euclaise/mathqa_programs huggingface dataset:
Problem: if x and y are integers , what is the least positive number of 24 x + 16 y ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: "24 x + 16 y = 8 ( 3 x + 2 y ) which will be a minimum positive number when 3 x + 2 y = 1 . 3 ( 1 ) + 2 ( - 1 ) = 1 then 8 ( 3 x + 2 y ) can have a minimum positive value of 8 . the answer is e ."
Answer: e
Python program:
a = 24 - 16
Problem: a certain company retirement plan has arule of 70 provision that allows an employee to retire when the employee ' s age plus years of employment with the company total at least 70 . in what year could a female employee hired in 1987 on her 32 nd birthday first be eligible to retire under this provision ?
Options: a ) 2003 , b ) 2004 , c ) 2005 , d ) 2006 , e ) 2007
Rationale: "she must gain at least 70 points , now she has 32 and every year gives her two more points : one for age and one for additional year of employment , so 32 + 2 * ( # of years ) = 70 - - > ( # of years ) = 19 - - > 1987 + 19 = 2006 . answer : d ."
Answer: d
Python program:
a = 70 - 32
b = a / 2
c = 1987 + b
Problem: a cistern is filled by a tap in 3 1 / 2 hours . due to leak in the bottom of the cistern , it takes half an hour longer to fill the cistern . if the cistern is full how long will it take the leak to empty it ?
Options: a ) 11 , b ) 12 , c ) 29 , d ) 28 , e ) 29
Rationale: 2 / 7 - 1 / x = 1 / 4 x = 28 answer : d
Answer: d
Python program:
a = 1 / 2
b = 3 + a 
c = 1 / b
d = 1 / 4
e = c - d
f = 1 / e
Problem: in the coordinate plane , points ( x , 1 ) and ( 10 , y ) are on line k . if line k passes through the origin and has slope 1 / 3 , then x + y =
Options: a ) 4.5 , b ) 7 , c ) 8 , d ) 19 / 3 , e ) 12
Rationale: "line k passes through the origin and has slope 1 / 3 means that its equation is y = 1 / 3 * x . thus : ( x , 1 ) = ( 3 , 1 ) and ( 10 , y ) = ( 10,10 / 3 ) - - > x + y = 3 + 10 / 3 = 19 / 3 . answer : d ."
Answer: d
Python program:
a = 10 * 3
b = 1 / 3
c = a * b
Problem: a 40 gallon solution of salt and water is 10 % salt . how many gallons of water must be added to the solution in order to decrease the salt to 8 % of the volume ?
Options: a ) 810 , b ) 12 , c ) 13 , d ) 14 , e ) 16
Rationale: "amount of salt = 4.0 assume x gallons of water are added . 4.0 / 40 + x = 8 / 100 400 = 8 x + 320 8 x = 80 x = 10 correct option : a"
Answer: a
Python program:
a = 10 - 8
b = 40 * a
c = b / 8
Problem: if 10 boys meet at a reunion and each boy shakes hands exactly once with each of the others , then what is the total number of handshakes
Options: a ) 41 , b ) 42 , c ) 43 , d ) 44 , e ) 45
Rationale: n ( n - 1 ) / 2 = 10 * 9 / 2 = 45 answer : e
Answer: e
Python program:
a = math.factorial(10)
b = 10 - 2
c = math.factorial(b)
d = math.factorial(2)
e = c * d
f = a / e
Problem: 6 x – 5 y + 3 z = 22 4 x + 8 y – 11 z = 7 5 x – 6 y + 2 z = 12 given the equations above , x + y + z = ?
Options: a ) 10 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: ( 6 x – 5 y + 3 z ) - ( 5 x – 6 y + 2 z ) = 22 - 12 or , x + y + z = 10 option a is the ans
Answer: a
Python program:
a = 5 * 2
Problem: the output of a factory is increased by 10 % to keep up with rising demand . to handle the holiday rush , this new output is increased by 60 % . by approximately what percent would the output of the factory now have to be decreased in order to restore the original output ?
Options: a ) 20 % , b ) 24 % , c ) 30 % , d ) 43 % , e ) 79 %
Rationale: "take it as original output = 100 . to meet demand increase by 10 % , then output = 110 . to meet holiday demand , new output increase by 60 % then output equals 176 to restore new holidy demand output to original 100 . final - initial / final * 100 = 76 / 176 * 100 = 8 / 33 * 100 = 43 % approxiamately . option d is correct ."
Answer: d
Python program:
a = 100 + 10 
b = a / 100
c = 100 + 60 
d = c / 100
e = b * d
f = e - 1
g = 100 + 10 
h = g / 100
i = 100 + 60 
j = i / 100
k = h * j
l = f / k
m = l * 100
Problem: car x began traveling at an average speed of 35 miles per hour . after 72 minutes , car y began traveling at an average speed of 38 miles per hour . when both cars had traveled the same distance , both cars stopped . how many miles did car x travel from the time car y began traveling until both cars stopped ?
Options: a ) 405 , b ) 420 , c ) 440 , d ) 447 , e ) 490
Rationale: "car y began travelling after 72 minutes or 1.2 hours . let t be the time for which car y travelled before it stopped . both cars stop when they have travelled the same distance . so , 35 ( t + 1.2 ) = 38 t t = 14 distance traveled by car x from the time car y began traveling until both cars stopped is 35 x 14 = 490 miles answer : - e"
Answer: e
Python program:
a = 72 / const_60
b = a * 35
c = 38 - 35
d = b / c
e = 35 * d
Problem: a certain car ' s price decreased by 2.5 % ( from the original price ) each year from 1996 to 2002 , during that time the owner of the car invested in a new carburetor and a new audio system for the car , which increased car ' s price by $ 2,500 . if the price of the car in 1996 was $ 22,000 , what is the car ' s price in 2002 ?
Options: a ) $ 18,400 , b ) $ 19,500 , c ) $ 20,200 , d ) $ 20,400 , e ) $ 21,200
Rationale: "price in 96 = 22000 price decrease each year = 2.5 / 100 * 22000 = 550 price in 97 = 22000 - 550 price in 98 = 22000 - 2 * 550 price in 99 = 22000 - 3 * 550 price in 00 = 22000 - 4 * 550 price in 01 = 22000 - 5 * 550 price in 02 = 22000 - 6 * 550 = 18700 investment in the car = 2500 net price of the car in 02 = 18700 + 2500 = $ 21200 correct option : e"
Answer: e
Python program:
a = 2 * 10
Problem: jerry travels 8 miles at an average speed of 40 miles per hour , stops for 15 minutes , and then travels another 20 miles at an average speed of 60 miles per hour . what is jerry ’ s average speed , in miles per hour , for this trip ?
Options: a ) 35 , b ) 42.5 , c ) 44 , d ) 50 , e ) 52.5
Rationale: total time taken by jerry = ( 8 / 40 ) * 60 minutes + 15 minutes + ( 20 / 60 ) * 60 minutes = 47 minutes average speed = total distance / total time = ( 8 + 20 ) miles / ( 47 / 60 ) hours = 28 * 60 / 47 = 35 miles per hour answer : option a
Answer: a
Python program:
a = 8 + 20 
b = 8 / 40
c = 15 / const_60
d = b + c 
e = 20 / 60
f = d + e 
g = a / f
Problem: john makes $ 40 a week from his job . he earns a raise and now makes $ 60 a week . what is the % increase ?
Options: a ) 16 % , b ) 16.66 % , c ) 18 % , d ) 21 % , e ) 50 %
Rationale: "increase = ( 20 / 40 ) * 100 = 50 % . e"
Answer: e
Python program:
a = 60 - 40
b = a / 40
c = b * 100
Problem: - 69 * 39 + 450 = ?
Options: a ) 2736 , b ) 2309 , c ) - 2801 , d ) - 2241 , e ) none of these
Rationale: "= > - 69 * ( 40 - 1 ) + 450 ; = > - ( 69 * 40 ) + 69 + 450 ; = > - 2760 + 519 = - 2241 . correct option : d"
Answer: d
Python program:
a = negate * (
b = a + 39
Problem: when n is divided by 24 , the remainder is 4 . what is the remainder when 3 n is divided by 8 ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "let n = 4 ( leaves a remainder of 4 when divided by 24 ) 3 n = 3 ( 4 ) = 12 , which leaves a remainder of 4 when divided by 8 . answer b"
Answer: b
Python program:
a = 4 - reminder
Problem: two pipes a and b can separately fill a cistern in 45 minutes and 60 minutes respectively . there is a third pipe in the bottom of the cistern to empty it . if all the three pipes are simultaneously opened , then the cistern is full in 40 minutes . in how much time , the third pipe alone can empty the cistern ?
Options: a ) 90 min , b ) 100 min , c ) 72 min , d ) 75 min , e ) 130 min
Rationale: "1 / 40 - ( 1 / 45 + 1 / 60 ) = - 1 / 72 third pipe can empty in 72 minutes answer : c"
Answer: c
Python program:
a = 1/(45)
b = 1/(60)
c = a + b 
d = 1/(40)
e = c - d
f = 1/(e)
Problem: a car takes 6 hours to cover a distance of 450 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 60 , b ) 50 , c ) 40 , d ) 70 , e ) 65
Rationale: "time = 6 distance = 450 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 450 / 9 = 50 kmph answer b ."
Answer: b
Python program:
a = 6 * 3
b = a / 2
c = 450 / b
Problem: a letter lock consists of 3 rings each marked with 6 different letters . the number of distinct unsuccessful attempts to open the lock is at the most - .
Options: a ) 216 , b ) 243 , c ) 215 , d ) 729 , e ) 728
Rationale: since each ring consists of six different letters , the total number of attempts possible with the three rings is = 6 * 6 * 6 = 216 . of these attempts , one of them is a successful attempt . maximum number of unsuccessful attempts = 216 - 1 = 215 . answer : c
Answer: c
Python program:
a = 6 * 6
b = a * 6
c = b - 1
Problem: average of money that group of 4 friends pay for rent each month is $ 800 . after one persons rent is increased by 16 % the new mean is $ 850 . what was original rent of friend whose rent is increased ?
Options: a ) 800 , b ) 900 , c ) 1000 , d ) 1100 , e ) 1250
Rationale: "0.16 x = 4 ( 850 - 800 ) 0.16 x = 200 x = 1250 answer e"
Answer: e
Python program:
a = 850 - 800
b = a * 4
c = 16 / 100
d = b / c
Problem: a person started from point a to point b and returned back to a with a speed of 60 kmh . if the distance between a and b is 120 km , calculate the time he travelled
Options: a ) 4 hours , b ) 2 hours , c ) 3 hours , d ) 6 hours , e ) 5 hours
Rationale: time = distance / speed total distance = ( from a - > b and from b - > a ) = 120 + 120 = 240 km speed = 60 kmh 240 / 60 = 4 answer : a
Answer: a
Python program:
a = 120 * 2
b = a / 60
Problem: a meeting has to be conducted with 5 managers . find the number of ways in which the managers may be selected from among 7 managers , if there are 2 managers who refuse to attend the meeting together .
Options: a ) 6 , b ) 8 , c ) 10 , d ) 11 , e ) 15
Rationale: "the total number of ways to choose 5 managers is 7 c 5 = 21 we need to subtract the number of groups which include the two managers , which is 5 c 3 = 10 . 21 - 10 = 11 the answer is d ."
Answer: d
Python program:
a = math.comb(7, 5)
b = 7 - 2
c = math.comb(b, 2)
d = a - c
Problem: ravi and sunil are partners in a business . ravi invests rs . 15,000 for 8 months and sunil invested rs . 8000 for 10 months then after one year ratio of their profits will be
Options: a ) 1 : 3 , b ) 2 : 3 , c ) 3 : 2 , d ) 3 : 1 , e ) 3 : 4
Rationale: "= ( 15000 * 8 ) : ( 8000 * 10 ) = 120000 : 80000 = 3 : 2 answer : c"
Answer: c
Python program:
a = 4 * 3
b = 10 * 2
c = a * b
d = c * 100
e = d * 4
f = 8000 * 10
g = e / f
Problem: on a saturday night , each of the rooms at a certain motel was rented for either $ 50 or $ 60 . if 10 of the rooms that were rented for $ 60 had instead been rented for $ 50 , then the total rent the motel charged for that night would have been reduced by 25 percent . what was the total rent the motel actually charged for that night ?
Options: a ) $ 400 , b ) $ 800 , c ) $ 1,000 , d ) $ 1,600 , e ) $ 2,400
Rationale: let total rent the motel charge for all rooms = x if 10 rooms that were rented for 60 $ had instead been rented for 50 $ , then total difference in prices = 10 $ * 10 = 100 $ total rent the motel charged would have been reduced by 25 % . 25 x = 100 = > x = 400 answer a
Answer: a
Python program:
a = 60 - 50
b = 10 * a
c = 25 / 100
d = b / c
Problem: if price of t . v set is reduced by 10 % , then its sale increases by 85 % , find net effect on sale value
Options: a ) 44 , b ) 45 , c ) 46 , d ) 67 , e ) 48
Rationale: - a + b + ( ( - a ) ( b ) / 100 ) = - 10 + 85 + ( - 10 * 85 ) / 100 = - 10 + 85 - 8.5 = 67 answer : d
Answer: d
Python program:
a = 100 - 10
b = a / 100
c = 100 + 85 
d = c / 100
e = b * d
f = e - 1
g = f * 100
Problem: a retailer buys a radio for rs 225 . his overhead expenses are rs 20 . he sellis the radio for rs 300 . the profit percent of the retailer is
Options: a ) 22.4 % , b ) 50 % , c ) 25 % , d ) 52 % , e ) none of these
Rationale: "explanation : cost price = ( 225 + 20 ) = 245 sell price = 300 gain = ( 55 / 245 ) * 100 = 22.4 % . answer : a"
Answer: a
Python program:
a = 225 + 20 
b = 300 / a
c = b * 100
d = c - 100
Problem: which number should replace both the asterisks in ( * / 18 ) x ( * / 162 ) = 1 ?
Options: a ) 27 , b ) 36 , c ) 54 , d ) 72 , e ) 90
Rationale: let ( y / 18 ) x ( y / 162 ) = 1 y ^ 2 = 18 x 162 = 18 x 18 x 9 y = ( 18 x 3 ) = 54 the answer is c .
Answer: c
Python program:
a = 162 * 18
b = math.sqrt(a)
Problem: anne bought doughnuts for a class breakfast party . she bought 5 chocolate doughnuts , 6 coconut doughnuts , and 11 jam - filled doughnuts . how many doughnuts did anne buy in all ?
Options: a ) 22 , b ) 36 , c ) 39 , d ) 21 , e ) 11
Rationale: "add the numbers of doughnuts . 5 + 6 + 11 = 22 . answer is a ."
Answer: a
Python program:
a = 5 + 6 
b = a + 11
Problem: a certain music store stocks 800 cellos and 600 violas . of these instruments , there are 120 cello - viola pairs , such that a cello and a viola were both made with wood from the same tree ( each tree can make at most one viola and one cello , so there are no pairs other than these 90 ) . if one viola and one cello are chosen at random , what is the probability that the two instruments are made with wood from the same tree ?
Options: a ) 3 / 16,000 , b ) 1 / 8,000 , c ) 3 / 1,600 , d ) 1 / 90 , e ) 2 / 45
Rationale: "solution provided by stanford 2012 is correct : 120 / 800 choosing one of the cellos which has a pair viola , 1 / 600 choosing the viola which is the pair of chosen cello - - > p = 120 / 800 * 1 / 600 = 1 / 8,000 . answer : b ."
Answer: b
Python program:
a = 120 / 800
b = 1 / 600
c = a * b
Problem: a man is walking at the rate of 10 km / hr crosses a bridge in 15 minutes . the length of the bridge is
Options: a ) 1000 meters , b ) 1050 meters , c ) 1200 meters , d ) 1250 meters , e ) 2500 meters
Rationale: "explanation : we need to get the answer in meters . so we will first of change distance from km / hour to meter / sec by multiplying it with 5 / 18 and also change 15 minutes to seconds by multiplying it with 60 . speed = 10 â ˆ — 5 / 18 = 25 / 9 m / sec time = 15 â ˆ — 60 seconds = 900 seconds distance = time â ˆ — speed / distance = 25 / 9 â ˆ — 900 = 2500 meter option e"
Answer: e
Python program:
a = 15 / const_60
b = 10 * a
c = b * 1000
Problem: 826924 × 9999 = ?
Options: a ) 8248402936 , b ) 8268413076 , c ) 8268413071 , d ) 8064329671 , e ) 8244563371
Rationale: "b 8268413076 826924 × 9999 = 826924 × ( 10000 - 1 ) = 826924 × 10000 - 826924 × 1 = 8269240000 - 826924 = 8268413076"
Answer: b
Python program:
a = 826924 / 9999
b = a * 100
Problem: the megatek corporation is displaying its distribution of employees by department in a circle graph . the size of each sector of the graph representing a department is proportional to the percentage of total employees in that department . if the section of the circle graph representing the manufacturing department takes up 144 ° of the circle , what percentage of megatek employees are in manufacturing ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 40 % , e ) 72 %
Rationale: answer : d 144 ° divided by 360 ° equals 0.4 , therefore the sector is equal to 40 % of the total
Answer: d
Python program:
a = 3600 / 10
b = 144 / a
c = b * 100
Problem: a train speeds past a pole in 15 seconds and a platfrom 100 m long in 25 seconds . its length is :
Options: a ) 100 m , b ) 125 m , c ) 130 m , d ) 150 m , e ) none
Rationale: "sol . let the length of the train be x metres and its speed be y m / sec . they , x / y = 15 ⇒ y = x / 15 ∴ x + 100 / 25 = x / 15 ⇔ x = 150 m . answer d"
Answer: d
Python program:
a = 2 - 1
b = 100 * a
Problem: gopi gives rs . 90 plus one turban as salary to his servant for one year . the servant leaves after 9 months and receives rs . 55 and the turban . find the price of the turban .
Options: a ) 27 , b ) 36 , c ) 29 , d ) 50 , e ) 11
Rationale: let the price of turban be x . thus , for one year the salary = ( 90 + x ) for 9 months he should earn 3434 ( 90 + x ) . now he gets one turban and rs . 55 . thus , 3434 ( 90 + x ) = 55 + x or 270 + 3 x = 220 + 4 x or x = 50 answer : d
Answer: d
Python program:
a = 90 - 55
b = 12 - 9
c = a / b
d = c * 12
e = d - 90
Problem: in a ratio which is equal to 2 : 4 , if the antecedent is 50 , then the consequent is ?
Options: a ) 72 , b ) 85 , c ) 100 , d ) 51 , e ) 80
Rationale: "we have 2 / 4 = 50 / x 2 x = 50 * 4 x = 100 consequent = 100 answer is c"
Answer: c
Python program:
a = 50 / 2
b = 50 + a
Problem: before leaving home for the town of madison , pete checks a map which shows that madison is 5 inches from his current location , gardensquare . pete arrives in madison 1.5 hours later and drove at an average speed of 60 miles per hour . at what scale , in inches per mile , is the map drawn ?
Options: a ) 1 / 3 , b ) 1 / 18 , c ) 1 / 10 , d ) 2 , e ) 30
Rationale: "pete covered 1.5 * 60 = 90 miles which correspond to 5 inches on the map - - > scale in inches per mile is 5 / 90 = 1 / 18 . answer : b ."
Answer: b
Python program:
a = 1 / 5
b = a * 60
c = 1 / b
Problem: the average of 50 numbers is 38 . if two numbers 45 and 55 are discarded , the average of the remaining set of numbers is
Options: a ) 38.5 , b ) 37.5 , c ) 37.0 , d ) 36.5 , e ) none of these
Rationale: average of the remaining set of numbers [ 50 x 38 - ( 45 + 55 ) ] / ( 50 - 2 ) = ( 1900 - 100 ) / 48 = 37.5 answer : b
Answer: b
Python program:
a = 50 * 38
b = a - 45
c = b - 55
d = 50 - 2
e = c / d
Problem: i bought two books ; for rs . 420 . i sold one at a loss of 15 % and other at a gain of 19 % and then i found each book was sold at the same price . find the cost of the book sold at a loss ?
Options: a ) 197 , b ) 245 , c ) 189 , d ) 278 , e ) 268
Rationale: "x * ( 85 / 100 ) = ( 420 - x ) 119 / 100 x = 245 answer : b"
Answer: b
Python program:
a = 100 + 19 
b = 420 * a
c = 100 - 15
d = 100 + 19 
e = c + d 
f = b / e
Problem: the ratio of the ages of mini and minakshi is 4 : 3 . the sum of their ages is 28 years . the ratio of their ages after 6 years will be
Options: a ) 2 : 3 , b ) 7 : 11 , c ) 5 : 4 , d ) 4 : 5 , e ) 11 : 9
Rationale: "let mini ’ s age = 4 x and minakshi ’ s age = 3 x then 4 x + 3 x = 28 x = 4 mini ’ s age = 16 years and minakshi ’ s age = 12 years ratio of their ages after 8 years = ( 16 + 6 ) : ( 12 + 6 ) = 22 : 18 = 11 : 9 answer : e"
Answer: e
Python program:
a = 4 + 3 
b = 28 / a
c = 4 * b
d = c + 6 
e = 4 + 3 
f = 28 / e
g = 3 * f
h = g + 6 
i = d / h
Problem: 50 men took a dip in a water tank 40 m long and 20 m broad on a religious day . if the average displacement of water by a man is 5 m 3 , then the rise in the water level in the tank will be :
Options: a ) 31.25 cm , b ) 25 cm , c ) 35 cm , d ) 50 cm , e ) none of these
Rationale: "explanation : total volume of water displaced = ( 5 x 50 ) m 3 = 250 m 3 rise in water level = 250 / 40 ã — 20 = 0.3125 m = 31.25 cm answer : a"
Answer: a
Python program:
a = 5 * 50
b = 40 * 20
c = a / b
Problem: if the price of petrol increases by 20 , by how much must a user cut down his consumption so that his expenditure on petrol remains constant ?
Options: a ) 16.7 % , b ) 20 % , c ) 24.67 % , d ) 33.33 % , e ) none of these
Rationale: "explanation : let us assume before increase the petrol will be rs . 100 . after increase it will be rs ( 100 + 20 ) i . e 120 . now , his consumption should be reduced to : - = ( 120 − 100 ) / 120 ∗ 100 . hence , the consumption should be reduced to 16.7 % . answer : a"
Answer: a
Python program:
a = 100 + 20 
b = 100 / a
c = 1 - b
d = c * 100
Problem: thirty percent of the women in a college class are science majors , and the non - science majors make up 60 % of the class . what percentage of the men are science majors if 40 % of the class are men ?
Options: a ) 35 % , b ) 45 % , c ) 55 % , d ) 65 % , e ) 75 %
Rationale: science majors make up 0.4 of the class . 60 % of the class are women and 0.3 * 0.6 = 0.18 of the class are female science majors . then 0.22 of the class are male science majors . 0.4 x = 0.22 x = 0.55 = 55 % the answer is c .
Answer: c
Python program:
a = 100 - 60
b = 10 * 3
c = b / 100
d = 100 - 40
e = c * d
f = a - e
g = f / 40
h = g * 100
Problem: a cargo ship carrying 4 kinds of items , doohickies , geegaws , widgets , and yamyams , arrives at the port . each item weighs 2 , 11 , 5 , and 7 pounds , respectively , and each item is weighed as it is unloaded . if , in the middle of the unloading process , the product of the individual weights of the unloaded items equals 104 , 350400 pounds , how many widgets have been unloaded ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 25 , e ) 20 , 870,080
Rationale: we need to know the number of widgets ( which weigh 5 pounds each ) . the number of times that 5 divides the number is related to the number of times that 10 divides the number . when we divide 104 , 350,400 by 100 , we get 104 , 350,400 = 1 , 043,504 * 5 ^ 2 * 2 ^ 2 . 1 , 043,504 is not divisible by 5 , thus there are 2 widgets . the answer is a .
Answer: a
Python program:
a = 1 + 1
Problem: what is the sum of all the composite numbers up to 18 ?
Options: a ) 228 , b ) 112 , c ) 80 , d ) 96 , e ) 100
Rationale: explanation : 4 + 6 + 8 + 9 + 10 + 12 + 14 + 15 + 16 + 18 = 112 answer : b
Answer: b
Python program:
a = 12 + 2 
b = a + 1 
c = 12 + 2 
d = 2 + 4 
e = d + 4 
f = 10 - 1
g = e + f 
h = 2 + 4 
i = h + 4 
j = g + i 
k = 10 + 2 
l = j + k 
m = c + l 
n = b + m 
o = 12 + 2 
p = o + 1 
q = p + 1 
r = n + q 
s = r + 18 
t = 2 + 4 
u = s + t
Problem: if 10,000 microns = 1 decimeter , and 1 , 000,000 angstroms = 1 decimeter , how many angstroms equal 1 micron ?
Options: a ) 100 , b ) 10,000 , c ) 100,000 , d ) 0.01 , e ) 0.0001
Rationale: "10,000 microns = 1 decimeter , and 1 , 000,000 angstroms = 1 decimeter 10,000 microns = 1 , 000,000 angstroms 1 micron = 100 answer : a"
Answer: a
Python program:
a = 100 * 100
b = 1 / a
c = 100 * 100
d = b * c
Problem: this year , mbb consulting fired 5 % of its employees and left remaining employee salaries unchanged . sally , a first - year post - mba consultant , noticed that that the average ( arithmetic mean ) of employee salaries at mbb was 10 % more after the employee headcount reduction than before . the total salary pool allocated to employees after headcount reduction is what percent of that before the headcount reduction ?
Options: a ) 98.5 % , b ) 100.0 % , c ) 102.8 % , d ) 104.5 % , e ) 105.0 %
Rationale: "100 employees , each earning 1 $ . after the cut , 95 are left , each earning 1.1 $ . 1.1 * 95 = 104.5 100 * 1 = 100 this gives you the answer . answer : c"
Answer: c
Python program:
a = 100 * 10
b = 100 + a 
c = 100 - 5
d = c + 4 
e = b * d
f = 100 * 10
g = e / f
Problem: during a certain two - week period , 75 percent of the movies rented from a video store were comedies , and of the remaining movies rented , there were 2 / 3 times as many dramas as action movies . if no other movies were rented during that two - week period and there were a action movies rented , then how many comedies , in terms of a , were rented during that two - week period ?
Options: a ) 5 a , b ) 10 a , c ) 15 a , d ) 18 a , e ) 25 a
Rationale: "movies : 75 % comedies . 25 % remaining genre . now in this 25 % , there are only 2 categories . action movies and drama movies . if action = x ; drama movies = 2 x / 3 . total 5 x / 3 . 5 x / 3 = 25 ; x = 15 action movies : 15 % drama movies : 10 % we can say that out of 100 z , : comedies : 75 z action : 15 z drama : 10 z now action movies were a this means : a = 15 z . z = a / 15 comedies : 75 z = 75 * ( a / 15 ) 5 a a is the answer ."
Answer: a
Python program:
a = 2 + 1 
b = 75 / a
c = math.floor(b)
Problem: rs 60000 is divided into two parts one part is given to a person with 10 % interest and another part is given to a person with 20 % interest . at the end of first year he gets profit 7000 find money given by 10 % ?
Options: a ) 30000 , b ) 40000 , c ) 50000 , d ) 60000 , e ) 70000
Rationale: "let first parrt is x and second part is y then x + y = 60000 - - - - - - - - - - eq 1 total profit = profit on x + profit on y 7000 = ( x * 10 * 1 ) / 100 + ( y * 20 * 1 ) / 100 70000 = x + 2 y - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - eq 2 70000 = 60000 + y so y = 10000 then x = 50000 - 10000 = 40000 first part = 40000 answer : b"
Answer: b
Python program:
a = 60000 * 20
b = a / 100
c = b - 7000
d = 10 / 100
e = c / d