euclaise/mathqa_programs huggingface dataset:
Problem: a train 120 m long crosses a platform 120 m long in 6 sec ; find the speed of the train ?
Options: a ) 144 kmph , b ) 58 kmph , c ) 54 kmph , d ) 94 kmph , e ) 59 kmph
Rationale: "d = 120 + 120 = 240 t = 6 s = 240 / 6 * 18 / 5 = 144 kmph answer : a"
Answer: a
Python program:
a = 120 * const_0_2778
b = 6 * a
c = b - 120
Problem: an investor can sell her microtron stock for 36 $ per share and her dynaco stock for 48 $ per share , if she sells 300 shares altogether , some of each stock , at an average price per share of 40 $ , how many shares of dynaco stock has she sold ?
Options: a ) 52 , b ) 75 , c ) 92 , d ) 100 , e ) 184
Rationale: "w 1 / w 2 = ( a 2 - aavg ) / ( aavg - a 1 ) = ( 48 - 40 ) / ( 40 - 36 ) = 8 / 4 = 2 / 1 = number of microtron stocks / number of dynaco stocks so for every 2 microtron stock , she sold 1 dynaco stock . so out of 300 total stocks , ( 1 / 3 ) th i . e . 300 / 3 = 100 must be dynaco stock . answer ( d )"
Answer: d
Python program:
a = 48 - 36
b = 40 / a
c = 300 * b
d = 36 + 48 
e = 48 - 36
f = d / e
g = c / f
Problem: working at constant rate , pump x pumped out half of the water in a flooded basement in 3 hours . the pump y was started and the two pumps , working independently at their respective constant rates , pumped out rest of the water in 3 hours . how many hours would it have taken pump y , operating alone at its own constant rate , to pump out all of the water that was pumped out of the basement ?
Options: a ) a . 20 , b ) b . 12 , c ) c . 14 , d ) d . 18 , e ) e . 24
Rationale: "rate of x = 1 / 8 rate of x + y = 1 / 6 rate of y = 1 / 6 - 1 / 8 = 1 / 24 20 hours a"
Answer: a
Python program:
a = 3 + 3 
b = 1 + a 
c = b + 1 
d = c + 1 
e = d + 1 
f = e + 1 
g = f + 3 
h = g + 1 
i = h + 1 
j = i + 1 
k = j + 1 
l = k + 1 
m = l + 1
Problem: two spherical balls lie on the ground touching . if one of the balls has a radius of 10 cm , and the point of contact is 12 cm above the ground , what is the radius of the other ball ?
Options: a ) 2 cm , b ) 5 / 2 cm , c ) 5 cm , d ) 15 / 2 cm , e ) none of the these
Rationale: "similar triangle properties . . 2 / r + 10 = 10 / r - 10 giving r = 15 / 2 . answer : d"
Answer: d
Python program:
a = 10 + 12 
b = a + 10
Problem: ( 753 x 753 + 247 x 247 - 753 x 247 ) / ( 753 x 753 x 753 + 247 x 247 x 247 ) = ?
Options: a ) 1 / 1000 , b ) 1 / 506 , c ) 253 / 500 , d ) 253 / 1000 , e ) none of these
Rationale: given exp . = ( a ^ 2 + b ^ 2 - ab ) / ( a ^ 3 + b ^ 3 ) = 1 / ( a + b ) = 1 / ( 753 + 247 ) = 1 / 1000 answer : a
Answer: a
Python program:
a = 753 * 753
b = 247 * 247
c = a + b 
d = 753 * 247
e = c - d
f = 753 * 753
g = f * 753
h = 247 * 247
i = h * 247
j = g + i 
k = e / j
Problem: the area of a square field is 7201 sq m . how long will a lady take to cross the field diagonally at the rate of 1.2 km / hr ?
Options: a ) 6 min , b ) 5 min , c ) 5.5 min , d ) 4 min , e ) 3 min
Rationale: "area of a square field = 7201 sq m let the side of square = a a ^ 2 = 7201 = > a = 84.86 diagonal = ( 2 ) ^ ( 1 / 2 ) * a = 1.414 * 84.86 = 120 speed of lady = 1.2 km / hour = 1200 m / hour = 20 m / min time taken by lady to cross the field diagonally = 120 / 20 = 6 min answer a"
Answer: a
Python program:
a = 1 * 2
b = 7201 / a
Problem: one pipe can fill a tank three times as fast as another pipe . if together the two pipes can fill the tank in 36 minutes , then the slower pipe alone will be able to fill the tank in :
Options: a ) 144 min , b ) 145 min , c ) 150 min , d ) 200 min , e ) 250 min
Rationale: "slower pipe alone fill the tank = x faster pipe will fill in x / 3 min 1 / x + 3 / x = 1 / 36 x = 144 min answer a"
Answer: a
Python program:
a = 1 + 4 
b = a * 36
Problem: the tax on a commodity is diminished by 22 % but its consumption is increased by 9 % . find the decrease percent in the revenue derived from it ?
Options: a ) 20 % , b ) 18 % , c ) 15 % , d ) 12 % , e ) 14 %
Rationale: "100 * 100 = 10000 78 * 109 = 8502 10000 - - - - - - - 1200 100 - - - - - - - ? = 15 % answer : c"
Answer: c
Python program:
a = 100 + 9 
b = 100 - 22
c = a * b
d = c / 100
e = 100 - d
Problem: each of the three people individually can complete a certain job in 4 , 6 , and 8 hours , respectively . what is the lowest fraction of the job that can be done in 1 hour by 2 of the people working together at their respective rates ?
Options: a ) 3 / 8 , b ) 5 / 12 , c ) 7 / 24 , d ) 11 / 36 , e ) 13 / 48
Rationale: "the two slowest people work at rates of 1 / 6 and 1 / 8 of the job per hour . the sum of these rates is 1 / 6 + 1 / 8 = 7 / 24 of the job per hour . the answer is c ."
Answer: c
Python program:
a = 1 / 6
b = 1 / 8
c = a + b
Problem: a man can row at 4 kmph in still water . if the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back , how far is the place ?
Options: a ) 2.4 km , b ) 2.9 km , c ) 3.4 km , d ) 1.9 km , e ) 5.6 km
Rationale: "explanation : speed in still water = 4 kmph speed of the current = 1 kmph speed downstream = ( 4 + 1 ) = 5 kmph speed upstream = ( 4 - 1 ) = 3 kmph let the required distance be x km total time taken = 1 hour â ‡ ’ x / 5 + x / 3 = 1 â ‡ ’ 3 x + 5 x = 15 â ‡ ’ 8 x = 15 â ‡ ’ x = 1.9 km answer : option d"
Answer: d
Python program:
a = 4 - 1
b = a * 3
c = b / 4
Problem: two numbers are respectively 20 % and 25 % more than a third number . the percentage that is first of the second is ?
Options: a ) 80 % , b ) 85 % , c ) 96 % , d ) 125 % , e ) 150 %
Rationale: "explanation : i ii iii 120 125 100 125 - - - - - - - - - - 120 100 - - - - - - - - - - - ? = > 96 % answer is c"
Answer: c
Python program:
a = 20 + 100 
b = 25 + 100 
c = a / b
d = c * 100
e = 100 - d
Problem: if 5 % more is gained by selling an article for rs . 360 than by selling it for rs . 340 , the cost of the article is
Options: a ) 289 , b ) 400 , c ) 200 , d ) 288 , e ) 111
Rationale: "explanation : let c . p . be rs . x . then , 5 % of x = 360 - 340 = 20 x / 20 = 20 = > x = 400 answer : b"
Answer: b
Python program:
a = 360 - 340
b = 5 / 100
c = a / b
Problem: weights of two friends ram and shyam are in the ratio 6 : 5 . if ram ' s weight is increased by 10 % and total weight of ram and shyam become 82.8 kg , with an increases of 15 % . by what percent did the weight of shyam has to be increased ?
Options: a ) 19 % , b ) 10 % , c ) 21 % , d ) 16 % , e ) none
Rationale: "solution : given ratio of ram and shayam ' s weight = 6 : 5 hence , ( x - 15 ) / ( 15 - 10 ) = 6 / 5 or , x = 21 % . answer : option c"
Answer: c
Python program:
a = 15 - 10
b = 6 / 5
c = a * b
d = 15 + c
Problem: how many of the positive factors of 36 , 84 and how many common factors are there in numbers ?
Options: a ) 2 , b ) 4 , c ) 3 , d ) 5 , e ) 6
Rationale: "factors of 36 - 1 , 2 , 3 , 4 , 6 , 9 , 12 , 18 , 36 factors of 84 - 1 , 2 , 3 , 4 , 6 , 7 , 12 , 14 , 21 , 28 , 42 , 84 comparing both , we have six common factors of 36 and 84 - 1,2 , 3,4 , 6,12 , answer ( e )"
Answer: e
Python program:
a = 84 / 36
Problem: jaclyn buys $ 20 000 worth of debentures in a company . she earns 9.5 % p . a . simple interest , paid to her quarterly ( that is , every 3 months ) . if the agreed period of the debenture was 18 months : calculate the amount of interest jaclyn will earn for each quarter
Options: a ) 475 , b ) 234 , c ) 289 , d ) 345 , e ) none of these
Rationale: "explanation : i = ( p x r x t ) / 100 = 30000 * 9.5 / 100 * ( 18 / 12 ) ^ 1 / 6 = 475 answer : a"
Answer: a
Python program:
a = 100 * 100
b = a * 9
c = b / 100
d = c / 4
Problem: if 5 parallel lines in a plane is intersected by a family of another 8 parallel lines , how many parallelograms are there in the network thus formed ?
Options: a ) 280 , b ) 63 , c ) 120 , d ) 160 , e ) 1260
Rationale: parallelogram can formed by 2 horizontal and 2 vertical lines for horizontal 5 c 2 for vertical 8 c 2 total parallelogram is 5 c 2 * 8 c 2 = 10 * 28 = 280 answer : a
Answer: a
Python program:
a = 5 - 1
b = 5 * a
c = b / 2
d = 8 - 1
e = 8 * d
f = e / 2
g = c * f
Problem: in a group of buffaloes and ducks , the number of legs are 24 more than twice the number of heads . what is the number of buffaloes in the group ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: let no . of buffaloes be x & no . of ducks be y buffaloes have 4 legs while ducks have 2 4 x + 2 y = 2 * ( x + y ) + 24 = > 4 x + 2 y - 2 x - 2 y = 24 = > x = 12 number of buffaloes in the group = 12 answer : a
Answer: a
Python program:
a = 24 / 2
Problem: a man started driving at a constant speed , from the site of a blast , the moment he heard the blast . he heard a second blast after a time of 30 mins and 24 seconds . if the second blast occurred exactly 30 mins after the first , how many meters was he from the site when he heard the second blast ? ( speed of sound = 330 m / s )
Options: a ) 6810 , b ) 7920 , c ) 9030 , d ) 10,140 , e ) 11,250
Rationale: the distance the sound traveled to the man is 24 * 330 = 7920 meters the answer is b .
Answer: b
Python program:
a = 330 * 24
Problem: what is the thousandths digit in the decimal equivalent of 57 / 5000 ?
Options: a ) 0 , b ) 1 , c ) 3 , d ) 5 , e ) 6
Rationale: 57 / 5000 = 57 / ( 5 * 10 ^ 3 ) = ( 57 / 5 ) * 10 ^ - 3 = 11.4 * 10 ^ - 3 = . 0114 thousandths digit = 1 answer b
Answer: b
Python program:
a = 57 / 5000
b = 100 * a
c = math.floor(b)
Problem: 6 / 8 of the population of the country of venezia lives in montague province , while the rest lives in capulet province . in the upcoming election , 80 % of montague residents support romeo , while 70 % of capulet residents support juliet ; each resident of venezia supports exactly one of these two candidates . rounded if necessary to the nearest percent , the probability that a juliet supporter chosen at random resides in capulet is
Options: a ) 28 % , b ) 54 % , c ) 45 % , d ) 72 % , e ) 78 %
Rationale: "total population = 80 ( assume ) . 6 / 8 * 80 = 60 people from montague . 2 / 8 * 80 = 20 people from capulet . 0.2 * 60 = 12 people from montague support juliet . 0.7 * 20 = 14 people from capulet support juliet . the probability that a juliet supporter chosen at random resides in capulet is 14 / ( 12 + 14 ) = ~ 54 answer : b ."
Answer: b
Python program:
a = 70 / 100
b = 8 - 6
c = b / 8
d = a * c
e = 100 - 80
f = e / 100
g = 6 / 8
h = f * g
i = 70 / 100
j = 8 - 6
k = j / 8
l = i * k
m = h + l 
n = d / m
o = n * 100
Problem: 45 persons can repair a road in 12 days , working 5 hours a day . in how many days will 30 persons , working 6 hours a day , complete the work ?
Options: a ) 10 , b ) 15 , c ) 13 , d ) 18 , e ) 19
Rationale: "let the required number of days be x . less persons , more days ( indirect proportion ) more working hours per day , less days ( indirect proportion ) persons 30 : 45 : : 12 : x working hours / day 6 : 5 30 x 6 x x = 45 x 5 x 12 x = ( 45 x 5 x 12 ) / ( 30 x 6 ) x = 15 answer b"
Answer: b
Python program:
a = 45 * 12
b = a * 5
c = 30 * 6
d = b / c
Problem: the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg . what is the weight of the new person ?
Options: a ) 75 , b ) 65 , c ) 85 , d ) 95 , e ) 80
Rationale: "total increase in weight = 8 × 2.5 = 20 if x is the weight of the new person , total increase in weight = x − 65 = > 20 = x - 65 = > x = 20 + 65 = 85 answer is c ."
Answer: c
Python program:
a = 8 * 2
b = a + 65
Problem: it takes 60 identical printing machines 4 hours to print 200,000 cards . how long would it take 50 of these machines to print the same total ?
Options: a ) 10 hr , b ) 5 hr , c ) 6 hr , d ) 4 hr 30 min , e ) 5 hr 12 min
Rationale: "50 % of 60 = 40 % or 0.30 4 hr x 60 min = 240 min 240 min x 0.30 = 72 min or 1 hr and 12 min 1 hr and 12 min + 4 hr = 5 hr and 12 min answer is e"
Answer: e
Python program:
a = 60 / 4
b = 200 / 0
c = a + b
Problem: in a party , there are rows arranged with 1220 and 30 chairs and there were 3 left in all the cases . when there were 11 rows . there were no chair left . if 30 chairs were added . then what will be the reminder ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: lcm of 12 , 2030 is 120 . so the number is in the form of 120 x + 3 which is divisible by 11 , by placing x = 3 , we get 363 which is divisible by 11 and the multiple of 120 when 3 is subtracted from 363 . so the no . is 363 . so when 30 is added to it and is divided by 11 we get remainder as 8 answer : a
Answer: a
Python program:
a = 11 - 3
Problem: for every integer n ≥ 3 , the function g ( n ) is defined as the product of all the odd integers from 1 to n , inclusive . what is the value of g ( 106 ) – g ( 103 ) ?
Options: a ) 100 , b ) 99 , c ) 98 , d ) 102 , e ) 104
Rationale: "g ( 106 ) = 1 * 3 * 5 * 7 * 9 * . . . * 99 * 101 * 103 * 105 g ( 103 ) = 1 * 3 * 5 * 7 * 9 * . . . * 99 * 101 * 103 g ( 106 ) - g ( 103 ) = 1 * 3 * 5 * 7 * 9 * . . . * 99 * 101 * 103 * 105 - 1 * 3 * 5 * 7 * 9 * . . . * 99 * 101 * 103 = 1 * 3 * 5 * 7 * 9 * . . . * 103 * ( 105 - 1 ) = 1 * 3 * 5 * 7 * 9 * . . . * 99 * 101 * 103 * 104 hence : e"
Answer: e
Python program:
a = 106 - 1
Problem: if x is 11 percent greater than 90 , then x =
Options: a ) 99.9 , b ) 91.0 , c ) 88.0 , d ) 70.9 , e ) 71.2
Rationale: "11 % of 90 = ( 90 * 0.11 ) = 9.9 11 % greater than 90 = 90 + 9.9 = 99.9 answer is clearly a ."
Answer: a
Python program:
a = 11 / 100
b = a * 90
c = 90 + b
Problem: the sides of a triangle are in the ratio 5 : 12 : 13 and its perimeter is 240 m , its area is ?
Options: a ) 150 , b ) 882 , c ) 277 , d ) 261 , e ) 120
Rationale: "5 x + 12 x + 13 x = 240 = > x = 8 a = 40 , b = 96 , c = 104 s = ( 40 + 96 + 104 ) / 2 = 120 answer : e"
Answer: e
Python program:
a = 5 + 12 
b = a + 13 
c = 240 / b
d = 240 * c
Problem: total 22 matches are conducted in knockout match type . how many players will be participated in that tournament ?
Options: a ) 24 , b ) 26 , c ) 21 , d ) 20 , e ) 19
Rationale: "21 players answer : c"
Answer: c
Python program:
a = 22 + 1
Problem: in an intercollegiate competition that lasted for 3 days , 150 students took part on day 1 , 110 on day 2 and 140 on day 3 . if 75 took part on day 1 and day 2 and 25 took part on day 2 and day 3 and 15 took part on all three days , how many students took part only on day 2 ?
Options: a ) 50 , b ) 35 , c ) 45 , d ) 25 , e ) 60
Rationale: "day 1 & 2 = 75 ; only day 1 & 2 ( 75 - 15 ) = 60 , day 2 & 3 = 25 ; only day 2 & 3 ( 25 - 15 ) = 10 , only day 2 = 110 - ( 60 + 10 + 15 ) = 25 answer : d"
Answer: d
Python program:
a = 15 + 75 
b = 75 + 25 
c = b + 15 
d = 110 - c
e = 15 + d 
f = e / 2
g = a + f 
h = 150 - g
Problem: jim drove 923 miles of a 1200 miles journey . how many more miles does he need to drive to finish his journey ?
Options: a ) 113 miles , b ) 277 miles , c ) 456 miles , d ) 887 miles , e ) 767 miles
Rationale: the number of miles to drive to finish his journey is given by 1200 - 923 = 277 miles correct answer b
Answer: b
Python program:
a = 1200 - 923
Problem: on increasing the price of t . v . sets by 70 % , their sale decreases by 20 % . what is the effect on the revenue receipts of the shop ?
Options: a ) 4 , b ) 5 , c ) 36 , d ) 2 , e ) 7
Rationale: "explanation : let the price be = rs . 100 , and number of units sold = 100 then , sale value = rs . ( 100 × 100 ) = rs . 10000 new sale value = rs . ( 170 × 80 ) = rs . 13600 increase % = 3600 / 10000 × 100 = 36 % answer : c"
Answer: c
Python program:
a = 100 + 70 
b = 100 + 70 
c = b * 20
d = c / 100
e = d + 100 
f = a - e
Problem: how many cubes of 10 cm edge can be put in a cubic box of 1 m edge ?
Options: a ) 4000 , b ) 2000 , c ) 3000 , d ) 5000 , e ) 1000
Rationale: "( 110 × 100 × 100 ) / 10 × 10 × 10 = 1000 answer is e ."
Answer: e
Python program:
a = volume_cube / (
Problem: a train running at the speed of 60 km / hr crosses a pole in 36 seconds . find the length of the train ?
Options: a ) 150 meter , b ) 600 meter , c ) 167 meter , d ) 719 meter , e ) 169 meter
Rationale: "speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 36 = 600 meter answer : b"
Answer: b
Python program:
a = 60 * 1000
b = a / 3600
c = b * 36
Problem: the area of a parallelogram is 128 sq m and its altitude is twice the corresponding base . then the length of the base is ?
Options: a ) 8
b ) 7
c ) 6
d ) 5
e ) 2
Rationale: 2 x * x = 128 = > x = 8 answer : a
Answer: a
Python program:
a = 128 / 2
b = math.sqrt(a)
Problem: the total marks obtained by a student in mathematics and physics is 60 and his score in chemistry is 20 marks more than that in physics . find the average marks scored in mathamatics and chemistry together ?
Options: a ) 40 , b ) 99 , c ) 88 , d ) 77 , e ) 66
Rationale: "let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 60 and c - p = 20 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 60 + 20 ) / 2 = 40 . answer : a"
Answer: a
Python program:
a = 60 + 20 
b = a / 2
Problem: a , b , and c were started a business , the total profit for one year is $ 56700 . the profit sharing ratio is 8 : 9 : 10 ( according to their investment they divide their profit ) . what is the profit of c ?
Options: a ) $ 5670 , b ) $ 18900 , c ) $ 21000 , d ) $ 13500 , e ) $ 27000
Rationale: a : b : c = 8 + 9 + 10 = 27 ; c ' share = 10 / 27 of the total profit . c will get = 10 / 27 * $ 56700 = $ 21000 . answer : c
Answer: c
Python program:
a = 8 + 9 
b = a + 10 
c = 10 / b
d = c * 56700
Problem: if the product of the integers from 1 to n is divisible by 1029 , what is the least possible value of n ?
Options: a ) 7 , b ) 14 , c ) 21 , d ) 28 , e ) 35
Rationale: 1029 = 7 x 7 x 7 x 3 n must include at least 7 , 2 * 7 , and 3 * 7 . the answer is c .
Answer: c
Python program:
a = 1029 / 3
b = 3 + 4 
c = a / b
d = 3 + 4 
e = c / d
f = e * 3
Problem: average families of 4 pay $ 3000 for their health insurance deductibles annually . there will be a 2 / 3 increase in the deductibles for next year . how much more will the average family pay in deductibles next year ?
Options: a ) $ 1000 , b ) $ 2000 , c ) $ 3000 , d ) $ 4000 , e ) $ 5000
Rationale: a certain percentage of questions in the quant section of the gmat are just ' math questions ' - you ' ll use a formula , do some calculations and you ' ll have the answer . this is one of those types of questions . you still have to write everything down and stay organized , but the work involved is relatively straight - forward . here , we ' re told that the current annual deductible is $ 3000 and that the deductible is to be increased by 2 / 3 . we ' re asked how much more will the deductible cost a family next year . original deductible = $ 3000 increase in deductible = 2 / 3 the answer is calculated by the equation : $ 3000 × 2 / 3 = $ 2000 . b
Answer: b
Python program:
a = 3000 * 2
b = a / 3
Problem: a certain university will select 1 of 3 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department . if none of the candidates is eligible for a position in both departments , how many different sets of 3 candidates are there to fill the 3 positions ?
Options: a ) 42 , b ) 70 , c ) 140 , d ) 135 , e ) 315
Rationale: "1 of 3 will be chosen for the math 2 of 10 will be chosen for the computer none of the 3 chosen people can be in more than one departments . we can choose any of the 3 candidates for the math dep . , which gives as 3 selections . we can choose 2 of the 10 candidates for the computer dep . , which gives us 2 selections and 8 rejections . so , the way to find how many different selections of 2 candidates we can have for the computer dep . , we do : 10 ! / 2 ! * 8 ! = ( 9 * 10 ) / 2 = 90 / 2 = 45 . we are multiplying our individual selections : 3 * 45 = 135 in the bolded part , we do n ' t have to multiply all of the numbers , as those in 8 ! are included in 10 ! , so we simplify instead . ans d"
Answer: d
Python program:
a = 10 * 3
b = a * 3
Problem: at the end of the month , a certain ocean desalination plant ’ s reservoir contained 6 million gallons of water . this amount is twice the normal level . if this amount represents 60 % of the reservoir ’ s total capacity , how many million gallons short of total capacity is the normal level ?
Options: a ) 15 , b ) 10 , c ) 5 , d ) 20 , e ) 25
Rationale: "the q talks of total capacity , normal level , present level , shortage etc . . so it is all about not going wrong in these terms 6 mg = 60 % of total . . total = 6 / . 6 = 10 mg . . normal level = 1 / 2 of 10 = 5 mg . . shortage of normal level = 10 - 5 = 5 mg . . c"
Answer: c
Python program:
a = 6 / 2
b = 60 / 100
c = a / b
Problem: two interconnected , circular gears travel at the same circumferential rate . if gear a has a diameter of 60 centimeters and gear b has a diameter of 50 centimeters , what is the ratio of the number of revolutions that gear a makes per minute to the number of revolutions that gear b makes per minute ?
Options: a ) 6 : 5 , b ) 9 : 25 , c ) 5 : 6 , d ) 25 : 9 , e ) can not be determined from the information provided
Rationale: "same circumferential rate means that a point on both the gears would take same time to come back to the same position again . hence in other words , time taken by the point to cover the circumference of gear a = time take by point to cover the circumference of gear b time a = 2 * pi * 25 / speed a time b = 2 * pi * 30 / speed b since the times are same , 50 pi / speed a = 60 pi / speed b speeda / speed b = 50 pi / 60 pi = 5 / 6 correct option : c"
Answer: c
Python program:
a = 50 / 2
b = circumface / (
Problem: a sum of money lent out at s . i . amounts to a total of $ 600 after 2 years and to $ 850 after a further period of 5 years . what was the initial sum of money that was invested ?
Options: a ) $ 500 , b ) $ 520 , c ) $ 540 , d ) $ 560 , e ) $ 580
Rationale: s . i for 5 years = $ 850 - $ 600 = $ 250 the s . i . is $ 50 / year s . i . for 2 years = $ 100 principal = $ 600 - $ 100 = $ 500 the answer is a .
Answer: a
Python program:
a = 850 - 600
b = 2 / 5
c = a * b
d = 600 - c
Problem: a train passes a station platform in 46 sec and a man standing on the platform in 16 sec . if the speed of the train is 54 km / hr . what is the length of the platform ?
Options: a ) 227 , b ) 240 , c ) 460 , d ) 450 , e ) 455
Rationale: "speed = 54 * 5 / 18 = 15 m / sec . length of the train = 15 * 16 = 240 m . let the length of the platform be x m . then , ( x + 240 ) / 46 = 15 = > x = 450 m . answer : d"
Answer: d
Python program:
a = 54 * const_0_2778
b = 16 * a
Problem: if the area of a square with sides of length 5 centimeters is equal to the area of a rectangle with a width of 4 centimeters , what is the length of the rectangle , in centimeters ?
Options: a ) 4 , b ) 8 , c ) 12 , d ) 7 , e ) 18
Rationale: "let length of rectangle = l 5 ^ 2 = l * 4 = > l = 25 / 4 = 7 answer d"
Answer: d
Python program:
a = 5 ** 2
b = a / 4
Problem: a rectangular grassy plot 110 m . by 65 m has a gravel path 2.5 m wide all round it on the inside . find the cost of gravelling the path at 80 paise per sq . metre
Options: a ) rs 680 , b ) rs 780 , c ) rs 880 , d ) rs 480 , e ) rs 980
Rationale: "area of the plot = 110 m * 65 m = 7150 sq . m area of plot excluding gravel = 105 m * 60 m = 6300 sq . m area of gravel = 7150 sq . m - 6300 sq . m = 850 sq . m cost of building it = 850 sq . m * 80 = 68000 p in rs = 68000 / 100 = rs 680 answer : a"
Answer: a
Python program:
a = 110 * 65
b = 2 * 5
c = 110 - b
d = 2 * 5
e = 65 - d
f = c * e
g = a - f
h = g * 80
i = h / 100
Problem: a certain board game is played by rolling a pair of fair 6 - sided dice and then moving one ' s piece forward the number of spaces indicated by the sum showing on the dice . a player is frozen if her opponent ' s piece comes to rest in the space already occupied by her piece . if player a is about to roll and is currently 8 spaces behind player b , what is the probability that player b will be frozen after player a rolls ?
Options: a ) 1 / 12 , b ) 5 / 36 , c ) 1 / 6 , d ) 1 / 3 , e ) 17 / 36
Rationale: no . of possible outcomes = 6 * 6 = 36 no . of outcomes that result a total of 8 ( as a is 8 spaces behind b ) = 5 ( ( 2,6 ) , ( 3,5 ) , ( 4,4 ) , ( 5,3 ) , ( 6,2 ) ) so , the probability = 5 / 36 ( option b )
Answer: b
Python program:
a = 4 + 1 
b = 6 * 6
c = a / b