euclaise/mathqa_programs huggingface dataset:
Problem: of the 12,210 employees of the anvil factory , 2 / 7 are journeymen . if half of the journeymen were laid off , what percentage of the total remaining employees would be journeymen ?
Options: a ) 14.3 % , b ) 13.67 % , c ) 33 % , d ) 28.6 % , e ) 49.67 %
Rationale: "the exam gives us a number that is easily divisible by 7 to pique our curiosity and tempt us into calculating actual numbers ( also because otherwise the ratio would be incorrect ) . since the question is about percentages , the actual numbers will be meaningless , as only the ratio of that number versus others will be meaningful . nonetheless , for those who are curious , each 1 / 7 portion represents ( 14210 / 7 ) 2,030 employees . this in turn means that 4,060 employees are journeymen and the remaining 10,150 are full time workers . if half the journeymen were laid off , that would mean 1 / 7 of the total current workforce would be removed . this statistic is what leads many students to think that since half the journeymen are left , the remaining journeymen would represent half of what they used to be , which means 1 / 7 of the total workforce . if 1 / 7 of the workforce is journeymen , and 1 / 7 is roughly 14.3 % , then answer choice a should be the right answer . in this case , though , it is merely the tempting trap answer choice . what changed between the initial statement and the final tally ? well , you let go of 1 / 7 of the workforce , so the total number of workers went down . the remaining workers are still 1 / 7 of the initial workers , but the group has changed . the new workforce is smaller than the original group , specifically 6 / 7 of it because 1 / 7 was eliminated . the remaining workers now account for 1 / 7 out of 6 / 7 of the force , which if we multiply by 7 gives us 1 out of 6 . this number as a percentage is answer choice b , 13.67 % . using the absolute numbers we calculated before , there were 4,060 journeymen employees out of 14,210 total . if 2,030 of them are laid off , then there are 2,030 journeyman employees left , but now out of a total of ( 14,210 - 2,030 ) 12,180 employees . 2,030 / 12,180 is exactly 1 / 6 , or 16.67 % . the answer will work with either percentages or absolute numbers , but the percentage calculation will be significantly faster and applicable to any similar situation . the underlying principle of percentages ( and , on a related note , ratios ) can be summed up in the brainteaser i like to ask my students : if you ’ re running a race and you overtake the 2 nd place runner just before the end , what position do you end up in ? the correct answer is 2 nd place . percentages , like ratios and other concepts of relative math , depend entirely on the context . whether 100 % more of something is better than 50 % more of something else depends on the context much more than the percentages quoted . when it comes to percentages on the gmat , the goal is to understand them enough to instinctively not fall into the traps laid out for you . b"
Answer: b
Python program:
a = 2 / 7
b = a / 2
c = 2 / 7
d = c / 2
e = 2 / 7
f = 1 - e
g = d + f 
h = b / g
i = h * 100
j = i * 3
Problem: given two sets a = { 11 , 44 , 55 } and b = { 01 } , if one number is chosen from each set at random , what is the probability that the sum of both numbers is an even number
Options: a ) 1 / 4 , b ) 1 / 8 , c ) 1 / 7 , d ) 1 / 2 , e ) 3
Rationale: one way to look at it : the number from set a can be anything . the number selected from set b will determine whether the sum is odd or even . for example , if a 4 is selected from set a , we need a 0 from set b to get an even sum . if a 5 is selected from set a , we need a 1 from set b to get an even sum . and so on . so , p ( sum is even ) = p ( select any number from set aandselect the number from set b that makes the sum even ) = p ( select any number from set a ) xp ( select the number from set b that makes the sum even ) = 1 x 1 / 2 = 1 / 2 = d
Answer: d
Python program:
a = 11 + 44 
b = a / 2
c = b / 55
Problem: what is the least value of x , so that 2 x 4472 is divisible by 9
Options: a ) 7 , b ) 8 , c ) 9 , d ) 3 , e ) 2
Rationale: "explanation : the sum of the digits of the number is divisible by 9 . then the number is divisible by 9 . 2 + x + 4 + 4 + 7 + 2 = 19 + x least value of x may be ' 8 ' , so that the total 19 + 8 = 27 is divisible by 9 . answer : option b"
Answer: b
Python program:
a = math.lcm(2, 4472)
b = a / 4472
c = b / 4
d = c / 4
Problem: a man saves 20 % of his monthly salary . if an account of dearness of things he is to increase his monthly expenses by 20 % , he is only able to save rs . 230 per month . what is his monthly salary ?
Options: a ) 5000 , b ) 5750 , c ) 2878 , d ) 2990 , e ) 2771
Rationale: "income = rs . 100 expenditure = rs . 80 savings = rs . 20 present expenditure 80 * ( 20 / 100 ) = rs . 96 present savings = 100 â € “ 96 = rs . 4 100 - - - - - - 4 ? - - - - - - - - - 230 = > 5750 answer : b"
Answer: b
Python program:
a = 230 * 100
b = 100 - 20
c = 100 - 20
d = 20 / 100
e = c * d
f = b + e 
g = 100 - f
h = a / g
Problem: a shipment of 250 smartphones contains 76 that are defective . if a customer buys two smartphones at random from the shipment , what is the approximate probability that both phones are defective ?
Options: a ) 1 / 250 , b ) 1 / 84 , c ) 1 / 11 , d ) 1 / 9 , e ) 1 / 3
Rationale: "probability of chosing one defective phone from a lot of 250 which ontains 76 defective phones is = ( 76 / 250 ) probability of chosing one defective phone from a lot of 249 ( we already picked one ) which ontains 75 ( we already picked one ) defective phones is = ( 75 / 249 ) combined probability of series of events = product of the probabilities = ( 76 / 250 ) * ( 75 / 249 ) 76 / 250 is close to ( 7 / 23 ) and ( 75 / 249 ) = ( 25 / 83 ) so answer is ( 7 / 23 ) * ( 25 / 83 ) = ( 1 / 11 ) so , answer will be c"
Answer: c
Python program:
a = 76 - 1
b = 76 * a
c = 250 - 1
d = 250 * c
e = b / d
Problem: if 48 machine can finish a job in 80 days , then how many more machines would be needed to finish the job in one - fifth less time ?
Options: a ) a . 4 , b ) b . 8 , c ) c . 10 , d ) d . 12 , e ) e . 16
Rationale: "you might think of this in a management context - we can use the principle of ' person - hours ' to solve any problem where we have identical workers . so , using simpler numbers , suppose you know that 6 identical employees , working simultaneously , would finish a job in 5 hours . then that job requires 6 * 5 = 30 total hours of person - work . if instead you wanted the job done in 3 hours , you ' d assign 30 / 3 = 10 employees to do the job , because you want to get a total of 30 hours of work from the employees . we can solve this problem identically . if 48 machines ( identical ones , i assume ) work simultaneously for 80 days , they will do a total of 48 * 80 machine - days of work . so the job requires 48 * 80 days of machine work in total . we instead want the job done in 1 / 5 less time , so in 64 days . so we ' ll need 48 * 80 / 64 = 60 machines , or 12 additional machines . d"
Answer: d
Python program:
a = 48 * 80
b = 3 / 4
c = b * 80
d = a / c
e = d - 48
Problem: a courtyard is 25 meter long and 16 meter board is to be paved with bricks of dimensions 20 cm by 10 cm . the total number of bricks required is
Options: a ) 16000 , b ) 18000 , c ) 20000 , d ) 22000 , e ) 24000
Rationale: "explanation : number of bricks = courtyard area / 1 brick area = ( 2500 × 160020 × 10 ) = 20000 answer : option c"
Answer: c
Python program:
a = 25 * 100
b = 16 * 100
c = a * b
d = 20 * 10
e = c / d
Problem: a train 108 m long is moving at a speed of 50 km / hr . it crosses a train 112 m long coming from opposite direction in 6 seconds . what is the speed of the second train ?
Options: a ) 82 kmph , b ) 76 kmph , c ) 44 kmph , d ) 58 kmph , e ) 56 kmph
Rationale: explanation : total distance = 108 + 112 = 220 m time = 6 s relative speed = distance / time = 220 / 6 m / s = 110 / 3 m / s = ( 110 / 3 ) × ( 18 / 5 ) km / hr = 132 km / hr = > 50 + speed of second train = 132 km / hr = > speed of second train = 132 - 50 = 82 km / hr answer : option a
Answer: a
Python program:
a = 112 + 108 
b = a / 6
c = const_0_2778 * 50
d = b - c
e = const_3_6 * d
Problem: john found that the average of 15 numbers is 40 . if 14 is added to each number then the mean of number is ?
Options: a ) 54 , b ) 45 , c ) 65 , d ) 78 , e ) 64
Rationale: ( x + x 1 + . . . x 14 ) / 15 = 40 54 option a
Answer: a
Python program:
a = 40 + 14
Problem: the perimeter of a square is equal to the perimeter of a rectangle of length 18 cm and breadth 14 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places )
Options: a ) 23.57 , b ) 23.54 , c ) 23.5 , d ) 24.55 , e ) 25.14
Rationale: "let the side of the square be a cm . perimeter of the rectangle = 2 ( 18 + 14 ) = 64 cm perimeter of the square = 64 cm i . e . 4 a = 64 a = 16 diameter of the semicircle = 16 cm circumference of the semicircle = 1 / 2 ( ∏ ) ( 16 ) = 1 / 2 ( 22 / 7 ) ( 16 ) = 25.14 cm to two decimal places answer : e"
Answer: e
Python program:
a = 14 + 18 
b = 2 * a
c = b / 4
d = c / 2
e = circumface / (
f = math.floor(e, 2)
Problem: when 6 is added to half of one - third of one - fifth of a number , the result is one - fifteenth of the number . find the number ?
Options: a ) 32 , b ) 180 , c ) 60 , d ) 27 , e ) 11
Rationale: "explanation : let the number be 26 + 1 / 2 [ 1 / 3 ( a / 5 ) ] = a / 15 = > 6 = a / 30 = > a = 180 answer : b"
Answer: b
Python program:
a = 2 + 6 
b = 3 * a
c = 1 / b
d = c / 2
e = 3 / 0
Problem: danny and steve are running towards each other , each one from his own house . danny can reach steve ' s house in 31 minutes of running , which is half the time it takes steve to reach danny ' s house . if the two started to run at the same time , how much time longer will it take steve to reach the halfway point between their houses than danny to reach the halfway point between their houses ?
Options: a ) 15.5 minutes , b ) 31 minutes , c ) 35 minutes , d ) 62 minutes , e ) 93 minutes
Rationale: "danny ' s time is 31 minutes . the time to reach halfway is 15.5 minutes . steve ' s time is 62 minutes . the time to reach halfway is 31 minutes . the time difference is 31 - 15.5 = 15.5 minutes the answer is a ."
Answer: a
Python program:
a = 31 / 2
Problem: in a group of 140 people , 90 have an age of more 30 years , and the others have an age of less than 20 years . if a person is selected at random from this group , what is the probability the person ' s age is less than 20 ?
Options: a ) 0.35 , b ) 0.55 , c ) 0.65 , d ) 0.75 , e ) 0.85
Rationale: "number of people whose age is less than 20 is given by 140 - 90 = 50 probability p that a person selected at random from the group is less than 20 is given by 50 / 140 = 0.35 correct answer a"
Answer: a
Python program:
a = 140 - 90
b = a / 140
Problem: if radius of a circle is reduced by 10 % , then how much % of its area will be reduced ?
Options: a ) 10 %
b ) 19 %
c ) 20 %
d ) 36 %
e ) 30 %
Rationale: let initial radius = a then , area = π a ^ 2 . new radius = 90 % of a = 9 a / 10 . new area = π * 81 a ^ 2 / 100 = 81 / 100 π a ^ 2 reduce in area = [ π a ^ 2 - 81 / 100 π a ^ 2 ] = 19 / 100 π a ^ 2 % reduce = [ ( 19 * π a ^ 2 / 100 ) * ( 1 * 100 / π a ^ 2 ) ] % = 19 % answer b
Answer: b
Python program:
a = 100 - 10
b = a / 100
c = b ** 2
d = 1 - c
e = d * 100
Problem: a rope of which a calf is tied is increased from 12 m to 21 m , how much additional grassy ground shall it graze ?
Options: a ) 933.4 , b ) 1219 , c ) 1210 , d ) 1212 , e ) 1312
Rationale: "π ( 212 – 122 ) = 933.4 answer : a"
Answer: a
Python program:
a = 21 ** 2
b = 10 ** 2
c = a - b
d = 12 * 2
e = d + 2 
f = 4 + 3 
g = e / f
h = c * g
Problem: in a school with 640 students , the average age of the boys is 12 years and that of the girls is 11 years . if the average age of the school is 11 years 9 months , then the number of girls in the school is
Options: a ) 160 , b ) 200 , c ) 250 , d ) 350 , e ) none
Rationale: sol . let the number of grils be x . then , number of boys = ( 640 - x ) . then , ( 11 3 / 4 × 640 ) ⇔ 11 x + 12 ( 640 - x ) ⇔ x = 7680 - 7520 ⇔ 160 . answer a
Answer: a
Python program:
a = 12 * 640
b = 9 / 12
c = 11 + b 
d = c * 640
e = a - d
Problem: if the average ( arithmetic mean ) of x , x + 2 , and x + 4 is 33 , what is the value of x ?
Options: a ) 30 , b ) 31 , c ) 32 , d ) 32 , e ) 37
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 = 33 x = 31 correct option : b"
Answer: b
Python program:
a = 4 * 2
b = 2 * 2
c = a - b
Problem: two persons a and b can complete a piece of work in 30 days and 45 days respectively . if they work together , what part of the work will be completed in 4 days ?
Options: a ) 2 / 5 , b ) 1 / 6 , c ) 1 / 4 , d ) 1 / 9 , e ) 2 / 9
Rationale: "a ' s one day ' s work = 1 / 30 b ' s one day ' s work = 1 / 45 ( a + b ) ' s one day ' s work = 1 / 30 + 1 / 45 = 1 / 18 the part of the work completed in 4 days = 4 ( 1 / 18 ) = 2 / 9 . answer e"
Answer: e
Python program:
a = 1 / 30
b = 1 / 45
c = a + b 
d = 4 * c
Problem: 30 pens and 75 pencils were purchased for 690 . if the average price of a pencil was 2.00 , find the average price of a pen .
Options: a ) 10 , b ) 11 , c ) 18 , d ) 13 , e ) 14
Rationale: "since average price of a pencil = 2 ∴ price of 75 pencils = 150 ∴ price of 30 pens = ( 690 – 150 ) = 540 ∴ average price of a pen = 540 ⁄ 60 = 18 answer c"
Answer: c
Python program:
a = 75 * 2
b = 690 - a
c = b / 30
Problem: if the price of a tv is first decreased by 20 % and then increased by 45 % , then the net change in the price will be :
Options: a ) 4 % increase , b ) 10 % increase , c ) 10 % decrease , d ) 16 % increase , e ) none of these
Rationale: "explanation : solution : let the original price be rs . 100 . new final price = 145 % of ( 80 % of 100 ) = rs . 145 / 100 * 80 / 100 * 100 = rs . 116 . . ' . increase = 16 % answer : d"
Answer: d
Python program:
a = 100 - 20
b = 100 + 45 
c = a * b
d = c / 100
e = d - 100
Problem: two dogsled teams raced across a 300 mile course in wyoming . team a finished the course in 3 fewer hours than team e . if team a ' s average speed was 5 mph greater than team e ' s , what was team e ' s average mph ?
Options: a ) 12 , b ) 15 , c ) 18 , d ) 20 , e ) 25
Rationale: this is a very specific format that has appeared in a handful of real gmat questions , and you may wish to learn to recognize it : here we have a * fixed * distance , and we are given the difference between the times and speeds of two things that have traveled that distance . this is one of the very small number of question formats where backsolving is typically easier than solving directly , since the direct approach normally produces a quadratic equation . say team e ' s speed was s . then team e ' s time is 300 / s . team a ' s speed was then s + 5 , and team a ' s time was then 300 / ( s + 5 ) . we need to find an answer choice for s so that the time of team a is 3 less than the time of team e . that is , we need an answer choice so that 300 / ( s + 5 ) = ( 300 / s ) - 3 . you can now immediately use number properties to zero in on promising answer choices : the times in these questions will always work out to be integers , and we need to divide 300 by s , and by s + 5 . so we want an answer choice s which is a factor of 300 , and for which s + 5 is also a factor of 300 . so you can rule out answers a and c immediately , since s + 5 wo n ' t be a divisor of 300 in those cases ( sometimes using number properties you get to the correct answer without doing any other work , but unfortunately that ' s not the case here ) . testing the other answer choices , if you try answer d , you find the time for team e is 15 hours , and for team a is 12 hours , and since these differ by 3 , as desired , d is correct .
Answer: d
Python program:
a = 300 / 5
b = a / 3
Problem: a and b can do a piece of work in 40 days and 50 days respectively . they work together for 10 days and b leaves . in how many days the whole work is completed ?
Options: a ) 28 days , b ) 60 days , c ) 20 days , d ) 30 days , e ) 40 days
Rationale: "explanation : ( a + b ) ’ s 10 days work = 10 [ 1 / 40 + 1 / 50 ] = 10 [ 5 + 4 / 200 ] = 9 / 20 a complete remaining work in 9 / 20 * 40 = 18 total work = 10 + 18 = 28 days answer : option a"
Answer: a
Python program:
a = 10 / 50
b = 10 / 40
c = a + b 
d = 10 - c
e = 10 / 50
f = d / e
Problem: sahil purchased a machine at rs 13000 , then got it repaired at rs 5000 , then gave its transportation charges rs 1000 . then he sold it with 50 % of profit . at what price he actually sold it .
Options: a ) rs . 22000 , b ) rs . 24500 , c ) rs . 26500 , d ) rs . 28500 , e ) none of these
Rationale: explanation : question seems a bit tricky , but it is very simple . just calculate all cost price , then get 150 % of cp . c . p . = 13000 + 5000 + 1000 = 19000 150 % of 19000 = 150 / 100 * 19000 = 28500 option d
Answer: d
Python program:
a = 13000 + 5000 
b = a + 1000 
c = 13000 + 5000 
d = c + 1000 
e = d / 100
f = e * 50
g = b + f
Problem: the area of a square field is a square feet and the perimeter is p feet . if 6 a = 6 ( 2 p + 9 ) , what is the perimeter of the field , in feet ? ( here a = a ^ 2 )
Options: a ) 28
b ) 36
c ) 40
d ) 56
e ) 84
Rationale: you can also solve this via using the given numbers in the answer choices ! of course you need to be aware of the basic properties as outlined by the other posts above ( a = x ^ 2 and p = 4 x ) starting with d you will notice that x = 14 is way too big for your area ( 14 ^ 2 ) and will not satisfy : 6 a = 6 ( 2 p + 9 ) or a = 2 p + 9 - - > eliminate d and e now pick b ( its either too big , then its a , or too small then you know its c or it is b itsself ) and picking b indeed solves the problem ! ( 36 / 4 - - > 9 ; a = 9 ^ 2 = 81 and 81 = 2 x 36 + 9 )
Answer: b
Python program:
a = 4 * 9
Problem: how many numbers from 10 to 43 are exactly divisible by 3 ?
Options: a ) 13 , b ) 11 , c ) 16 , d ) 17 , e ) 18
Rationale: "12 , 15 , 18 , 21 , 24 , 27 , 30 , 33 , 36 , 39 , 42 . 11 numbers . 10 / 3 = 3 and 43 / 3 = 14 = = > 14 - 3 = 11 . therefore 11 digits b )"
Answer: b
Python program:
a = 43 / 3
b = math.floor(a)
c = b * 3
d = 10 / 3
e = math.floor(d)
f = e + 1 
g = f * 3
h = c - g
i = h / 3
j = i + 1
Problem: working together , printer a and printer b would finish the task in 30 minutes . printer a alone would finish the task in 50 minutes . how many pages does the task contain if printer b prints 3 pages a minute more than printer a ?
Options: a ) 200 , b ) 400 , c ) 600 , d ) 800 , e ) 900
Rationale: "30 * a + 30 * b = x pages in 30 mins printer a will print = 30 / 50 * x pages = 3 / 5 * x pages thus in 30 mins printer printer b will print x - 3 / 5 * x = 2 / 5 * x pages also it is given that printer b prints 3 more pages per min that printer a . in 30 mins printer b will print 90 more pages than printer a thus 3 / 5 * x - 2 / 5 * x = 90 = > x = 400 pages answer : b"
Answer: b
Python program:
a = const_60 / 0
b = a - 1
c = 3 / b
d = c * const_60
Problem: train speed 36 kph . dist travelled in 3 minutes in meters
Options: a ) 1600 , b ) 1700 , c ) 1800 , d ) 1900 , e ) 2000
Rationale: 36 kmph = 10 m / sec d = 10 * 180 = 1800 meters answer : c
Answer: c
Python program:
a = 3 / const_60
b = 36 * a
c = b * 1000
Problem: 300 first - time customers of a fashion store were surveyed for their shopping experience right after leaving the store . 60 % of the customers in the survey had purchased clothes for less than $ 100 . 40 % of the customers in the survey reported they were overall satisfied with their purchase . 65 % of the customers that had purchased clothes for less than $ 100 reported they were overall satisfied with their purchase . what percent of the customers surveyed purchased clothes for at least $ 100 and reported that they were not overall satisfied with their purchase ?
Options: a ) 1 , b ) 25 , c ) 35 , d ) 45 , e ) 75
Rationale: "out of 300 - 180 purchased for less than 100 $ 120 for more out of 300 - 120 responded as satisfied and 180 responded disatisfied out of 180 ( purchased less than 100 $ ) - 65 % = 117 responded as satisfied , so remaining satisfied are 120 - 117 = 3 so 3 is what percentage of 300 - 1 % so the answer should be a"
Answer: a
Python program:
a = 40 / 100
b = a * 300
c = 65 / 100
d = 60 / 100
e = 300 * d
f = c * e
g = b - f
h = g / 300
i = h * 100
Problem: in a company of 148 employees , 92 are females . a total of 78 employees have advanced degrees and the rest have a college degree only . if 31 employees are males with college degree only , how many employees are females with advanced degrees ?
Options: a ) 50 , b ) 51 , c ) 52 , d ) 53 , e ) 54
Rationale: "the number of males is 148 - 92 = 56 . the number of males with advanced degrees is 56 - 31 = 25 . the number of females with advanced degrees is 78 - 25 = 53 . the answer is d ."
Answer: d
Python program:
a = 148 - 92
b = a - 31
c = 78 - b
Problem: a cycle is bought for rs . 900 and sold for rs . 1260 , find the gain percent ?
Options: a ) 39 % , b ) 20 % , c ) 40 % , d ) 74 % , e ) 83 %
Rationale: "900 - - - - 360 100 - - - - ? = > 40 % answer : c"
Answer: c
Python program:
a = 1260 - 900
b = a / 900
c = b * 100
Problem: a van takes 6 hours to cover a distance of 288 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 ) 50 kmph , b ) 60 kmph , c ) 32 kmph , d ) 80 kmph , e ) 90 kmph
Rationale: time = 6 distence = 288 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 288 / 9 = 32 kmph c
Answer: c
Python program:
a = 3 / 2
b = a * 6
c = 288 / b
Problem: a goods train runs at the speed of 72 km / hr and crosses a 250 m long platform in 30 sec . what is the length of the goods train ?
Options: a ) 299 , b ) 277 , c ) 350 , d ) 270 , e ) 281
Rationale: "speed = 72 * 5 / 18 = 20 m / sec . time = 30 sec . let the length of the train be x meters . then , ( x + 250 ) / 30 = 20 x = 350 m . answer : c"
Answer: c
Python program:
a = 72 / 3600
b = a * 1000
c = b * 30
d = c - 250
Problem: the ratio of the adjacent angles of a parallelogram is 8 : 10 . also , the ratio of the angles of quadrilateral is 5 : 6 : 7 : 12 . what is the sum of the smaller angle of the parallelogram and the second largest angle of the quadrilateral ?
Options: a ) 168 ° , b ) 228 ° , c ) 156 ° , d ) 224 ° , e ) 164 °
Rationale: "the measures of the adjacent angles of a parallelogram add up to be 180 ° given so , 8 x + 10 x = 180 ° or , 18 x = 180 ° or , x = 10 ° hence the angles of the parallelogram are 80 ° and 100 ° further it is given we know sum of all the four angles of a quadrilateral is 360 ° so , 5 y + 6 y + 7 y + 12 y = 360 ° or , 5 y + 6 y + 7 y + 12 y = 360 ° or , 30 y = 360 ° or , y = 12 ° hence the angles of the quadrilateral are 60 ° , 72 , 84 ° and 144 ° will be 80 ° + 84 ° = 164 ° answer : e"
Answer: e
Python program:
a = 8 * 2
b = a * 10
c = b + 100 
d = c * 2
e = 5 + 6 
f = e + 7 
g = f + 12 
h = d / g
i = h * 10
Problem: if the price of a certain computer increased 30 percent from d dollars to 364 dollars , then 2 d =
Options: a ) 540 , b ) 570 , c ) 619 , d ) 649 , e ) 560
Rationale: before price increase price = d after 30 % price increase price = d + ( 30 / 100 ) * d = 1.3 d = 364 ( given ) i . e . d = 364 / 1.3 = $ 280 i . e . 2 d = 2 * 280 = 560 answer : option e
Answer: e
Python program:
a = 100 + 30 
b = a / 100
c = 364 / b
d = c * 2
Problem: find the value of 72518 x 9999 = m ?
Options: a ) 456578972 , b ) 436567874 , c ) 653658791 , d ) 725117481 , e ) 725107482
Rationale: "72518 x 9999 = 72518 x ( 10000 - 1 ) = 72518 x 10000 - 72518 x 1 = 725180000 - 72518 = 725107482 e"
Answer: e
Python program:
a = 9999 - 4
b = a * 72518