euclaise/mathqa_programs huggingface dataset:
Problem: | 8 - 3 | - | 4 - 6 | = ?
Options: a ) 3 , b ) 2 , c ) 1 , d ) 0 , e ) 4
Rationale: "| 8 - 3 | - | 4 - 6 | = | 5 | - | - 2 | = 5 - 2 = 3 correct answer a"
Answer: a
Python program:
a = 8 - 3
b = 6 - 4
c = a - b
Problem: if x is an integer and 2.134 × 10 ^ x is less than 240,000 , what is the greatest possible value for x ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: "x is an integer and 2.134 × 10 x is less than 240,000 , what is the greatest possible value for x ? for 2.134 × 10 x is less than 240,000 to remain true , the greatest number is 213,400 , which makes x = 5 c . 5"
Answer: c
Python program:
a = 240 / 0
b = math.log(a)
c = math.log(10)
d = b / c
e = math.floor(d)
Problem: two trains of length 90 m and 100 m are 200 m apart . they start moving towards each other on parallel tracks , at speeds 71 kmph and 89 kmph . after how much time will the trains meet ?
Options: a ) 47 / 10 , b ) 46 / 10 , c ) 45 / 10 , d ) 42 / 10 , e ) 43 / 10
Rationale: "they are moving in opposite directions , relative speed is equal to the sum of their speeds . relative speed = ( 71 + 89 ) * 5 / 18 = 44.4 mps . the time required = d / s = 200 / 44.4 = 45 / 10 sec . answer : c"
Answer: c
Python program:
a = 71 + 89 
b = a * const_0_2778
c = 200 / b
Problem: in a class of 40 students , 2 students did not borrow any books from the library , 12 students each borrowed 1 book , 10 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?
Options: a ) 3 , b ) 5 , c ) 8 , d ) 13 , e ) 15
Rationale: "total # of students = 40 avg # of books per student = 2 total # of books = 40 * 2 = 80 # of student borrowed at least 3 books = 40 - 2 - 12 - 10 = 16 # of books borrowed by above 16 students = 80 - ( 12 * 1 ) - ( 10 * 2 ) = 48 considering that 15 out of above 16 students borrowed only 3 books , # of books borrowed = 15 * 3 = 45 so maximum # of books borrowed by any single student = 48 - 45 = 3 option a"
Answer: a
Python program:
a = 40 * 2
b = 12 * 1
c = b + 10 
d = c + 2 
e = 40 - d
f = e - 1
g = f * 3
h = 12 * 1
i = 10 * 2
j = h + i 
k = g + j 
l = a - k
Problem: of the 20210 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 ) 16.67 % , 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 , 49.67 % . 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 . e
Answer: e
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: find the total number of prime factors in the expression ( 4 ) ^ 13 x ( 7 ) ^ 5 x ( 11 ) ^ 2
Options: a ) 26 , b ) 22 , c ) 25 , d ) 27 , e ) 33
Rationale: ( 4 ) ^ 13 x ( 7 ) ^ 5 x ( 11 ) ^ 2 = ( 2 x 2 ) ^ 13 x ( 7 ) ^ 5 x ( 11 ) ^ 2 = 2 ^ 13 x 2 ^ 13 x 7 ^ 5 x 11 ^ 2 = 2 ^ 26 x 7 ^ 5 x 11 ^ 2 total number of prime factors = ( 26 + 5 + 2 ) = 33 . answer is e .
Answer: e
Python program:
a = 2 * 13
b = a + 5 
c = b + 2
Problem: the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 650 resolutions ?
Options: a ) 724 m , b ) 704 m , c ) 915.2 m , d ) 278 m , e ) 927 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 650 resolutions . = 650 * 2 * 22 / 7 * 22.4 = 91520 cm = 915.2 m answer : c"
Answer: c
Python program:
a = 3 + 4 
b = a * 3
c = b + 1 
d = 3 + 4 
e = c / d
f = e * 22
g = f * 2
h = g * 650
i = h / 100
Problem: a man is 22 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is ?
Options: a ) 20 , b ) 25 , c ) 27 , d ) 22 , e ) 91
Rationale: "let the son ' s present age be x years . then , man ' s present age = ( x + 22 ) years . ( x + 22 ) + 2 = 2 ( x + 2 ) x + 24 = 2 x + 4 = > x = 20 . answer : a"
Answer: a
Python program:
a = 2 * 2
b = a - 2
c = 22 - b
d = 2 - 1
e = c / d
Problem: a can run 2 km distance in 2 min . , while b can run this distance in 2 min 40 sec . by how much distance can a beat b ?
Options: a ) 150 m , b ) 100 m , c ) 500 m , d ) 180 m , e ) 190 m
Rationale: a takes time 2 minutes = 120 sec b takes time 2.40 minutes = 160 sec diffrence = 160 - 120 = 40 sec now we are to find distance covered in 40 sec by b 160 sec = 2000 m 1 sec = 25 / 2 m 40 sec = 40 x 25 / 2 = 500 m answer : c
Answer: c
Python program:
a = 2 * 1000
b = 2 * const_60
c = a / b
d = 2 * 1000
e = 2 * const_60
f = e + 40 
g = d / f
h = c - g
i = 2 * const_60
j = h * i
Problem: stacy and heather are 20 miles apart and walk towards each other along the same route . stacy walks at constant rate that is 2 mile per hour faster than heather ' s constant rate of 5 miles / hour . if heather starts her journey 24 minutes after stacy , how far from the original destination has heather walked when the two meet ?
Options: a ) 5 miles , b ) 7 miles , c ) 9 miles , d ) 10 miles , e ) 12 miles
Rationale: "original distance between s and h = 20 miles . speed of s = 5 + 2 = 7 mph , speed of h = 5 mph . time traveled by h = t hours - - - > time traveled by s = t + 24 / 60 = t + 2 / 5 hours . now , the total distances traveled by s and h = 20 miles - - - > 7 * ( t + 2 / 5 ) + 5 * t = 20 - - - > t = 86 / 60 hours . thus h has traveled for 86 / 60 hours giving you a total distance for h = 5 * 86 / 60 = 7 miles . b is thus the correct answer . p . s . : based on the wording of the question , you should calculatehow far from theoriginal destination has heather walkedwhen the two meet . ' original destination ' for h does not make any sense . original destination for h was situated at a distance of 20 miles ."
Answer: b
Python program:
a = 2 + 5 
b = a / const_60
c = 24 * b
d = 20 - c
e = 2 + 5 
f = 5 + e 
g = d / f
h = g * 5
Problem: two trains of equal length are running on parallel lines in the same directions at 46 km / hr . and 36 km / hr . the faster trains pass the slower train in 36 seconds . the length of each train is :
Options: a ) 82 m , b ) 50 m , c ) 72 m , d ) 80 m , e ) none of these
Rationale: "explanation : the relative speed of train is 46 - 36 = 10 km / hr = ( 10 x 5 ) / 18 = 25 / 9 m / s 10 × 518 = 259 m / s in 36 secs the total distance travelled is 36 x 25 / 9 = 100 m . therefore the length of each train is = 100 / 2 = 50 m . answer b"
Answer: b
Python program:
a = 46 - 36
b = a * 1000
c = b / 3600
d = c * 36
e = d / 2
Problem: divide rs . 1400 among a , b and c so that a receives 1 / 3 as much as b and c together and b receives 2 / 3 as a and c together . a ' s share is ?
Options: a ) 346 , b ) 368 , c ) 350 , d ) 337 , e ) 639
Rationale: "a + b + c = 1400 a = 1 / 3 ( b + c ) ; b = 2 / 3 ( a + c ) a / ( b + c ) = 1 / 3 a = 1 / 4 * 1400 = > 350 answer : c"
Answer: c
Python program:
a = 1400 / 3
Problem: if the sum of a number and its square is 72 , what is the number ?
Options: a ) 15 , b ) 26 , c ) 8 , d ) 91 , e ) none of these
Rationale: "let the number be x . then , x + x 2 = 72 ( x + 9 ) ( x - 8 ) = 0 x = 8 answer : c"
Answer: c
Python program:
a = math.sqrt(72)
b = math.floor(a)
Problem: sarah is driving to the airport . after driving at 20 miles per hour for one hour , she realizes that if she continues at that same average rate she will be an hour late for her flight . she then travels 50 miles per hour for the rest of the trip , and arrives 30 minutes before her flight departs . how many miles did she drive in all ?
Options: a ) 140 , b ) 175 , c ) 210 , d ) 70 , e ) 280
Rationale: "after driving at 20 miles per hourfor one hour , this distance left to cover is d - 20 . say this distance is x miles . now , we know that the difference in time between covering this distance at 20 miles per hour and 50 miles per hour is 1 + 1 / 2 = 3 / 2 hours . so , we have that x / 20 - x / 50 = 3 / 2 - - > 5 x / 100 - 2 x / 100 = 3 / 2 - - > 3 x / 100 = 3 / 2 - - > x = 50 . total distance = x + 20 = 70 miles . answer : d"
Answer: d
Python program:
a = 20 - 30
b = 30 - a
Problem: there are 13 stations between hyderabad and bangalore . how many second class tickets have to be printed , so that a passenger can travel from any station to any other station ?
Options: a ) 288 , b ) 267 , c ) 261 , d ) 211 , e ) 210
Rationale: "the total number of stations = 15 from 15 stations we have to choose any two stations and the direction of travel ( i . e . , hyderabad to bangalore is different from bangalore to hyderabad ) in 15 p ₂ ways . 15 p ₂ = 15 * 14 = 210 . answer : e"
Answer: e
Python program:
a = 13 + 1 
b = 13 + 1 
c = b + 1 
d = a * c
Problem: the difference between the local value and the face value of 4 in the numeral 98625147 is
Options: a ) 36 , b ) 63 , c ) 34 , d ) 30 , e ) 33
Rationale: "explanation : ( local value of 4 ) - ( face value of 4 ) = ( 40 - 4 ) = 36 a )"
Answer: a
Python program:
a = 4 * 1000
b = a - 4
Problem: a boat moves upstream at the rate of 1 km in 30 minutes and down stream 1 km in 12 minutes . then the speed of the current is :
Options: a ) 1.5 kmph , b ) 2 kmph , c ) 3 kmph , d ) 2.5 kmph , e ) 3.5 kmph
Rationale: "rate upstream = ( 1 / 30 * 60 ) = 2 kmph rate down stream = 1 / 12 * 60 = 5 kmph rate of the current = ½ ( 5 - 2 ) = 1.5 kmph answer : a"
Answer: a
Python program:
a = 1 / 12
b = a * const_60
c = 1 / 30
d = c * const_60
e = b - d
f = e / 2
Problem: if five machines working at the same rate can do 3 / 4 of a job in 30 minutes , how many minutes would it take two machines working at the same rate to do 3 / 5 of the job ?
Options: a ) 45 , b ) 60 , c ) 75 , d ) 80 , e ) 100
Rationale: using the std formula m 1 d 1 h 1 / w 1 = m 2 d 2 h 2 / w 2 substituting the values we have 5 * 1 / 2 * 4 / 3 = 2 * 5 / 3 * x ( converted 30 min into hours = 1 / 2 ) 10 / 3 = 10 / 3 * x x = 1 hour so 60 minutes answer : b
Answer: b
Python program:
a = 3 / 5
b = 3 / 4
c = b / 5
d = c / 30
e = d * 2
f = a / e
Problem: a circular racetrack is 3 miles in length and has signs posted to indicate each 1 / 10 mile increment . if a race car starts at a random location on the track and travels exactly one half mile , what is the probability that the car ends within a half mile of the sign indicating 2 1 / 2 miles ?
Options: a ) 1 / 6 , b ) 3 / 10 , c ) 1 / 3 , d ) 1 / 2 , e ) 2 / 3
Rationale: the car ends within a half mile of the sign indicating 2 1 / 2 miles means that the car will end in one mile interval , between the signs indicating 2 and 3 miles . now , it does n ' t matter where the car starts or what distance it travels , the probability will be p = ( favorable outcome ) / ( total # of outcomes ) = 1 / 3 ( as the car starts at random point end travels some distance afterwards we can consider its end point as the point where he randomly appeared , so the probability that the car appeared within 1 mile interval out of total 3 miles will be 1 / 3 ) . answer : c .
Answer: c
Python program:
a = 3 * 10
b = 10 / a
Problem: the cost price of a radio is rs . 2400 and it was sold for rs . 2100 , find the loss % ?
Options: a ) 12.5 % , b ) 11 % , c ) 13 % , d ) 15 % , e ) 12.8 %
Rationale: "2400 - - - - 300 100 - - - - ? = > 12.5 % answer : a"
Answer: a
Python program:
a = 2400 - 2100
b = a / 2400
c = b * 100
Problem: the ages of two persons differ by 20 years . if 5 years ago , the older one be 5 times as old as the younger one , then their present ages , in years , are
Options: a ) 25 , 5 , b ) 30 , 10 , c ) 35 , 15 , d ) 50 , 30 , e ) none of these
Rationale: "let the ages be ’ x ’ and ’ y ’ years now . then x - y = 20 . . . ( i ) ( x - 5 ) = 5 ( y - 5 ) . . . ( ii ) from ( i ) and ( ii ) , 20 + y - 5 = 5 y - 25 y = 10 and x = 30 . answer : b"
Answer: b
Python program:
a = 20 * 5
b = 5 - 1
c = a / b
d = c + 5 
e = d - 20
Problem: the sum of 4 th and 20 th term of a . p . is equal to the sum of 8 th , 15 th and 12 th term . find the term which is 0
Options: a ) 10 , b ) 7 , c ) 11 , d ) 5 , e ) 3
Rationale: t 4 + t 20 = t 8 + t 15 + t 12 = > a + 3 d + a + 19 d = a + 7 d + a + 14 d + a + 11 d = > a + 10 d = 0 = > t 11 = 0 i . e . 11 th term is zero . answer : c
Answer: c
Python program:
a = 8 + 15 
b = a + 12 
c = 4 + 20 
d = b - c
Problem: a particular library has 75 books in a special collection , all of which were in the library at the beginning of the month . these book are occasionally loaned out through an inter - library program . if , by the end of the month , 80 percent of books that were loaned out are returned and there are 64 books in the special collection at that time , how many books of the special collection were loaned out during that month ?
Options: a ) 20 , b ) 30 , c ) 35 , d ) 40 , e ) 55
Rationale: "there are 11 books less ( 75 - 64 ) which represents 20 % of the loaned books ( 100 - 80 ) so total loaned out books = 55 answer e"
Answer: e
Python program:
a = 75 - 64
b = 80 / 100
c = 1 - b
d = a / c
Problem: a 6 - liter solution is 20 % alcohol . how many liters of pure alcohol must be added to produce a solution that is 50 % alcohol ?
Options: a ) 2.4 , b ) 2.7 , c ) 3.0 , d ) 3.3 , e ) 3.6
Rationale: "let x be the amount of pure alcohol required . 0.2 ( 6 ) + x = 0.5 ( x + 6 ) 0.5 x = 3 - 1.2 x = 3.6 liters the answer is e ."
Answer: e
Python program:
a = 6 * 20
b = a / 100
c = b * 2
d = 6 - c
Problem: how many multiples of 2 are there between 1 and 52 , exclusive ?
Options: a ) 21 , b ) 22 , c ) 25 , d ) 26 , e ) 28
Rationale: "25 multiples of 2 between 1 and 52 exclusive . from 2 * 1 upto 2 * 25 , ( 1,2 , 3,4 , . . . , 25 ) . hence , 25 multiples ! correct option is c"
Answer: c
Python program:
a = 52 - 1
b = a / 2
c = b + 1
Problem: the length of a room is 6 m and width is 4.75 m . what is the cost of paying the floor by slabs at the rate of rs . 900 per sq . metre .
Options: a ) 25650 , b ) 25750 , c ) 26550 , d ) 26750 , e ) 25725
Rationale: "area = 6 × 4.75 sq . metre . cost for 1 sq . metre . = rs . 900 hence total cost = 6 × 4.75 × 900 = 6 × 4275 = rs . 25650 answer is a ."
Answer: a
Python program:
a = 6 * 4
b = 900 * a
Problem: nails and screws are manufactured at a uniform weight per nail and a uniform weight per screw . if the total weight of one screw and one nail is half that of 6 screws and one nail , then the total weight of 3 screws , and 3 nails is how many times that of 2 screws and 4 nails ?
Options: a ) a . 4 , b ) b . 5 / 2 , c ) c . 2 , d ) d . 3 / 2 , e ) e . 5 / 4
Rationale: "let the weight of nail be n and that of screw be s . . so s + w = 1 / 2 * ( 6 s + 1 n ) . . . or 1 n = 4 s . . lets see the weight of 3 s and 3 n = 3 s + 3 * 4 s = 15 s . . and weight of 2 s and 4 n = 2 s + 4 * 2 s = 10 s . . ratio = 15 s / 10 s = 15 / 10 = 3 / 2 d"
Answer: d
Python program:
a = 3 * 4
b = a + 3 
c = b / 10
Problem: a box contains 10 tablets of medicine a and 14 tablets of medicine b . what is the least number of tablets that should be taken from the box to ensure that at least two tablets of each kind are among the extracted .
Options: a ) 12 , b ) 16 , c ) 17 , d ) 19 , e ) 21
Rationale: the worst case scenario will be if we remove all 14 tablets of medicine b first . the next 2 tablets we remove have to be of medicine a , so to guarantee that at least two tablets of each kind will be taken we should remove minimum of 14 + 2 = 16 tablets . answer : b .
Answer: b
Python program:
a = 14 + 2
Problem: a and b together can do a work in 6 days . if a alone can do it in 15 days . in how many days can b alone do it ?
Options: a ) 10 , b ) 99 , c ) 77 , d ) 55 , e ) 21
Rationale: "1 / 6 – 1 / 15 = 1 / 10 = > 10 answer : a"
Answer: a
Python program:
a = 1 / 6
b = 1 / 15
c = a - b
d = 1/(c)
e = 2 + 3 
f = 2 / e
g = d + f
Problem: the sum of present age of abe and the age before 7 years is 27 . find the present age of abe . what will be his age after 7 years ?
Options: a ) 25 , b ) 24 , c ) 27 , d ) 28 , e ) 29
Rationale: "present age = x before 7 yrs , y = x - 7 after 7 yrs , z = x + 7 by the qn , x + ( x - 7 ) = 27 2 x - 7 = 27 2 x = 27 + 7 x = 34 / 2 x = 17 z = x + 7 = 17 + 7 = 24 answer : b"
Answer: b
Python program:
a = 27 + 7 
b = a / 2
c = b + 7
Problem: a , b and c invested rs . 6600 , rs . 4400 and rs . 11000 respectively , in a partnership business . find the share of a in profit of rs . 12100 after a year ?
Options: a ) rs . 3300 , b ) rs . 3100 , c ) rs . 3500 , d ) rs . 4200 , e ) rs . 3400
Rationale: "6600 : 4400 : 11000 3 : 2 : 5 3 / 10 * 11000 = rs . 3300 answera"
Answer: a
Python program:
a = 6600 + 4400 
b = a + 11000 
c = 6600 / b
d = c * 12100
Problem: a man drive his car to the office at 20 miles / hr . after reaching office , he realize that its a new year holiday so he went back home at a speed of 30 miles / hr . discounting the time spent in the stoppage what was his average speed of his journey ?
Options: a ) 23 miles , b ) 25 miles , c ) 22 miles , d ) 24 miles , e ) 26 miles
Rationale: d 24 miles / hr ( not 25 miles / hr which might be guessed by many ) d : distance traveled t 1 : time of going to office t 2 : time of returning back y : average speed d = 20 * t 1 t 1 = d / 20 d = 30 * t 2 t 2 = d / 30 2 d = y ( t 2 + t 1 ) 2 d = y ( d / 20 + d / 30 ) 2 d = y ( 3 d / 60 + 2 d / 60 ) 2 d = y ( 5 d / 60 ) y = 120 d / 5 d = > y = 24
Answer: d
Python program:
a = 20 + 30 
b = a / 2
c = b - 1
Problem: walking 7 / 6 of his usual rate , a boy reaches his school 4 min early . find his usual time to reach the school ?
Options: a ) 11 , b ) 15 , c ) 16 , d ) 28 , e ) 19
Rationale: "speed ratio = 1 : 7 / 6 = 6 : 7 time ratio = 7 : 6 1 - - - - - - - - 7 4 - - - - - - - - - ? è 28 m answer : d"
Answer: d
Python program:
a = 4 * 7
Problem: find the principle on a certain sum of money at 5 % per annum for 2 2 / 5 years if the amount being rs . 896 ?
Options: a ) 1000 , b ) 800 , c ) 2889 , d ) 2777 , e ) 2991
Rationale: "896 = p [ 1 + ( 5 * 12 / 5 ) / 100 ] p = 800 answer : b"
Answer: b
Python program:
a = 2 * 5
b = a + 2 
c = b / 5
d = c * 5
e = d / 100
f = e + 1 
g = 896 / f
Problem: a number is said to be prime saturated if the product of all the different positive prime factors of g is less than the square root of g . what is the greatest two digit prime saturated integer ?
Options: a ) 99 , b ) 98 , c ) 97 , d ) 96 , e ) 95
Rationale: "g = 96 = 3 * 32 = 3 * 2 ^ 5 answer is d ."
Answer: d
Python program:
a = 2 * 3
b = 100 - 10
c = a + b
Problem: a person saved $ 10 in buying an item on sale . if he spent $ 600 for the item , approximately how much percent he saved in the transaction ?
Options: a ) 8 % , b ) 1.6 % , c ) 2 % , d ) 5 % , e ) 6 %
Rationale: "actual price = 600 + 10 = $ 610 saving = 10 / 610 * 100 = 100 / 61 = 1.6 % approximately answer is b"
Answer: b
Python program:
a = 10 + 600 
b = 10 / a
c = b * 600
d = math.floor(c)
e = d + 1
Problem: an article is bought for rs . 705 and sold for rs . 900 , find the gain percent ?
Options: a ) 27.65 % , b ) 33 1 / 2 % , c ) 33 1 / 3 % , d ) 33 5 / 3 % , e ) 35 1 / 3 %
Rationale: "705 - - - - 195 100 - - - - ? = > 27.65 % answer : a"
Answer: a
Python program:
a = 900 * 100
b = a / 705
c = 100 - b
Problem: what will be the percentage increase in the area of the cube ' s surface if each of the cube ' s edges grows by 10 % ?
Options: a ) 25 % , b ) 28 % , c ) 21 % , d ) 30 % , e ) 32 %
Rationale: "the question is very easy . my logic is the following : a surface = 6 * a ^ 2 after 10 % increase a surface = 6 * ( ( 1.1 a ) ^ 2 ) = 6 * 1.21 * a ^ 2 the increase in the surface area = ( 6 * 1.21 * a ^ 2 - 6 * a ^ 2 ) / 6 * a ^ 2 = ( 6 * a ^ 2 ( 1.21 - 1 ) ) / ( 6 * a ^ 2 ) = 1.21 - 1 = 0.21 = 21 % answer : c"
Answer: c
Python program:
a = 10 / 100
b = 1 + a 
c = b ** 2
d = c - 1
e = d * 100
Problem: how many positive integers less than 500 can be formed using the numbers 1 , 2,3 , and 5 for digits , each digit being used only once .
Options: a ) 34 , b ) 677 , c ) 197 , d ) 177 , e ) 191
Rationale: "single digit numbers = 4 double digit numbers = 4 x 3 = 12 three digit numbers = 3 x 3 x 2 x 1 = 18 total = 34 answer : a"
Answer: a
Python program:
a = 500 - 1
b = a - 4
c = b - 1
Problem: a certain clock marks every hour by striking a number of times equal to the hour , and the time require for a stroke is exactly equal to the time interval between strokes . at 6 : 00 the time lapse between the beginning of the first stoke and the end of the last stroke is 22 seconds . at 11 : 00 , how many seconds elapse between the beginning of the first stroke and the end of the last stroke ?
Options: a ) 34 , b ) 38 , c ) 36 , d ) 40 , e ) 42
Rationale: "at 6 ' o clock , there would be 6 strikes . first strike , then a short interval , the second strike , then a short interval and so on till the 6 th strike . so there would be in all 5 intervals between 6 strikes . similarly , between 11 strikes , there would be 10 intervals . according to the question , the time spent in the strike and the interval is same . at 6 ' o clock , the 6 strikes and the 5 intervals together take 22 sec so each strike and each interval takes 2 secs . at 11 ' o clock , the 11 strikes and 10 intervals will take 2 * ( 11 + 10 ) = 42 secs e"
Answer: e
Python program:
a = 11 - 1
b = a + 11 
c = 6 - 1
d = c + 6 
e = 22 / d
f = b * e