euclaise/mathqa_programs huggingface dataset:
Problem: a man rows his boat 120 km downstream and 60 km upstream , taking 2 hours each time . find the speed of the stream ?
Options: a ) 6 , b ) 15 , c ) 17 , d ) 18 , e ) 2
Rationale: "speed downstream = d / t = 120 / ( 2 ) = 60 kmph speed upstream = d / t = 60 / ( 2 ) = 30 kmph the speed of the stream = ( 60 - 30 ) / 2 = 15 kmph answer : b"
Answer: b
Python program:
a = 120 / 2
b = 60 / 2
c = a - b
d = c / 2
Problem: there are 14 slate rocks , 20 pumice rocks , and 10 granite rocks randomly distributed in a certain field . if 2 rocks are chosen at random and without replacement , what is the probability that both rocks will be slate rocks ?
Options: a ) 1 / 5 , b ) 11 / 22 , c ) 81 / 724 , d ) 91 / 946 , e ) 101 / 987
Rationale: "14 / 44 * 13 / 43 = 91 / 946 the answer is d ."
Answer: d
Python program:
a = 14 + 20 
b = a + 10 
c = 14 / b
d = 14 - 1
e = 14 + 20 
f = e + 10 
g = f - 1
h = d / g
i = c * h
Problem: my grandson is about as many days as my son in weeks , and my grandson is as many months as i am in years . my grandson , my son and i together are 150 years . can you tell my son age in years ?
Options: a ) 63 years , b ) 60 years , c ) 50 years , d ) 53 years , e ) 46 years
Rationale: let m be my age in years . if s is my son ' s age in years , then my son is 52 s weeks old . if g is my grandson ' s age in years , then my grandson is 365 g days old . thus , 365 g = 52 s . since my grandson is 12 g months old , 12 g = m . since my grandson , my son and i together are 150 years , g + s + m = 100 . the above system of 3 equations in 3 unknowns ( g , s and m ) can be solved as follows : 52 s / 365 + s + 12 x ( 52 s / 365 ) = 150 or 52 s + 365 s + 365 x ( 624 s / 365 ) = 365 x 150 or s = 54,750 / 1,041 = 53 years answer = d
Answer: d
Python program:
a = 10 + 10 
b = 150 / a
c = b * 12
Problem: a merchant sells an item at a 20 % discount , but still makes a gross profit of 20 percent of the cost . what percent t of the cost would the gross profit on the item have been if it had been sold without the discount ?
Options: a ) 20 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 75 %
Rationale: "let the market price of the product is mp . let the original cost price of the product is cp . selling price ( discounted price ) = 100 % of mp - 20 % mp = 80 % of mp . - - - - - - - - - - - - - - - - ( 1 ) profit made by selling at discounted price = 20 % of cp - - - - - - - - - - - - - - ( 2 ) apply the formula : profit t = selling price - original cost price = > 20 % of cp = 80 % of mp - 100 % cp = > mp = 120 cp / 80 = 3 / 2 ( cp ) now if product is sold without any discount , then , profit = selling price ( without discount ) - original cost price = market price - original cost price = mp - cp = 3 / 2 cp - cp = 1 / 2 cp = 50 % of cp thus , answer should bec ."
Answer: c
Python program:
a = 100 - 20
b = a - 20
c = 100 - b
Problem: in a race of 1000 m , a can beat by 100 m , in a race of 800 m , b can beat c by 100 m . by how many meters will a beat c in a race of 900 m ?
Options: a ) 122.9 m , b ) 127.5 m . , c ) 191.25 m , d ) 222.9 m , e ) 12289 m
Rationale: "when a runs 1000 m , b runs 900 m and when b runs 800 m , c runs 700 m . when b runs 900 m , distance that c runs = ( 900 * 700 ) / 800 = 6300 / 8 = 787.5 m . in a race of 1000 m , a beats c by ( 1000 - 787.5 ) = 212.5 m to c . in a race of 900 m , the number of meters by which a beats c = ( 900 * 212.5 ) / 1000 = 191.25 m . answer : c"
Answer: c
Python program:
a = 1000 - 100
b = 800 - 100
c = a * b
d = c / 800
e = 1000 - d
Problem: if rs . 7500 are borrowed at c . i at the rate of 4 % per annum , then after 3 years the amount to be paid is ?
Options: a ) 3377 , b ) 2688 , c ) 2688 , d ) 8436 , e ) 1268
Rationale: a = 7500 ( 26 / 25 ) ^ 3 = 8436 answer : d
Answer: d
Python program:
a = 100 + 4 
b = a / 100
c = 100 + 4 
d = c / 100
e = b * d
f = 7500 * e
Problem: two friends decide to get together ; so they start riding bikes towards each other . they plan to meet halfway . each is riding at 6 mph . they live 36 miles apart . one of them has a pet carrier pigeon and it starts flying the instant the friends start traveling . the pigeon flies back and forth at 21 mph between the 2 friends until the friends meet . how many miles does the pigeon travel ?
Options: a ) 54 , b ) 66 , c ) 68 , d ) 60 , e ) 63
Rationale: "e 63 it takes 3 hours for the friends to meet ; so the pigeon flies for 3 hours at 21 mph = 63 miles"
Answer: e
Python program:
a = 36 / 2
b = a / 6
c = 21 * b
Problem: the sum of number of boys and girls in a school is 400 . if the number of boys is x , then the number of girls becomes x % of the total number of students . the number of boys is ?
Options: a ) 50 , b ) 40 , c ) 60 , d ) 80 , e ) 70
Rationale: "we have x + x % of 400 = 400 x + x / 100 * 400 = 400 5 * x = 400 x = 80 answer is d"
Answer: d
Python program:
a = 400 / 100
b = a + 1 
c = 400 / b
Problem: a customer bought a product at the shop . however , the shopkeeper increased the price of the product by 15 % so that the customer could not buy the required amount of the product . the customer managed to buy only 60 % of the required amount . what is the difference in the amount of money that the customer paid for the second purchase compared to the first purchase ?
Options: a ) 27 % , b ) 29 % , c ) 31 % , d ) 33 % , e ) 35 %
Rationale: "let x be the amount of money paid for the first purchase . the second time , the customer paid 0.6 ( 1.15 x ) = 0.69 x . the difference is 31 % . the answer is c ."
Answer: c
Python program:
a = 15 / 100
b = a + 1 
c = 60 / 100
d = b * c
e = 1 - d
f = e * 100
Problem: the h . c . f . of two numbers is 12 and their l . c . m . is 600 . if one of the number is 30 , find the other ?
Options: a ) 100 , b ) 240 , c ) 120 , d ) 200 , e ) 150
Rationale: "other number = 12 * 600 / 30 = 240 answer is b"
Answer: b
Python program:
a = 12 * 30
Problem: if xy = 1 , x / y = 36 , for positive numbers x and y , y = ?
Options: a ) 1 / 2 , b ) 2 , c ) 1 / 3 , d ) 3 , e ) 1 / 6
Rationale: "very easy question . 2 variables and 2 easy equations . xy = 1 - - - > x = 1 / y - ( i ) x / y = 36 - - - > replacing ( i ) here - - - > 1 / ( y ^ 2 ) = 36 - - - > y ^ 2 = 1 / 36 - - - > y = 1 / 6 or - 1 / 6 the question states that x and y are positive integers . therefore , y = 1 / 6 is the answer . answer e ."
Answer: e
Python program:
a = 1 / 36
b = math.sqrt(a)
Problem: for covering 88 km a wheel revolve 1000 times . what is the radius of wheel ?
Options: a ) 14 m , b ) 24 m , c ) 28 m , d ) 40 m , e ) none of the above
Rationale: distance travel in 1 round = 88000 / 1000 m = 88 m perimeter = 88 m , 2 π r = 882 r = [ 88 * 7 / 22 ] = 28 m hence , diameter = 28 m answer c
Answer: c
Python program:
a = 88 / 1000
b = 3 + 4 
c = a * b
d = c / 2
e = 10 * 2
f = e + 2 
g = d / f
h = g * 1000
i = h * 2
Problem: a car covers a distance of 642 km in 6 ½ hours . find its speed ?
Options: a ) 104 kmph , b ) 176 kmph , c ) 298 kmph , d ) 186 kmph , e ) 107 kmph
Rationale: 642 / 6 = 107 kmph answer : e
Answer: e
Python program:
a = 642 / 6
Problem: a can complete a certain job in 18 days . b is 80 % more efficient than a . in how many days can b complete the same job ?
Options: a ) 6 , b ) 6.25 , c ) 7 , d ) 7.5 , e ) 10
Rationale: "let , total work unit = 180 units a can finish in 18 days = 180 unit work i . e . a can finish in 1 days = 10 unit work i . e . b can finish in 1 days = 10 + ( 80 / 100 ) * 10 = 18 unit work days in which b will complete the work alone = 180 / 18 = 10 days answer : option e"
Answer: e
Python program:
a = 18 * 80
b = a / 100
Problem: i sold a book at a profit of 12 % . had i sold it for $ 18 more , 18 % would have been gained . find the cost price ?
Options: a ) $ 100 , b ) $ 250 , c ) $ 300 , d ) $ 200 , e ) $ 180
Rationale: "118 % of cost - 112 % of cost = $ 18 6 % of cost = $ 18 cost = 18 * 100 / 6 = $ 300 answer is c"
Answer: c
Python program:
a = 18 * 12
b = 18 - 12
c = a / b
d = c * 100
e = d / 12
Problem: the speed of a boat in still water is 20 km / hr and the rate of current is 5 km / hr . the distance travelled downstream in 21 minutes is :
Options: a ) 9.75 , b ) 5.75 , c ) 8.75 , d ) 6.75 , e ) 5.15
Rationale: "explanation : speed downstream = ( 20 + 5 ) kmph = 25 kmph distance travelled = ( 25 * ( 21 / 60 ) ) km = 8.75 km . answer : c"
Answer: c
Python program:
a = 21 / const_60
b = 20 + 5 
c = a * b
Problem: if the price of an article went up by 25 % , then by what percent should it be brought down to bring it back to its original price ?
Options: a ) 20 % , b ) 2 / 8 % , c ) 2 / 1 % , d ) 1 / 3 % , e ) 2 / 7 %
Rationale: let the price of the article be rs . 100 . 25 % of 100 = 25 . new price = 100 + 25 = rs . 125 required percentage = ( 125 - 100 ) / 125 * 100 = 25 / 125 * 100 = 20 % . answer : a
Answer: a
Python program:
a = 100 + 25 
b = 25 / a
c = b * 100
Problem: a retailer buys 40 pens at the market price of 36 pens from a wholesaler , if he sells these pens giving a discount of 1 % , what is the profit % ?
Options: a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) none of them
Rationale: "let the market price of each pen be rs 1 then , c . p of 40 pens = rs 36 s . p of 40 pens = 99 % of rs 40 = rs 39.60 profit % = ( ( 3.60 * 100 ) / 36 ) % = 10 % answer is b ."
Answer: b
Python program:
a = 1 / 100
b = 1 - a
c = 36 / 40
d = b - c
e = 36 / 40
f = d / e
g = 100 * f
Problem: given a circular wheel of 3.62 m radius how many revolutions will the will make to travel a distance of 1 km ?
Options: a ) 22754.3 , b ) 22254.2 , c ) 25754.2 , d ) 22753.2 , e ) 22254.2
Rationale: 2 * 22 / 7 * 3.62 * x = 22754.3 x = 1000 answer : a
Answer: a
Python program:
a = 10 + 1 
b = a * 2
c = 3 + 4 
d = b / c
e = d * 2
f = e * 3
g = f * 1000
Problem: find the least number must be subtracted from 427398 so that remaining no . is divisible by 15 ?
Options: a ) 2 , b ) 3 , c ) 5 , d ) 7 , e ) 8
Rationale: "on dividing 427398 by 15 we get the remainder 3 , so 3 should be subtracted b"
Answer: b
Python program:
a = 427398 / 15
b = math.floor(a)
c = b * 15
d = 427398 - c
Problem: if 15 students in a class average 73 % on an exam and 10 students average 88 % on the same exam , what is the average in percent for all 25 students ?
Options: a ) 77 % , b ) 78 % , c ) 79 % , d ) 80 % , e ) 81 %
Rationale: "( 15 * 73 + 10 * 88 ) / 25 = 79 % the answer is c ."
Answer: c
Python program:
a = 15 * 73
b = 10 * 88
c = a + b 
d = c / 25
Problem: if the price of a tv is first decreased by 10 % and then increased by 30 % , then the net change in the price will be :
Options: a ) 4 % increase , b ) 17 % increase , c ) 10 % decrease , d ) 6 % increase , e ) none of these
Rationale: "explanation : solution : let the original price be rs . 100 . new final price = 130 % of ( 10 % of 100 ) = rs . 130 / 100 * 90 / 100 * 100 = rs . 117 . . ' . increase = 17 % answer : b"
Answer: b
Python program:
a = 100 - 10
b = 100 + 30 
c = a * b
d = c / 100
e = d - 100
Problem: if the true discount on a sum due 2 years hence at 14 % per annum be rs . 168 , the sum due is :
Options: a ) rs . 768 , b ) rs . 968 , c ) rs . 1960 , d ) rs . 2400 , e ) none
Rationale: solution p . w = 100 xt . d . / r x t = 100 x 168 / 14 x 2 = 600 . ∴ sum = ( p . w . + td . ) = rs . 768 . answer a
Answer: a
Python program:
a = 100 * 168
b = 14 * 2
c = a / b
d = c + 168
Problem: the difference between the ages of two persons is 30 years . fifteen years ago , the elder one was twice as old as the younger one . the present age of the younger person is ?
Options: a ) 30 yr , b ) 25 yr , c ) 45 yr , d ) 40 yr , e ) 50 yr
Rationale: "let their ages be x years and ( x + 30 ) years then , ( x + 30 ) - 15 = 2 ( x - 15 ) x + 15 = 2 x - 30 x = 45 answer is c"
Answer: c
Python program:
a = 3 + 2 
b = 30 - a
c = 30 - b
d = 3 + 2 
e = 30 - d
f = e * 2
g = c + f
Problem: a store owner estimates that the average price of type a products will increase by 20 % next year and that the price of type b products will increase by 11 % next year . this year , the total amount paid for type a products was $ 3500 and the total price paid for type b products was $ 8600 . according to the store owner ' s estimate , and assuming the number of products purchased next year remains the same as that of this year , how much will be spent for both products next year ?
Options: a ) $ 13,746 , b ) $ 15,325 , c ) $ 16,000 , d ) $ 16,225 , e ) $ 17,155
Rationale: "cost of type a products next year = 1.20 * 3500 = 4200 cost of type b products next year = 1.11 * 8300 = 9546 total 4200 + 9546 = 13746 answer : a"
Answer: a
Python program:
a = 3 / 4
b = a * 1000
Problem: a soft drink company had 6000 small and 10000 big bottles in storage . if 12 % of small 15 % of big bottles have been sold , then the total bottles remaining in storage is
Options: a ) 15360 , b ) 13780 , c ) 15060 , d ) 14930 , e ) 16075
Rationale: "6000 + 10000 - ( 0.12 * 6000 + 0.15 * 10000 ) = 13780 . answer : b ."
Answer: b
Python program:
a = 6000 + 10000 
b = 12 / 100
c = 6000 * b
d = 15 / 100
e = d * 10000
f = c + e 
g = a - f
Problem: in a race where 18 cars are running , the chance that car x will win is 1 / 8 , that y will win is 1 / 12 and that z will win is 1 / 6 . assuming that a dead heat is impossible , find the chance that one of them will win .
Options: a ) 1 / 140 , b ) 1 / 180 , c ) 3 / 12 , d ) 3 / 8 , e ) 57 / 120
Rationale: "required probability = p ( x ) + p ( y ) + p ( z ) ( all the events are mutually exclusive ) . = 1 / 8 + 1 / 12 + 1 / 6 = 3 / 8 answer : d"
Answer: d
Python program:
a = 1 / 8
b = 1 / 12
c = a + b 
d = 1 / 6
e = c + d
Problem: the average marks of 25 students in a class is 100 . but a student mark is wrongly noted as 60 instead of 10 then find the correct average marks ?
Options: a ) a ) 78 , b ) b ) 82 , c ) c ) 98 , d ) d ) 91 , e ) e ) 85
Rationale: "correct avg marks = 100 + ( 10 - 60 ) / 25 avg = 100 - 2 = 98 answer is c"
Answer: c
Python program:
a = 100 * 25
b = a - 60
c = b + 10 
d = c / 25
Problem: what is the sum of the local values of the digits 2 , 3 , 4 , 5 in the number 2345 ?
Options: a ) 2345 , b ) 4500 , c ) 5000 , d ) 6000 , e ) 7000
Rationale: 2000 + 300 + 40 + 5 = 2345 answer a
Answer: a
Python program:
a = 2 * 1000
b = 3 * 100
c = a + b 
d = 10 * 4
e = c + d 
f = 5 + e
Problem: a started a business with an investment of rs . 70000 and after 6 months b joined him investing rs . 120000 . if the profit at the end of a year is rs . 91000 , then the share of b is ?
Options: a ) a ) 44500 , b ) b ) 42000 , c ) c ) 44098 , d ) d ) 43007 , e ) e ) 44098
Rationale: "ratio of investments of a and b is ( 70000 * 12 ) : ( 120000 * 6 ) = 7 : 6 total profit = rs . 91000 share of b = 6 / 13 ( 91000 ) = rs . 42000 answer : b"
Answer: b
Python program:
a = const_60 * 100
b = 91000 - a
Problem: 54671 - 14456 - 33490 = ?
Options: a ) 2449 , b ) 5449 , c ) 6749 , d ) 6725 , e ) 6468
Rationale: "d if we calculate we will get 6725"
Answer: d
Python program:
a = 54671 / 100
b = a * 14456
c = 1 / 3
d = 54671 / 100
e = d * 14456
f = c * e
g = b - f
Problem: if p and q are positive integers each greater than 1 , and 17 ( p + 1 ) = 28 ( q + 1 ) , what is the least possible value of p + q ?
Options: a ) 36 , b ) 42 , c ) 44 , d ) 43 , e ) none
Rationale: "17 ( p + 1 ) = 29 ( q + 1 ) - - > ( p + 1 ) / ( q + 1 ) = 28 / 17 - - > the least positive value of p + 1 is 28 , so the least value of p is 27 and the least positive value of q + 1 is 17 , so the least value of q is 16 - - > the least value of p + q is 27 + 16 = 43 . answer : d"
Answer: d
Python program:
a = 28 + 17 
b = a - 2
Problem: a thief is spotted by a policeman from a distance of 225 meters . when the policeman starts the chase , the thief also starts running . if the speed of the thief be 8 km / hr and that of the policeman 10 km / hr , how far the thief will have run before he is overtaken ?
Options: a ) 350 m , b ) 200 m , c ) 400 m , d ) 900 m , e ) none of them
Rationale: "relative speed of the policeman = ( 10 - 8 ) km / hr = 2 km / hr . time taken by police man to cover ( 225 m / 1000 ) x 1 / 2 hr = 9 / 80 hr . in 9 / 80 hrs , the thief covers a distance of 8 x 9 / 80 km = 9 / 10 km = 900 m answer is d ."
Answer: d
Python program:
a = 225 * 8
b = 10 - 8
c = a / b
Problem: a , b , c can complete a piece of work in 24,6 and 12 days respectively . working together , they will complete the same work in how many days ?
Options: a ) 13 / 8 , b ) 26 / 11 , c ) 24 / 7 , d ) 12 / 13 , e ) 1 / 2
Rationale: "( a + b + c ) ' s 1 day work = ( 1 / 24 ) + ( 1 / 6 ) + ( 1 / 12 ) = 7 / 24 a , b , c together will complete the work in 24 / 7 days answer is c"
Answer: c
Python program:
a = 1/(12)
b = 1/(3)
c = 4 + 4 
d = c + 1 
e = 1/(d)
f = b + e 
g = a + f 
h = 1/(g)
Problem: mary works 9 hours per day on monday , wednesday and friday , and 5 hours per day on tuesday and thursday . she does not work on saturday and sunday . she earns $ 407 per week . how much does she earn in dollars per hour ?
Options: a ) 12 , b ) 10 , c ) 9 , d ) 8 , e ) 11
Rationale: so , she works 27 hours in 3 days so , she works 10 hours in 2 days so in a week she works 37 hours ( 27 + 10 ) and earns $ 407 so , hourly wage is 407 / 37 = > 11 hence answer will be ( e ) 11
Answer: e
Python program:
a = 9 * 3
b = 5 * 2
c = a + b 
d = 407 / c
Problem: when a number is divided by 4 & then multiply by 12 the answer is 9 what is the no . ?
Options: a ) 3 , b ) 5 , c ) 5.6 , d ) 5.7 , e ) 6.5
Rationale: if $ x $ is the number , x / 4 * 12 = 9 = > 3 x = 9 = > x = 3 a
Answer: a
Python program:
a = 9 / 12
b = a * 4
Problem: a toy store ' s revenue in november was 3 / 5 of its revenue in december and its revenue in january was 3 / 4 of its revenue in november , then the store ' s revenue in december was how many times the average ( arithmetic mean ) of its revenues in november and january ?
Options: a ) 1 / 4 , b ) 1 / 2 , c ) 2 / 3 , d ) 2 , e ) 4
Rationale: let dec rev = 100 then nov rev is 3 / 5 ( 100 ) = > 60 therefore jan rev = 3 / 4 ( nov rev ) = 3 / 4 ( 60 ) = > 45 hence dec rev = x * ( nov rev + jan rev ) / 2 100 = x * ( 60 + 45 ) / 2 x = 100 / 52.5 = > 1.90 = 2 ans ) d
Answer: d
Python program:
a = 3 / 4
b = a + 1 
c = 3 / 5
d = b * c
e = d / 2
f = 1 / e
Problem: of the goose eggs laid at a certain pond , 1 / 4 hatched and 4 / 5 of the geese that hatched from those eggs survived the first month . of the geese that survived the first month , 2 / 5 did not survive the first year . if 120 geese survived the first year and if no more than one goose hatched from each egg , how many goose eggs were laid at the pond ?
Options: a ) 600 , b ) 700 , c ) 800 , d ) 900 , e ) 1000
Rationale: "let x be the number of eggs that were laid . ( 3 / 5 ) ( 4 / 5 ) ( 1 / 4 ) x = 120 ( 12 / 100 ) x = 120 x = 1000 the answer is e ."
Answer: e
Python program:
a = 4 / 5
b = 1 - a
c = 120 / b
d = 4 / 5
e = c / d
f = 1 / 4
g = e / f
Problem: in a graduate physics course , 60 percent of the students are male and 30 percent of the students are married . if two - sevenths of the male students are married , what fraction of the female students is single ?
Options: a ) 2 / 7 , b ) 17 / 30 , c ) 1 / 2 , d ) 27 / 40 , e ) 5 / 7
Rationale: "let assume there are 100 students of which 60 are male and 40 are females if 30 are married then 70 will be single . now its given that two - sevenths of the male students are married that means 2 / 7 of 60 = 17 males are married if 30 is the total number of students who are married and out of that 17 are males then the remaining 13 will be females who are married . total females = 40 married females = 13 then single females = 40 - 13 = 27 we need to find the fraction of female students who are single i . e single female students / total female student = 27 / 40 [ d ]"
Answer: d
Python program:
a = 10 / 30
Problem: calculate the average of first 18 even numbers is ?
Options: a ) 21 , b ) 29 , c ) 19 , d ) 14 , e ) 10
Rationale: explanation : sum of 10 even numbers = 18 * 19 = 342 average = 342 / 18 = 19 answer : option c
Answer: c
Python program:
a = 18 + 1
Problem: an empty fuel tank with a capacity of 200 gallons was filled partially with fuel a and then to capacity with fuel b . fuel a contains 12 % ethanol by volume and fuel b contains 16 % ethanol by volume . if the full fuel tank contains 22 gallons of ethanol , how many gallons of fuel a were added ?
Options: a ) 160 , b ) 150 , c ) 250 , d ) 80 , e ) 50
Rationale: "say there are a gallons of fuel a in the tank , then there would be 200 - a gallons of fuel b . the amount of ethanol in a gallons of fuel a is 0.12 a ; the amount of ethanol in 200 - a gallons of fuel b is 0.16 ( 200 - a ) ; since the total amount of ethanol is 22 gallons then 0.12 a + 0.16 ( 200 - a ) = 22 - - > a = 250 . answer : c ."
Answer: c
Python program:
a = 16 / 100
b = 200 * a
c = b - 22
d = 16 / 100
e = 12 / 100
f = d - e
g = c / f
Problem: in a class of 36 students 26 play football and play 20 long tennis , if 17 play above , many play neither ?
Options: a ) 7 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: "26 + 20 - 17 = 29 36 - 29 = 7 play neither answer is a"
Answer: a
Python program:
a = 26 + 20 
b = a - 17
c = 36 - b
Problem: on dividing a number by 56 , we get 29 as remainder . on dividing the same number by 8 , what will be the remainder ?
Options: a ) 5 , b ) 7 , c ) 9 , d ) 11 , e ) 12
Rationale: "formula : ( divisor * quotient ) + remainder = dividend . soln : ( 56 * q ) + 29 = d - - - - - - - ( 1 ) d % 8 = r - - - - - - - - - - - - - ( 2 ) from equation ( 2 ) , ( ( 56 * q ) + 29 ) % 8 = r . = > assume q = 1 . = > ( 56 + 29 ) % 8 = r . = > 85 % 8 = r = > 5 = r . a )"
Answer: a
Python program:
a = 29 ** 2
b = a / 56
c = 29 ** 2
d = c / 56
e = math.floor(d)
f = b - e
g = f * 56
Problem: given that p is a positive even integer with a positive units digit , if the units digit of p ^ 3 minus the units digit of p ^ 2 is equal to 0 , what is the units digit of p + 2 ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "p is a positiveeveninteger with apositive units digit - - > the units digit of p can be 2 , 4 , 6 , or 8 - - > in order the units digit of p ^ 3 - p ^ 2 to be 0 , the units digit of p ^ 3 and p ^ 2 must be the same . thus the units digit of p can be 0 , 1 , 5 or 6 . intersection of values is 6 , thus the units digit of p + 2 is 6 + 2 = 8 . answer : b ."
Answer: b
Python program:
a = 3 + 3 
b = a + 2
Problem: dan ' s age after 18 years will be 5 times his age 6 years ago . what is the present age of dan ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "let dan ' s present age be x . x + 18 = 5 ( x - 6 ) 4 x = 48 x = 12 the answer is c ."
Answer: c
Python program:
a = 6 * 5
b = 18 + a 
c = 5 - 1
d = b / c
Problem: the end of a blade on an airplane propeller is 10 feet from the center . if the propeller spins at the rate of 1,980 revolutions per second , how many miles will the tip of the blade travel in one minute ? ( 1 mile = 5,280 feet )
Options: a ) 200 π , b ) 450 π , c ) 300 π , d ) 480 π , e ) 1,200 π
Rationale: "distance traveled in 1 revolution = 2 π r = 2 π 10 / 5280 revolutions in one second = 1980 revolutions in 60 seconds ( one minute ) = 1980 * 60 total distance traveled = total revolutions * distance traveled in one revolution 1980 * 60 * 2 π 10 / 5280 = 450 π b is the answer"
Answer: b
Python program:
a = 2 * 100
b = 2 + 3 
c = b * 1000
d = a + c 
e = 10 / d
f = e * 2
g = 2 * 10
h = 2 + g 
i = 3 + 4 
j = h / i
k = f * j
l = k * 1
m = l * const_60