 47 / 120 answer : d"
Answer: d
Python program:
a = 1 / 6
b = 1 / 10
c = a + b 
d = 1 / 8
e = c + d
Problem: in a box of 12 pens , a total of 3 are defective . if a customer buys 2 pens selected at random from the box , what is the probability that both pen will be defective ?
Options: a ) 1 / 6 , b ) 2 / 9 , c ) 6 / 11 , d ) 9 / 16 , e ) 3 / 4
Rationale: "method - 1 there are 9 fine pieces of pen and 3 defective in a lot of 12 pens i . e . probability of first pen being defective = ( 1 / 3 ) i . e . probability of second pen being defective = ( 1 / 2 ) probability of both pen being defective = ( 1 / 2 ) * ( 1 / 3 ) = 1 / 6 answer : option a"
Answer: a
Python program:
a = 12 - 3
b = a / 12
c = 12 - 3
d = c - 1
e = 12 - 1
f = d / e
g = b * f
Problem: the timing of a college is from 12 p . m to 4.20 p . m . five lectures are held in the given duration and a break of 5 minutes after each lecture is given to the students . find the duration of each lecture .
Options: a ) 52 minutes , b ) 45 minutes , c ) 30 minutes , d ) 48 minutes , e ) 44 minutes
Rationale: explanation : total time a student spends in college = 4 hours 20 minutes = 260 minutes as there are 5 lectures , the number of breaks between lectures is 4 . total time of the break = 20 minutes hence , the duration of each lecture is = ( 260 – 20 ) / 5 = 48 minutes answer d
Answer: d
Python program:
a = 4 * 2
b = a / 5
Problem: after decreasing 50 % in the price of an article costs rs . 1200 . find the actual cost of an article ?
Options: a ) 1200 , b ) 50 , c ) 2400 , d ) 100 , e ) 600
Rationale: "cp * ( 50 / 100 ) = 1200 cp = 24 * 100 = > cp = 2400 answer : c"
Answer: c
Python program:
a = 50 / 100
b = 1 - a
c = 1200 / b
Problem: mary ' s income is 60 % more than tim ' s income and tim ' s income is 30 % less than juan ' s income . what % of juan ' s income is mary ' s income .
Options: a ) 112 % , b ) b . 100 % , c ) 96 % , d ) 80 % , e ) 64 %
Rationale: "even i got 96 % j = 100 t = 100 * 0.7 = 70 m = 70 * 1.6 = 112 if mary ' s income is x percent of j m = j * x / 100 x = m * 100 / j = 112 * 100 / 100 = 112 ans : a"
Answer: a
Python program:
a = 100 - 30
b = 100 - 30
c = 60 / 100
d = b * c
e = a + d
Problem: a telephone company needs to create a set of 3 - digit area codes . the company is entitled to use only digits 2 , 4 and 5 , which can be repeated . if the product of the digits in the area code must be even , how many different codes can be created ?
Options: a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 30
Rationale: we have 3 places ( - - - ) to fill & we can use only digits 2 , 4 , 5 first place can be filled in 3 ways 2 nd place can be filled in 3 ways because we can repeat the digits 3 rd place can be filled in 3 ways because we can repeat the digits total no of codes = 3 x 3 x 3 = 27 but one combination ( 555 ) will not be even so total no of even codes = 27 - 1 = 26 answer d
Answer: d
Python program:
a = 3 ** 3
b = a - 1
Problem: which no . need to add to 859622 to get a number exactly divisible by 456 ?
Options: a ) 345652 , b ) 547678 , c ) 356789 , d ) 778990 , e ) 859622
Rationale: "dividend = quotient * divisor + reminder 859622 / 456 gives quotient = 1885 and reminder = 62 . so , the next number divisible by 456 is 456 places infront of 456 * 1885 which means 456 – 62 = 394 should be added to 859622 . e"
Answer: e
Python program:
a = 859622 - reminder
Problem: a 250 meter long train crosses a man standing on the platform in 12 sec . what is the speed of the train ?
Options: a ) 228 , b ) 108 , c ) 1266 , d ) 75 , e ) 211
Rationale: "s = 250 / 12 * 18 / 5 = 75 kmph answer : d"
Answer: d
Python program:
a = 250 / 12
b = a * const_3_6
Problem: in what time will a train 120 m long cross an electric pole , it its speed be 185 km / hr ?
Options: a ) 2.3 sec , b ) 2.9 sec , c ) 2.7 sec , d ) 8.7 sec , e ) 8.5 sec
Rationale: "speed = 185 * 5 / 18 = 51 m / sec time taken = 120 / 51 = 2.3 sec . answer : a"
Answer: a
Python program:
a = 185 * const_0_2778
b = 120 / a
Problem: a dishonest dealer professes to sell goods at the cost price but uses a weight of 750 grams per kg , what is his percent ?
Options: a ) 25 % , b ) 33 % , c ) 29 % , d ) 55 % , e ) 45 %
Rationale: "750 - - - 250 100 - - - ? = > 33.33 % answer : b"
Answer: b
Python program:
a = 100 / 750
b = 3 + 2 
c = b * 2
d = 100 * c
e = a * d
f = e - 100
Problem: what ratio must a shopkeeper mix peas and soybean of rs . 16 and rs . 25 / kg , as to obtain a mixture of rs . 21 ?
Options: a ) 10 : 7 , b ) 9 : 8 , c ) 4 : 5 , d ) 13 : 11 , e ) 14 : 8
Rationale: "correct option : ( c ) use rule of alligation , to determine the ratio the required ratio of soybean and peas = 4 : 5"
Answer: c
Python program:
a = 25 - 21
b = 21 - 16
c = a / b