euclaise/mathqa_programs huggingface dataset:
Problem: when positive integer x is divided by 9 , the quotient is y and the remainder is 4 . when 2 x is divided by 7 , the quotient is 2 y and the remainder is 1 . what is the value of 5 y – x ?
Options: a ) - 3 , b ) 3 , c ) - 4 , d ) 4 , e ) - 5
Rationale: "( 1 ) x = 9 y + 4 ( 2 ) 2 x = 14 y + 1 ( 2 ) - ( 1 ) : x = 5 y - 3 5 y - x = 3 the answer is b ."
Answer: b
Python program:
a = 2 * 4
b = a - 1
c = 7 * 2
d = 2 * 9
e = c - d
f = b / e
g = 5 * f
h = 2 * 4
i = h - 1
j = 7 * 2
k = 2 * 9
l = j - k
m = i / l
n = 9 * m
o = n + 4 
p = g - o
Problem: a school has 4 maths 3 physics and 3 chemistry teachers each teacher can teach 2 subjects max what is he minimum number of teachers required
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "total subjects = 4 + 3 + 3 = 10 max subjects by 1 teacher = 2 so , min of teachers required = 10 / 2 = 5 answer : b"
Answer: b
Python program:
a = 4 + 3 
b = a + 3 
c = b / 2
Problem: two stations a and b are 245 km apart on a straight line . one train starts from a at 7 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 ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 1
Rationale: "suppose they meet x hours after 7 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 ) = 245 45 x = 270 x = 6 . so , they meet at 1 p . m . answer : option e"
Answer: e
Python program:
a = 245 - 20
b = 25 + 20 
c = a / b
d = 8 + c
Problem: for any integer p , * p is equal to the product of all the integers between 1 and p , inclusive . how many prime numbers are there between * 6 + 3 and * 6 + 6 , inclusive ?
Options: a ) one , b ) none , c ) two , d ) three , e ) four
Rationale: "generally * p or p ! will be divisible by all numbers from 1 to p . therefore , * 6 would be divisible by all numbers from 1 to 6 . = > * 6 + 3 would give me a number which is a multiple of 3 and therefore divisible ( since * 6 is divisible by 3 ) in fact adding anyprimenumber between 1 to 6 to * 6 will definitely be divisible . so the answer is none ( a ) ! supposing if the question had asked for prime numbers between * 6 + 3 and * 6 + 11 then the answer would be 1 . for * 6 + 3 and * 6 + 13 , it is 2 and so on . . . b"
Answer: b
Python program:
a = 6 * 3
b = a * 2
c = b * 4
d = c + 6 
e = 6 * 3
f = e * 2
g = f * 4
h = g + 3 
i = d - h
j = i - 1
Problem: the tax on a commodity is diminished by 35 % but its consumption is increased by 15 % . find the decrease percent in the revenue derived from it ?
Options: a ) 18 % , b ) 72 % , c ) 32 % , d ) 25.25 % , e ) 52.25 %
Rationale: "100 * 100 = 10000 65 * 115 = 7475 10000 - - - - - - - 2525 100 - - - - - - - ? = 25.25 % answer : d"
Answer: d
Python program:
a = 100 + 15 
b = 100 - 35
c = a * b
d = c / 100
e = 100 - d
Problem: a university cafeteria offers 4 flavors of pizza - pepperoni , chicken , hawaiian and vegetarian . if a customer has an option ( but not the obligation ) to add extra cheese , mushrooms or both to any kind of pizza , how many different pizza varieties are available ?
Options: a ) 4 , b ) 8 , c ) 12 , d ) 16 , e ) 32
Rationale: there are 4 flavors of pizza and each can be : 1 . without cheese and mushrooms ; 2 . with cheese ; 3 . with mushrooms ; 4 . with cheese and mushrooms . so , the total number of pizza varieties is 4 * 4 = 16 . answer : d .
Answer: d
Python program:
a = 4 * 4
Problem: find the least number of five digits which is exactly divisible by 12 , 15 and 18 ?
Options: a ) 1080 , b ) 10080 , c ) 10025 , d ) 11080 , e ) 12080
Rationale: "lcm = 180 180 ) 10000 ( 55 9900 - - - - - - - - - 100 10000 + 180 - 100 = 10080 answer : b"
Answer: b
Python program:
a = 10 * 1000
b = a - 1
c = b / 15
d = c + 1 
e = math.floor(d)
f = e * 15
g = f / 4
h = g / 100
i = h + 2
Problem: a tank can be filled by pipe a in 5 hours and by pipe b in 8 hours , each pump working on its own . when the tank is full and a drainage hole is open , the water is drained in 20 hours . if initially the tank was empty and someone started the two pumps together but left the drainage hole open , how long does it take for the tank to be filled ?
Options: a ) 2.6 hours , b ) 3.6 hours , c ) 4.6 hours , d ) 5.6 hours , e ) none of these
Rationale: let ' s first find the rates of the pumps and the drainage hole pump a : 1 / 5 , pump b : 1 / 8 , drainage hole : 1 / 20 let t be the time for the pumps to fill the tank . the pumps , add water into the tank however the drainage hole drains water out of the tank , hence t ( 1 / 5 + 1 / 8 - 1 / 20 ) = 1 solve for t t = 3.6 hours answer b
Answer: b
Python program:
a = 1 / 8
b = 1 / 5
c = a + b 
d = 1 / 20
e = c - d
f = 1 / e
Problem: a and b invests rs . 3000 and rs . 5000 respectively in a business . if a doubles his capital after 6 months . in what ratio should a and b divide that year ' s profit ?
Options: a ) 8 : 8 , b ) 9 : 8 , c ) 9 : 7 , d ) 9 : 5 , e ) 9 : 10
Rationale: ( 3 * 6 + 6 * 6 ) : ( 5 * 12 ) 54 : 60 = > 9 : 10 answer : e
Answer: e
Python program:
a = 3000 * 6
b = 3000 * 2
c = b * 6
d = a + c 
e = 6 + 6 
f = 5000 * e
g = d / f
Problem: express a speed of 720 kmph in meters per second ?
Options: a ) 120 mps , b ) 200 mps , c ) 181 mps , d ) 190 mps , e ) 125 mps
Rationale: "720 * 5 / 18 = 200 mps answer : b"
Answer: b
Python program:
a = const_0_2778 * 720
Problem: 84 / 12 / 0.8 = ?
Options: a ) 8.17 , b ) 7.14 , c ) 6.23 , d ) 4.35 , e ) 8.75
Rationale: "e 8.75 ? = 84 / ( 12 * 0.8 ) = 8.75"
Answer: e
Python program:
a = 84 / 12
Problem: from a pack of cards , two cards are drawn one after the other , with replacement . what is the probability that the first card is a club and the second card is a king ?
Options: a ) 2 / 13 , b ) 1 / 26 , c ) 5 / 26 , d ) 1 / 52 , e ) 17 / 52
Rationale: "p ( club ) = 1 / 4 p ( king ) = 1 / 13 p ( club then a king ) = 1 / 4 * 1 / 13 = 1 / 52 the answer is d ."
Answer: d
Python program:
a = 3 * 4
b = a + 1 
c = b / const_52
d = 2 / const_52
e = c * d
Problem: the length of a rectangular plot is 20 mtr more than its breadth . if the cost of fencingthe plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ?
Options: a ) 50 m
b ) 60 m
c ) 65 m
d ) 75 m
e ) 80 m
Rationale: let breadth = x metres . then , length = ( x + 20 ) metres . perimeter = 5300 m = 200 m . 26.50 2 [ ( x + 20 ) + x ] = 200 2 x + 20 = 100 2 x = 80 x = 40 . hence , length = x + 20 = 60 m b
Answer: b
Python program:
a = 5300 / 26
b = 20 * 2
c = a - b
d = c / 4
e = d + 20
Problem: define r * by the equation r * = π - r . then ( ( − π ) * ) * =
Options: a ) − 2 π , b ) - 1 , c ) − π , d ) 2 π , e ) 4 π
Rationale: for r * f ( f ( − π ) ) = f ( π − ( − π ) ) = f ( π + π ) = f ( 2 π ) = π − 2 π = − π = c
Answer: c
Python program:
a = 10 + 4 
b = a * 100
c = 12 + 4 
d = b + c 
e = d / 1000
f = e / 10
g = f + 3 
h = 10 + 4 
i = h * 100
j = 12 + 4 
k = i + j 
l = k / 1000
m = l / 10
n = m + 3 
o = 10 + 4 
p = o * 100
q = 12 + 4 
r = p + q 
s = r / 1000
t = s / 10
u = t + 3 
v = n - negate
w = g - v
Problem: how many multiples of 5 are there between 5 to 100 ?
Options: a ) 9 , b ) 18 , c ) 17 , d ) none of these , e ) can not be determined
Rationale: "explanation : as you know , multiples of 5 are integers having 0 or 5 in the digit to the extreme right ( i . e . the units place ) . so the numbers are 10 , 15 , 20 , 25 , 30 , 35 , 40 , 45 , 50 , 55 , 60 , 65 , 70 , 75 , 80 , 85 , 90 , 95 . answer : b"
Answer: b
Python program:
a = 100 - 5
b = a / 5
c = b + 1
Problem: a store reported total sales of $ 385 million for february of this year . if the total sales for the same month last year was $ 320 million , approximately what was the percent increase r in sales ?
Options: a ) 2 % , b ) 17 % , c ) 20 % , d ) 65 % , e ) 83 %
Rationale: last year ' s sales = $ 320 million ; this year ' s sales = $ 385 million ; increase r = $ 65 million . now , 20 % of $ 320 million is $ 64 million , which is very close to actual increase of $ 65 million . answer : c .
Answer: c
Python program:
a = 385 - 320
b = a / 320
c = b * 100
Problem: a person travels equal distances with speeds of 3 km / hr , 6 km / hr , 9 km / hr . and takes a total time of 11 minutes . find the total distance ?
Options: a ) 1 km , b ) 500 mts , c ) 900 mts , d ) 2 km , e ) 250 mts
Rationale: "let the each distance be x km total distance = 3 x then total time , ( x / 3 ) + ( x / 6 ) + ( x / 9 ) = 11 / 60 x = 0.3 total distance = 3 * 0.3 = 0.9 km = 900 meters correct option is c"
Answer: c
Python program:
a = 11 / const_60
b = 1 / 3
c = 1 / 6
d = b + c 
e = 1 / 9
f = d + e 
g = a / f
h = g * 3
i = h * 1000
Problem: a bag of potatoes weighs 28 lbs divided by half of its weight . how much does the bag of potatoes weight ?
Options: a ) 20 lb , b ) 14 lb , c ) 10 lb , d ) 15 lb , e ) 5 lb
Rationale: "sol . 28 ÷ 2 = 14 . answer : b"
Answer: b
Python program:
a = 28 / 1
Problem: pipe a can fill a tank in 2 hours . due to a leak at the bottom , it takes 4 hours for the pipe a to fill the tank . in what time can the leak alone empty the full tank ?
Options: a ) 2 , b ) 5 , c ) 6 , d ) 4 , e ) 1
Rationale: "let the leak can empty the full tank in x hours 1 / 2 - 1 / x = 1 / 4 = > 1 / x = 1 / 2 - 1 / 4 = 1 / 4 = > x = 4 . answer : d"
Answer: d
Python program:
a = 4 * 2
b = 4 - 2
c = a / b
Problem: the total age of a and b is 15 years more than the total age of b and c . c is how many year younger than a
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "explanation : given that a + b = 15 + b + c = > a ? c = 15 + b ? b = 15 = > c is younger than a by 15 years answer : option e"
Answer: e
Python program:
a = 15 * 1
Problem: 306 ã · ? ã — 15 + 270 = 405
Options: a ) 24 , b ) 25 , c ) 34 , d ) 39 , e ) 43
Rationale: explanation : 306 ã · ? ã — 15 = 405 - 270 = 135 ( 306 ã — 15 ) / ? = 135 ? = ( 306 ã — 15 ) / 135 = 34 answer : option c
Answer: c
Python program:
a = 405 - 270
b = a + 15 
c = b * 2
d = c / 10
e = 405 - 270
f = e + 15 
g = f * 2
h = g / 10
i = h / 10
j = d + i 
k = j + 1
Problem: two trains of equal length , running with the speeds of 60 and 40 kmph , take 50 seconds to cross each other while they are running in the same direction . what time will they take to cross each other if they are running in opposite directions ?
Options: a ) 10 sec , b ) 11 sec , c ) 77 sec , d ) 99 sec , e ) 67 sec
Rationale: "rs = 60 - 40 = 20 * 5 / 18 = 100 / 18 t = 50 d = 50 * 100 / 18 = 2500 / 9 rs = 60 + 40 = 100 * 5 / 18 t = 2500 / 9 * 18 / 500 = 10 sec answer : a"
Answer: a
Python program:
a = 60 - 40
b = const_0_2778 * a
c = b * 50
d = 60 + 40 
e = const_0_2778 * d
f = 1/(e)
g = c * f
Problem: eddy and freddy start simultaneously from city a and they travel to city b and city c respectively . eddy takes 3 hours and freddy takes 4 hours to complete the journey . if the distance between city a and city b is 540 kms and city a and city c is 300 kms . what is the ratio of their average speed of travel ? ( eddy : freddy )
Options: a ) 8 / 3 , b ) 3 / 8 , c ) 8 / 5 , d ) 12 / 5 , e ) 5 / 3
Rationale: "distance traveled by eddy = 540 km time taken by eddy = 3 hours average speed of eddy = 540 / 3 = 180 km / hour distance traveled by freddy = 300 km time taken by freddy = 4 hours average speed of freddy = 300 / 4 = 75 km / hour ratio of average speed of eddy to freddy = 180 / 75 = 12 / 5 answer d"
Answer: d
Python program:
a = 540 / 3
b = 300 / 4
c = a / b
Problem: in the first 10 overs of a cricket game , the run rate was only 3.4 . what should be the run rate in the remaining 40 overs to reach the target of 282 runs ?
Options: a ) 4.25 , b ) 5 , c ) 6.2 , d ) 7 , e ) 7.5
Rationale: "required run rate = 282 - ( 3.4 x 10 ) = 248 248 / 40 = 6.2 c )"
Answer: c
Python program:
a = 10 * 3
b = 282 - a
c = b / 40
Problem: the average weight of a group of boys is 20 kg . after a boy of weight 32 kg joins the group , the average weight of the group goes up by 1 kg . find the number of boys in the group originally ?
Options: a ) 12 , b ) 11 , c ) 18 , d ) 24 , e ) 10
Rationale: "let the number off boys in the group originally be x . total weight of the boys = 20 x after the boy weighing 32 kg joins the group , total weight of boys = 20 x + 32 so 20 x + 32 = 21 ( x + 1 ) = > x = 11 . answer : b"
Answer: b
Python program:
a = 20 + 1 
b = 32 - a
c = b + 1
Problem: a football team lost 5 yards and then gained 11 . what is the team ' s progress ?
Options: a ) 2 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: "for lost , use negative . for gain , use positive . progress = - 5 + 11 = 6 yards d"
Answer: d
Python program:
a = 11 - 5
Problem: two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post . if the length of each train be 160 m , in what time will they cross other travelling in opposite direction ?
Options: a ) 17 sec , b ) 12 sec , c ) 16 sec , d ) 15 sec , e ) 18 sec
Rationale: "speed of the first train = 120 / 10 = 12 m / sec . speed of the second train = 120 / 5 = 8 m / sec . relative speed = 12 + 8 = 20 m / sec . required time = ( 160 + 160 ) / 20 = 16 sec . answer : c"
Answer: c
Python program:
a = 160 * 2
b = speed + ( 
c = a / b
Problem: last year a worker saved 10 % of her annual salary . this year , she made 10 % more money than last year and she saved 12 % of her salary . the amount she saved this year was what percent of the amount she saved last year ?
Options: a ) 126 % , b ) 128 % , c ) 130 % , d ) 132 % , e ) 134 %
Rationale: "let x be the worker ' s salary last year . last year , she saved 0.1 x . this year , she saved 0.12 ( 1.1 x ) = 0.132 x 0.132 x / 0.1 x = 132 % the answer is d ."
Answer: d
Python program:
a = 10 + 100 
b = 12 / 100
c = a * b
d = 10 / c
e = 100 * d
Problem: what is the median of a set of consecutive integers if the sum of nth number from the beginning and nth number from the end is 120 ?
Options: a ) 60 , b ) 25 , c ) 50 , d ) 75 , e ) 100
Rationale: "surprisingly no one answered this easy one . property of a set of consecutive integerz . mean = median = ( first element + last element ) / 2 = ( second element + last but one element ) / 2 = ( third element + third last element ) / 2 etc . etc . so mean = median = 120 / 2 = 60 answer is a"
Answer: a
Python program:
a = 120 / 2
Problem: how many distinct integer values of n satisfy the inequality | | n - 3 | + 4 | ≤ 14 ?
Options: a ) 15 , b ) 12 , c ) 17 , d ) 18 , e ) 19
Rationale: "so i can write this as in - 3 i + 4 < = 14 or in - 3 i < = 10 so n can have - 7 to 13 = 12 true values . . . . b"
Answer: b
Python program:
a = 3 * 4
b = a + 1
Problem: a sum of money at simple interest amounts to 815 in 3 years and to 854 in 4 years . the sum is :
Options: a ) 698 , b ) 387 , c ) 373 , d ) 593 , e ) 372
Rationale: "a 698 s . i . for 1 year = ( 854 - 815 ) = 39 . s . i . for 3 years = ( 39 x 3 ) = 117 . principal = ( 815 - 117 ) = 698 ."
Answer: a
Python program:
a = 854 - 815
b = a * 3
c = b / 4
d = 815 - c
Problem: a woman spends 15 % of her income in house rent , 15 % of the rest on his children ’ s education , 10 % of the rest miscellaneous causes and 15 % in medical expenses . if she now posses rs . 5548 then her income is ?
Options: a ) 10058 , b ) 10068 , c ) 10078 , d ) 10088 , e ) 10038
Rationale: x * ( 85 / 100 ) * ( 85 / 100 ) * ( 90 / 100 ) * ( 85 / 100 ) = 5548 x * 0.85 * 0.85 * 0.9 * 0.85 = 5548 x = 5548 / 0.5527 x = 10038 answer : e
Answer: e
Python program:
a = 15 / 100
b = 1 - a
c = 15 / 100
d = 1 - c
e = b * d
f = 10 / 100
g = 1 - f
h = e * g
i = 15 / 100
j = 1 - i
k = h * j
l = 5548 / k
Problem: a student got twice as many sums wrong as he got right . if he attempted 48 sums in all , how many did he solve correctly ?
Options: a ) 12 , b ) 16 , c ) 18 , d ) 24 , e ) 26
Rationale: "explanation : suppose the boy got x sums right and 2 x sums wrong . then , x + 2 x = 48 3 x = 48 x = 16 . answer : b"
Answer: b
Python program:
a = 1 + 2 
b = 48 / a
Problem: a worker is paid a regular rate of rs . 20 for completing a survey . the worker completes 50 surveys per week . for any survey involving the use of her cellphone , she is paid at a rate of that is 10 % higher than her regular rate . if she completed 35 surveys involving the use of her cellphone , how much did she get that week ?
Options: a ) 570 , b ) 670 , c ) 1070 , d ) 470 , e ) 2070
Rationale: "amount earned by using her cell phone = 35 * 22 = 770 amount earned as usual = 15 * 20 = 300 total = 770 + 300 = 1070 answer : c"
Answer: c
Python program:
a = 20 * 50
b = 10 / 50
c = 20 * b
d = 35 * c
e = a + d
Problem: reeya obtained 50 , 60 , 70 , 80 and 80 out of 100 in different subjects , what will be the average
Options: a ) 70 , b ) 75 , c ) 80 , d ) 85 , e ) 68
Rationale: "explanation : ( 50 + 60 + 70 + 80 + 80 / 5 ) = 68 option e"
Answer: e
Python program:
a = 50 + 60 
b = a + 70 
c = b + 80 
d = c + 80 
e = 4 + 1 
f = d / e
Problem: 5 goats ’ s and 10 hens are brought for rs . 2500 . if the average price of a hen be rs . 50 . what is the average price of a goat .
Options: a ) 425 , b ) 375 , c ) 350 , d ) 400 , e ) 500
Rationale: explanation : average price of a hen = rs . 50 total price of 10 hens = 10 * 50 = rs . 500 but total price of 5 goats and 10 hens = rs . 2500 total price of 5 goats is = 2500 - 500 = 2000 average price of a goat = 2000 / 5 = rs . 400 answer : d
Answer: d
Python program:
a = 10 * 50
b = 2500 - a
c = b / 5
Problem: kareena , saif , and a puppy start walking down a road . they start at the same time , from the same point , in the same direction . the saif walks at 5 miles / hour kareena at 6 miles / hour . the puppy runs from saif to kareena and back again with a constant speed of 10 miles / hour . the puppy does not slow down on the turn . how far does the puppy travel in 1 hour ?
Options: a ) 10 miles , b ) 14 miles , c ) 12 miles , d ) 20 miles , e ) 30 miles
Rationale: a 10 miles speed us 10 miles / hour
Answer: a
Python program:
a = 10 * 1
Problem: if m is a positive integer and m ^ 2 is divisible by 39 , then the largest positive integer that must divide m is ?
Options: a ) 3 , b ) 6 , c ) 8 , d ) 12 , e ) 13
Rationale: "m ^ 2 is divisible by 48 so m ^ 2 must be multiple of 48 . if the value of m is multiples of 13 then it will satisfy the condition . if we if m is 12 or 24 or 36 then it ans is e but if m = 39 then answer should be 16 . is the question right ? or am i missing some thing ? e"
Answer: e
Python program:
a = 39 / 3
b = a / 3
c = 3 * b
Problem: a man can row 6 kmph in still water . when the river is running at 1.2 kmph , it takes him 1 hour to row to a place and back . what is the total distance traveled by the man ?
Options: a ) 7.76 kms , b ) 8.76 kms , c ) 5.76 kms , d ) 3.76 kms , e ) 4.76 kms
Rationale: "explanation : speed in still water = 6 kmph stream speed = 1.2 kmph down stream = 7.2 kmph up stream = 4.8 kmph x / 7.2 + x / 4.8 = 1 x = 2.88 total distance = 2.88 x 2 = 5.76 kms answer : c"
Answer: c
Python program:
a = 6 + 1 
b = 6 - 1
c = a * b
d = 6 + 1 
e = 6 - 1
f = d + e 
g = c / f
h = g * 2
Problem: for any integer k greater than 1 , the symbol k * denotes the product of all integers between 1 and k , inclusive . if k * is a multiple of 315 what is the least possible value of k ?
Options: a ) 5 , b ) 7 , c ) 9 , d ) 11 , e ) 13
Rationale: 315 = 3 * 3 * 5 * 7 thus k must include numbers at least up to the number 7 . the answer is b .
Answer: b
Python program:
a = 315 / 3
b = a / 3
c = 1 + 4 
d = b / c
Problem: find the value of a from ( 15 ) ^ 2 x 8 ^ 3 ã · 256 = a .
Options: a ) 250 , b ) 420 , c ) 440 , d ) 650 , e ) 450
Rationale: given exp . = ( 15 ) ^ 2 x 8 ^ 3 ã · 256 = a = 225 x 512 ã · 256 = 450 e
Answer: e
Python program:
a = 15 ** 2
b = 8 ** 3
c = a * b
d = c / 256
Problem: the sum of two prime numbers is 85 . what is the product of these two prime numbers ?
Options: a ) 85 , b ) 91 , c ) 115 , d ) 133 , e ) 166
Rationale: since there is only one even prime number ( 2 ) , and the sum of two odd numbers is even , the product of these two numbers must be even . correct answer e
Answer: e
Python program:
a = 85 - 2
b = a * 2
Problem: a and b can do a work in 15 days , b and c in 30 days , c and a in 45 days . if a , b and c work together , they will complete the work in ?
Options: a ) 10 days , b ) 16 days , c ) 20 days , d ) 25 days , e ) 22 days
Rationale: "a + b 1 day work = 1 / 15 b + c 1 day work = 1 / 30 c + a 1 day work = 1 / 45 adding we get 2 ( a + b + c ) = 1 / 15 + 1 / 30 + 1 / 45 = 11 / 90 a + b + c 1 day work = 11 / 180 a , b , c can finish the work in 180 / 11 days = 16 days approximately answer is b"
Answer: b
Python program:
a = 1/(15)
b = 1/(30)
c = a + b 
d = 1/(45)
e = c + d 
f = e / 2
g = 1 / f
Problem: a woman invested $ 1,000 , part at 5 % and the rest at 6 % . her total investment with interest at the end of the year was $ 1,053 . how much did she invest at 5 % ?
Options: a ) $ 500 , b ) $ 600 , c ) $ 700 , d ) $ 900 , e ) $ 950
Rationale: "et x be the portion invested at 5 % and let ( 1 - x ) be the rest which is invested at 6 % the question states that the return after 1 year is ( 1053 / 1000 ) - 1 = 0.053 = 5.3 % we want to find the dollar amount invested in x using our defined variables , put together the equation and solve for x ( the percentage of 1000 invested at 5 % ) 0.05 x + 0.06 ( 1 - x ) = 0.053 ( 0.05 ) x + 0.06 - ( 0.06 ) x = 0.053 - 0.01 x = - 0.007 x = - 0.007 / - 0.01 = 7 / 10 = 70 % so x = 70 % of the 1000 which is 700 answer : c"
Answer: c
Python program:
a = 5 * 2
b = a * 100
c = 5 * 2
d = c * 100
e = 5 * 2
f = e * 5
g = f + 4 
h = d + g 
i = 5 * 2
j = i * 100
k = h - j
l = k * 100
m = 5 * 2
n = m * 100
o = 5 * n
p = l - o
q = b - p
Problem: 6 ! / ( 6 - 3 ) ! = ?
Options: a ) 120 , b ) 346 , c ) 356 , d ) 366 , e ) 396
Rationale: 6 ! / 6 - 3 ) ! = 6 ! / 3 ! = 6 * 5 * 4 = 120 . hence , the correct answer is a .
Answer: a
Python program:
a = math.factorial(6)
b = 6 - 3
c = math.factorial(b)
d = a / c
Problem: x is a positive integer less than 500 . when x is divided by 7 , the remainder is 1 ; when x is divided by 3 , the remainder is 2 . how many x are there ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: "when x divided by 7 and leave reminder 1 . x could be 1 , 8,15 , . . . . when divided by 3 and leave reminder 2 - x could be 2 , 5,8 , . . . . so x must be of the form 21 m + 8 where m = 0 , 1,2 , . . . . . first no will be 8 and last no will be 491 . so total no . less than 500 will be 24 . answer : d"
Answer: d
Python program:
a = reminder * (
b = a + 3 
c = b - reminder
Problem: the expression x # y denotes the product of the consecutive multiples of 3 between x and y , inclusive . what is the sum of the exponents in the prime factorization of 21 # 27 ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "first , let ' s translate the expression 21 # 27 , using the definition given : 21 # 27 = 21 × 24 × 27 we need the prime factorization of this product . let ' s factor out 3 from each multiple . 21 # 27 = 3 ^ 3 ( 7 × 8 × 9 ) now let ' s replace each consecutive integer with its prime factorization : 21 # 27 = 3 ^ 3 ( 7 × 2 ^ 3 × 3 ^ 2 ) let ' s group the prime bases : 21 # 27 = 2 ^ 3 × 3 ^ 5 × 7 the sum of the exponents is 3 + 5 + 1 = 9 the answer is d ."
Answer: d
Python program:
a = 2 + 2 
b = 3 + a 
c = 2 + 2 
d = b + c 
e = 2 + 2 
f = 3 + e 
g = d + f
Problem: the average age of the boys in a class is 16 years and that of the girls is 15 years . the average age for the whole class is
Options: a ) 27 , b ) 29 , c ) 11 , d ) data inadequate , e ) 28
Rationale: clearly , to find the average , we ought to know the number of boys , girls or students in the class , neither of which has been given . so , the data provided is inadequate answer : d
Answer: d
Python program:
a = 16 + 15 
b = a / 2