euclaise/mathqa_programs huggingface dataset:
Problem: if price of t . v set is reduced by 22 % , then its sale increases by 86 % , find net effect on sale value
Options: a ) 44 , b ) 45 , c ) 46 , d ) 47 , e ) 48
Rationale: "- a + b + ( ( - a ) ( b ) / 100 ) = - 22 + 86 + ( - 22 * 86 ) / 100 = - 22 + 86 - 19 = 45 answer : b"
Answer: b
Python program:
a = 100 - 22
b = a / 100
c = 100 + 86 
d = c / 100
e = b * d
f = e - 1
g = f * 100
Problem: there are 76 lights which are functional and each is controlled by a separate on / off switch . two children a and b start playing with the switches . a starts by pressing every third switch till he reaches the end . b , thereafter , presses every fifth switch till he too reaches the end . if all switches were in off position at the beggining , how many lights are switched on by the end of this operation ?
Options: a ) 28 , b ) 30 , c ) 32 , d ) 34 , e ) 36
Rationale: "editing my solution : number of switches = 76 number of switches turned on by a : 3 , 6 , . . . 75 = 25 number of switches turned on by b : 5 , 10 , . . . . 75 = 15 few switches are turned on by a and later turned off by b : lcm ( 3,5 ) = 15 x = 15 , 30 , . . . . 90 = 6 . subtract the above 6 switches from both a and b as they are turned off . number of switches that are turned on = ( 25 - 6 ) + ( 15 - 6 ) = 28 answer : a"
Answer: a
Python program:
a = 76 / 3
b = math.floor(a)
c = 1 + 4 
d = 76 / c
e = math.floor(d)
f = b + e 
g = 1 + 4 
h = 3 * g
i = 76 / h
j = math.floor(i)
k = j * 2
l = f - k
Problem: each month , after jill pays for rent , utilities , food , and other necessary expenses , she has one fifth of her net monthly salary left as discretionary income . of this discretionary income , she puts 30 % into a vacation fund , 20 % into savings , and spends 35 % on eating out and socializing . this leaves her with $ 99 dollar , which she typically uses for gifts and charitable causes . what is jill ’ s net monthly salary ?
Options: a ) $ 2400 , b ) $ 3300 , c ) $ 6000 , d ) $ 6400 , e ) $ 9600
Rationale: "let x be the monthly salary 15 % of 1 / 5 * x = 99 x = 3300 answer b"
Answer: b
Python program:
a = 3 + 2 
b = 100 * a
c = 30 + 20 
d = c + 35 
e = 100 - d
f = 99 / e
g = b * f
Problem: a goat is tied to one corner of a square plot of side 12 m by a rope 7 m long . find the area it can graze ?
Options: a ) 32
b ) 36.5
c ) 38.5
d ) 39
e ) 39.5
Rationale: area covered by goat = pi * r ^ 2 / 4 ( here we divide by 4 because rope is tied at the corner of the plot and only 1 / 4 part , the goat can graze ) where r = 7 m = length of rope so area = ( 22 / 7 ) * 7 * 7 / 4 = 38.5 sq m answer : c
Answer: c
Python program:
a = circle_area / (
Problem: a retailer bought a hat at wholesale and marked it up 60 % to its initial price of $ 24 . by how many more dollars does he need to increase the price to achieve a 100 % markup ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "let x be the wholesale price . then 1.6 x = 24 and x = 24 / 1.6 = 15 . to achieve a 100 % markup , the price needs to be $ 30 . the retailer needs to increase the price by $ 6 more . the answer is d ."
Answer: d
Python program:
a = 100 + 60 
b = a / 100
c = 24 / b
d = c * 2
e = d - 24
Problem: the cube root of . 000343 is
Options: a ) 0.7 , b ) 0.07 , c ) 0.007 , d ) 7 , e ) none of these
Rationale: "explanation : ( . 000343 ) 1 / 3 = ( 343 / 106 ) 1 / 3 = ( 7 * 7 * 7 / 102 * 102 * 102 ) 1 / 3 = 7 / 102 = 7 / 100 = 0.07 answer b"
Answer: b
Python program:
a = 343 / 1000
b = a / 1000
c = 1 / 3
d = b ** c
Problem: a crow leaves its nest , and flies back and forth from its nest to a nearby ditch to gather worms . the distance between the nest and the ditch is 200 meters . in one and a half hours , the crow manages to bring worms to its nest 15 times . what is the speed of the crow in kilometers per hour ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 6
Rationale: "the distance between the nest and the ditch is 200 meters . 15 times mean = a crow leaves its nest , and flies back ( going and coming back ) i . e . 2 times we get total 30 rounds . so the distance is 30 * 200 = 6000 . d = st 6000 / 1.5 = t , i think we can take 6000 meters as 6 km , then only we get t = 4 . ( 1000 meters = 1 km ) d )"
Answer: d
Python program:
a = 15 * 2
b = 200 * a
c = b / 1000
d = 15 / 10
e = c / d
Problem: 3 seventh of a number is 12 more than 40 % of that number . what will be the 30 % of that number ?
Options: a ) a ) 148 , b ) b ) 210 , c ) c ) 63 , d ) d ) 248 , e ) e ) 258
Rationale: 3 / 7 x – 40 / 100 x = 12 x = 35 * 12 35 * 12 * 30 / 100 = 126 / 2 = 63 answer : c
Answer: c
Python program:
a = 30 / 100
b = 3 + 4 
c = 3 / b
d = 40 / 100
e = c - d
f = 12 / e
g = a * f
h = g / 2
Problem: the sum of 4 consecutive even numbers is 36 . find the sum of the squares of these numbers ?
Options: a ) 296 , b ) 252 , c ) 344 , d ) 388 , e ) none of these
Rationale: let the four numbers be x , x + 2 , x + 4 and x + 6 . = > x + x + 2 + x + 4 + x + 6 = 36 = > 4 x + 12 = 36 = > x = 6 the numbers are 6 , 8 , 10 and 12 . sum of their squares = 62 + 82 + 102 + 122 = 36 + 64 + 100 + 144 = 344 . answer : c
Answer: c
Python program:
a = 4 + 10 
b = a ** 2
c = 12 * 12
d = b + c
Problem: two trains , each 150 m long , moving in opposite directions , cross other in 8 sec . if one is moving twice as fast the other , then the speed of the faster train is ?
Options: a ) 90 , b ) 98 , c ) 60 , d ) 88 , e ) 12
Rationale: "let the speed of the slower train be x m / sec . then , speed of the train = 2 x m / sec . relative speed = ( x + 2 x ) = 3 x m / sec . ( 150 + 150 ) / 8 = 3 x = > x = 25 / 2 . so , speed of the faster train = 50 / 2 = 25 * 18 / 5 = 90 km / hr . answer : a"
Answer: a
Python program:
a = 150 + 150 
b = 1 + 2 
c = 8 * b
d = a / c
e = d * 2
f = e * 3600
g = f / 1000
Problem: with an average speed of 40 km / hr a car reaches its destination on time . if it goes with an average speed of 35 km / h , it is late by 15 minutes . the total journey is ?
Options: a ) 30 km , b ) 40 km , c ) 70 km , d ) 80 km , e ) 90 km
Rationale: let the total journey be x km . x / 35 - x / 40 = 15 / 60 solving for x , we get x = 70 therefore , total journey = 70 km . answer : c
Answer: c
Python program:
a = math.gcd(40, 35)
b = 40 / a
c = 15 / const_60
d = b * c
e = 35 * d
Problem: find the remainder q when 12 ^ 190 is divided by 1729 ?
Options: a ) 12 , b ) 1 , c ) 1728 , d ) 1717 , e ) 4
Rationale: 12 ^ ( 190 ) can be written as . ( ( 12 ^ 3 ) ^ 63 ) * 12 . 12 ^ 3 when divided by 1729 gives a remainder q - 1 . so in the numerator we have - 12 . now acccording to remainder theorm the answer will be 1729 - 12 = 1717 . d
Answer: d
Python program:
a = 1729 - 12
Problem: how much 70 % of 100 is greater than 60 % of 80 ?
Options: a ) 18 , b ) 99 , c ) 22 , d ) 26 , e ) 71
Rationale: "( 70 / 100 ) * 100 – ( 60 / 100 ) * 80 70 - 48 = 22 answer : c"
Answer: c
Python program:
a = 70 * 100
b = a / 100
c = 60 * 80
d = c / 100
e = b - d
Problem: the main line train starts at 5.00 am and the harbor line train starts at 5.02 am . each train has the frequency of 10 minutes . if a guy goes in the morning at a random time what is the probability of he getting main line train ?
Options: a ) . 5 , b ) 0.6 , c ) 0.4 , d ) 0.7 , e ) 0.8
Rationale: out of 10 minutes there is only 2 minutes chance of getting harbour line train and there is 8 minutes chance for getting main line train . so , probability = 8 / 10 = 0.8 answer : e
Answer: e
Python program:
a = 10 - 2
b = a / 10
Problem: an uneducated retailer marks all his goods at 60 % above the cost price and thinking that he will still make 25 % profit , offers a discount of 25 % on the marked price . what is his actual profit on the sales ?
Options: a ) 20 % , b ) 13.50 % , c ) 14 % , d ) 14.50 % , e ) none
Rationale: "sol . let c . p . = rs . 100 . then , marked price = rs . 160 . s . p . = 75 % of rs . 160 = rs . 120 . ∴ gain % = 20 % . answer a"
Answer: a
Python program:
a = 60 / 100
b = 1 + a 
c = 60 / 100
d = 1 + c 
e = 25 / 100
f = d * e
g = b - f
h = g - 1
i = h * 100
Problem: a plane flies 420 miles with the wind and 350 miles against the wind in the same length of time . if the speed of the wind is 23 mph , what is the speed of the plain in still air ?
Options: a ) 253 mph . , b ) 275 mph . , c ) 296 mph . , d ) 278 mph . , e ) 235 mph .
Rationale: the speed of the plane in still air = x miles / hour the speed of the wind is 23 mph speed with the wind = ( x + 23 ) mph speed against the wind = ( x – 23 ) mph time = distance / speed according to the problem , 420 / ( x + 23 ) = 350 / ( x – 23 ) 420 ( x – 23 ) = 350 ( x + 23 ) 420 x – 9660 = 350 x + 805 420 x – 350 x = 8050 + 9660 70 x = 17710 x = 17710 / 70 x = 253 therefore , the speed of the plane in still air = 253 mph . correct answer a
Answer: a
Python program:
a = 350 * 23
b = 420 * 23
c = a + b 
d = 420 - 350
e = c / d
Problem: rs 80000 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 9000 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 = 80000 - - - - - - - - - - eq 1 total profit = profit on x + profit on y 9000 = ( x * 10 * 1 ) / 100 + ( y * 20 * 1 ) / 100 90000 = x + 2 y - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - eq 2 90000 = 80000 + y so y = 10000 then x = 80000 - 10000 = 70000 first part = 70000 answer : e"
Answer: e
Python program:
a = 80000 * 20
b = a / 100
c = b - 9000
d = 10 / 100
e = c / d
Problem: at the end of year x , automobile installment credit accounted for 43 % of all outstanding consumer installment credit . at that time automobile finance companies extended $ 50 billion of credit , or 1 / 4 of the automobile installment credit . how many billion dollars of consumer installment credit was outstanding at that time ?
Options: a ) 450 , b ) 465.12 , c ) 475 , d ) 500.15 , e ) 200
Rationale: system of equations a = ( 43 / 100 ) c ( 1 / 4 ) a = 50 - - > a = 200 substitution 200 = ( 43 / 100 ) c c = ( 100 / 43 ) 200 calculate 200 / 43 * 100 - the the correct answer is 465.12 . the correct answer is b .
Answer: b
Python program:
a = 50 * 4
b = 43 / 100
c = a / b
Problem: what is the lowest positive integer that is divisible by 1 through 3 , inclusive ?
Options: a ) 12 , b ) 6 , c ) 8 , d ) 18 , e ) 33
Rationale: "the integer should be divisible by : 1 , 2 , and 3 . the least common multiple of these integers is lcm = 1 * 2 * 3 = 6 answer : b"
Answer: b
Python program:
a = math.lcm(1, 3)
Problem: a courier charges for packages to a certain destination are 65 cents for the first 250 grams and 10 cents for each additional 100 grams or part thereof . what could be the weight in grams of a package for which the charge is $ 1.85 ?
Options: a ) 1680 , b ) 1420 , c ) 1120 , d ) 970 , e ) 740
Rationale: "the charge is 65 cents for the first 250 grams . this leaves a charge of $ 1.85 - $ 0.65 = $ 1.20 the charge for the next 1100 grams is $ 1.10 which leaves a charge of $ 0.10 the weight is somewhere between 1350 and 1450 . the answer is b ."
Answer: b
Python program:
a = 65 / 100
b = 1 - 85
c = 10 / 100
d = c / 100
e = d * 250
f = b + e 
g = 10 / 100
h = g / 100
i = f / h
Problem: during a certain two - week period , 60 percent of the movies rented from a video store were comedies , and of the remaining movies rented , there were 4 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 ) 14 , b ) 12 , c ) 10 , d ) 8 , e ) 7.5
Rationale: "total movies = 100 . comedies = 60 . action + drama = 40 . since there were 5 times as many dramas as action movies , then action + 4 * action = 40 - - > action = a = 8 . comedies = 60 = 7.5 a . answer : e"
Answer: e
Python program:
a = 4 + 1 
b = 60 / a
c = math.floor(b)
Problem: a fruit seller sells mangoes at the rate of rs . 9 per kg and thereby loses 20 % . at what price per kg , he should have sold them to make a profit of 5 %
Options: a ) rs 8.81 , b ) rs 9.81 , c ) rs 10.81 , d ) rs 11.81 , e ) none of these
Rationale: "explanation : 85 : 9 = 105 : x x = ( 9 × 105 / 85 ) = rs 11.81 option d"
Answer: d
Python program:
a = 100 + 5 
b = 9 * a
c = 100 - 20
d = b / c
Problem: if 21 / 22 = 0 . 95.45 , what is the 57 th digit to the right of the decimal point of the fraction ?
Options: a ) 1 , b ) 4 , c ) 5 , d ) 7 , e ) 9
Rationale: we are not concerned what 21 / 22 means . . we have to look at the decimal . . 0.9544 means 0.95454545 . . . . so leaving first digit to the right of decimal , all odd numbered digits are 4 and all even numbered are 5 . . here 57 is odd , so ans is 4 answer is b
Answer: b
Python program:
a = 2 * 2
Problem: an army ’ s recruitment process included n rounds of selection tasks . for the first a rounds , the rejection percentage was 60 percent per round . for the next b rounds , the rejection percentage was 50 percent per round and for the remaining rounds , the selection percentage was 70 percent per round . if there were 20000 people who applied for the army and 196 were finally selected , what was the value of n ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 10
Rationale: "step ( 1 ) 8000 accepted . step ( 2 ) another 40 % of 8000 = 3200 accepted . here it is quiet observable that if we further deduct candidate by 60 % it would change our probablity of easy going 2000 candidate . so i would get to second stage of recruitment where 50 % is accepted step ( 3 ) 50 % of 3200 = 1600 step ( 4 ) 50 % of 1600 = 800 step ( 5 ) 50 % of 800 = 400 step ( 6 ) 50 % of 400 = 200 70 % of 400 = 280 and last step of accepting 70 % of 280 = 196 ( our target ) total 8 steps required . ans d"
Answer: d
Python program:
a = 1 + 4 
b = 2 + a 
c = b + 2
Problem: how many multiples of 5 are there between 50 and 500 ?
Options: a ) 128 , b ) 91 , c ) 89 , d ) 61 , e ) 60
Rationale: "it should be mentioned whether 50 and 500 are inclusive . if 50 and 500 are inclusive , then the answer is ( 500 - 50 ) / 5 + 1 = 91 . if 50 and 500 are not inclusive , then the answer is ( 495 - 55 ) / 5 + 1 = 89 . since oa is c , then we have not inclusive case ."
Answer: c
Python program:
a = 500 - 50
b = a / 5
c = b + 1
Problem: two stations a and b are 110 km apart on a straight line . one train starts from a at 4 a . m . and travels towards b at 20 kmph . another train starts from b at 8 a . m . and travels towards a at a speed of 25 kmph . at what time will they meet ?
Options: a ) 15 a . m , b ) 10 a . m , c ) 7 a . m , d ) 02 a . m , e ) 05 a . m
Rationale: "suppose they meet x hours after 4 a . m . distance covered by a in x hours = 20 x km . distance covered by b in ( x - 1 ) hours = 25 ( x - 1 ) km . therefore 20 x + 25 ( x - 1 ) = 110 45 x = 135 x = 3 . so , they meet at 7 a . m . answer : c"
Answer: c
Python program:
a = 110 - 20
b = 25 + 20 
c = a / b
d = 8 + c
Problem: the height of the wall is 6 times its width and lenght of the wall is 7 times its height . if the volume of the wall be 16128 cu . m . its width is
Options: a ) 4 m
b ) 5 m
c ) 6 m
d ) 7 m
e ) 8 m
Rationale: explanation : let width = x then , height = 6 x and length = 42 x 42 x × 6 x × x = 16128 x = 4 answer : a
Answer: a
Python program:
a = 6 * 7
b = a * 6
c = 16128 / b
d = 1 / 3
e = c ** d
Problem: find the sum of all odd numbers upto 100 .
Options: a ) 200 , b ) 1000 , c ) 2500 , d ) 3140 , e ) 3200
Rationale: "sol . the given numbers are 1 , 3 , 5 , 7 , . . . , 99 . this is an a . p . with a = 1 and d = 2 . let it contain n terms . then , 1 + ( n - 1 ) x 2 = 99 or n = 50 .  required sum = ( n / 2 ) ( first term + last term ) = 50 ( 1 + 99 ) / 2 = 2500 . answer c 2500"
Answer: c
Python program:
a = 100 / 2
b = a / 2
c = b / 2
d = c / 2
e = d / 2
f = 100 / e
g = f / 2
h = 100 / 2
i = h / 2
j = i / 2
k = j / 2
l = k / 2
m = 100 / l
n = m / 2
o = math.sqrt(n)
p = 1 + o 
q = g + p
Problem: two stations p and q are 110 km apart on a straight track . one train starts from p at 7 a . m . and travels towards q at 20 kmph . another train starts from q at 8 a . m . and travels towards p at a speed of 25 kmph . at what time will they meet ?
Options: a ) 10.30 , b ) 10 , c ) 8.45 , d ) 9.3 , e ) 11
Rationale: "explanation : assume both trains meet after x hours after 7 am distance covered by train starting from p in x hours = 20 x km distance covered by train starting from q in ( x - 1 ) hours = 25 ( x - 1 ) total distance = 110 = > 20 x + 25 ( x - 1 ) = 110 = > 45 x = 135 = > x = 3 means , they meet after 3 hours after 7 am , ie , they meet at 10 am . answer : b"
Answer: b
Python program:
a = 110 + 25 
b = 20 + 25 
c = a / b
d = c + 7
Problem: a milk man has 10 liters of milk . if he mixes 5 liters of water , which is freely available , in 20 liters of pure milk . if the cost of pure milk is rs . 18 per liter , then the profit of the milkman , when he sells all the mixture at cost price is :
Options: a ) 20 % , b ) 15 % , c ) 33.33 % , d ) 18 % , e ) none of these
Rationale: "explanation : when the water is freely available and all the water is sold at the price of the milk , then the water gives the profit on the cost of 10 liters of milk . therefore , profit percentage = 15 % . answer : b"
Answer: b
Python program:
a = 20 + 5 
b = a + 10 
c = 5 / 2
d = c + 3 
e = b + d 
f = e * 18
g = 10 * 18
h = f - g
i = 10 * 18
j = h / i
k = j * 100
Problem: if * stands for / , / stands for - , + stands for * and - stands for + , then 9 / 8 * 7 + 5 - 10 = ?
Options: a ) 13.3 , b ) 10.8 , c ) 10.7 , d ) 11.4 , e ) 12.5
Rationale: 9 / 8 * 7 + 5 - 10 this expression becomes 9 - 8 / 7 * 5 + 10 after exchanging the symbols then the values for it would be 9 - 1.142 * 5 + 10 = 13.290 ( app ) = 13.3 answer : a
Answer: a
Python program:
a = 8 / 7
b = a * 5
c = 9 - b
d = 10 + c
Problem: hcf and lcm two numbers are 12 and 396 respectively . if one of the numbers is 36 , then the other number is ?
Options: a ) 36 , b ) 66 , c ) 132 , d ) 264 , e ) 152
Rationale: "12 * 396 = 36 * x x = 132 answer : c"
Answer: c
Python program:
a = 12 * 396
b = a / 36
Problem: what is the tens digit of 36 ^ 30 ?
Options: a ) 1 , b ) 7 , c ) 5 , d ) 3 , e ) 9
Rationale: "36 ^ 10 = 6 ^ 20 ( 6 ^ 2 ) = 6 * 6 = 36 ( 6 ^ 3 ) = 36 * 6 = . 16 ( 6 ^ 4 ) = . 16 * 6 = . . 96 ( 6 ^ 5 ) = . . 96 * 6 = . . 76 ( 6 ^ 6 ) = . . 76 * 6 = . . . 56 ( 6 ^ 7 ) = . . . . 56 * 6 = . . . . 36 if you see there is a pattern here in tens digits 3 , 1,9 , 7,5 , 3,1 and so on . . . continue the pattern up to 6 ^ 30 ( dont actually calculate full values ) and answer is b : 7"
Answer: b
Python program:
a = 4 + 1 
b = 36 ** reminder
c = reminder / (
d = math.floor(c, 100)
Problem: a 4 digit number is such that the product of all of its digits is 126 . the sum of all the digits is equal to the 2 digit number formed by using thousands digit and tens digit ( 1000 digit in tens place & 10 digit in units place ) which in turn is equal to 19 . then difference of units and 1000 place of the number is , given that this difference is positive .
Options: a ) 1692 , b ) 1792 , c ) 1795 , d ) 1892 , e ) 1992
Rationale: the number is 1792 . let the number be represented as 1000 x + 100 y + 10 z + t acc to ques , xyzt = 126 x + y + z + t = 10 x + z = 19 so , number in thousands and tens place are 1 and 9 respectively . the remaining factor is 14 which is 7 * 2 so the number is 1792 . answer : b
Answer: b
Python program:
a = 19 - 10
b = 126 / a
c = b / 2
d = c * 100
e = 1000 + d 
f = 19 - 10
g = f * 10
h = e + g 
i = h + 2
Problem: p and q started a business investing rs . 54,000 and rs . 18,000 respectively . in what ratio the profit earned after 2 years be divided between p and q respectively ?
Options: a ) 3 : 1 , b ) 4 : 3 , c ) 5 : 4 , d ) 6 : 5 , e ) 17 : 4
Rationale: "p : q = 54000 : 18000 = 3 : 1 . answer : a"
Answer: a
Python program:
a = 2 + 3 
b = a + 3 
c = 2 + 3 
d = c * 2
e = b * d
f = 2 + 3 
g = e + f 
h = 2 + 3 
i = h * 2
j = 3 * i
k = 2 + 3 
l = j + k 
m = g / l
Problem: a man loses 1 / 3 rd of his money , then wins rs . 10 loses 1 / 3 rd of what he has and wins rs . 20 and finds that he has exactly what be had at the beginning . what was the amount he originally bad ?
Options: a ) 25 , b ) 36 , c ) 10 , d ) 48 , e ) 45
Rationale: let x be that amount so accordind to question , eqn will be like : ( ( ( x - x / 3 ) + 10 ) - ( ( ( x - x / 3 ) + 10 ) / 3 ) ) + 20 = x = > ( ( 2 x / 3 + 10 ) - ( ( 2 x / 3 + 10 ) / 3 ) ) + 20 = x = > 3 x - 4 x / 3 = 80 = > x = 48 answer : d
Answer: d
Python program:
a = 1 / 3
b = 1 - a
c = b * 10
d = c + 20 
e = 1 / 3
f = 1 - e
g = 1 / 3
h = 1 - g
i = f * h
j = 1 - i
k = d / j
Problem: what is the probability of getting sum of 10 on rolling three dices ?
Options: a ) 28 / 216 , b ) 27 / 216 , c ) 29 / 216 , d ) 26 / 216 , e ) 25 / 216
Rationale: "the no of ways to roll three dies is 6 ^ 3 = 216 the possibles of getting sum as 10 is 631 = 3 ! = 6 622 = 3 ! / 2 ! = 3 541 = 3 ! = 6 523 = 3 ! = 6 442 = 3 ! / 2 ! = 3 433 = 3 ! / 2 ! = 3 total possibles for getting sum as 10 is 27 the probabilty is 27 / 216 answer : b"
Answer: b
Python program:
a = 3 + 3 
b = math.comb(a, 3)
c = 2 / b
Problem: for any integer n greater than 1 , # n denotes the product of all the integers from 1 to n , inclusive . how many prime numbers are there between # 6 + 2 and # 6 + 6 , inclusive ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: "given that n * denotes the product of all the integers from 1 to n , inclusive so , 6 * + 2 = 6 ! + 2 and 6 * + 6 = 6 ! + 6 . now , notice that we can factor out 2 our of 6 ! + 2 so it can not be a prime number , we can factor out 3 our of 6 ! + 3 so it can not be a prime number , we can factor out 4 our of 6 ! + 4 so it can not be a prime number , . . . the same way for all numbers between 6 * + 2 = 6 ! + 2 and 6 * + 6 = 6 ! + 6 , inclusive . which means that there are no primes in this range . answer : a ."
Answer: a
Python program:
a = 1 + 1
Problem: a carpenter worked alone for 1 day on a job that would take him 6 more days to finish . he and another carpenter completed the job in 7 more days . how many days would it have taken the second carpenter to do the complete job working alone ?
Options: a ) 4.5 , b ) 7.5 , c ) 9.5 , d ) 14.5 , e ) 24.5
Rationale: "a carpenter worked only 1 day on something that takes him 6 more days . means ; carpenter finishes his work in 7 days . let his buddy finish the same task in x days . respective rates per day : 1 / 7 and 1 / x to complete 1 work : first guy worked for 5 days @ rate = 1 / 7 per day . second one worked for 7 days @ rate = 1 / x per day expression : days * rate = work 5 * 1 / 7 + 7 * 1 / x = 1 5 x + 49 = 7 x 2 x = 49 x = 24.5 days . ans : e"
Answer: e
Python program:
a = 1 + 6 
b = 7 * a
c = b / 2
Problem: for an agricultural experiment , 300 seeds were planted in one plot and 200 were planted in a second plot . if exactly 25 percent of the seeds in the first plot germinated and exactly 35 percent of the seeds in the second plot germinated , what percent of the total number of seeds germinated ?
Options: a ) 12 % , b ) 26 % , c ) 29 % , d ) 30 % , e ) 60 %
Rationale: in the first plot 25 % of 300 seeds germinated , so 0.25 x 300 = 75 seeds germinated . in the second plot , 35 % of 200 seeds germinated , so 0.35 x 200 = 70 seeds germinated . since 75 + 70 = 145 seeds germinated out of a total of 300 + 200 = 500 seeds , the percent of seeds that germinated is ( 145 / 500 ) x 100 % , or 29 % . answer : c .
Answer: c
Python program:
a = 25 / 100
b = a * 300
c = 35 / 100
d = c * 200
e = b + d 
f = 300 + 200 
g = e / f
h = g * 100
Problem: on the first day of her vacation , louisa traveled 240 miles . on the second day , traveling at the same average speed , she traveled 420 miles . if the 240 - mile trip took 3 hours less than the 420 - mile trip , what was the average speed , in miles per hour ?
Options: a ) 65 , b ) 50 , c ) 55 , d ) 60 , e ) 58
Rationale: "( time ) * ( rate ) = ( distance ) - - > ( rate ) = ( distance ) / ( time ) - - > given : ( rate ) = 240 / t = 420 / ( t + 3 ) - - > 4 / t = 7 / ( t + 3 ) - - > 4 t + 12 = 7 t - - - - > 3 t = 12 . t = 4 - - - - > ( rate ) = 240 / 4 = 60 answer : d"
Answer: d
Python program:
a = 420 - 240
b = a / 3