euclaise/mathqa_programs huggingface dataset:
Problem: find the expenditure on digging a well 14 m deep and of 3 m diameter at rs . 17 per cubic meter ?
Options: a ) 2998 , b ) 2799 , c ) 2890 , d ) 1683 , e ) 2780
Rationale: "22 / 7 * 14 * 3 / 2 * 3 / 2 = 99 m 2 99 * 17 = 1683 answer : d"
Answer: d
Python program:
a = 3 / 2
b = volume_cylinder * (
Problem: 1370 , 1320 , 1070 , x , - 6430
Options: a ) - 180 , b ) 6530 , c ) 6630 , d ) 6730 , e ) 6830
Rationale: "1370 - 50 * ( 5 ^ 0 ) = 1320 1320 - 50 * ( 5 ^ 1 ) = 1070 1070 - 50 * ( 5 ^ 2 ) = - 180 - 180 - 50 * ( 5 ^ 3 ) = - 6430 answer : a ."
Answer: a
Python program:
a = negate - (
Problem: if ( 27 / 4 ) x - 18 = 3 x + 27 what is the value of x ?
Options: a ) 12 , b ) - 12 , c ) 1 / 12 , d ) - 1 / 12 , e ) 3
Rationale: ( 27 / 4 ) x - 18 = 3 x + 27 = > 27 x - 72 = 12 x + 108 = > 15 x = 180 = > x = 12 answer : a
Answer: a
Python program:
a = 27 + 18 
b = 27 / 4
c = b - 3
d = a / c
Problem: if the average marks of 3 classes of 55 , 60 and 45 students respectively is 50 , 55 , 60 , then find the average marksof all the students is
Options: a ) 53 , b ) 53.5 , c ) 54.68 , d ) 55.6 , e ) 67.2
Rationale: required average = 55 x 50 + 60 x 55 + 45 x 60 55 + 60 + 45 = 2750 + 3300 + 2700 160 = 8750 160 = 54.68 c
Answer: c
Python program:
a = 55 * 50
b = 60 * 55
c = a + b 
d = 45 * 60
e = c + d 
f = 55 + 50 
g = 60 + f 
h = e / g
Problem: the batting average of a particular batsman is 63 runs in 46 innings . if the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs , find his highest score .
Options: a ) 179 , b ) 208 , c ) 210 , d ) 223 , e ) 248
Rationale: explanation : total runs scored by the batsman = 63 * 46 = 2898 runs now excluding the two innings the runs scored = 58 * 44 = 2552 runs hence the runs scored in the two innings = 2898 – 2552 = 346 runs . let the highest score be x , hence the lowest score = x – 150 x + ( x - 150 ) = 346 2 x = 496 x = 248 runs answer e
Answer: e
Python program:
a = 63 * 46
b = 46 - 2
c = 58 * b
d = a - c
e = 150 + d 
f = e / 2
Problem: a lady builds 10 cm length , 13 cm width , and 5 cm height box using 5 cubic cm cubes . what is the minimum number of cubes required to build the box ?
Options: a ) 107 , b ) 108 , c ) 130 , d ) 150 , e ) 145
Rationale: "number of cubes required = volume of box / volume of cube = 10 * 13 * 5 / 5 = 130 cubes answer : c"
Answer: c
Python program:
a = 10 * 13
b = a * 5
c = b / 5
Problem: a train 275 m long is running with a speed of 60 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 8 , b ) 6 , c ) 5 , d ) 15 , e ) 1
Rationale: "speed of train relative to man = 60 + 6 = 66 km / hr . = 66 * 5 / 18 = 55 / 3 m / sec . time taken to pass the men = 275 * 3 / 55 = 15 sec . answer : d"
Answer: d
Python program:
a = 60 + 6 
b = a * const_0_2778
c = 275 / b
Problem: when 2 + 3 = 65 , 3 + 4 = 125 , 4 + 5 = 205 , then 5 + 6 = ?
Options: a ) 285 , b ) 305 , c ) 315 , d ) 350 , e ) 245
Rationale: "2 + 3 = > 2 ã — 3 = 6 = > 6 ã — 10 + 5 = 65 3 + 4 = > 3 ã — 4 = 12 = > 12 ã — 10 + 5 = 125 4 + 5 = > 4 ã — 5 = 20 = > 20 ã — 10 + 5 = 205 then 5 + 6 = > 5 ã — 6 = 30 = > 30 ã — 10 + 5 = 305 answer : b"
Answer: b
Python program:
a = 5 * 6
b = a * 10
c = b + 2
Problem: a certain experimental mathematics program was tried out in 2 classes in each of 22 elementary schools and involved 31 teachers . each of the classes had 1 teacher and each of the teachers taught at least 1 , but not more than 3 , of the classes . if the number of teachers who taught 3 classes is n , then the least and greatest possible values of n , respectively , are
Options: a ) 0 and 13 , b ) 0 and 14 , c ) 1 and 10 , d ) 1 and 6 , e ) 2 and 8
Rationale: "one may notice that greatest possible values differ in each answer choice in contrast to the least values , which repeat . to find out the greatest value you should count the total classes ( 22 * 2 = 44 ) , then subtract the total # of teachers since we know from the question that each teacher taught at least one class ( 44 - 31 = 13 ) . thus we get a number of the available extra - classes for teachers , and all that we need is just to count how many teachers could take 2 more classes , which is 13 / 2 = 6.5 . so the greatest possible value of the # of teachers who had 3 classes is 6 . only answer d has this option ."
Answer: d
Python program:
a = 22 * 2
b = a - 31
c = b / 2
Problem: a is twice as good a work man as b and together they finish a piece of work in 24 days . the number of days taken by a alone to finish the work is :
Options: a ) 28 days . , b ) 16 days . , c ) 12 days . , d ) 24 days . , e ) 36 days .
Rationale: "solution ( a ’ s 1 day ’ s work ) : ( b ’ s 1 day ’ s work ) = 2 : 1 . ( a + b ) ' s 1 day ’ s work = 1 / 24 divide 1 / 14 in the ratio 2 : 1 . ∴ a ’ s 1 day ’ s work = ( 1 / 24 x 2 / 3 ) = 1 / 36 hence , a alone can finish the work in 36 days . answer e"
Answer: e
Python program:
a = 1/(24)
b = 2 + 1 
c = a / b
d = 1/(c)
Problem: what will be the difference between simple and compound interest at 12 % per annum on a sum of rs . 1000 after 4 years ?
Options: a ) 94.19 , b ) 94.12 , c ) 93.5 , d ) 64.1 , e ) 64.11
Rationale: "s . i . = ( 1000 * 12 * 4 ) / 100 = rs . 480 c . i . = [ 1000 * ( 1 + 12 / 100 ) 4 - 1000 ] = rs . 573.5 difference = ( 573.5 - 480 ) = rs . 93.5 answer : c"
Answer: c
Python program:
a = 12 / 100
b = a + 1 
c = b ** 4
d = 1000 * c
e = d - 1000
f = 12 / 100
g = 1000 * f
h = g * 4
i = e - h
Problem: a train 360 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 290 m long ?
Options: a ) 40 sec , b ) 52 sec , c ) 45 sec , d ) 48 sec , e ) 50 sec
Rationale: "speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 360 + 290 = 650 m required time = 650 * 2 / 25 = 52 sec answer : b"
Answer: b
Python program:
a = 45 - 290
b = a * const_0_2778
c = 360 / b
Problem: q ' = 3 q - 3 , what is the value of ( 7 ' ) ' ?
Options: a ) 6 , b ) 106 , c ) 206 , d ) 306 , e ) 406
Rationale: "( 7 ' ) ' = ( 3 * 7 - 3 ) ' = 18 ' = 18 * 18 - 18 = 306 answer d"
Answer: d
Python program:
a = 3 * 7
b = a - 3
c = b * 3
d = c - 3
e = 7 - 1
f = d * e
Problem: find the ratio in which rice at rs . 7.20 a kg be mixed with rice at rs . 5.50 a kg to produce a mixture worth rs . 6.30 a kg
Options: a ) 2 : 0 , b ) 2 : 3 , c ) 2 : 1 , d ) 8 : 9 , e ) 2 : 8
Rationale: "by the rule of alligation : cost of 1 kg rice of 1 st kind cost of 1 kg rice of 2 nd kind required ratio = 80 : 90 = 8 : 9 answer : d"
Answer: d
Python program:
a = 6 - 30
b = 7 - 20
c = a / b
Problem: a grocer has a sale of rs . 5400 , rs . 9000 , rs . 6300 , rs . 7200 and rs . 4500 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 5600 ?
Options: a ) s . 1200 , b ) s . 5400 , c ) s . 5400 , d ) s . 4999 , e ) s . 5000
Rationale: "total sale for 5 months = rs . ( 5400 + 9000 + 6300 + 7200 + 4500 ) = rs . 32400 . required sale = rs . [ ( 5600 x 6 ) - 32400 ] = rs . ( 33600 - 32400 ) = rs . 1200 . option a"
Answer: a
Python program:
a = 5 + 1 
b = a * 5600
c = 5400 + 9000 
d = c + 6300 
e = d + 7200 
f = e + 4500 
g = b - f
Problem: marginal cost is the cost of increasing the quantity produced ( or purchased ) by one unit . if the fixed cost for n products is $ 12000 and the marginal cost is $ 200 , and the total cost is $ 16000 , what is the value of n ?
Options: a ) 20 , b ) 50 , c ) 60 , d ) 80 , e ) 100
Rationale: total cost for n products = fixed cost for n products + n * marginal cost - - > $ 16,000 = $ 12,000 + n * $ 200 - - > n = 20 . answer : a .
Answer: a
Python program:
a = 16000 - 12000
b = a / 200
Problem: $ 392 is divided among a , b , and c so that a receives half as much as b , and b receives half as much as c . how much money is c ' s share ?
Options: a ) $ 212 , b ) $ 216 , c ) $ 220 , d ) $ 224 , e ) $ 228
Rationale: "let the shares for a , b , and c be x , 2 x , and 4 x respectively . 7 x = 392 x = 56 4 x = 224 the answer is d ."
Answer: d
Python program:
a = 1 / 2
b = a + 1 
c = b + 2 
d = 392 / c
e = d * 2
Problem: the cyclist walking at a constant rate of 15 miles per hour is passed by a car traveling in the same direction along the same path at 60 miles per hour . the car stops to wait for the cyclist for 6 minutes after passing her , while the cyclist continues to go at her constant rate , how many minutes must the car wait until the cyclist catches up ?
Options: a ) 9 , b ) 10 , c ) 12 , d ) 15 , e ) 18
Rationale: for the 6 minutes the car continues to overtake the cyclist , she is going at 45 miles per hour faster than the cyclist . once the car stops , the cyclist is going at 15 miles per hour while the car is at rest so the amount of time the cyclist will take to cover the distance between them is going to be in the ratio of the relative speeds . 45 / 15 * 6 or 18 minutes answer is ( e )
Answer: e
Python program:
a = 60 - 15
b = 6 / const_60
c = a * b
d = c / 15
e = d * const_60
Problem: the value for d = ( 0.889 × 55 ) / 9.97 to the nearest tenth is
Options: a ) 0.5 , b ) 4.63 , c ) 4.9 , d ) 7.7 , e ) 49.1
Rationale: if we read the q , we can easily home on to the answer , , the numerator is clearly between 40 and 50 . . denomiator is close to 10 . . so d = ( 0.889 × 55 ) / 9.97 is between 4 and 5 . . it may tempt us to solve it since ther are two values between 4 and 5 . . but the catch is innearest tenth 4.63 can be called nearest to hundreth and no tenth , so can be eliminated . . 4.9 is our answer . . . c
Answer: c
Python program:
a = 0 * 889
b = a / 9
c = b * 10
d = math.floor(c)
e = d / 10
Problem: find the least number which when divided by 37 and 7 leaves a remainder of 2 in each case .
Options: a ) 259 , b ) 261 , c ) 263 , d ) 265 , e ) 267
Rationale: the least number which when divided by different divisors leaving the same remainder in each case = lcm ( different divisors ) + remainder left in each case . hence the required least number = lcm ( 37 , 7 ) + 2 = 261 . answer : b
Answer: b
Python program:
a = math.lcm(37, 7)
b = 2 + a
Problem: a cubical tank is filled with water to a level of 1 foot . if the water in the tank occupies 16 cubic feet , to what fraction of its capacity is the tank filled with water ?
Options: a ) 1 / 2
b ) 1 / 3
c ) 1 / 4
d ) 1 / 5
e ) 1 / 6
Rationale: the volume of water in the tank is h * l * b = 16 cubic feet . since h = 1 , then l * b = 16 and l = b = 4 . since the tank is cubical , the capacity of the tank is 4 * 4 * 4 = 64 . the ratio of the water in the tank to the capacity is 16 / 64 = 1 / 4 the answer is c .
Answer: c
Python program:
a = math.sqrt(16)
b = 16 / volume_cube
Problem: by approximately what percent is x greater than 2 / 5 if ( 3 / 5 ) ( x ) = 1 ?
Options: a ) 723 % , b ) 156 % , c ) 316 % , d ) 37 % , e ) 29 %
Rationale: "what percent is x greater than 2 / 5 if ( 3 / 5 ) ( x ) = 1 ? = > x = 5 / 3 % change = [ ( 5 / 3 - 2 / 5 ) / ( 2 / 5 ) ] * 100 = 316.5 % = 316 % approx ans , c"
Answer: c
Python program:
a = 2 / 5
b = 5 - a
c = 2 / 5
d = b / c
e = d * 100
Problem: a furniture store owner decided to drop the price of her recliners by 20 % to spur business . by the end of the week she had sold 60 % more recliners . what is the percentage increase of the gross ?
Options: a ) 10 % , b ) 15 % , c ) 20 % , d ) 28 % , e ) 50 %
Rationale: "say a recliner is actually worth $ 100 if she sells 100 recliners then she earns $ 10000 after the discount of 20 % , she will earn $ 80 per recliner and she sells 60 % more ie . , 160 recliners hence her sales tields 160 * 80 = $ 12800 increase in sales = 12800 - 10000 = $ 2800 so % increase = 2800 * 100 / 10000 = 28 % d is the answer"
Answer: d
Python program:
a = 20 / 100
b = 1 - a
c = 60 / 100
d = 1 + c 
e = b * d
f = e * 100
g = f - 100
Problem: 10 play kabadi , 25 play kho kho only , 5 play both gmaes . then how many in total ?
Options: a ) 30 , b ) 35 , c ) 38 , d ) 40 , e ) 45
Rationale: "10 play kabadi = > n ( a ) = 10 , 5 play both gmaes . = > n ( anb ) = 5 25 play kho kho only , = > n ( b ) = n ( b only ) + n ( anb ) = 25 + 5 = 30 total = > n ( aub ) = n ( a ) + n ( b ) - n ( anb ) = 10 + 30 - 5 = 35 answer : b"
Answer: b
Python program:
a = 25 + 5 
b = 10 + a 
c = b - 5
Problem: if the area of a square with sides of length 8 centimeters is equal to the area of a rectangle with a width of 4 centimeters , what is the length of the rectangle , in centimeters ?
Options: a ) 4 , b ) 8 , c ) 12 , d ) 16 , e ) 18
Rationale: "let length of rectangle = l 8 ^ 2 = l * 4 = > l = 64 / 4 = 16 answer d"
Answer: d
Python program:
a = 8 ** 2
b = a / 4
Problem: the average salary of 15 people in the shipping department at a certain firm is $ 21,000 . the salary of 5 of the employees is $ 25,000 each and the salary of 4 of the employees is $ 16,000 each . what is the average salary of the remaining employees ?
Options: a ) $ 19,250 , b ) $ 18,500 , c ) $ 21,000 , d ) $ 15,850 , e ) $ 12,300
Rationale: "total salary . . . 15 * 21 k = 315 k 5 emp @ 25 k = 125 k 4 emp @ 16 k = 64 k remaing 6 emp sal = 315 k - 125 k - 64 k = 126 k average = 126 k / 6 = 21000 ans : c"
Answer: c
Python program:
a = 5 * 4
b = 4 * 4
c = a * b
d = 5 * 5
e = d * 5
f = c - e
g = 4 * 15
h = f - g
i = 2 + 5 
j = h / i
Problem: walking at the rate of 3 kmph a man cover certain distance in 6 hr 40 min . running at a speed of 18 kmph the man will cover the same distance in .
Options: a ) 40 min , b ) 25 min , c ) 54 min , d ) 65 min , e ) 58 min
Rationale: "distance = speed * time 3 * 20 / 3 = 20 km new speed = 18 kmph therefore time = 20 / 18 = 10 / 9 = 54 min answer : c ."
Answer: c
Python program:
a = 40 / const_60
b = 6 + a 
c = 3 * b
d = c / 18
e = d * const_60
Problem: in the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30 . in the sport formulation , the ratio of flavoring to corn syrup is three times as great as in the standard formulation , and the ratio of flavoring to water is half that of the standard formulation . if a large bottle of thesportformulation contains 5 ounces of corn syrup , how many ounces of water does it contain ?
Options: a ) 15
b ) 30
c ) 45
d ) 75
e ) 90
Rationale: standard : fl : corn s : water = 1 : 12 : 30 sport : fl : corn s : water = 3 : 12 : 180 this simplifies to 1 : 4 : 60 if the large bottle has a capacity of x ounces , then 4 x / 65 = 5 . so , x = 325 / 4 ounces . water = ( 60 / 65 ) * ( 325 / 4 ) = 60 * 3 / 4 = 75 ounces . ans d
Answer: d
Python program:
a = 1 / 12
b = a * 3
c = 1 / 30
d = c / 2
e = b / d
f = e * 5
Problem: two brothers took the gmat exam , the higher score is u and the lower one is v . if the difference between the two scores is equal to their average , what is the value of v / u ?
Options: a ) 3 , b ) 2 , c ) 1 / 2 , d ) 1 / 3 , e ) there is n ' t enough data to answer the question .
Rationale: answer is d : 1 / 3 u - v = ( u + v ) / 2 solving for v / u = 1 / 3 d
Answer: d
Python program:
a = 1 / 3
Problem: two trains 131 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 ) 7.16 , b ) 7.16 , c ) 7.12 , d ) 7.35 , e ) 7.11
Rationale: "t = ( 131 + 165 ) / ( 80 + 65 ) * 18 / 5 t = 7.35 answer : d"
Answer: d
Python program:
a = 131 + 165 
b = 80 + 65 
c = b * const_0_2778
d = a / c
Problem: in the rectangular coordinate system , if the line x = 6 y + 5 passes through points ( m , n ) and ( m + 2 , n + p ) , what is the value of p ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 5 , e ) 1 / 6
Rationale: "x = 6 y + 5 , and thus y = x / 6 - 5 / 6 the slope is 1 / 6 . the slope of a line through points ( m , n ) and ( m + 2 , n + p ) is ( n + p - n ) / ( m + 2 - m ) = p / 2 p / 2 = 1 / 6 and thus p = 1 / 3 the answer is b ."
Answer: b
Python program:
a = 2 / 6
Problem: the temperature of a certain cup of coffee 6 minutes after it was poured was 120 degrees fahrenheit . if the temperature f of the coffee t minutes after it was poured can be determined by the formula f = 120 * 2 ^ ( - at ) + 60 , where f is in degrees fahrenheit and a is a constant . then the temperature of the coffee 30 minutes after it was poured was how many degrees fahrenheit ?
Options: a ) 65 , b ) 63.75 , c ) 80 , d ) 85 , e ) 90
Rationale: "first , we have to find a . we know that after t = 6 minutes the temperature f = 120 degrees . hence : 120 = 120 * ( 2 ^ - 6 a ) + 60 60 = 120 * ( 2 ^ - 6 a ) 60 / 120 = 2 ^ - 6 a 1 / 2 = 2 ^ - 6 a 2 ^ - 1 = 2 ^ - 6 a - 1 = - 6 a 1 / 6 = a now we need to find f after t = 30 minutes : f = 120 * ( 2 ^ - 1 / 6 * 30 ) + 60 f = 120 * ( 2 ^ - 5 ) + 60 f = 120 * ( 1 / 2 ^ 5 ) + 60 f = 120 * 1 / 32 + 60 f = 3.75 + 60 = 63.75 answer b !"
Answer: b
Python program:
a = 60 / 6
b = 1 - 2
c = a * b
d = 2 ** c
e = d * 120
f = e + 60
Problem: a man can row his boat with the stream at 16 km / h and against the stream in 8 km / h . the man ' s rate is ?
Options: a ) 4 kmph , b ) 2 kmph , c ) 7 kmph , d ) 8 kmph , e ) 3 kmph
Rationale: "ds = 16 us = 8 s = ? s = ( 16 - 8 ) / 2 = 4 kmph answer : a"
Answer: a
Python program:
a = 16 - 8
b = a / 2
Problem: 2.09 can be expressed in terms of percentage as
Options: a ) 2.09 % , b ) 20.9 % , c ) 209 % , d ) 0.209 % , e ) none of these
Rationale: "explanation : while calculation in terms of percentage we need to multiply by 100 , so 2.09 * 100 = 209 answer : option c"
Answer: c
Python program:
a = 2 * 9
Problem: johnny bought 6 peanut butter cans at an average price ( arithmetic mean ) of 36.5 ¢ . if johnny returned two cans to the retailer , and the average price of the remaining cans was 30 ¢ , then what is the average price , in cents , of the two returned peanut butter cans ?
Options: a ) 5.5 , b ) 11 , c ) 47.5 , d ) 66 , e ) 49.5
Rationale: total price of six cans = 6 * 36.5 = 219 total price of 4 cans = 4 * 30 = 120 total rice of two cans = 219 - 120 = 99 average price of two cans = 99 / 2 = 49.5 c another way to do it is this : assume that the four leftover cans were of 30 c each . the avg was 36.5 c initially because the two cans were 36.5 c each and were providing another 6.5 c of cost to other 4 cans . so cost of the two cans = 2 * 36.5 + 4 * 6.5 = 99 avg cost of the two cans = 99 / 2 = 49.5 c answer ( e )
Answer: e
Python program:
a = 6 * 36
b = 6 - 2
c = b * 30
d = a - c
e = d / 2
Problem: a clockwise rotation around point z ( that is , a rotation in the direction of the arrow ) transforms the shaded quadrilateral to the unshaded quadrilateral . the angle of rotation is approximately
Options: a ) 180 o , b ) 270 o , c ) 360 o , d ) 45 o , e ) 135 o
Rationale: the measure of \ pzq formed by the bottom edge of the shaded quadrilateral , zq , and this same edge after the rotation , zp , is approximately 90 . the transformation of the shaded quadrilateral to the unshaded quadrilateral is a clockwise rotation around point z through an an - gle equal to the measure of re ex angle pzq . the measure of \ pzq added to the measure of re ex \ pzq is equal to the measure of one complete rotation , or 360 . therefore , the measure of re ex angle pzq is approximately 360 o - 90 o or 270 o . thus the clockwise rotation around point z is through an angle of approximately 270 o correct answer b
Answer: b
Python program:
a = 3600 / 10
b = 3600 / 10
c = b / 4
d = a - c
Problem: find the compound interest on $ 66,000 at 20 % per annum for 9 months , compounded quarterly
Options: a ) 2532.12 , b ) 2552.2 , c ) 9524.32 , d ) 10403.25 , e ) 20512.54
Rationale: "principal = $ 66000 ; time = 9 months = 3 quarters ; rate = 20 % per annum = 5 % per quarter . amount = $ [ 66000 x ( 1 + ( 5 / 100 ) ) ^ 3 ] = $ 76403.25 ci . = $ ( 76403.25 - 66000 ) = $ 10403.25 answer d ."
Answer: d
Python program:
a = 9 / 100
b = 1 + a 
c = b ** 20
d = 66 * 0
e = d - 66
Problem: if | x | = 4 x - 1 , then x = ?
Options: a ) 3 , b ) 1 / 2 , c ) 1 and 1 / 2 , d ) - 1 / 2 , e ) - 1
Rationale: "answer : a approach : substituted option a i . e x = 1 . inequality satisfied ."
Answer: a
Python program:
a = 4 - 1
b = 1 / a
Problem: an uneducated retailer marks all his goods at 40 % above the cost price and thinking that he will still make 25 % profit , offers a discount of 25 % on the marked price . what is his actual profit on the sales ?
Options: a ) 12.50 % , b ) 13.50 % , c ) 5 % , d ) 14.50 % , e ) none
Rationale: sol . let c . p . = rs . 100 . then , marked price = rs . 140 . s . p . = 75 % of rs . 140 = rs . 105 . ∴ gain % = 5 % . answer c
Answer: c
Python program:
a = 40 / 100
b = 1 + a 
c = 40 / 100
d = 1 + c 
e = 25 / 100
f = d * e
g = b - f
h = g - 1
i = h * 100
Problem: dick and jane each saved $ 4,000 in 1989 . in 1990 dick saved 10 percent more than in 1989 , and together he and jane saved a total of $ 6,500 . approximately what percent less did jane save in 1990 than in 1989 ?
Options: a ) 20 % , b ) 70 % , c ) 50 % , d ) 30 % , e ) 40 %
Rationale: "1990 dick saved = $ 4400 jane saved = $ 2100 ( jane saved $ 2800 less than she did the prior year ) jane saved approximately $ 2800 / 4000 $ ( 70 % ) less in 1990 answer : b"
Answer: b
Python program:
a = 10 / 100
b = a + 1 
c = 2 - b
d = 1 - c
e = d * 100
Problem: the area of a sector of a circle of radius 5 cm formed by an arc of length 3.5 cm is ?
Options: a ) 0.35 cm 2
b ) 17.5 cm 2
c ) 8.75 cm 2
d ) 55 cm 2
e ) 50 cm 2
Rationale: explanation : ( 5 * 3.5 ) / 2 = 8.75 answer is c
Answer: c
Python program:
a = 1 / 2
b = 5 * 3
c = a * b
Problem: if one positive integer is greater than another positive integer by 3 , and the difference of their cubes is 189 , what is their sum ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "1 ^ 3 = 1 2 ^ 3 = 8 3 ^ 3 = 27 4 ^ 3 = 64 5 ^ 3 = 125 6 ^ 3 = 216 the two numbers are 3 and 6 . the answer is d ."
Answer: d
Python program:
a = 3 ** 3
b = 3 ** 3
c = b ** 2
d = 3 ** 3
e = 189 - d
f = e ** 2
g = c + f 
h = math.sqrt(g)
i = a + h 
j = 3 ** 2
k = j * 2
l = i / k
m = 3 ** 3
n = 3 ** 3
o = n ** 2
p = 3 ** 3
q = 189 - p
r = q ** 2
s = o + r 
t = math.sqrt(s)
u = m + t 
v = 3 ** 2
w = v * 2
x = u / w
y = x - 3
z = l + y
Problem: there are 16 bees in the hive , then 5 more fly . how many bees are there in all ?
Options: a ) 20 , b ) 33 , c ) 12 , d ) 17 , e ) 25
Rationale: 16 + 5 = 20 . answer is a .
Answer: a
Python program:
a = 16 + 5
Problem: a special municipal payroll tax charges not tax on a payroll less than $ 250,000 and only 0.1 % on a company ’ s payroll above $ 250,000 . if belfried industries paid $ 200 in this special municipal payroll tax , then they must have had a payroll of
Options: a ) $ 450,000 , b ) $ 202,000 , c ) $ 220,000 , d ) $ 400,000 , e ) $ 2 , 200,000
Rationale: "answer : a , ( with different approach ) : the 200 paid is 0.1 % of the additional amount above 250,000 . let it be x now 0.1 % of x = 200 therefore x = 200,000 total = 250,000 + x = 450,000"
Answer: a
Python program:
a = 200 * 100
b = a * 10
Problem: an auction house charges a commission of 16 % on the first $ 50,000 of the sale price of an item , plus 10 % on the amount of of the sale price in excess of $ 50,000 . what was the price of a painting for which the house charged a total commission of $ 24,000 ?
Options: a ) $ 115,000 , b ) $ 160,000 , c ) $ 210,000 , d ) $ 240,000 , e ) $ 365,000
Rationale: "say the price of the house was $ x , then 0.16 * 50,000 + 0.1 * ( x - 50,000 ) = 24,000 - - > x = $ 210,000 ( 16 % of $ 50,000 plus 10 % of the amount in excess of $ 50,000 , which is x - 50,000 , should equal to total commission of $ 24,000 ) . answer : c ."
Answer: c
Python program:
a = 16 * 10
b = a + 10
Problem: two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 13 kmph and 21 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ?
Options: a ) 11 , b ) 408 , c ) 2881 , d ) 287 , e ) 221
Rationale: "1 h - - - - - 5 ? - - - - - - 60 12 h rs = 13 + 21 = 34 t = 12 d = 34 * 12 = 408 answer : b"
Answer: b
Python program:
a = 21 - 13
b = 60 / a
c = b * 13
d = 21 - 13
e = 60 / d
f = e * 21
g = c + f