euclaise/mathqa_programs huggingface dataset:
Problem: a part - time employee whose hourly wage was increased by 10 percent decided to reduce the number of hours worked per week so that the employee ' s total weekly income would remain unchanged . by what percent should the number of hours worked be reduced ?
Options: a ) 9.09 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: let original hourly wage be x and let the no of hours worked be y total wage will be = x * y after the increment the wage will be = 1.1 x now we need to find number of hours worked so that x * y = 1.1 x * z i . e z = x * y / 1.1 x = 1 / 1.1 y % decrease = ( y - 1 / 1.1 y ) / y * 100 = 1 - 1 / 1.1 * 100 = 9.09 % thus my answer is a .
Answer: a
Python program:
a = 10 + 100 
b = a / 100
c = b * 10
d = 1 / c
e = d * 100
Problem: a company has 15 managers and 75 associates . the 15 managers have an average salary of $ 150,000 . the 75 associates have an average salary of $ 30,000 . what is the average salary for the company ?
Options: a ) $ 35,000 , b ) $ 45,000 , c ) $ 50,000 , d ) $ 65,000 , e ) $ 75,000
Rationale: "another method is to get ratios say 30000 = a and we know the # of people are in 1 : 5 ratio average = ( 5 a * 1 + a * 5 ) / 6 = 10 a / 6 = 50000 answer is c . $ 50,000"
Answer: c
Python program:
a = 3 * 3
b = a * 10
c = 100 * 10
d = b * c
e = 3 * 10
f = 100 * 10
g = e * f
h = d + g 
i = 75 + 15 
j = h / i
Problem: the volume of a sphere with radius r is ( 4 / 3 ) * pi * r ^ 3 and the surface area is 4 * pi * r ^ 3 . if a sperical balloon has a volume of 2304 pi cubic centimeters , what is hte surface area of the balloon in square centimeters ?
Options: a ) a . 40
b ) b . 100
c ) c . 400
d ) d . 1,800
e ) e . 10,000
Rationale: the surface area is 4 . pi . r ^ 2 ( its area remember not volume ) as 4 / 3 . pi . r ^ 3 = 2304 pi r = 12 so area = 4 . pi . r ^ 2 = 576 . pi = 576 x 3.14 = 1800 ( approx ) d
Answer: d
Python program:
a = const_180 / 1000
Problem: in the above number , a and b represent the tens and units digits , respectively . if the above number is divisible by 35 , what is the greatest possible value of b x a ?
Options: a ) 0 , b ) 10 , c ) 20 , d ) 30 , e ) 35
Rationale: "i also was confused when i was looking forabove number : d as far as i understood , 35 is a factor of ab . in other words , the values of b ( units digits can be 5 or 0 . better to have option for 5 in this case to havebigger result ) . now let ' s try 35 x 1 ( a = 3 , b = 5 respectively we have = 15 ) . but we do n ' t have this number in answer choices , move on . ( avoid even multiples of 2,4 , 6,8 etc ( we will have 0 in units thus making our result 0 ) 35 x 3 = 105 ( a = 0 b = 5 respectively . hey ! that ' s 0 now . 35 x 5 = 175 ( a = 7 , b = 5 respectively . increasing trend , we have 35 now ) . this is the greatest possible value of b x a . imo e ."
Answer: e
Python program:
a = 3 + 4 
b = 2 + 3 
c = a * b
Problem: if 2 x - y = 4 then 6 x - 3 y = ?
Options: a ) 15 , b ) 12 , c ) 18 , d ) 10 , e ) 14
Rationale: 6 x - 3 y = 3 * ( 2 x - y ) = 3 * 4 = 12 answer : b
Answer: b
Python program:
a = 2 * 3
b = a + 6
Problem: find 3486 / 189
Options: a ) 18.44 , b ) 18.48 , c ) 18.42 , d ) 18.49 , e ) 18.41
Rationale: first we make the denominator 200 . i . e . , we are introducing an error of 11 which is 11189 = 11711189 = 117 th of the denominator . now 3486200 = 17.433486200 = 17.43 but this answer is less than actual answer . so we have to increase it by 1 / 17 th part of it . 117 × 17.43 ≃ 1117 × 17.43 ≃ 1 so final answer = 17.43 + 1 = 18.43 actual answer = 18.44 answer : a
Answer: a
Python program:
a = 3486 / 189
Problem: mary and mike enter into a partnership by investing $ 600 and $ 400 respectively . at the end of one year , they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business . if mary received $ 1000 more than mike did , what was the profit made by their business in that year ?
Options: a ) $ 8500 , b ) $ 9500 , c ) $ 7000 , d ) $ 7500 , e ) $ 6500
Rationale: "explanatory answer let the profit made during the year be $ 3 x therefore , $ x would have been shared equally and the remaining $ 2 x would have been shared in the ratio 6 : 4 . i . e . , 60 % of 2 x would go to mary and 40 % of 2 x would go to mike . hence , mary would get ( 60 - 40 ) % of 2 x more than mike or 20 % of 2 x = $ 1000 i . e . , ( 20 / 100 ) * 2 x = 1000 or 2 x = 5000 . hence , the profit made by the company during the year $ 3 x = $ 7500 . answer : d"
Answer: d
Python program:
a = 600 / 1000
b = 400 / 1000
c = a - b
d = 1 / 3
e = 1 - d
f = c * e
g = 1000 / f
Problem: a bookstore has a shelf that contains biographies which normally sell for $ 20 each and mysteries that normally sell for $ 12 each . during a sale , the biographies and mysteries are discounted at different rates so that a customer saves a total of $ 19 from the normal price by buying 5 discounted biographies and 3 discounted mysteries . if the sum of the discount rates for the two types of books is 27 percent , what is the discount rate on mysteries ?
Options: a ) 10 % , b ) 11 % , c ) 12.5 % , d ) 13 % , e ) 14 %
Rationale: "let b be the discount on biographies and m be the discount on mysteries so . , b + m = 0.27 - - - - - ( 1 ) and ( 20 * 5 + 12 * 3 ) - ( 20 * 5 * ( 1 - b ) + 12 * 3 * ( 1 - m ) ) = 19 - - > 100 ( 1 - ( 1 - b ) ) + 36 ( 1 - ( 1 - m ) = 19 100 b + 36 m = 19 - - - - - - ( 2 ) solving 12 . , we get m = 0.125 = 12.5 % c"
Answer: c
Python program:
a = 20 * 2
b = 20 + 27 
c = b + 1 
d = a / c
e = 1 - d
f = e * 100
Problem: after a storm deposits 120 billion gallons of water into the city reservoir , the reservoir is 80 % full . if the original contents of the reservoir totaled 200 billion gallons , the reservoir was approximately what percentage full before the storm ?
Options: a ) 45 % , b ) 48 % , c ) 50 % , d ) 58 % , e ) 65 %
Rationale: "when the storm deposited 120 billion gallons , volume of water in the reservoir = 200 + 120 = 320 billion gallons if this is only 80 % of the capacity of the reservoir , the total capacity of the reservoir = 320 / 0.8 = 400 billion gallons therefore percentage of reservoir that was full before the storm = ( 200 / 400 ) * 100 = 50 % option c"
Answer: c
Python program:
a = 120 + 200 
b = 80 / 100
c = a / b
d = 200 / c
e = d * 100
Problem: find the ones digit of 73 ^ 356
Options: a ) 1 , b ) 5 , c ) 6 , d ) 7 , e ) 9
Rationale: "the units digit of 73 ^ 356 will be the same as the units digit of 3 ^ 356 . 3 ^ 1 = 3 - - > the units digit is 3 ; 3 ^ 2 = 9 - - > the units digit is 9 ; 3 ^ 3 = 27 - - > the units digit is 7 ; 3 ^ 4 = 81 - - > the units digit is 1 ; 3 ^ 5 = 243 - - > the units digit is 3 again ; . . . so , as you can see the units digit repeats in blocks of 4 : { 3 , 9 , 7 , 1 } , { 3 , 9 , 7 , 1 } , . . . now , since 356 = 356 + 0 = ( multiple of 4 ) + 0 , then the units digit of 3 ^ 356 will be thus 1 . answer : a ."
Answer: a
Python program:
a = 3 + 4 
b = a * 10
c = 73 - b
d = 356 / 4
e = math.floor(d)
f = e * 4
g = 356 - f
h = c ** g
i = 2 * 10
j = h - i
Problem: a classroom has 3 electric lamps . from a collocation of 10 electric bulbs of which 6 are good , 3 are selected at random and put in the lamps . find the probability that the room is lighted .
Options: a ) 1 / 6 , b ) 4 / 120 , c ) 29 / 30 , d ) 1 / 9 , e ) none of these
Rationale: explanation : out of 10 electric bulbs , 3 are selected in 10 c 3 ways . so , number of possible outcomes = t = 10 c 3 = 120 . the room is lighted i . e at least one fo the 3 bulbs chosen at random is a good bulb . wherever ' at least one ' is present , it is easier to do the problem using complement of the event ( i . e room is dark and all 3 bulbs are bad ) . p ( room is dark ) = f / t = p ( none of the bulbs is good ) = > 4 c 3 / 120 . [ since 4 bulbs are bad ] . p ( room is lighted ) = 1 - ( 4 c 3 / 120 ) . [ room is lighted if at least one bulb is good ] . or p ( at least one ) = 1 - ( 4 / 120 ) . = 29 / 30 . answer : c
Answer: c
Python program:
a = math.comb(10, 3)
b = 10 - 6
c = math.comb(b, 3)
d = a - c
e = math.comb(10, 3)
f = d / e
Problem: if a population of women in a town is 90 % of men . what is the population of men as a % of population of women ?
Options: a ) 108 % , b ) 105 % , c ) 111 % , d ) 112 % , e ) 114 %
Rationale: we ' re told that the number of women in a town is equal to 90 % of the number of men in that town . if . . . . men = 10 women = 9 we ' re asked for the number of men , as a percentage of the number of women . m / w = 10 / 9 = 1 1 / 9 = 1.111111 = 111 % answer : c
Answer: c
Python program:
a = 100 / 90
b = a * 100
Problem: two trains 135 meters and 165 meters in length respectively are running in opposite directions , one at the rate of 80 km and the other at the rate of 65 kmph . in what time will they be completely clear of each other from the moment they meet ?
Options: a ) 7.18 , b ) 7.12 , c ) 7.3 , d ) 7.45 , e ) 7.51
Rationale: "t = ( 135 + 165 ) / ( 80 + 65 ) * 18 / 5 t = 7.45 answer : d"
Answer: d
Python program:
a = 135 + 165 
b = 80 + 65 
c = b * const_0_2778
d = a / c
Problem: 4 numbers are in the ratio 2 : 3 : 4 : 5 add up to give a sum of 1344 . find the biggest number .
Options: a ) 480 , b ) 239 , c ) 270 , d ) 282 , e ) 112
Rationale: answer : a
Answer: a
Python program:
a = 2 + 3 
b = a + 4 
c = b + 5 
d = 1344 / c
e = d * 5
Problem: rs . 700 is divided among a , b , c so that a receives half as much as b and b half as much as c . then c ' s share is :
Options: a ) rs 200 , b ) rs 300 , c ) rs 400 , d ) rs 500 , e ) rs 600
Rationale: let c = x . then b = x / 2 and a = x / 4 a : b : c = 1 : 2 : 4 . c ' s share rs . [ ( 4 / 7 ) x 700 ) = 400 answer : c
Answer: c
Python program:
a = 1 + 2 
b = 4 + a 
c = 4 / b
d = c * 700
Problem: a is twice as good a workman as b and they took 8 days together to do the work b alone can do it in ?
Options: a ) 25 days , b ) 88 days , c ) 21 days , d ) 11 days , e ) 24 days
Rationale: "wc = 2 : 1 2 x + x = 1 / 8 x = 1 / 24 = > 24 days answer : e"
Answer: e
Python program:
a = 2 + 1 
b = 8 * a
c = b / 2
d = c * 2
Problem: find the greatest number that will divide 150 , 230 and 175 leaving 50 , 5 and 25 as remainders respectively
Options: a ) 19 , b ) 17 , c ) 32 , d ) 9 , e ) 8
Rationale: explanation : answer will be hcf of ( 150 - 50 , 230 - 5 , 175 - 25 ) hcf of ( 100 , 225 , 150 ) = 32 option c
Answer: c
Python program:
a = 5 * 4
b = 12 + a
Problem: how long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 170 m in length ?
Options: a ) 16.8 , b ) 17.8 , c ) 15.9 , d ) 13.2 , e ) 12.4
Rationale: "d = 110 + 170 = 280 m s = 60 * 5 / 18 = 50 / 3 t = 280 * 3 / 50 = 16.8 sec answer a"
Answer: a
Python program:
a = 110 + 170 
b = 60 * const_0_2778
c = a / b
Problem: for any positive integer n , the sum of the first n positive integers equals n ( n + 1 ) / 2 . what is the sum x of all the even integers between 99 and 301 ?
Options: a ) 10,100 , b ) 20,200 , c ) 22,650 , d ) 40,200 , e ) 45,150
Rationale: "i would solve it in a different way . first of all , total number of even integers between 99 and 301 are , ( 301 - 99 ) / 2 = 202 / 2 = 101 average = ( 301 + 99 ) / 2 = 400 / 2 = 200 sum x = average * total count = 200 * 101 = 20,200 answer is b"
Answer: b
Python program:
a = 301 - 1
b = 99 + 1 
c = a - b
d = c / 2
e = d + 1
Problem: in track last week , the boys ran 27 laps . the girls ran 9 more laps . each lap is a 3 - fourth of a mile . how many miles did the girls run ?
Options: a ) 24 miles , b ) 25 miles , c ) 26 miles , d ) 27 miles , e ) 28 miles
Rationale: the girls ran 27 + 9 = 36 laps . 36 x 3 / 4 = 108 / 4 , which reduces to 27 . the girls ran 27 miles correct answer d
Answer: d
Python program:
a = 3 / 4
b = 27 + 9 
c = a * b
Problem: if tim had lunch at $ 50.20 and he gave 20 % tip , how much did he spend ?
Options: a ) $ 30.60 , b ) $ 60.60 , c ) $ 70.60 , d ) $ 40.60 , e ) $ 60.24
Rationale: "the tip is 20 % of what he paid for lunch . hence tip = 20 % of 50.20 = ( 20 / 100 ) * 50.20 = $ 10.04 total spent 50.20 + 10.04 = $ 60.24 correct answer e"
Answer: e
Python program:
a = 50 * 20
b = a / 100
c = 50 + 20
Problem: if the operation € is defined for all x and y by the equation x € y = 2 * x * y , then 8 € ( 4 € 5 ) =
Options: a ) 80 , b ) 120 , c ) 160 , d ) 640 , e ) 760
Rationale: "working inside out , ( 4 € 5 ) = 2 * 4 * 5 = 40 8 € 40 = 2 * 8 * 40 = 640 hence , answer is d"
Answer: d
Python program:
a = 2 * 8
b = 2 * 4
c = b * 5
d = a * c
Problem: a and b started a business in partnership investing rs . 20,000 and rs . 15,000 respectively . after 6 months , c joined them with rs . 20,000 . whatwill be b ' s share in total profit of rs . 24,000 earned at the end of 2 years from the startingof the business ?
Options: a ) s . 5,000 , b ) s . 5,500 , c ) s . 5,700 , d ) s . 6,500 , e ) s . 7,200
Rationale: "a : b : c = ( 20,000 x 24 ) : ( 15,000 x 24 ) : ( 20,000 x 18 ) = 4 : 3 : 3 . b ' s share = rs . 24000 x 3 / 10 = rs . 7,200 . e"
Answer: e
Python program:
a = 4 + 1 
b = a * 4
c = 3 * 4
d = 2 * c
e = b * d
Problem: every year an amount increases by 1 / 6 th of itself . how much will it be after two years if its present value is rs . 64000 ?
Options: a ) 87111 , b ) 81007 , c ) 81008 , d ) 81066 , e ) 81022
Rationale: "64000 * 7 / 6 * 7 / 6 = 87111 answer : a"
Answer: a
Python program:
a = 1 / 6
b = a * 64000
c = 64000 + b 
d = 1 / 6
e = 1 / 6
f = e * 64000
g = 64000 + f 
h = d * g
i = c + h
Problem: a factory has three types of machines , each of which works at its own constant rate . if 7 machine as and 11 machine bs can produce 305 widgets per hour , and if 8 machine as and 22 machine cs can produce 600 widgets per hour , how many widgets could one machine a , one machine b , and one machine c produce in one 8 - hour day ?
Options: a ) 400 , b ) 440 , c ) 550 , d ) 625 , e ) 700
Rationale: let machine a produce a widgets per hour . b produce b widgets per hour and c produce c widgets per hour . 7 a + 11 b = 305 - - - ( 1 ) 8 a + 22 c = 600 - - - ( 2 ) dividing ( 2 ) by 2 4 a + 11 c = 300 . . . . . ( 3 ) adding ( 1 ) ( 3 ) 11 a + 11 b + 11 c = 605 a + b + c = 55 per hour so for eight hrs = 55 * 8 = 440 = answer = b
Answer: b
Python program:
a = 600 / 11
b = a * 8
Problem: how many odd numbers between 10 and 1200 are the squares of integers ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: "the numbers are the squares of 5 , 7 , 9 , . . . , 33 which includes 15 numbers . the answer is d ."
Answer: d
Python program:
a = 10 + 4
Problem: alok ordered 16 chapatis , 5 plates of rice , 7 plates of mixed vegetable and 5 ice - cream cups . the cost of each chapati is rs . 6 , that of each plate of rice is rs . 45 and that of mixed vegetable is rs . 70 . the amount that alok paid the cashier was rs . 961 . find the cost of each ice - cream cup ?
Options: a ) 25 , b ) 30 , c ) 29 , d ) 12 , e ) 20
Rationale: "explanation : let the cost of each ice - cream cup be rs . x 16 ( 6 ) + 5 ( 45 ) + 7 ( 70 ) + 6 ( x ) = 961 96 + 225 + 490 + 5 x = 961 5 x = 150 = > x = 30 . answer : b"
Answer: b
Python program:
a = 16 * 5
b = 961 - a
c = 5 * 45
d = b - c
e = 7 * 70
f = d - e
g = f / 5
Problem: 300 liters of a mixture contains milk and water in the ratio 3 : 2 if 15 liters of this mixture be replaced by 15 liters of milk , the ratio of milk to water in the new mixture would be ?
Options: a ) 12 : 8 , b ) 12 : 4 , c ) 13 : 8 , d ) 14 : 5 , e ) 13 : 5
Rationale: "quantity of milk in 300 liters if mix = 300 * 3 / 5 = 180 liters quantity of milk in 315 liters of new mix = 180 + 15 = 195 liters quantity of water in it = 315 - 195 = 120 liters ratio of milk and water in new mix = 90 : 20 = 13 : 8 answer isc"
Answer: c
Python program:
a = 15 - 1
b = a * 2
c = 3 * 2
d = b / c
Problem: a car started running at a speed of 30 km / hr and the speed of the car was increased by 2 km / hr at the end of every hour . find the total distance covered by the car in the first 12 hours of the journey .
Options: a ) 342 km , b ) 352 km , c ) 642 km , d ) 742 km , e ) 492 km
Rationale: "the total distance covered by the car in the first 12 hours = 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44 + 46 + 48 + 50 + 52 = sum of 12 terms in ap whose first term is 30 and last term is 52 = 12 / 2 [ 30 + 52 ] = 492 km . answer : e"
Answer: e
Python program:
a = 2 * 12
b = 30 + a 
c = b + 30 
d = c / 2
Problem: a chemical supply company has 60 liters of a 25 % hno 3 solution . how many liters of pure undiluted hno 3 must the chemists add so that the resultant solution is a 50 % solution ?
Options: a ) 12 , b ) 15 , c ) 20 , d ) 24 , e ) 30
Rationale: "60 liters of a 25 % hno 3 solution means hno 3 = 15 liters in 60 liters of the solution . now , let x be the pure hno 3 added . as per question , 15 + x = 50 % of ( 60 + x ) or x = 30 . hence , e"
Answer: e
Python program:
a = 60 / 2
b = 60 * 25
c = b / 100
d = a - c
e = d * 2
Problem: in a 500 m race , the ratio of the speeds of two contestants a and b is 3 : 4 . a has a start of 140 m . then , a wins by
Options: a ) 60 m , b ) 40 m , c ) 20 m , d ) 10 m , e ) 50 m
Rationale: "solution to reach the winning post a will have to cover a distance of ( 500 - 140 ) m , i . e , 360 m . while a covers 3 m , b covers 4 m . while a covers 360 m , b covers ( 4 / 3 x 360 ) m = 480 m thus , when a reaches the winning post , b covers 480 m and therefore remains 20 m behind . ∴ a wins by 20 m . answer c"
Answer: c
Python program:
a = 500 - 140
b = a * 4
c = b / 3
d = 500 - c
Problem: pipe a can fill a tank in 2 hours . due to a leak at the bottom , it takes 3 hours for the pipe a to fill the tank . in what time can the leak alone empty the full tank ?
Options: a ) 10 , b ) 9 , c ) 7 , d ) 6 , e ) 5
Rationale: "let the leak can empty the full tank in x hours 1 / 2 - 1 / x = 1 / 3 = > 1 / x = 1 / 2 - 1 / 3 = ( 3 - 2 ) / 6 = 1 / 6 = > x = 6 . answer : d"
Answer: d
Python program:
a = 3 * 2
b = 3 - 2
c = a / b
Problem: a certain bus driver is paid a regular rate of $ 16 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 752 in total compensation , how many total hours did he work that week ?
Options: a ) 36 , b ) 40 , c ) 44 , d ) 48 , e ) 52
Rationale: "for 40 hrs = 40 * 16 = 640 excess = 752 - 640 = 112 for extra hours = . 75 ( 16 ) = 12 + 16 = 28 number of extra hrs = 112 / 28 = 28 / 7 = 4 total hrs = 40 + 4 = 44 answer c 44"
Answer: c
Python program:
a = 16 * 40
b = 752 - a
c = 100 + 75 
d = 16 * c
e = d / 100
f = b / e
g = 40 + f
Problem: if the weight of 12 meters long rod is 12.2 kg . what is the weight of 6 meters long rod ?
Options: a ) 7.2 kg . , b ) 10.8 kg . , c ) 12.4 kg . , d ) 6.1 kg , e ) none
Rationale: "answer ∵ weight of 12 m long rod = 12.2 kg ∴ weight of 1 m long rod = 12.2 / 12 kg ∴ weight of 6 m long rod = 12.2 x 6 / 12 = 6.1 kg option : d"
Answer: d
Python program:
a = 6 * 12
b = a / 12
Problem: x starts a business with rs . 45000 . y joins in the business after 3 months with rs . 45000 . what will be the ratio in which they should share the profit at the end of the year ?
Options: a ) 1 : 2 , b ) 2 : 1 , c ) 3 : 2 , d ) 2 : 3 , e ) 4 : 3
Rationale: "ratio in which they should share the profit = ratio of the investments multiplied by the time period = 45000 × 12 : 45000 × 9 = 45 × 12 : 45 × 9 = 3 × 12 : 2 × 9 = 4 : 3 answer is e ."
Answer: e
Python program:
a = 45000 * 12
b = 4 + 3 
c = 45000 * b
d = a / c
Problem: find the fraction which has the same ratio to 2 / 5 that 3 / 7 has to 6 / 5
Options: a ) 2 / 4 , b ) 6 / 78 , c ) 4 / 7 , d ) 3 / 5 , e ) 1 / 7
Rationale: "p : 2 / 5 = 3 / 7 : 6 / 5 as the product of the means is equal to the product of the extremes . p * 6 / 5 = 2 / 5 * 3 / 7 p * 6 / 5 = 6 / 35 p = 1 / 7 = > p = 1 / 7 answer : e"
Answer: e
Python program:
a = 3 / 7
b = 6 / 5
c = a / b
d = 2 / 5
e = c * d
Problem: a student traveled 25 percent of the distance of the trip alone , continued another 20 miles with a friend , and then finished the last half of the trip alone . how many miles long was the trip ?
Options: a ) 60 , b ) 80 , c ) 100 , d ) 120 , e ) 150
Rationale: "let x be the total length of the trip . 0.25 x + 20 miles + 0.5 x = x 20 miles = 0.25 x x = 80 miles the answer is b ."
Answer: b
Python program:
a = 1/(25)
b = 1 - a
c = 1 / 2
d = b - c
e = 20 / d
Problem: david obtained 72 , 60 , 35 , 62 and 84 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology what are his average marks ?
Options: a ) 75 , b ) 62.6 , c ) 87 , d ) 165 , e ) 11
Rationale: explanation : average = ( 72 + 60 + 35 + 62 + 84 ) / 5 = 313 / 5 = 62.6 . answer : b
Answer: b
Python program:
a = 72 + 60 
b = a + 35 
c = b + 62 
d = c + 84 
e = 2 + 3 
f = d / e
Problem: mohit sold an article for $ 12000 . 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 ) 25000 , c ) 10000 , 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 = 12000 - 10 / 100 ( 12000 ) = 12000 - 1200 = $ 10800 = > 1.08 x = 10800 = > x = 10000 c"
Answer: c
Python program:
a = 12000 * 10
b = a / 100
c = 12000 - b
d = 100 + 8 
e = c / d
f = e * 100
Problem: a certain store sold pens for $ 0.35 each and pencils for $ 0.25 each . if a customer purchased both pens and pencils from the store for a total of $ 1.80 , what total number of pens and pencils did the customer purchase ?
Options: a ) 6 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "answer : algebraically , the question looks like this : 2.5 = 0.35 x + 0.25 y there are three possible numbers of pens that fit that requirement : 1 pen : $ 0.35 2 pens : $ 0.70 3 pens : $ 1.05 and 3 pencils for $ 0.25 each . that ' s 3 pens and 3 pencils for a total of 6 pens and pencils . choice ( a ) is correct ."
Answer: a
Python program:
a = 0 + 35 
b = 1 / 80
c = b * 2
Problem: what profit percent is made by selling an article at a certain price , if by selling at 1 / 2 rd of that price , there would be a loss of 20 % ?
Options: a ) 20 % , b ) 29 % , c ) 60 % , d ) 27 % , e ) 28 %
Rationale: "sp 2 = 1 / 2 sp 1 cp = 100 sp 2 = 80 1 / 2 sp 1 = 80 sp 1 = 160 100 - - - 160 = > 60 % answer : c"
Answer: c
Python program:
a = 100 - 20
b = 1 / 2
c = a / b
d = c - 100
Problem: williams works at a resort from the beginning of march to the end of september . during the month of august this past year , he made 10 times the average ( arithmetic mean ) of his monthly totals in tips for the other months . his total tips for august were what fraction of his total tips for all of the months he worked ?
Options: a ) 5 / 8 , b ) 7 / 8 , c ) 6 / 8 , d ) 2 / 9 , e ) 1 / 7
Rationale: "first notice the number of months for which he worked - march to sept i . e . 7 months avg of monthly totals in tips for months other than august = x tips in august = 10 x total tips for all months = 6 * x + 10 x = 16 x tips for august / total tips for all months = 10 x / 16 x = 5 / 8 answer : a"
Answer: a
Python program:
a = 3 + 4 
b = a - 1
c = 10 + b 
d = 10 / c
Problem: how many seconds will it take for a car that is traveling at a constant rate of 77 miles per hour to travel a distance of 21 yards ? ( 1 mile = 1,160 yards )
Options: a ) . 1 , b ) 0.3 , c ) 0.6 , d ) 2 , e ) 1.6
Rationale: "speed = 77 miles / hr = 37.64 yard / s distance = 21 yards time = distance / speed = 21 / 37.64 = 0.6 sec ans - c"
Answer: c
Python program:
a = 77 / 3600
b = 77 + 77 
c = b - 4
d = c * 10
e = a * d
f = 21 / e
Problem: by selling an article at rs . 400 , a profit of 25 % is made . find its cost price ?
Options: a ) 228 , b ) 320 , c ) 287 , d ) 480 , e ) 811
Rationale: "sp = 400 cp = ( sp ) * [ 100 / ( 100 + p ) ] = 400 * [ 100 / ( 100 + 25 ) ] = 400 * [ 100 / 125 ] = rs . 320 answer : b"
Answer: b
Python program:
a = 400 * 100
b = 100 + 25 
c = a / b