euclaise/mathqa_programs huggingface dataset:
Problem: a lady grows cauliflower in her garden that is in the shape of a square . each cauliflower takes 1 square foot of area in her garden . this year , she has increased her output by 223 cauliflower when compared to last year . the shape of the area used for growing the cauliflower has remained a square in both these years . how many cauliflowers did she produce this year ?
Options: a ) 12541
b ) 12542
c ) 12544
d ) 12545
e ) can not be determined
Rationale: explanatory answer the shape of the area used for growing cauliflower has remained a square in both the years . let the side of the square area used for growing cauliflower this year be x ft . therefore , the area of the ground used for cultivation this year = x 2 sq . ft . let the side of the square area used for growing cauliflower last year be y ft . therefore , the area of the ground used for cultivation last year = y 2 sq . ft . as the number of cauliflower grown has increased by 223 , the area would have increased by 223 sq ft because each cauliflower takes 1 sq ft space . hence , x 2 - y 2 = 223 ( x + y ) ( x - y ) = 223 . 223 is a prime number and hence it will have only two factors . i . e . , 223 and 1 . therefore , 223 can be expressed as product of 2 numbers in only way = 223 * 1 i . e . , ( x + y ) ( x - y ) = 223 * 1 so , ( x + y ) should be 223 and ( x - y ) should be 1 . solving the two equations we get x = 112 and y = 111 . therefore , number of cauliflower produced this year = x 2 = 1122 = 12544 . alternative approach : use answer choices the area in both the years are squares of two numbers . that rules out choice a , b and d . as 12541,12542 and 12545 are not the square of any number . check choice c : if this year ' s produce is 12544 , last year ' s produce would have been 12544 - 223 = 12321 12321 is the square of 111 . so , 12544 is the answer . choice c .
Answer: c
Python program:
a = 223 - 1
b = a / 2
c = b ** 2
d = c + 223
Problem: 12 . what is the dividend . divisor 17 , the quotient is 9 and the remainder is 9 .
Options: a ) 150 , b ) 162 , c ) 154 , d ) 158 , e ) 144
Rationale: "d = d * q + r d = 17 * 9 + 9 d = 153 + 9 d = 162 answer b"
Answer: b
Python program:
a = 17 * 9
b = a + 9
Problem: a boat can travel with a speed of 13 km / hr in still water . if the speed of the stream is 4 km / hr . find the time taken by the boat to go 68 km downstream ?
Options: a ) 2 hours , b ) 3 hours , c ) 4 hours , d ) 5 hours , e ) none
Rationale: "solution speed downstream = ( 13 + 4 ) km / hr = 17 km / hr . time taken to travel 68 km downstream = ( 68 / 17 ) hrs = 4 hrs . answer c"
Answer: c
Python program:
a = 13 + 4 
b = 68 / a
Problem: find the cost of fencing around a circular field of diameter 42 m at the rate of rs . 3 a meter ?
Options: a ) 138 , b ) 390 , c ) 393 , d ) 279 , e ) 222
Rationale: "2 * 22 / 7 * 21 = 131 131 * 3 = rs . 393 answer : c"
Answer: c
Python program:
a = 42 / 2
b = circumface * (
Problem: the volumes of two cones are in the ratio 1 : 15 and the radii of the cones are in the ratio of 1 : 2 . what is the length of the wire ?
Options: a ) 3 : 5 , b ) 3 : 9 , c ) 3 : 2 , d ) 2 : 2 , e ) 3 : 8
Rationale: "the volume of the cone = ( 1 / 3 ) π r 2 h only radius ( r ) and height ( h ) are varying . hence , ( 1 / 3 ) π may be ignored . v 1 / v 2 = r 1 ^ 2 . h 1 / r 2 ^ 2 . h 2 = > 1 / 15 = ( 1 ) ^ 2 h 1 / ( 2 ) ^ 2 h 2 = > h 1 / h 2 = 3 / 5 i . e . h 1 : h 2 = 3 : 5 answer : a"
Answer: a
Python program:
a = 1 / 15
b = 1 / 2
c = b ** 2
d = a / c
Problem: the average salary of all the workers in a workshop is rs . 6750 . the average salary of 7 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 ) a ) 23 , b ) b ) 21 , c ) c ) 52 , d ) d ) 56 , e ) e ) 12
Rationale: "let the total number of workers be x . then , 6750 x = ( 12000 * 7 ) + 6000 ( x - 7 ) = > 750 x = 42000 = x = 56 . answer : d"
Answer: d
Python program:
a = 12000 - 6750
b = 7 * a
c = 6750 - 6000
d = b / c
e = 7 + d
Problem: each light bulb at a hotel is either incandescent or fluorescent . at a certain moment , forty percent of the incandescent bulbs are switched on , and eighty percent of the fluorescent bulbs are switched on . if 70 percent of all the bulbs are switched on at this moment , what percent of the bulbs that are switched on are incandescent ?
Options: a ) 10 % , b ) 14 % , c ) 18 % , d ) 22 % , e ) 26 %
Rationale: "let i be the number of incandescent bulbs . let f be the number of fluorescent bulbs . 0.4 i + 0.8 f = 0.7 ( i + f ) 0.1 f = 0.3 i f = 3 i this means that for every 1 incandescent bulb , there are 3 fluorescent bulbs . the percent of bulbs that are switched on which are incandescent is : 0.4 i / ( 0.4 i + 0.8 f ) = 0.4 i / ( 0.4 i + 0.8 * 3 i ) = 0.4 i / 2.8 i = 1 / 7 which is about 14 % . the answer is b ."
Answer: b
Python program:
a = 100 - 70
b = 2 / const_0_25
c = b + 2 
d = c * 4
e = a * d
f = e / 100
Problem: on dividinng 109 by a number , the quotient is 9 and the remainder is 1 . find the divisor .
Options: a ) 12 , b ) 14 , c ) 15 , d ) 16 , e ) 17
Rationale: d = ( d - r ) / q = ( 109 - 1 ) / 9 = 108 / 9 = 18 a
Answer: a
Python program:
a = 109 / 9
b = math.floor(a)
Problem: what is the compound interest paid on a sum of rs . 700 for the period of 2 years at 10 % per annum .
Options: a ) 130 , b ) 620 , c ) 147 , d ) 120 , e ) none of these
Rationale: "solution = interest % for 1 st year = 10 interest % for 2 nd year = 10 + 10 % of 10 = 10 + 10 * 10 / 100 = 11 total % of interest = 10 + 11 = 21 total interest = 21 % 700 = 700 * ( 21 / 100 ) = 147 answer c"
Answer: c
Python program:
a = 10 / 100
b = 1 + a 
c = b ** 2
d = 700 * c
e = d - 700
Problem: a train covers a distance of 15 km in 10 min . if it takes 10 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 240 m , b ) 150 m , c ) 120 m , d ) 200 m , e ) 165 m
Rationale: "speed = ( 15 / 10 * 60 ) km / hr = ( 90 * 5 / 18 ) m / sec = 25 m / sec . length of the train = 20 * 10 = 200 m . answer : d"
Answer: d
Python program:
a = 15 / 10
b = a - 10
c = 15 / b
Problem: fresh grapes contain 65 % by weight while dried grapes contain 10 % water by weight . what is the weight of dry grapes available from 400 kg of fresh grapes ?
Options: a ) 105.00 kg , b ) 115.60 kg , c ) 125.00 kg , d ) 130.50 kg , e ) 155.55 kg
Rationale: "from the question we know : 400 kg * 65 % = 260 kg of water in the fresh grapes 400 kg - 260 kg of water = 140 kg of non - water mass we are looking for the weight of the dry grapes ( x ) . since the question tells us that 10 % of the weight of the dry graps is water and we know that 140 kg is non - water mass we can set up the following equation : x = 1 / 10 ( x ) + 140 kg 9 / 10 ( x ) = 140 kg x = 155.55 kg answer - e"
Answer: e
Python program:
a = 100 - 65
b = a * 400
c = b / 100
d = 100 - 10
e = c / d
f = e * 100
Problem: in a fuel station the service costs $ 2.20 per vehicle and every liter of fuel costs $ 0.70 . assuming that you fill up 4 mini - vans and 2 trucks , what will be the total cost , if a mini - van ' s tank is 65 liters and a truck ' s tank is 120 % bigger and they are all empty ?
Options: a ) $ 382.10 , b ) $ 395.40 , c ) $ 404.30 , d ) $ 416.80 , e ) $ 426.50
Rationale: "the service cost of 4 vans and 2 trucks is 6 * 2.20 $ 13.20 the fuel in 4 vans is 4 * 65 = 260 liters the fuel in 2 trucks is 2 * 65 * 2.2 = 286 liters the total fuel ( vans + trucks ) = 546 liters the total fuel cost is 546 * 0.7 = $ 382.20 the total cost is $ 382.20 + $ 13.20 = $ 395.40 the answer is b ."
Answer: b
Python program:
a = 120 * 65
b = a / 100
c = b + 65 
d = c * 2
e = d * 0
f = 4 * 65
g = f * 0
h = e + g 
i = 4 + 2 
j = 2 * 20
k = h + j
Problem: a group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 7 with 4 students left over . what is the sum of the two smallest possible values of n ?
Options: a ) 66 , b ) 70 , c ) 74 , d ) 78 , e ) 82
Rationale: "n = 4 k + 1 = 7 j + 4 let ' s start at 1 = 4 ( 0 ) + 1 and keep adding 4 until we find a number in the form 7 j + 4 . 1 , 5 , 9 , 13 , 17 , 21 , 25 = 7 ( 3 ) + 4 the next such number is 25 + 4 * 7 = 53 . 25 + 53 = 78 the answer is d ."
Answer: d
Python program:
a = 7 * 2
b = a + 4 
c = 2 * 4
d = 7 * c
e = d + 4 
f = b + e
Problem: if an integer n is to be chosen at random from the integers 1 to 84 , inclusive , what is the probability that n ( n + 1 ) ( n + 2 ) will be divisible by 8 ?
Options: a ) 9 / 14 , b ) 3 / 8 , c ) 1 / 2 , d ) 5 / 8 , e ) 3 / 4
Rationale: "n ( n + 1 ) ( n + 2 ) will be divisible by 8 when n is a multiple of 2 or when ( n + 1 ) is a multiple of 8 . thus when n is even , this whole expression will be divisible by 8 . from 1 to 84 , there are 42 even integers . now when ( n + 1 ) is multiple by 8 , we have 12 such values for ( n + 1 ) probability that n ( n + 1 ) ( n + 2 ) will be divisible by 8 = ( 42 + 12 ) / 84 = 54 / 84 = 9 / 14 ans is a"
Answer: a
Python program:
a = 84 / 2
b = 84 / 8
c = a + b 
d = c / 84
Problem: an auto assembly plant performs 6 functions with each frame that arrives : add axles , add wheels to the axles , install the windshield to the frame , install the instrument panel , install the steering wheel , and install the interior seating . once those 6 tasks are performed , each car goes to a separate building for finishing touches . if these tasks can be arranged along a linear assembly line in any order , except that the axles must be installed before the wheels can be added , how many y ways can the assembly line be arranged ?
Options: a ) 120 , b ) 240 , c ) 360 , d ) 480 , e ) 720
Rationale: c ) 360 short way : there are 6 c ! ways to do the six tasks . half will have wheels before axles and half will have axles before wheels . so we want y = 6 c ! / 2 - > 720 / 2 = 360
Answer: c
Python program:
a = math.factorial(4)
b = 4 + 3 
c = b + 2 
d = c + 1 
e = a * d
f = 6 - 1
g = math.factorial(f)
h = e + g
Problem: company x provides bottled water to its employees in 5 liter bottles , $ 3 each . at least how many 5 l bottles must company x buy monthly , so that new contract with $ 50 fixed monthly rate and $ 1 for 20 l bottle each paid off ? ( assume that no other costs apply )
Options: a ) 15 , b ) 17 , c ) 19 , d ) 20 , e ) 21
Rationale: let the no . of 5 liter bottles be x , so the no . of 20 l bottles will be x / 4 ( to equate the vol . ) since the total cost will be equal , 3 x = 50 + x / 4 so x = 18.18 or 19 . answer is ( c ) .
Answer: c
Python program:
a = 1 / 1
b = 5 - a
c = 50 / b
Problem: if a ( a - 7 ) = 8 and b ( b - 7 ) = 8 , where a ≠ b , then a + b =
Options: a ) − 48 , b ) − 2 , c ) 2 , d ) 7 , e ) 48
Rationale: "i . e . if a = - 1 then b = 8 or if a = 8 then b = - 1 but in each case a + b = - 1 + 8 = 7 answer : option d"
Answer: d
Python program:
a = 7 + 8 
b = 7 - 8
c = a + b 
d = c - 1
e = d - 1
f = e - 1
g = f - 1
Problem: by selling an article at rs . 800 , a shopkeeper makes a profit of 25 % . at what price should he sell the article so as to make a loss of 30 % ?
Options: a ) s . 429 , b ) s . 480 , c ) s . 429 , d ) s . 488 , e ) s . 419
Rationale: "sp = 800 profit = 25 % cp = ( sp ) * [ 100 / ( 100 + p ) ] = 800 * [ 100 / 125 ] = 640 loss = 30 % = 30 % of 640 = rs . 192 sp = cp - loss = 640 - 192 = rs . 448 answer : d"
Answer: d
Python program:
a = 800 * 100
b = 25 + 100 
c = a / b
d = 800 * 100
e = 25 + 100 
f = d / e
g = f * 30
h = g / 100
i = c - h
Problem: if the cost price of 50 articles is equal to the selling price of 15 articles , then the gain or loss percent is ?
Options: a ) 16 , b ) 127 , c ) 12 , d ) 18 , e ) 233
Rationale: "percentage of profit = 35 / 15 * 100 = 233 % answer : e"
Answer: e
Python program:
a = 100 * 15
b = a / 50
c = 100 - b
d = 100 * 15
e = d / 50
f = c / e
g = 100 * f
Problem: if the function q is defined by the formula q = 5 e / ( 4 x ( z ^ 2 ) ) , by what factor will q be multiplied if e is quadrupled , x is doubled , and z is tripled ?
Options: a ) 1 / 9 , b ) 2 / 9 , c ) 4 / 9 , d ) 3 / 9 , e ) 2 / 27
Rationale: we just need to find the factor thats all , e - > quadrupled - > 4 e x - > doubled - > 2 x z - > tripled - > 3 z hence , z ^ 2 = 9 z ^ 2 e is in numerator , and x * z in denominator . hence , additional factor being introduced = 4 / 2 * 9 = 4 / 18 = 2 / 9 = b
Answer: b
Python program:
a = 5 + 4 
b = 2 / a
Problem: a man rows his boat 95 km downstream and 60 km upstream , taking 2 hours each time . find the speed of the stream ?
Options: a ) 76 kmph , b ) 6 kmph , c ) 9 kmph , d ) 8 kmph , e ) 4 kmph
Rationale: "speed downstream = d / t = 95 / ( 2 ) = 48 kmph speed upstream = d / t = 60 / ( 2 ) = 30 kmph the speed of the stream = ( 48 - 30 ) / 2 = 9 kmph answer : c"
Answer: c
Python program:
a = 95 / 2
b = 60 / 2
c = a - b
d = c / 2
Problem: a shopkeeper bought 600 oranges and 400 bananas . he found 15 % of oranges and 6 % of bananas were rotten . find the percentage of fruits in good condition ?
Options: a ) 92.5 % , b ) 88.6 % , c ) 85.2 % , d ) 96.8 % , e ) 78.9 %
Rationale: "total number of fruits shopkeeper bought = 600 + 400 = 1000 number of rotten oranges = 15 % of 600 = 15 / 100 × 600 = 9000 / 100 = 90 number of rotten bananas = 6 % of 400 = 24 therefore , total number of rotten fruits = 90 + 24 = 114 therefore number of fruits in good condition = 1000 - 114 = 886 therefore percentage of fruits in good condition = ( 886 / 1000 × 100 ) % = ( 88600 / 1000 ) % = 88.6 % answer : b"
Answer: b
Python program:
a = 600 + 400 
b = 15 / 100
c = 600 * b
d = 6 / 100
e = 400 * d
f = c + e 
g = a - f
h = 600 + 400 
i = g / h
j = i * 100
Problem: if a farmer sells 20 of his chickens , his stock of feed will last for 3 more days than planned , but if he buys 15 more chickens , he will run out of feed 4 days earlier than planned . if no chickens are sold or bought , the farmer will be exactly on schedule . how many chickens does the farmer have ?
Options: a ) 40 , b ) 60 , c ) 80 , d ) 90 , e ) 100
Rationale: let x = total feed required for the planned period n = number of chicken t = total time of the planned feed x = nt 1 ) x = ( n - 15 ) * ( t + 4 ) 2 ) x = ( n + 20 ) * ( t - 3 ) equating 1 & 2 ( n - 15 ) * ( t + 4 ) = ( n + 20 ) * ( t - 3 ) 7 n = 35 t n = 5 t x = n * n / 5 substituting this value in 1 n * n / 5 = ( n - 15 ) * ( n / 5 + 4 ) 5 n = 300 n = 60 b
Answer: b
Python program:
a = 2 + 3 
b = 4 * 3
c = a * b
Problem: which number can we add to 987654 to get a number exactly divisible by 456 ?
Options: a ) 18 , b ) 24 , c ) 30 , d ) 36 , e ) 42
Rationale: "987654 / 456 = 2165 with a remainder of 414 . we need to add 456 - 414 = 42 the answer is e ."
Answer: e
Python program:
a = 456 - reminder
Problem: if 25 % of a number is subtracted from a second number , the second number reduces to its 4 - sixth . what is the ratio of the first number to the second number ?
Options: a ) 5 : 3 , b ) 4 : 3 , c ) 6 : 3 , d ) 3 : 4 , e ) 5 : 4
Rationale: explanation : let the numbers be p & q q - p / 4 = 4 q / 6 = > q - 4 q / 6 = p / 4 = > 2 q / 6 = p / 4 = > p / q = 4 / 3 answer b
Answer: b
Python program:
a = 3 * 2
b = 4 / a
c = 1 - b
d = 25 / 100
e = c / d
Problem: the weight of a glass of jar is 10 % of the weight of the jar filled with coffee beans . after some of the beans have been removed , the weight of the jar and the remaining beans is 60 % of the original total weight . what fraction part of the beans remain in the jar ?
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 2 / 5 , d ) 1 / 2 , e ) 5 / 9
Rationale: "let weight of jar filled with beans = 100 g weight of jar = 10 g weight of coffee beans = 90 g weight of jar and remaining beans = 60 g weight of remaining beans = 50 g fraction remaining = 50 / 90 = 5 / 9 answer is e ."
Answer: e
Python program:
a = 60 - 10
b = 100 - 10
c = a / b
Problem: the length of a room is 5.5 m and width is 3.75 m . what is the cost of paying the floor by slabs at the rate of rs . 800 per sq . metre .
Options: a ) 16200 , b ) 16350 , c ) 16500 , d ) 16750 , e ) 16250
Rationale: "area = 5.5 × 3.75 sq . metre . cost for 1 sq . metre . = rs . 800 hence , total cost = 5.5 × 3.75 × 800 = 5.5 × 3000 = rs . 16500 answer is c ."
Answer: c
Python program:
a = 5 * 5
b = 800 * a
Problem: the sum of the even numbers between 1 and n is 105 * 106 , where n is an odd number , then n = ?
Options: a ) 187 , b ) 193 , c ) 199 , d ) 205 , e ) 211
Rationale: let n - 1 = 2 a . 2 + 4 + . . . + 2 a = 2 * ( 1 + 2 + . . . + a ) = 2 * ( a ) ( a + 1 ) / 2 = ( a ) ( a + 1 ) = 105 * 106 then a = 105 and n = 211 . the answer is e .
Answer: e
Python program:
a = 105 * 2
b = a + 1
Problem: in township k each property is taxed at 8 percent of its assessed value . if the assessed value of a property in township k is increased from $ 20,000 to $ 24,000 , by how much will the property tax increase ?
Options: a ) $ 32 , b ) $ 50 , c ) $ 320 , d ) $ 400 , e ) $ 500
Rationale: "property tax as a percentage of its assessed value = 8 % increase in assessed value of the property = 24000 - 20000 = 4,000 $ increase in property tax = ( 8 / 100 ) * 4000 = 320 $ answer c"
Answer: c
Python program:
a = 3 + 4 
b = a * 4
c = b * 1000
d = 4 + 1 
e = d * 4
f = e * 1000
g = c - f
h = g * 8
i = h / 100
Problem: if ( 20 ) ² is subtracted from the square of a number , the answer so obtained is 4321 . what is the number ?
Options: a ) 68
b ) 69
c ) 70
d ) 71
e ) 72
Rationale: x ^ 2 = 4321 + 400 = 4721 4761 = 69 * 69 x = 69 answer : b
Answer: b
Python program:
a = 2 * 10
b = a ** 2
c = 4321 + b 
d = math.sqrt(c)
Problem: how many integers between 1 and 10 ^ 17 are such that the sum of their digits is 2 ?
Options: a ) 133 , b ) 143 , c ) 153 , d ) 163 , e ) 173
Rationale: "the integers with a sum of 2 are : 2 , 20 , 200 , . . . , 2 * 10 ^ 16 and there are 17 integers in this list . also , these integers have a sum of 2 : 11 101 , 110 1001 , 1010 , 1100 etc . . . the number of integers in this list is 1 + 2 + . . . + 16 thus , the total number of integers is 1 + 2 + . . . + 16 + 17 = 17 * 18 / 2 = 153 the answer is c ."
Answer: c
Python program:
a = 2 * 100
b = 3 + 4 
c = b * 10
d = a + c 
e = d + 2 
f = 10 - e
Problem: excluding stoppages , the speed of a bus is 60 kmph and including stoppages , it is 45 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 10 min , b ) 12 min , c ) 18 min , d ) 20 min , e ) 15 min
Rationale: "due to stoppages , it covers 15 km less . time taken to cover 15 km = ( 15 / 60 x 60 ) min = 15 min answer : e"
Answer: e
Python program:
a = 60 - 45
b = a / 60
c = const_60 * b
Problem: the average monthly income of p and q is rs . 5050 . the average monthly income of q and r is rs . 6250 and the average monthly income of p and r is rs . 5200 . the monthly income of p is :
Options: a ) 4050 , b ) 3500 , c ) 4000 , d ) 4500 , e ) 5000
Rationale: let p , q and r represent their respective monthly incomes . then , we have : p + q = ( 5050 x 2 ) = 10100 . . . . ( i ) q + r = ( 6250 x 2 ) = 12500 . . . . ( ii ) p + r = ( 5200 x 2 ) = 10400 . . . . ( iii ) adding ( i ) , ( ii ) and ( iii ) , we get : 2 ( p + q + r ) = 33000 or p + q + r = 16500 . . . . ( iv ) subtracting ( ii ) from ( iv ) , we get p = 4000 . p ' s monthly income = rs . 4000 . answer : c
Answer: c
Python program:
a = 5050 + 5200 
b = a - 6250
Problem: if ( 1 / 2 ) ^ 23 ( 1 / 81 ) ^ k = 1 / 18 ^ 23 , then k =
Options: a ) 8 , b ) 12 , c ) 16 , d ) 24 , e ) 46 / 4
Rationale: "i ' m going to focus on denominator only . . ( 2 ^ 23 ) . ( ( 3 ^ 4 ) ^ k = 18 ^ 23 ( 2 ^ 23 ) . ( ( 3 ^ 4 k ) = ( 2 . 3 ^ 2 ) ^ 23 ( 2 ^ 23 ) . ( ( 3 ^ 4 k ) = ( 2 ^ 23 ) . ( 3 ^ 2 ) ^ 23 hence 4 k = 46 k = 46 / 4 answer e i hope it ' s quite clear"
Answer: e
Python program:
a = 23 * 2
b = a / 4
Problem: the average wages of a worker during a fortnight comprising 15 consecutive working days was $ 90 per day . during the first 7 days , his average wages was $ 87 per day and the average wages during the last 7 days was $ 90 per day . what was his wage on the 8 th day ?
Options: a ) $ 83 , b ) $ 90 , c ) $ 92 , d ) $ 97 , e ) $ 111
Rationale: "average daily wage of a worker for 15 consecutive working days = 90 $ during the first 7 days , the daily average daily wage = 87 $ during the last 7 days , the daily average daily wage = 90 $ wage on 8 th day = 90 * 15 - ( 87 * 7 + 90 * 7 ) = 1350 - ( 609 + 630 ) = 1350 - 1239 = 111 answer e"
Answer: e
Python program:
a = 90 * 15
b = 87 * 7
c = 90 * 7
d = b + c 
e = a - d
Problem: a vendor bought toffees at 6 for a rupee . how many for a rupee must he sell to gain 80 % ?
Options: a ) 10.8 , b ) 20.8 , c ) 28.8 , d ) 18.8 , e ) 17.8
Rationale: "c . p . of 6 toffees = re . 1 s . p . of 6 toffees = 480 % of re . 1 = rs . 24 / 5 for rs . 24 / 5 , toffees sold = 6 . for re . 1 , toffees sold = 6 x 24 / 5 = 28.8 . answer c"
Answer: c
Python program:
a = 80 / 100
b = 1 + a 
c = 6 * b
Problem: find the average of all the numbers between 11 and 34 which are divisible by 10 ?
Options: a ) 10 , b ) 20 , c ) 25 , d ) 30 , e ) 15
Rationale: "average = ( 20 + 30 ) 2 = 50 / 2 = 25 answer is c"
Answer: c
Python program:
a = 11 + 4 
b = 34 - 4
c = a + b 
d = c / 2
Problem: a certain company expects quarterly earnings of $ 0.80 per share of stock , half of which will be distributed as dividends to shareholders while the rest will be used for research and development . if earnings are greater than expected , shareholders will receive an additional $ 0.04 per share for each additional $ 0.10 of per share earnings . if quarterly earnings are $ 1.10 per share , what will be the dividend paid to a person who owns 400 shares of the company ' s stock ?
Options: a ) $ 208 , b ) $ 96 , c ) $ 104 , d ) $ 120 , e ) $ 240
Rationale: "eps actual > eps expected . each gets and additional . 12 per share . thus . 52 * 400 - - > $ 208 answer is a"
Answer: a
Python program:
a = 0 / 80
b = 1 - 10
c = b * 10
d = c * 0
e = a + d 
f = e * 400
Problem: the content of several smaller cylinders ( 3 meter diameter and 6 meter height ) were to be emptied into a larger cylinder ( 20 meter diameter and 10 meter height ) , how many smaller cylinders will fill up the larger cylinder ?
Options: a ) 20
b ) 10
c ) 50
d ) 74
e ) 73
Rationale: calculate the volume of the larger cylinder and divide it by the volume of the smaller cylinder . volume of cylinder = π r 2 h larger cylinder volume = 3141.59 smaller cylinder volume = 42.41 therefore the number of cylinders b that can be filled to capacity = 3141.59 / 42.41 = 74.1 answer is d 74 smaller cylinders can be filled to capacity .
Answer: d
Python program:
a = 20 / 2
b = volume_cylinder / (
Problem: if n is a positive integer and the product of all integers from 1 to n , inclusive , is a multiple of 840 , what is the least possible value of n ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: 840 = 2 * 2 * 2 * 3 * 5 * 7 , so n must be at least 7 . the answer is c .
Answer: c
Python program:
a = 840 / 2
b = a / 3
c = b / 4
d = 10 / 2
e = c / d
Problem: among all sales staff at listco corporation , college graduates and those without college degrees are equally represented . each sales staff member is either a level - 1 or level - 2 employee . level - 1 college graduates account for 10 % of listco ' s sales staff . listco employs 72 level - 1 employees , 30 of whom are college graduates . how many sales staff members without college degrees are level - 2 employees ?
Options: a ) 108 , b ) 42 , c ) 56 , d ) 32 , e ) 58
Rationale: "i ' m going in on this one . so let ' s say that we have the following so we know that l 1 = 72 and that c and l 1 = 0.10 x , we should set up a double set matrix btw but anyways , i ' m just explaining the point with this problem . now we are told that 0.10 x = 30 , therefore the grand total is 300 . now we know that l 2 is 300 - 72 = 228 . we also learn that c and no c are equally represented thus 150 each . therefore no c and no l 2 will be 150 - 42 = 108 . thus a is the correct answer choice"
Answer: a
Python program:
a = 10 / 100
b = 30 / a
c = b - 72
d = c / 2