euclaise/mathqa_programs huggingface dataset:
Problem: arun and tarun can do a work in 10 days . after 4 days tarun went to his village . how many days are required to complete the remaining work by arun alone . arun can do the work alone in 60 days .
Options: a ) 36 days . , b ) 17 days . , c ) 18 days . , d ) 19 days . , e ) 20 days .
Rationale: "they together completed 4 / 10 work in 4 days . balance 6 / 10 work will be completed by arun alone in 60 * 6 / 10 = 36 days . answer : a"
Answer: a
Python program:
a = 60 / 10
b = a * 4
c = 60 - b
Problem: in a school with 5 classes , each class has 2 students less then the previous class . how many students are there in the largest class if the total number of students at school is 95 ?
Options: a ) 17 , b ) 19 , c ) 21 , d ) 23 , e ) 25
Rationale: "total classes = 5 total students = 95 . average = 19 if the classes had average number of students : 19 19 19 19 19 given case = 23 21 19 17 15 hence number of students in the largest class = 23 correct option : d"
Answer: d
Python program:
a = 2 + 2 
b = 2 + a 
c = 2 + 2 
d = c + 2 
e = b + d 
f = 2 + 2 
g = f + 2 
h = g + 2 
i = e + h 
j = 95 - i
k = j / 5
l = 2 + 2 
m = l + 2 
n = m + 2 
o = k + n
Problem: jane and thomas are among the 6 people from which a committee of 3 people is to be selected . how many different possible committees of 3 people can be selected from these 6 people if at least one of either jane or thomas is to be selected ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: the total number of ways to choose 3 people from 6 is 6 c 3 = 20 . the number of committees without jane or thomas is 4 c 3 = 4 . there are 20 - 4 = 16 possible committees which include jane and / or thomas . the answer is c .
Answer: c
Python program:
a = math.comb(6, 1)
b = math.comb(6, 1)
c = a + b 
d = math.comb(4, 1)
e = c + d
Problem: when 1 / 20 % of 4,000 is subtracted from 1 / 10 of 4,000 , the difference is
Options: a ) 50 , b ) 200 , c ) 380 , d ) 398 , e ) 400
Rationale: "( 1 / 10 ) * 4000 - ( 1 / 20 * 100 ) * 4000 = 400 - 2 = 398 answer d"
Answer: d
Python program:
a = 1/(10)
b = 100 * 10
c = 4 + 4 
d = b * c
e = a * d
Problem: the average weight of a class is x pounds . when a new student weighing 60 pounds joins the class , the average decreases by 1 pound . in a few months the student ’ s weight increases to 110 pounds and the average weight of the class becomes x + 4 pounds . none of the other students ’ weights changed . what is the value of x ?
Options: a ) 85 , b ) 86 , c ) 88 , d ) 90 , e ) 92
Rationale: "when the student weighs 80 pounds the average weight is x - 1 pounds ; when the student weighs 110 pounds the average weight is x + 4 pounds . so , the increase in total weight of 110 - 80 = 30 pounds corresponds to the increase in average weight of ( x + 4 ) - ( x - 1 ) = 5 pounds , which means that there are 30 / 5 = 6 students ( including the new one ) . so , initially there were 5 student . total weight = 5 x + 80 = 6 ( x - 1 ) - - > x = 88 pounds . answer : c ."
Answer: c
Python program:
a = 60 + 4 
b = 4 + 1 
c = a + b
Problem: if a train , travelling at a speed of 180 kmph , crosses a pole in 5 sec , then the length of train is ?
Options: a ) 250 m , b ) 112 m , c ) 117 m , d ) 125 m , e ) 123 m
Rationale: "a a = 180 * 5 / 18 * 5 = 250 m"
Answer: a
Python program:
a = 180 * const_0_2778
b = a * 5
Problem: if 6 < x < 10 < y < 17 , then what is the greatest possible positive integer difference of x and y ?
Options: a ) 3 , b ) 4 , c ) 10 , d ) 6 , e ) 7
Rationale: "let x = 6.1 and y = 16.1 greatest possible difference = 16.1 - 6.1 = 10 answer c"
Answer: c
Python program:
a = 17 - 6
b = a - 1
Problem: 9 spheres of the same size are made from melting a solid cylinder of 16 cm diameter and 12 cm height . what is the diameter of each sphere ?
Options: a ) 4 cm
b ) 6 cm
c ) 8 cm
d ) 10 cm
e ) 12 cm
Rationale: volume of cylinder = pi * r ^ 2 * h volume of a sphere = 4 * pi * r ^ 3 / 3 9 * 4 * pi * r ^ 3 / 3 = pi * r ^ 2 * h r ^ 3 = r ^ 2 * h / 12 = 64 cm ^ 3 r = 4 cm d = 8 cm the answer is c .
Answer: c
Python program:
a = 16 / 2
b = volume_cylinder / (
c = b * math.pi
d = c / 3
e = d / 4
f = e / 9
g = f / 4
h = g * 4
Problem: a survey was sent to 90 customers , 7 of whom responded . then the survey was redesigned and sent to another 63 customers , 9 of whom responded . by approximately what percent did the response rate increase from the original survey to the redesigned survey ?
Options: a ) 2 % , b ) 6 % , c ) 14 % , d ) 28 % , e ) 63 %
Rationale: "case 1 : ( 7 / 90 ) = x / 100 x = 8 % case 2 : ( 9 / 63 ) = y / 100 y = 14 % so percent increase is = ( y - x ) = ( 14 - 8 ) % = 6 % answer is b"
Answer: b
Python program:
a = 9 / 63
b = 7 / 90
c = a - b
d = c * 100
e = math.floor(d)
Problem: a car started running at a speed of 29 km / hr and the speed of the car was increased by 2 km / hr at the end of every hour . find the total distance covered by the car in the first 10 hours of the journey .
Options: a ) 41 km , b ) 76 km , c ) 25 km , d ) 15 km , e ) 30 km
Rationale: "a 41 km the total distance covered by the car in the first 10 hours = 32 + 34 + 36 + 38 + 40 + 42 + 44 + 46 + 48 + 50 = sum of 10 terms in ap whose first term is 32 and last term is 50 = 10 / 2 [ 32 + 50 ] = 410 km ."
Answer: a
Python program:
a = 2 * 10
b = 29 + a 
c = b + 29 
d = c / 2
Problem: q is as much younger than r as he is older than t . if the sum of the ages of r and t is 50 years . what is definitely the difference between r and q ' s age ?
Options: a ) 50 , b ) 99 , c ) 88 , d ) 77 , e ) 23
Rationale: "r - q = r - t q = t . also r + t = 50 ; r + q = 50 so , ( r - q ) can not be determined . answer : d"
Answer: d
Python program:
a = 50 / 2
Problem: a deer passed a certain tree at a constant speed of 50 miles per hour while being chased by a cheetah . then , 2 minutes later , the cheetah passed the same tree at a constant speed of 60 miles per hour . if both animals maintained their speeds , how long after the cheetah passed the tree did the cheetah catch up with the deer ?
Options: a ) 30 min , b ) 3 min , c ) 1 hr , d ) 1 min , e ) 2 min
Rationale: when the cheetah is at the tree , the deer is 50 / 30 miles ahead on the highway . ( the distance covered in 2 min ) every hour , cheetah runs 10 miles more than the deer . how many hours will it takes it to cover 50 / 30 miles more ? the answer is ( 50 / 30 ) / 10 = 1 / 60 = 1 min answer d
Answer: d
Python program:
a = 60 / 60
Problem: a computer manufacturer produces a certain electronic component at a cost of $ 150 per component . shipping costs for delivering the components are $ 1 per unit . further , the manufacturer has costs of $ 19,500 a month related to the electronic component regardless of how many it produces . if the manufacturer produces and sells 250 components a month , what is the lowest price it can sell them for such that the costs do n ' t exceed the revenues ?
Options: a ) 199 , b ) 249 , c ) 233 , d ) 215 , e ) 229
Rationale: "$ 19500 is a fixed cost each component is $ 151 ( $ 150 to produce , $ 1 to ship ) manufacturer will be producing and selling 250 components so therefore the equation to find price would be 250 * p = 19500 + ( 250 * 150 ) + ( 250 * 1 ) p = ( 19500 + 37500 + 250 ) / 250 p = 229 answer : e"
Answer: e
Python program:
a = 4 * 4
b = a * 1000
c = 1 * 100
d = b + c 
e = 150 + 1 
f = e * 250
g = d + f 
h = g / 250
Problem: the minimum number of tiles of size 16 by 24 required to form a square by placing them adjacent to one another is
Options: a ) 4 tiles
b ) 5 tiles
c ) 6 tiles
d ) 7 tiles
e ) 8 tiles
Rationale: lcm of 16,24 = 48 48 * 48 is the minimum size of square made with 16 by 24 tiles number of tiles required = area of square / area of one tile = 48 * 48 / ( 16 * 24 ) = 6 tiles answer : c
Answer: c
Python program:
a = 24 / 4
Problem: sandy bought 65 books for $ 1380 from one shop and 55 books for $ 900 from another shop . what is the average price that sandy paid per book ?
Options: a ) $ 13 , b ) $ 15 , c ) $ 17 , d ) $ 19 , e ) $ 21
Rationale: average price per book = ( 1380 + 900 ) / ( 65 + 55 ) = 2280 / 120 = $ 19 the answer is d .
Answer: d
Python program:
a = 1380 + 900 
b = 65 + 55 
c = a / b
Problem: the simple interest on rs . 23 for 3 months at the rate of 5 paise per rupeeper month is
Options: a ) 3.45 , b ) 4.5 , c ) 2.25 , d ) 3.21 , e ) none
Rationale: sol . s . i . = rs . [ 23 * 5 / 100 * 3 ] = rs . 3.45 answer a
Answer: a
Python program:
a = 23 * 3
b = a * 5
c = b / 100
Problem: the weight of a glass of jar is 15 % of the weight of the jar filled with coffee beans . after some of the beans have been removed , the weight of the jar and the remaining beans is 60 % of the original total weight . what fraction part of the beans remain in the jar ?
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 2 / 5 , d ) 9 / 17 , e ) 9 / 23
Rationale: "let weight of jar filled with beans = 100 g weight of jar = 15 g weight of coffee beans = 85 g weight of jar and remaining beans = 60 g weight of remaining beans = 45 g fraction remaining = 45 / 85 = 9 / 17 answer is d ."
Answer: d
Python program:
a = 60 - 15
b = 100 - 15
c = a / b
Problem: how many numbers from 10 to 1000 are exactly divisible by 9 ?
Options: a ) 100 , b ) 10 , c ) 11 , d ) 12 , e ) 14
Rationale: "10 / 9 = 1 and 1000 / 9 = 111 = = > 111 - 1 = 100 . therefore 100 answer : a"
Answer: a
Python program:
a = 1000 / 9
b = math.floor(a)
c = b * 9
d = 10 / 9
e = math.floor(d)
f = e + 1 
g = f * 9
h = c - g
i = h / 9
j = i + 1
Problem: in a factory , an average of 50 tv ' s are produced per day for the fist 25 days of the months . a few workers fell ill for the next 5 days reducing the daily avg for the month to 48 sets / day . the average production per day for day last 5 days is ?
Options: a ) 20 , b ) 36 , c ) 48 , d ) 38 , e ) 59
Rationale: "production during these 5 days = total production in a month - production in first 25 days . = 30 x 48 - 25 x 50 = 190 ∴ average for last 5 days = 190 / 5 = 38 d"
Answer: d
Python program:
a = 25 + 5 
b = a * 48
c = 25 * 50
d = b - c
e = d / 5
Problem: pradeep has to obtain 40 % of the total marks to pass . he got 200 marks and failed by 20 marks . the maximum marks are
Options: a ) 300 , b ) 600 , c ) 550 , d ) 1000 , e ) 900
Rationale: "explanation : let their maximum marks be x . then , 40 % of x = 200 + 20 = > 40 / 100 x = 220 x = ( 22000 / 40 ) x = 550 . answer : c"
Answer: c
Python program:
a = 200 + 20 
b = 40 / 100
c = a / b
Problem: a batsman makes a score of 56 runs in the 17 th inning and thus increases his averages by 3 . what is his average after 17 th inning ?
Options: a ) 25 , b ) 8 , c ) 27 , d ) 29 , e ) 39
Rationale: "let the average after 17 innings = x total runs scored in 17 innings = 17 x average after 16 innings = ( x - 3 ) total runs scored in 16 innings = 16 ( x - 3 ) total runs scored in 16 innings + 56 = total runs scored in 17 innings = > 16 ( x - 3 ) + 56 = 17 x = > 16 x - 48 + 56 = 17 x = > x = 8 answer is b ."
Answer: b
Python program:
a = 17 * 3
b = 56 - a
c = b + 3
Problem: if 2 x + y = 6 and x + 2 y = 5 , then ( x + y ) / 3 =
Options: a ) 1 , b ) 4 / 3 , c ) 17 / 5 , d ) 11 / 9 , e ) 4
Rationale: we have two equations : 2 x + y = 6 x + 2 y = 5 notice that something nice happens when we add them . we get : 3 x + 3 y = 11 divide both sides by 3 to get : x + y = 11 / 3 so , ( x + y ) / 3 = 11 / 9 answer : d
Answer: d
Python program:
a = 6 * 2
b = a - 5
c = 2 * 2
d = c - 1
e = b / d
f = 6 * 2
g = f - 5
h = 2 * 2
i = h - 1
j = g / i
k = 2 * j
l = 6 - k
m = e + l 
n = m / 3
Problem: what is the value of ( 12 + 22 + 32 + 42 + - - - - - + 102 )
Options: a ) 295 , b ) 324 , c ) 385 , d ) 391 , e ) 399
Rationale: "explanation : ( 12 + 22 + … . . + n 2 ) = ( 1 / 6 ) n ( n + 1 ) ( 2 n + 1 ) here , n = 10 therefore , ( 12 + 22 + … . . + 102 ) = ( 1 / 6 ) 10 ( 10 + 1 ) ( 2 x 10 + 1 ) = ( 1 / 6 ) x 10 x 11 x 21 = 385 answer : c"
Answer: c
Python program:
a = 12 ** negate
Problem: if m and n are positive integers and m = 15 n - 1 , what is the remainder when m is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: this question asks what is . . . ( the answer ) , so we know that the answer will be consistent . as such , we can test values to quickly get the solution . we ' re told that m and n are positive integers and m = 15 n - 1 . we ' re asked for the remainder when m is divided by 5 . if . . . . n = 1 m = 14 14 / 5 = 2 remainder 4 final answer : e
Answer: e
Python program:
a = 15 * 2
b = a - 1
c = 5 * 5
d = b - c
Problem: a man has $ 10,000 to invest . he invests $ 4000 at 5 % and $ 3500 at 4 % . in order to have a yearly income of $ 500 , he must invest the remainder at :
Options: a ) 4.6 % , b ) 3.6 % , c ) 6.4 % , d ) 7.8 % , e ) 8.9 %
Rationale: "c 6.4 % income from $ 4000 at 5 % in one year = $ 4000 of 5 % . = $ 4000 × 5 / 100 . = $ 4000 × 0.05 . = $ 200 . income from $ 3500 at 4 % in one year = $ 3500 of 4 % . = $ 3500 × 4 / 100 . = $ 3500 × 0.04 . = $ 140 . total income from 4000 at 5 % and 3500 at 4 % = $ 200 + $ 140 = $ 340 . remaining income amount in order to have a yearly income of $ 500 = $ 500 - $ 340 . = $ 160 . total invested amount = $ 4000 + $ 3500 = $ 7500 . remaining invest amount = $ 10000 - $ 7500 = $ 2500 . we know that , interest = principal × rate × time interest = $ 160 , principal = $ 2500 , rate = r [ we need to find the value of r ] , time = 1 year . 160 = 2500 × r × 1 . 160 = 2500 r 160 / 2500 = 2500 r / 2500 [ divide both sides by 2500 ] 0.064 = r r = 0.064 change it to a percent by moving the decimal to the right two places r = 6.4 % therefore , he invested the remaining amount $ 2500 at 6.4 % in order to get $ 500 income every year ."
Answer: c
Python program:
a = 4000 / 100
b = a * 5
c = 500 - b
d = 3500 / 100
e = d * 4
f = c - e
g = 100 * 100
h = g - 4000
i = h - 3500
j = i / 100
k = f / j
Problem: workers decided to raise rs . 3 lacs by equal contribution from each . had they contributed rs . 50 eachextra , the contribution would have been rs . 3.25 lacs . how many workers were they ?
Options: a ) 350 , b ) 400 , c ) 500 , d ) 550 , e ) 590
Rationale: "n * 50 = ( 325000 - 300000 ) = 25000 n = 25000 / 50 = 500 c"
Answer: c
Python program:
a = 3 - 25
b = a * 1000
c = b * 100
d = c / 50
Problem: in the xy - coordinate system , if ( m , n ) and ( m 1 2 , n 1 k ) are two points on the line with the equation x 5 2 y 1 5 , then k 5
Options: a ) 1 / 2 , b ) 1 , c ) 2 , d ) 5 / 2 , e ) 4
Rationale: step 1 : analyze the question for any question involving the equation of a line , a good place to start is the slope - intercept form of the line , y = mx 1 b . remember that if you have two points on a line , you can derive the entire equation , and if you have an equation of the line , you can calculate any points on that line . step 2 : state the task we are solving for k , which is the amount by which the y - coordinate increases when the x - coordinate increases by 2 . step 3 : approach strategically the slope of a line is the ratio between the change in y and the change in x . in other words , every time the x - coordinate increases by 1 , the y - coordinate increases by the amount of the slope . the equation of the line in the question stem is defined as x = 2 y + 5 . we must isolate y to have slope - intercept form : so the slope of this line is 1 / 2 . this means that for every change of + 1 in the x direction , there is a change of + 1 / 2 in the y direction . then we know that , because there is an increase in 2 units in the x direction when moving from m to m + 2 , there must be a change of 1 unit in the y direction when moving from n to n + k . so k = 1 . since there are variables that eventually cancel ( m and n are not part of the answers ) , we can pick numbers . let ’ s say that you choose the y - coordinate of the point ( m , n ) to be 0 to allow for easier calculations . using the equation we ’ re given to relate x - and y - coordinates , we can calculate the x - coordinate : so ( m , n ) is the point ( 5 , 0 ) . now we ’ ll plug our values of m and n into the next point : ( m + 2 , n + k ) . that yields ( 7 , k ) . all we have to do is plug an x - coordinate of 7 into the equation to solve for k , the y - coordinate : answer is b
Answer: b
Python program:
a = 1 / 2
b = 2 * a
Problem: if 625 ^ ( - x ) + 25 ^ ( - 2 x ) + 5 ^ ( - 4 x ) = 11 , what is the value of x ?
Options: a ) - 4 , b ) - 1 / 4 , c ) 0 , d ) 1 / 4 , e ) 4
Rationale: we ' re told that 625 ^ ( - x ) + 25 ^ ( - 2 x ) + 5 ^ ( - 4 x ) = 15 . we ' re asked for the value of x . since each of the calculated terms must be positive ( regardless of what the exponent is ) , we can use thebasesto our advantage . . . . . with answer a , we ' d have 625 ^ 4 , which is much bigger than 15 ( and we ' d be adding to that big number ) . eliminate a . with answer e , we ' d have 625 ^ ( - 4 ) , which would create a tiny fraction ( and we ' d add some other fractions to it , so the total would be much too small ) . eliminate e . with answer d , we ' d have 625 ^ ( - 1 / 4 ) , which will also be a fraction ( just not as tiny as the one in answer e ) , but the total would still be too small . eliminate d . with answer c , anything to the ' 0 power ' is 1 , so we ' d have 1 + 1 + 1 = 3 . this is not 15 . eliminate c . d
Answer: d
Python program:
a = 1 / 4
Problem: find √ ? / 13 = 4 ?
Options: a ) 76 , b ) 5776 , c ) 304 , d ) 2704 , e ) none
Rationale: "answer let √ n / 13 = 4 then √ n = 13 x 4 = 52 ∴ n = 52 x 52 = 2704 . correct option : d"
Answer: d
Python program:
a = 4 * 13
b = a ** 2
Problem: an athlete runs 200 metres race in 25 seconds . what is his speed ?
Options: a ) 23 , b ) 38 , c ) 37 , d ) 30 , e ) 28.8
Rationale: "speed = distance / time = 200 / 25 = 8 m / s = 8 * 18 / 5 = 28.8 km / hr answer : e"
Answer: e
Python program:
a = 200 / 25
b = a * const_3_6
Problem: how many odd prime numbers are there less than 125 ?
Options: a ) 29 , b ) 34 , c ) 44 , d ) 54 , e ) 64
Rationale: odd prime number less than 125 : 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41 , 43 , 47 , 53 , 59 , 61 , 67 , 71 , 73 , 79 , 83 , 89 , 97 , 101 , 103 , 107 , 109 , 113 there is 29 the odd prime number answer is a
Answer: a
Python program:
a = 125 - 100
b = a + 4
Problem: the radius of a semi circle is 3.1 cm then its perimeter is ?
Options: a ) 15.94 , b ) 12.41 , c ) 16.1 , d ) 32.92 , e ) 32.3
Rationale: "36 / 7 r = 6.3 = 15.94 answer : a"
Answer: a
Python program:
a = circumface / (
b = a + 2
Problem: a , band c can do a piece of work in 11 days , 5 days and 55 days respectively , working alone . how soon can the work be done if a is assisted by band c on alternate days ?
Options: a ) 5 days , b ) 8 days , c ) 9 days , d ) 10 days , e ) 11 days
Rationale: ( a + b ) ' s 1 day ' s work = 1 / 11 + 1 / 5 = 16 / 55 ( a + c ) ' s 1 day ' s work = 1 / 11 + 1 / 55 = 6 / 55 work done in 2 day ' s = 16 / 55 + 6 / 55 = 2 / 5 2 / 5 th work done in 2 days work done = 5 / 2 * 2 = 5 days answer : a
Answer: a
Python program:
a = 55 / 11
b = 55 / 5
c = a + b 
d = 55 / 11
e = 55 / 55
f = d + e 
g = c + f 
h = g / 2
i = 55 / h
Problem: find the number of shares that can be bought for rs . 8200 if the market value is rs . 20 each with brokerage being 2.5 % .
Options: a ) 237 , b ) 270 , c ) 177 , d ) 166 , e ) 111
Rationale: "explanation : cost of each share = ( 20 + 2.5 % of 20 ) = rs . 20.5 therefore , number of shares = 8200 / 20.5 = 400 answer : c"
Answer: c
Python program:
a = 2 / 5
b = 20 + a 
c = 8200 / b
d = math.floor(c)
Problem: two trains 300 m and 400 m long run at the speed of 36 kmph and 18 kmph in opposite directions in parallel tracks . the time which they take to cross each other is ?
Options: a ) 5.6 sec , b ) 46.67 sec , c ) 10.8 sec , d ) 12.6 sec , e ) 15 sec
Rationale: "relative speed = 36 + 18 = 54 kmph * 5 / 18 = 15 m / s distance covered in crossing each other = 300 + 400 = 700 m required time = 700 * 1 / 15 = 46.67 sec answer is b"
Answer: b
Python program:
a = 300 + 400 
b = 36 + 18 
c = b * const_0_2778
d = a / c
Problem: if 1 / ( x + 2 ) + 1 / ( x - 2 ) = 1 / ( x + 2 ) , what is the value of x ?
Options: a ) - 1 , b ) 2 , c ) 1 , d ) - 2 , e ) 0
Rationale: "if we solve the question , we get x = - 2 . option : d"
Answer: d
Python program:
a = 1 + 1 
b = a - 1
Problem: find the compound interest on $ 1200 for 1 year at 20 % p . a . if ci is component yearly ?
Options: a ) $ 120 , b ) $ 150 , c ) $ 240 , d ) $ 250 , e ) $ 300
Rationale: "a = p ( 1 + r / 100 ) ^ t = 1200 ( 1 + 20 / 100 ) ^ 1 = 1200 * 6 / 5 = $ 1440 ci = a - p = 1440 - 1200 = $ 240 answer is c"
Answer: c
Python program:
a = 20 / 100
b = 1 + a 
c = b ** 1
d = 1200 * c
e = d - 1200
Problem: if the sides of a cube are in the ratio 5 : 4 . what is the ratio of their diagonals ?
Options: a ) 4 : 3 , b ) 5 : 4 , c ) 4 : 7 , d ) 3 : 4 , e ) 4 : 5
Rationale: "explanation : diagonal of a cube = a √ 3 where a is side a 1 : a 2 = 5 : 4 d 1 : d 2 = 5 : 4 where √ 3 cancelled both side answer : b"
Answer: b
Python program:
a = 5 / 4
Problem: bob wants to run a mile in the same time as his sister . if bob ’ s time for a mile is currently 10 minutes 40 seconds and his sister ’ s time is currently 9 minutes 17 seconds , by what percent does bob need to improve his time in order run a mile in the same time as his sister ?
Options: a ) 3 % , b ) 5 % , c ) 8 % , d ) 10 % , e ) 13 %
Rationale: bob ' s time = 640 secs . his sis ' time = 557 secs . percent increase needed = ( 640 - 557 / 640 ) * 100 = 83 / 640 * 100 = 13 % . ans ( e ) .
Answer: e
Python program:
a = 10 * 10
b = 9 * const_60
c = b + 17 
d = 10 * const_60
e = d + 40 
f = c / e
g = 1 - f
h = a * g
Problem: a train sets off at 9 : 00 am at the speed of 70 km / h . another train starts at 10 : 30 am in the same direction at the rate of 80 km / h . at what time will the second train catch the first train ?
Options: a ) 7 : 00 , b ) 8 : 00 , c ) 9 : 00 , d ) 10 : 00 , e ) 11 : 00
Rationale: in one hour and thirty minutes the first train travels 105 km . the second train catches the first train at a rate of 80 km / h - 70 km / h = 10 km / h . the second train will catch the first train in 105 / 10 = 10.5 hours , so at 9 : 00 pm . the answer is c .
Answer: c
Python program:
a = 1 / 2
b = 70 * a
c = 70 + b 
d = 80 - 70
e = c / d
Problem: working together , jose and jane can complete an assigned task in 15 days . however , if jose worked alone and complete half the work and then jane takes over the task and completes the second half of the task , the task will be completed in 45 days . how long will jose take to complete the task if he worked alone ? assume that jane is more efficient than jose
Options: a ) 26 days , b ) 31 days , c ) 50 days , d ) 65 days , e ) 36 days
Rationale: "assume : jose does 1 job in x days , so jose does 1 / x job in a day jane does 1 job in y days , so jane does 1 / y job in a day together , they does ( x + y ) / xy job in a day . this is equals to 1 / 20 . so ( x + y ) / xy = 1 / 15 15 ( x + y ) = xy next , we ' re told 1 job takes 45 days to complete if jose and jane each does half the work . so since jose does 1 job in x days , he wil need x / 2 days to do half the job . jane similarly will need y / 2 days to do the other half . x / 2 + y / 2 = 45 x + y = 90 so xy = 1350 the answer choices are : 25 days 30 days 60 days 65 days 36 days from the answer choices , so i ' ll go for 50 days for jose and 27 days for jane . answer : c"
Answer: c
Python program:
a = 3 * 15
Problem: in an electric circuit , two resistors with resistances x and y are connected in parallel . if r is the combined resistance of these two resistors , then the reciprocal of r is equal to the sum of the reciprocals of x and y . what is r if x is 4 ohms and y is 6 ohms ?
Options: a ) 5 / 12 , b ) 7 / 12 , c ) 12 / 5 , d ) 7 / 5 , e ) 11 / 5
Rationale: "1 / r = 1 / x + 1 / y 1 / r = 1 / 4 + 1 / 6 = 5 / 12 r = 12 / 5 the answer is c ."
Answer: c
Python program:
a = 6 * 4
b = 4 + 6 
c = a / b