euclaise/mathqa_programs huggingface dataset:
Problem: in 1950 , richard was 4 times as old as robert . in 1955 , richard was 3 times as old as robert . in which year was richard 1.3 times as old as robert ?
Options: a ) 1960 , b ) 1965 , c ) 1970 , d ) 1975 , e ) 2040
Rationale: "in 1950 : ri = 4 ro - - - - - - - - - - - - - - eq 1 in 1955 : ri + 5 = 3 ( ro + 5 ) - - - - - - - - - eq 2 thus in 1950 , solving eq 1 and eq 2 ro = 10 , ri = 40 now for each year we can calculate : 1960 : ri = 50 , ro = 20 1965 : ri = 55 , ro = 25 2040 : ri = 100 , ro = 130 thus ans : e"
Answer: e
Python program:
a = 4 + 3 
b = 1 + 3 
c = 1950 + b
Problem: the simple interest on a sum of money will be rs . 800 after 10 years . if the principal is trebled after 5 years what will be the total interest at the end of the tenth year ?
Options: a ) 8981 , b ) 3799 , c ) 1200 , d ) 1600 , e ) 1732
Rationale: "p - - - 10 - - - - 800 p - - - 5 - - - - - 400 3 p - - - 5 - - - - - 1200 - - - - - - = > 1600 answer : d"
Answer: d
Python program:
a = 800 / 10
b = a * 5
c = b * 3
d = 800 / 10
e = d * 5
f = c + e
Problem: a certain clock marks every hour by striking a number of times equal to the hour , and the time required for a stroke is exactly equal to the time interval between strokes . at 6 : 00 the time lapse between the beginning of the first stroke and the end of the last stroke is 66 seconds . at 12 : 00 , how many seconds elapse between the beginning of the first stroke and the end of the last stroke ?
Options: a ) a . 138 , b ) b . 50 , c ) c . 48 , d ) d . 46 , e ) e . 44
Rationale: "at 6 : 00 it ' ll chime 6 times . if we assume that the time taken to chime is x , then time between chimes is also x . so you have 6 chimes , which is 6 x and 5 time intervals between chimes . this means that 11 x = 66 seconds . thus x = 6 seconds . by a similar logic , at 12 : 00 , there are 12 chimes and 11 intervals so the total time is ( 12 + 11 ) x = 23 x = 138 seconds . answer a"
Answer: a
Python program:
a = 1 + 4 
b = 6 + a 
c = 66 / b
d = 1 + 4 
e = 6 + d 
f = 12 + e 
g = c * f
Problem: each week , harry is paid x dollars per hour for the first 30 hours and 1.5 x dollars for each additional hour worked that week . each week , annie is paid x dollars per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week annie worked a total of 50 hours . if harry and annie were paid the same amount last week , how many hours did harry work last week ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 60
Rationale: "annie earned 40 x + 10 ( 2 x ) = 60 x let h be the number of hours that harry worked . harry earned 30 x + 1.5 x ( h - 30 ) = 60 x ( 1.5 x ) ( h ) = 75 x h = 50 hours the answer is c ."
Answer: c
Python program:
a = 40 + 2 
b = a - 30
c = b / 1
d = c + 30
Problem: a box measuring 25 inches long by 30 inches wide by 15 inches deep is to be filled entirely with identical cubes . no space is to be left unfilled . what is the smallest number of cubes that can accomplish this objective ?
Options: a ) 80 , b ) 82 , c ) 84 , d ) 88 , e ) 90
Rationale: "least number of cubes will be required when the cubes that could fit in are biggest . 5 is the biggest number that could divide all three , 25 , 30 and 15 . thus side of cube must be 5 , and total number of cubes = 25 / 5 * 30 / 5 * 15 / 5 = 90 ans e ."
Answer: e
Python program:
a = 25 * 30
b = a * 15
c = 15 / 2
d = b / volume_cube
Problem: in lottery , there are 10 prizes and 25 blanks . a lottery is drawn at random . what is the probability of getting a prize ?
Options: a ) 1 / 7 , b ) 2 / 7 , c ) 3 / 7 , d ) 4 / 7 , e ) 1
Rationale: total number of outcomes possible , n ( s ) = 10 + 25 = 35 . total number of prize , n ( e ) = 10 p ( e ) = n ( e ) / n ( s ) = 10 / 35 = 2 / 7 answer is option b
Answer: b
Python program:
a = 10 + 25 
b = 10 / a
Problem: 0.999991 + 0.111119 = ?
Options: a ) 1 , b ) 1.0001 , c ) 1.0021 , d ) 1.11111 , e ) 1.1111
Rationale: "0.999991 + 0.111119 = 0.999991 + 0.11111 + 0.00009 = ( 0.999991 + 0.00009 ) + 0.11111 = 1 + 0.11111 = 1.11111 d"
Answer: d
Python program:
a = 0 / 999991
b = a * 100
Problem: from january 1 , 1991 , to january 1 , 1993 , the number of people enrolled in health maintenance organizations increased by 30 percent . the enrollment on january 1 , 1993 , was 45 million . how many million people , to the nearest million , were enrolled in health maintenance organizations on january 1 , 1991 ?
Options: a ) 35 , b ) 39 , c ) 40 , d ) 41 , e ) 42
Rationale: "1.30 x = 45 - - > 13 / 10 * x = 45 - - > x = 45 * 10 / 13 = 450 / 13 = ~ 35 . answer : a ."
Answer: a
Python program:
a = 100 + 30 
b = 100 / a
c = b * 45
Problem: if $ 5,000 is invested in an account that earns 10 % interest compounded semi - annually , then the interest earned after one year would be how much greater than if the $ 5,000 had been invested at 8 % simple yearly interest ?
Options: a ) $ 4 , b ) $ 8 , c ) $ 12 , d ) $ 16 , e ) $ 10
Rationale: solution amount ( ci ) = p + ( 1 + r / n ) ^ nt = 5000 + ( 1 + 0.10 / 2 ) ^ 2 = 5410 amount ( si ) = p + ptr / 100 = 5000 + ( 5000 * 1 * 10 / 100 ) = 5400 difference = 5410 - 5400 = 10 $ e
Answer: e
Python program:
a = 10 * 1
Problem: line q has the equation 5 y – 3 x = 15 . if line s is perpendicular to q , has an integer for its y - intercept , and intersects q in the second quadrant , then how many possible line s ’ s exist ? ( note : intersections on one of the axes do not count . )
Options: a ) 9 , b ) 11 , c ) 13 , d ) 15 , e ) 17
Rationale: "5 y - 3 x = 15 and so y = 3 x / 5 + 3 when x = 0 , then y = 3 . when y = 0 , then x = - 5 the slope is 3 / 5 , so the slope of line s is - 5 / 3 . through the point ( - 5 , 0 ) , 0 = - 5 ( - 5 ) / 3 + c the y - intercept is c = - 25 / 3 < - 8 . thus the perpendicular line s can have y - intercepts from - 8 up to 2 . the number of possible lines is 8 + 2 + 1 = 11 the answer is b ."
Answer: b
Python program:
a = 15 / 5
b = a - 2
c = 15 / 3
d = 15 / 5
e = c + d 
f = b + e
Problem: mr . kramer , the losing candidate in a two - candidate election , received 942,568 votes , which was exactly 35 percent of all votes cast . approximately what percent of the remaining votes would he need to have received in order to have won at least 50 percent of all the votes cast ?
Options: a ) 10 % , b ) 12 % , c ) 15 % , d ) 17 % , e ) 23 %
Rationale: "lets assume that candidate got 35 % votes and total votes is 100 . candidate won = 35 remaining = 65 to get 50 % , candidate requires 15 votes from 100 which is 15 % and 15 votes from 65 . 15 / 65 = 23.07 which is approx 23 % . hence the answer is e"
Answer: e
Python program:
a = 50 / 100
b = 35 / 100
c = a - b
d = 35 / 100
e = 1 - d
f = c / e
g = f * 100
Problem: a family pays $ 900 per year for an insurance plan that pays 80 percent of the first $ 1,000 in expenses and 100 percent of all medical expenses thereafter . in any given year , the total amount paid by the family will equal the amount paid by the plan when the family ' s medical expenses total .
Options: a ) $ 1,000 , b ) $ 1,200 , c ) $ 1,300 , d ) $ 1,800 , e ) $ 2,200
Rationale: "upfront payment for insurance plan = 900 $ family needs to pay 20 % of first 1000 $ in expense = 200 $ total amount paid by family when medical expenses are equal to or greater than 1000 $ = 900 + 200 = 1100 $ total amount paid by insurance plan for first 1000 $ = 900 $ total amount paid by family will equal amount paid by plan when medical expense = 1300 $ ( since insurance plan will pay 100 % of amount that exceeds 1100 $ ) answer c"
Answer: c
Python program:
a = 1 - 0
Problem: at 1 : 00 pm , there were 10.0 grams of bacteria . the bacteria increased to x grams at 4 : 00 pm , and 28.9 grams at 7 : 00 pm . if the amount of bacteria present increased by the same fraction during each of the 3 - hour periods , how many grams of bacteria were present at 4 : 00 pm ?
Options: a ) 16.2 , b ) 16.4 , c ) 16.6 , d ) 16.8 , e ) 17.0
Rationale: "let x be the factor by which the bacteria increases every three hours . at 4 : 00 pm , the amount of bacteria was 10 x and at 7 : 00 pm it was 10 x ^ 2 . 10 x ^ 2 = 28.9 x ^ 2 = 2.89 x = 1.7 at 4 : 00 pm , the amount of bacteria was 10 ( 1.7 ) = 17 grams . the answer is e ."
Answer: e
Python program:
a = 28 / 9
b = math.sqrt(a)
c = b * 10
Problem: rahul played weel in this season . his current batting averagge is 53 . if he score 78 runs in today match . his batting average will become 58 . how many matches had he played in this season .
Options: a ) 4 , b ) 10 , c ) 9 , d ) 6 , e ) 5
Rationale: "53 x + 78 = 58 ( x + 1 ) = > 5 x = 20 = > x = 4 answer : a"
Answer: a
Python program:
a = 78 - 58
b = 58 - 53
c = a / b
Problem: the length of a rectangle is two - fifths of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 1225 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 10 units ?
Options: a ) 140 sq . units
b ) 158 sq . units
c ) 187 sq . units
d ) 607 sq . units
e ) 815 sq . units
Rationale: given that the area of the square = 1225 sq . units = > side of square = √ 1225 = 35 units the radius of the circle = side of the square = 35 units length of the rectangle = 2 / 5 * 35 = 14 units given that breadth = 10 units area of the rectangle = lb = 14 * 10 = 140 sq . units answer : a
Answer: a
Python program:
a = math.sqrt(1225)
b = 10 / 2
c = a / b
d = 2 * c
e = 10 * d
Problem: 33 1 / 3 % of 390 ?
Options: a ) 80 , b ) 90 , c ) 110 , d ) 120 , e ) 130
Rationale: "33 1 / 3 % = 1 / 3 1 / 3 × 390 = 130 e )"
Answer: e
Python program:
a = 1 / 3
b = 33 + a 
c = b * 390
d = c / 100
Problem: sale of rs 6835 , rs . 9927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs , 6600 ?
Options: a ) 5591 , b ) 2477 , c ) 2877 , d ) 2676 , e ) 1881
Rationale: "total sale for 5 months = rs . ( 6435 + 6927 + 6855 + 7230 + 6562 ) = rs . 34009 . required sale = rs . [ ( 6600 x 6 ) - 34009 ] = rs . ( 39600 - 34009 ) = rs . 5591 answer : a"
Answer: a
Python program:
a = 6835 + 9927 
b = a + 6855 
c = b + 7230 
d = c + 6562 
e = d / 5
f = e - 6600
g = f * 5
Problem: a man ' s regular pay is $ 3 per hour up to 40 hours . overtime is twice the payment for regular time . if he was paid $ 186 , how many hours overtime did he work ?
Options: a ) 8 , b ) 5 , c ) 9 , d ) 6 , e ) 11
Rationale: at $ 3 per hour up to 40 hours , regular pay = $ 3 x 40 = $ 120 if total pay = $ 168 , overtime pay = $ 186 - $ 120 = $ 66 overtime rate ( twice regular ) = 2 x $ 3 = $ 6 per hour = > number of overtime hours = $ 66 / $ 6 = 11 ans is e
Answer: e
Python program:
a = 3 * 40
b = 186 - a
c = 3 * 2
d = b / c
Problem: 6 workers should finish a job in 8 days . after 3 days came 4 workers join them . how many days c do they need to finish the same job ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: let rate of one worker be r = > ( 6 * r ) * 8 = 1 ( rate * time = work ) = > r = 1 / 48 = > work remaining after 3 days 1 - ( 3 * 6 ) / 48 = 30 / 48 after 4 ppl joined in ( ( 6 + 4 ) * time ) / 48 = 30 / 48 time c = 3 days to finish the task imo a
Answer: a
Python program:
a = 6 * 8
b = 3 * 6
c = a - b
d = 6 + 4 
e = c / d
Problem: a man can row 9 kmph in still water . when the river is running at 1.2 kmph , it takes him 1 hour to row to a place and black . what is the total distance traveled by the man ?
Options: a ) 5.98 , b ) 9.98 , c ) 9.06 , d ) 9.87 , e ) 9.82
Rationale: "m = 9 s = 1.2 ds = 7.2 us = 10.8 x / 10.8 + x / 7.8 = 1 x = 4.53 d = 4.53 * 2 = 9.06 answer : c"
Answer: c
Python program:
a = 9 + 1 
b = 9 - 1
c = a * b
d = 9 + 1 
e = 9 - 1
f = d + e 
g = c / f
h = g * 2
Problem: jacob is 12 years old . he is 4 times as old as his brother . how old will jacob be when he is twice as old ?
Options: a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 18
Rationale: "j = 12 ; j = 4 b ; b = 12 / 4 = 3 ; twice as old so b = 3 ( now ) + ( 3 ) = 6 ; jacob is 12 + 6 = 18 answer : e"
Answer: e
Python program:
a = 12 * 4
Problem: a type q machine can complete a job in 5 hours and a type b machine can complete the job in 7 hours . how many hours will it take 2 type q machines and 3 type b machines working together and independently to complete the job ?
Options: a ) 1 / 5 , b ) 29 / 35 , c ) 5 / 6 , d ) 35 / 29 , e ) 35 / 12
Rationale: now d should be the answer . q need 5 hours to complete and b needs 7 hours to compete so 2 q + 3 b will complete 2 / 5 + 3 / 7 or 29 / 35 portion of the job in 1 hour so the whole job will take 35 / 29 hours . . . . = d
Answer: d
Python program:
a = 1 / 5
b = 2 * a
c = 3 * b
Problem: a fellow borrowed a certain sum of money at 3 % per annum at simple interest and in 3 years the interest amounted to rs . 1820 less than the sum lent . what was the sum lent ?
Options: a ) 1050 , b ) 1220 , c ) 1250 , d ) 2000 , e ) 1110
Rationale: "p - 1820 = ( p * 3 * 3 ) / 100 p = 2000 answer : d"
Answer: d
Python program:
a = 3 * 3
b = a / 100
c = 1 - b
d = 1820 / c
Problem: a sum amounts to rs . 3969 in 2 years at the rate of 5 % p . a . if interest was compounded yearly then what was the principal ?
Options: a ) s . 3600 , b ) s . 5000 , c ) s . 4500 , d ) s . 4800 , e ) s . 5800
Rationale: "ci = 3969 , r = 5 , n = 2 ci = p [ 1 + r / 100 ] ^ 2 = p [ 1 + 5 / 100 ] ^ 2 3969 = p [ 21 / 20 ] ^ 2 3969 [ 20 / 21 ] ^ 2 3600 answer : a"
Answer: a
Python program:
a = 5 / 100
b = a + 1 
c = b ** 2
d = 3969 / c
Problem: a polling company surveyed a certain country , and it found that 35 % of that country ’ s registered voters had an unfavorable impression of both of that state ’ s major political parties and that 20 % had a favorable impression only of party r . if one registered voter has a favorable impression of both parties for every two registered voters who have a favorable impression only of party b , then what percentage of the country ’ s registered voters have a favorable impression of both parties ( assuming that respondents to the poll were given a choice between favorable and unfavorable impressions only ) ?
Options: a ) 15 , b ) 20 , c ) 30 , d ) 35 , e ) 45
Rationale: "s = 100 not ( r and b ) = 35 only r = 20 ( r and b ) / b = 1 / 2 let ( r and b ) = x only b = 2 x so now , 20 + 35 + x + 2 x = 100 x = 15 a ans"
Answer: a
Python program:
a = 35 + 20 
b = 100 - a
c = b / 3
Problem: how many pieces of 85 cm length can be cut from a rod of 38.25 meters long ?
Options: a ) 25 , b ) 35 , c ) 45 , d ) 55 , e ) 65
Rationale: "number of pieces = 3825 / 85 = 45 the answer is c ."
Answer: c
Python program:
a = 38 * 25
b = a / 85
Problem: gretzky street begins at orr street and runs directly east for 5.6 kilometers until it ends when it meets howe street . gretzky street is intersected every 350 meters by a perpendicular street , and each of those streets other than orr street and howe street is given a number beginning at 1 st street ( one block east of orr street ) and continuing consecutively ( 2 nd street , 3 rd street , etc . . . ) until the highest - numbered street one block west of howe street . what is the highest - numbered street that intersects gretzky street ?
Options: a ) 12 th , b ) 13 th , c ) 14 th , d ) 15 th , e ) 16 th
Rationale: 5.6 km / 350 m = 16 . however , the street at the 5.6 - km mark is not 16 th street ; it is howe street . therefore , the highest numbered street is 15 th street . the answer is d .
Answer: d
Python program:
a = 5 * 6
b = a / 350
c = b - 1
Problem: the average weight of 19 students is 15 kg . by the admission of a new student the average weight is reduced to 14.9 kg . the weight of the new student is ?
Options: a ) 10.6 kg , b ) 10.8 kg , c ) 11 kg , d ) 13 kg , e ) none
Rationale: "answer weight of new student = total weight of all 20 students - total weight of initial 19 students = ( 20 x 14.9 - 19 x 15 ) kg = 13 kg . correct option : d"
Answer: d
Python program:
a = 19 + 1 
b = a * 14
c = 19 * 15
d = b - c
Problem: the difference between a two - digit number and the number obtained by interchanging the digits is 36 . what is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ?
Options: a ) 4 , b ) 8 , c ) 16 , d ) 12 , e ) 14
Rationale: "since the number is greater than the number obtained on reversing the digits , so the ten ' s digit is greater than the unit ' s digit . let ten ' s and unit ' s digits be 2 x and x respectively . then , ( 10 x 2 x + x ) - ( 10 x + 2 x ) = 36 9 x = 36 x = 4 . required difference = ( 2 x + x ) - ( 2 x - x ) = 2 x = 8 . answer : b"
Answer: b
Python program:
a = 2 * 10
b = a + 1 
c = b - 10
d = c - 2
e = 36 / d
f = 2 * 10
g = f + 1 
h = g - 10
i = h - 2
j = 36 / i
k = j * 2
l = e + k 
m = 2 * 10
n = m + 1 
o = n - 10
p = o - 2
q = 36 / p
r = q * 2
s = 2 * 10
t = s + 1 
u = t - 10
v = u - 2
w = 36 / v
x = r - w
y = l - x
Problem: excluding stoppages , the average speed of a bus is 80 km / hr and including stoppages , the average speed of the bus is 40 km / hr . for how many minutes does the bus stop per hour ?
Options: a ) 15 min , b ) 18 min , c ) 16 min , d ) 20 min , e ) 30 min
Rationale: "in 1 hr , the bus covers 80 km without stoppages and 40 km with stoppages . stoppage time = time take to travel ( 80 - 40 ) km i . e 40 km at 80 km / hr . stoppage time = 40 / 80 hrs = 30 min answer : e"
Answer: e
Python program:
a = 1 * const_60
b = 40 / 80
c = b * const_60
d = a - c
Problem: what is the smallest integer n for which 25 ^ n > 5 ^ 12 ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "to solve , we want to get the bases the same . thus we need to break 25 ^ n into prime factors . 25 ^ n = ( 5 ^ 2 ) ^ n = 5 ^ ( 2 n ) ( remember that when we have a power to a power , we multiply the exponents . ) we can use the new value in the given inequality : 5 ^ ( 2 n ) > 5 ^ 12 since we have the same bases on either side of the inequality we can drop the bases and set up an equation involving just the exponents . 2 n > 12 n > 6 because n is greater than 6 , the smallest integer that satisfies the inequality 25 ^ n > 5 ^ 12 is 7 . the answer is b ."
Answer: b
Python program:
a = 12 / 3
b = math.floor(a)
c = b + 1
Problem: a bottle contains a certain solution . in the bottled solution , the ratio of water to soap is 3 : 4 , and the ratio of soap to salt is five times this ratio . the solution is poured into an open container , and after some time , the ratio of water to soap in the open container is quartered by water evaporation . at that time , what is the ratio of water to salt in the solution ?
Options: a ) 26 : 64 , b ) 64 : 9 , c ) 9 : 64 , d ) 9 : 60 , e ) 20 : 64
Rationale: "water : soap = 3 : 4 soap : salt = 15 : 20 = > for 15 soap , salt = 20 = > for 4 soap , salt = ( 20 / 15 ) * 4 = 80 / 15 = 16 / 3 so , water : soap : salt = 3 : 4 : 16 / 3 = 9 : 12 : 16 after open container , water : soap : salt = 2.25 : 12 : 16 so , water : salt = 2.25 : 16 = 9 : 64 answer : c"
Answer: c
Python program:
a = 4 * 3
b = a * 3
c = 4 * 4
d = c * 4
e = b / d
Problem: by selling an article for $ 110 , a person gains $ 10 . what is the gain % ?
Options: a ) 25 % , b ) 30 % , c ) 50 % , d ) 20 % , e ) 10 %
Rationale: "s . p . = $ 110 gain = $ 10 c . p . = 110 - 10 = 100 gain % = 10 / 100 * 100 % = 10 % answer is e"
Answer: e
Python program:
a = 10 * 100
b = 110 - 10
c = a / b
Problem: tough and tricky questions : functions . let a be a positive integer . let n # a equal n ^ ( 2 a ) if a is odd and n ^ ( 3 a ) if a is even . then ( 4 # 3 ) + ( 3 # 4 ) – ( 3 # 3 ) is equal to
Options: a ) 64 , b ) 82 , c ) 128 , d ) 512 , e ) 4096
Rationale: answer : 4 ^ 6 + 3 ^ 6 - 3 ^ 6 = 4 ^ 6 = 4096 ans e
Answer: e
Python program:
a = 2 * 3
b = 4 ** a
Problem: find the smallest number of 6 digits which is exactly divisible by 111 .
Options: a ) 100011 , b ) 111111 , c ) 101111 , d ) 201111 , e ) 211111
Rationale: smallest number of 6 digits is 100000 . on dividing 100000 by 111 , we get 100 as remainder . number to be added = ( 111 - 100 ) - 11 . hence , required number = 100011 option a
Answer: a
Python program:
a = 100 * 100
b = 10 * a
c = b - 100
d = c + 111
Problem: a company recently conducted a survey and found that 35,000 of its customers live in rural areas . if the number of customers who live in urban areas is 140 percent greater than the number of customers who live in rural areas , how many customers live in urban areas ?
Options: a ) 78,000 , b ) 80,000 , c ) 82,000 , d ) 84,000 , e ) 86,000
Rationale: "the number of customers in urban areas is 35,000 + 1.4 * 35,000 = 84,000 . the answer is d ."
Answer: d
Python program:
a = 4 * 2
b = 100 - a
Problem: in plutarch enterprises , 60 % of the employees are marketers , 20 % are engineers , and the rest are managers . marketers make an average salary of $ 50,000 a year , and engineers make an average of $ 80,000 . what is the average salary for managers if the average for all employees is also $ 80,000 ?
Options: a ) $ 80,000 , b ) $ 130,000 , c ) $ 240,000 , d ) $ 290,000 , e ) $ 340,000
Rationale: "for sake of ease , let ' s say there are 10 employees : 6 marketers , 2 engineers , and 2 manager . average company salary * number of employees = total company salary > > > $ 80,000 * 10 = $ 800,000 subtract the combined salaries for the marketers ( 6 * $ 50,000 ) and the engineers ( 2 * $ 80,000 ) > > > $ 800,000 - $ 300,000 - $ 160,000 = $ 340,000 . the correct answer is e ."
Answer: e
Python program:
a = 60 + 20 
b = a * 1000
c = b * 100
d = 60 + 20 
e = d * 1000
f = 20 * e
g = c - f
h = 20 / 2
i = h * 20
j = i * 1000
k = j * 60
l = g - k
m = l / 20
Problem: two stations a and b are 20 km apart on a straight line . one train starts from a at 7 a . m . and travels towards b at 20 kmph . another train starts from b at 8 a . m . and travels towards a at a speed of 25 kmph . at what time will they meet ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 8
Rationale: "suppose they meet x hours after 7 a . m . distance covered by a in x hours = 20 x km . distance covered by b in ( x - 1 ) hours = 25 ( x - 1 ) km . therefore 20 x + 25 ( x - 1 ) = 20 45 x = 45 x = 1 . so , they meet at 8 a . m . answer : option e"
Answer: e
Python program:
a = 20 - 20
b = 25 + 20 
c = a / b
d = 8 + c
Problem: a bag contains 6 red , 3 yellow and 4 green balls . 3 balls are drawn randomly . what is the probability that the balls drawn contain balls of different colours ?
Options: a ) 2 / 7 , b ) 3 / 5 , c ) 3 / 11 , d ) 1 / 4 , e ) 7 / 16
Rationale: "total number of balls = 6 + 3 + 4 = 13 n ( s ) = 13 c 3 = 286 n ( e ) = 6 c 1 * 3 c 1 * 4 c 1 = 72 probability = 72 / 286 = 1 / 4 answer is d"
Answer: d
Python program:
a = math.comb(4, 2)
b = 6 + 3 
c = math.comb(b, 1)
d = a * c
e = 6 + 3 
f = e + 4 
g = math.comb(f, 6)
h = d / g
Problem: a crate measures 2 feet by 8 feet by 12 feet on the inside . a stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides . what is the radius , in feet , of the pillar with the largest volume that could still fit in the crate ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 12
Rationale: "we can find the radius of all the three cases of cylinders . the only crux to find the answer faster is that : voulme is pi * r ^ 2 * h . the volume is a function of r ^ 2 . so r has to be the highest to find the largest volume . so r = 2 for the surface 8 * 12 face . volume = 8 pi answer a"
Answer: a
Python program:
a = 8 * 12
b = a * 2
c = b / 12
d = c / 8
Problem: if 0.3 of a number is equal to 0.06 of another number , the ratio of the numbers i
Options: a ) 3 : 15 , b ) 1 : 2 , c ) 3 : 20 , d ) 20 : 3 , e ) none
Rationale: "sol . 0.3 a = 0.06 b â ‡ ” a / b = 0.06 / 0.30 = 6 / 30 = 3 / 15 . â ˆ ´ a : b = 3 : 15 . answer a"
Answer: a
Python program:
a = 0 * 6
b = 0 * 3
c = a / b
Problem: if the average ( arithmetic mean ) of x , x + 2 , and x + 4 is 93 , what is the value of x ?
Options: a ) 95 , b ) 91 , c ) 102 , d ) 101 , e ) 85
Rationale: "am of x , x + 2 , and x + 4 = x + ( x + 2 ) + ( x + 4 ) / 3 = 3 x + 6 / 3 = x + 2 given that x + 2 = 93 x = 91 answer : b"
Answer: b
Python program:
a = 4 * 2
b = 2 * 2
c = a - b