euclaise/mathqa_programs huggingface dataset:
Problem: if x , y , and z are positive integers , and 4 x = 5 y = 8 z , then the least possible value of x + y + z is
Options: a ) 15 , b ) 23 , c ) 37 , d ) 42 , e ) 60
Rationale: "take lcm of 4,5 and 8 = 40 now 4 x = 40 = > x = 10 5 y = 40 = > y = 8 8 z = 40 = > z = 5 10 + 8 + 5 = 23 . option b ."
Answer: b
Python program:
a = 4 * 5
b = a * 8
c = b / 2
d = c / 4
e = 4 * 5
f = e * 8
g = f / 2
h = g / 5
i = d + h 
j = 4 * 5
k = j * 8
l = k / 2
m = l / 8
n = i + m
Problem: find the principal which yields a simple interest of rs . 20 and compound interest of rs . 28 in two years , at the same percent rate per annum ?
Options: a ) s . 25 , b ) s . 48 , c ) s . 42 , d ) s . 20 , e ) s . 60
Rationale: "explanation : si in 2 years = rs . 20 , si in 1 year = rs . 10 ci in 2 years = rs . 28 % rate per annum = [ ( ci – si ) / ( si in 1 year ) ] * 100 = [ ( 28 – 20 ) / 20 ] * 100 = 40 % p . a . let the principal be rs . x time = t = 2 years % rate = 40 % p . a . si = ( prt / 100 ) 20 = ( x * 40 * 2 ) / 100 x = rs . 25 answer : a"
Answer: a
Python program:
a = 28 - 20
b = a * 100
c = b / 2
Problem: joshua and jose work at an auto repair center with 2 other workers . for a survey on health care insurance , 2 of the 6 workers will be randomly chosen to be interviewed . what is the probability that joshua and jose will both be chosen ?
Options: a ) 1 / 15 , b ) 1 / 12 , c ) 1 / 9 , d ) 1 / 6 , e ) 1 / 3
Rationale: "two methods 1 ) probability of chosing josh first = 1 / 4 probability of chosing jose second = 1 / 3 total = 1 / 12 probability of chosing jose first = 1 / 4 probability of chosing josh second = 1 / 3 total = 1 / 12 final = 1 / 12 + 1 / 12 = 1 / 6 d"
Answer: d
Python program:
a = math.factorial(6)
b = math.factorial(2)
c = math.factorial(2)
d = b * c
e = a / d
f = math.factorial(6)
g = e / f
Problem: in a certain accounting class of 100 students , 70 % of the students took the final exam on the assigned day while the rest of the students took the exam on a make - up date . if the students on the assigned day had an average score of 60 % , and the students on the make - up date had an average score of 90 % , what was the average score for the entire class ?
Options: a ) 65 % , b ) 67 % , c ) 69 % , d ) 72 % , e ) 75 %
Rationale: "70 % of the class scored 60 % and 30 % of the class scored 90 % . the difference between 60 % and 90 % is 30 % . the average will be 60 % + 0.3 ( 30 % ) = 69 % . the answer is c ."
Answer: c
Python program:
a = 70 * 60
b = 100 - 70
c = 90 * b
d = a + c 
e = d / 100
Problem: of 90 applicants for a job , 42 had at least 4 years ' experience , 54 had degrees , and 8 had less than 4 years ' experience and did not have a degree . how many of the applicants had at least 4 years ' experience and a degree ?
Options: a ) 10 , b ) 8 , c ) 14 , d ) 16 , e ) 12
Rationale: "90 - 8 = 82 82 - 42 - 54 = - 14 then 14 are in the intersection between 4 years experience and degree . answer : c"
Answer: c
Python program:
a = 42 + 54 
b = 90 - 8
c = a - b
d = 54 - 42
e = c + d
Problem: a shopkeeper sold an article at $ 1110 and gained a 20 % profit . what was the cost price ?
Options: a ) $ 850 , b ) $ 875 , c ) $ 900 , d ) $ 925 , e ) $ 950
Rationale: "let x be the cost price . 1.2 x = 1110 x = 1110 / 1.2 = 925 the answer is d ."
Answer: d
Python program:
a = 1110 + 20 
b = 100 / a
c = 100 * 0
Problem: two trains running in opposite directions cross a pole placed on the platform in 47 seconds and 31 seconds respectively . if they cross each other in 33 seconds , what is the ratio of their speeds ?
Options: a ) 1 : 7 , b ) 8 : 7 , c ) 6 : 7 , d ) 6 : 5 , e ) 4 : 7
Rationale: explanation : let the speed of the trains be x and y respectively length of train 1 = 47 x length of train 2 = 31 y relative speed = x + y time taken to cross each other = 33 s = > = 33 = > ( 47 x + 31 y ) = 33 ( x + y ) = > 14 x = 2 y = > x / y = 2 / 14 = 1 / 7 = 1 : 7 answer : a
Answer: a
Python program:
a = 33 - 31
b = 47 - 33
c = a / b
Problem: if 25 % of a class averages 80 % on a test , 50 % of the class averages 65 % on the test , and the remainder of the class averages 90 % on the test , what is the overall class average ?
Options: a ) 60 % , b ) 65 % , c ) 70 % , d ) 75 % , e ) 80 %
Rationale: "this question is a weighted average question with a series of dependent variables . the remaining portion of the class represents 100 % - 25 % - 50 % = 25 % of the class converting the portions of the class population to decimal weights , we find : class average = 0.25 x 80 + 0.50 x 65 + 0.25 x 90 = 75 the class average is 75 % final answer d ) 75 %"
Answer: d
Python program:
a = 25 * 80
b = 50 * 65
c = a + b 
d = 25 + 50 
e = 100 - d
f = e * 90
g = c + f 
h = g / 100
Problem: a dog is tied to a tree by a long nylon cord . if the dog runs from the due north side of the tree to the due south side of the tree with the cord extended to its full length at all items , and the dog ran approximately 30 feet , what was the approximate length of the nylon cord s , in feet ?
Options: a ) 30 , b ) 25 , c ) 15 , d ) 10 , e ) 5
Rationale: "because the cord was extended to its full length at all items , the dog ran along a semi - circular path , from north to south . the circumference of a full circle is 2 * pi * r , but since we only care about the length of half the circle , the semi - circle path is pi * r . s = pi * r = 30 . round pi = 3 , then r = 10 . chord is about 10 feet long . d"
Answer: d
Python program:
a = 30 / 3
Problem: if xy > 0 , 1 / x + 1 / y = 6 , and 1 / xy = 12 , then ( x + y ) / 6 = ?
Options: a ) 1 / 12 , b ) 1 / 6 , c ) 1 / 5 , d ) 5 , e ) 6
Rationale: "( 1 / x + 1 / y ) = 6 canbe solved as { ( x + y ) / xy } = 12 . substituting for 1 / xy = 12 , we get x + y = 6 / 12 = = > ( x + y ) / 6 = 6 / ( 12 * 6 ) = 1 / 12 . a"
Answer: a
Python program:
a = 6 / 12
b = a / 12
Problem: how many 4 digit numbers have no repeat digits , do not contain zero , and have a sum of digits d equal to 28 ?
Options: a ) 14 , b ) 24 , c ) 28 , d ) 48 , e ) 96
Rationale: first , look for all 4 digits without repeat that add up to 28 . to avoid repetition , start with the highest numbers first . start from the largest number possible 9874 . then the next largest number possible is 9865 . after this , you ' ll realize no other solution . clearly the solution needs to start with a 9 ( cuz otherwise 8765 is the largest possible , but only equals 26 ) . with a 9 , you also need an 8 ( cuz otherwise 9765 is the largest possible , but only equals 27 ) . with 98 __ only 74 and 65 work . so you have two solutions . each can be rearranged in 4 ! = 24 ways . so d = 24 + 24 = 48 . d
Answer: d
Python program:
a = math.factorial(4)
b = a * 4
c = b / 2
Problem: a basket contains 8 apples , of which 1 is spoiled and the rest are good . if we select 2 apples from the basket simultaneously and at random , what is the probability that the 2 apples selected will include the spoiled apple ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 5 , e ) 1 / 6
Rationale: "the total number of ways to choose 2 apples is 8 c 2 = 28 the number of ways that include the spoiled apple is 7 c 1 = 7 p ( the spoiled apple is included ) = 7 / 28 = 1 / 4 the answer is c ."
Answer: c
Python program:
a = 8 - 1
b = math.comb(a, 1)
c = math.comb(8, 2)
d = b / c
Problem: a train is 460 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 140 meter length
Options: a ) 20 seconds , b ) 30 seconds , c ) 40 seconds , d ) 48 seconds , e ) none of these
Rationale: "explanation : speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 460 + 140 = 600 meter time = distance / speed = 600 ∗ 2 / 25 = 48 seconds option d"
Answer: d
Python program:
a = 460 + 140 
b = 45 * 1000
c = b / 3600
d = a / c
Problem: of the 645 speckled trout in a certain fishery that contains only speckled and rainbow trout , the number of males is 45 more than twice the number of females . if the ratio of female speckled trout to male rainbow trout is 4 : 3 and the ratio of male rainbow trout to all trout is 3 : 20 , how many female rainbow trout are there ?
Options: a ) 192 , b ) 195 , c ) 200 , d ) 205 , e ) 208
Rationale: it will be easier if you draw a table for this one . let t be the total trout . total speckled trout ( st ) = 645 if female speckled trout = fst then male speckled trout = 45 + 2 fst therefore 45 + 2 fst + fst = 645 we solve and get fst = 200 and mst = 445 ratio of fst to mrt = 4 : 3 we have fst = 200 solve ratio to get mrt = 150 now ratio of mrt to t = 3 : 20 we have mrt = 150 solve ratio to get t = 1000 now unless youve drawn the table it might get a little complex . from above we have mst and mrt mst + mrt = 445 + 150 = 595 so t - 595 = total female trouts 1000 - 595 = 405 female trouts we have from above that fst = 200 so ( whew ! ) frt = 405 - 200 = 205 answer is d
Answer: d
Python program:
a = 645 - 45
b = a / 3
c = b * 3
d = c / 4
e = d * 20
f = e / 3
g = f - 645
h = 645 - 45
i = h / 3
j = i * 3
k = j / 4
l = g - k
Problem: find compound interest on rs . 8000 at 15 % per annum for 2 years 4 months , compounded annually
Options: a ) 3109 , b ) 3115 , c ) 3250 , d ) 3500 , e ) 4000
Rationale: "time = 2 yrs 4 mos = 2 ( 4 / 12 ) yrs = 2 ( 1 / 3 ) yrs . amount = rs . [ 8000 x ( 1 + ( 15 / 100 ) ) ^ 2 x ( 1 + ( ( 1 / 3 ) * 15 ) / 100 ) ] = rs . 11109 . : . c . i . = rs . ( 11109 - 8000 ) = rs . 3109 . answer a"
Answer: a
Python program:
a = 8000 * 15
b = a / 100
c = 8000 + b 
d = 8000 * 15
e = d / 100
f = 8000 + e 
g = f * 15
h = g / 100
i = c + h 
j = i - 8000
Problem: it costs $ 3 for the first 1 / 3 hour to use the laundry machine at the laundromat . after the first ¼ hour it costs $ 12 per hour . if a certain customer uses the laundry machine for 2 hours and 35 minutes , how much will it cost him ?
Options: a ) $ 30 . , b ) $ 31 , c ) $ 32 . , d ) $ 33 . , e ) $ 34 .
Rationale: "2 hrs 35 min = 155 min first 20 min - - - - - - > $ 3 time left is 135 min . . . now , 60 min costs $ 12 1 min costs $ 12 / 60 155 min costs $ 12 / 60 * 155 = > $ 31 so , total cost will be $ 31 + $ 3 = > $ 34 hence answer will be c"
Answer: c
Python program:
a = 12 * 2
b = a + 3 
c = 12 / const_60
d = 35 / 3
e = c * d
f = b + e
Problem: which number should replace both the asterisks in ( * / 21 ) x ( * / 84 ) = 1 ?
Options: a ) 21 , b ) 42 , c ) 63 , d ) 72 , e ) 168
Rationale: "let ( y / 21 ) x ( y / 84 ) = 1 y ^ 2 = 21 x 84 = 21 x 21 x 4 y = ( 21 x 2 ) = 42 the answer is b ."
Answer: b
Python program:
a = 84 * 21
b = math.sqrt(a)
Problem: a train 140 m in length crosses a telegraph post in 16 seconds . the speed of the train is ?
Options: a ) 30.5 kmph , b ) 31.5 kmph , c ) 32.5 kmph , d ) 33.5 kmph , e ) 21.5 kmph
Rationale: "s = 140 / 16 * 18 / 5 = 31.5 kmph answer : b"
Answer: b
Python program:
a = 140 / 16
b = const_3_6 * a
Problem: how much water must be added to 52 litres of milk at 1 1 ⁄ 2 litres for 20 so as to have a mixture worth 10 2 ⁄ 3 a litre ?
Options: a ) 10 litres , b ) 13 litres , c ) 15 litres , d ) 18 litres , e ) none of these
Rationale: c . p . of 1 litre of milk = ( 20 × 2 ⁄ 3 ) = 40 ⁄ 3 ∴ ratio of water and milk = 8 ⁄ 3 : 32 ⁄ 3 = 8 : 32 = 1 : 4 ∴ quantity of water to be added to 52 litres of milk = ( 1 ⁄ 4 × 52 ) litres = 13 litres . answer b
Answer: b
Python program:
a = 1 / 2
b = 1 + a 
c = 20 / b
Problem: a train 500 m long takes 10 sec to cross a man walking at 5 kmph in a direction opposite to that of the train . find the speed of the train ?
Options: a ) 175 kmph , b ) 150 kmph , c ) 162 kmph , d ) 145 kmph , e ) 100 kmph
Rationale: "let the speed of the train be x kmph speed of the train relative to man = x + 5 = ( x + 5 ) * 5 / 18 m / sec 500 / [ ( x + 5 ) * 5 / 18 ] = 10 10 ( x + 5 ) = 1800 x = 175 kmph answer is a"
Answer: a
Python program:
a = 500 / 10
b = a / const_0_2778
c = b - 5
Problem: a card is drawn from a pack of 52 cards . the probability of getting a face card ?
Options: a ) 2 / 15 , b ) 2 / 13 , c ) 1 / 15 , d ) 4 / 13 , e ) 5 / 7
Rationale: "clearly in the 52 cards out of which there are 16 face cards . probability of getting a face card = 16 / 52 = 4 / 13 correct option is d"
Answer: d
Python program:
a = 4 * 4
b = 52 - a
c = b / 52
Problem: in what time will a railway train 90 m long moving at the rate of 44 kmph pass a telegraph post on its way ?
Options: a ) 3 , b ) 5 , c ) 4.3 , d ) 6.5 , e ) 7.4
Rationale: "t = 90 / 44 * 18 / 5 = 7.4 sec answer : e"
Answer: e
Python program:
a = 44 * const_0_2778
b = 90 / a
Problem: in what ratio mental a at rs . 68 per kg be mixed with another metal at rs . 96 per kg so that cost of alloy ( mixture ) is rs . 72 per kg ?
Options: a ) 6 : 1 , b ) 4 : 7 , c ) 3 : 7 , d ) 9 : 5 , e ) 9 : 8
Rationale: "( 96 - 72 ) / ( 72 - 68 ) = 24 / 4 = 6 / 1 answer : a"
Answer: a
Python program:
a = 96 - 72
b = 96 - 68
c = a / b
d = 96 - 72
e = 96 - 68
f = d / e
g = 1 - f
h = c / g
Problem: john was 43 years old when he married betty . they just celebrated their fifth wedding anniversary , and betty ' s age is now 7 / 8 of john ' s . how old is betty ?
Options: a ) 24 , b ) 26 , c ) 42 , d ) 30 , e ) 32
Rationale: "assume betty ' s age on marriage = x years . john ' s age on marriage = 43 john ' s age after 5 years = 48 years . betty ' s age after 5 years = x + 5 given : x + 5 = 7 / 8 ( 48 ) = 42 therefore betty ' s current age = 42 option c"
Answer: c
Python program:
a = 7 / 8
b = 43 + 4 
c = a * b
Problem: what is 120 % of 13 / 24 of 720 ?
Options: a ) 372 , b ) 434 , c ) 468 , d ) 512 , e ) 564
Rationale: "120 % * 13 / 24 * 360 = 1.2 * 13 * 30 = 468 the answer is c ."
Answer: c
Python program:
a = 3 + 2 
b = a * 2
c = 3 * 4
d = c * 100
e = b * d
f = 3 + 4 
g = 3 + 2 
h = f * g
i = 3 + 2 
j = i * 2
k = h * j
l = e + k 
m = 3 + 3 
n = l + m 
o = 120 * n
p = o / 100
Problem: a “ palindromic integer ” is an integer that remains the same when its digits are reversed . so , for example , 43334 and 516615 are both examples of palindromic integers . how many 6 - digit palindromic integers are both even and greater than 700,000 ?
Options: a ) 60 , b ) 100 , c ) 180 , d ) 240 , e ) 300
Rationale: "the first digit and last digit are the same so the only possibility is 8 . the second and third digits can be any number from 0 to 9 . the total number of palindromic integers is 1 * 10 * 10 = 100 the answer is b ."
Answer: b
Python program:
a = 6 - 4
b = a * 10
c = b * 10
Problem: mike took a taxi to the airport and paid $ 2.50 to start plus $ 0.25 per mile . annie took a different route to the airport and paid $ 2.50 plus $ 5.00 in bridge toll fees plus $ 0.25 per mile . if each was charged exactly the same amount , and annie ' s ride was 16 miles , how many miles was mike ' s ride ?
Options: a ) 32 , b ) 36 , c ) 40 , d ) 44 , e ) 48
Rationale: "the cost of annie ' s ride was 2.5 + 5 + ( 0.25 * 16 ) = $ 11.50 let x be the distance of mike ' s ride . the cost of mike ' s ride is 2.5 + ( 0.25 * x ) = 11.5 0.25 * x = 9 x = 36 miles the answer is b ."
Answer: b
Python program:
a = 2 + 50 
b = 0 * 25
c = a + b 
d = c - 2
e = d / 0
Problem: if a man walks at a rate of 5 kmph , he misses a train by 7 minutes . however , if he walks at the rate of 6 kmph , he reaches the station 5 minutes before the arrival of the train . find the distance covered by him to reach the station .
Options: a ) 8 , b ) 4 , c ) 15 , d ) 6 , e ) 12
Rationale: let the required distance x km difference in the times taken at two speeds = 12 min = 1 / 5 hr ( x / 5 ) - ( x / 6 ) = 1 / 5 x = 6 the required distance is 6 km answer is d
Answer: d
Python program:
a = 7 / const_60
b = a * 5
c = 5 / const_60
d = c * 6
e = b + d 
f = 7 / const_60
g = e + f 
h = g * 5
Problem: the milk level in a rectangular box measuring 62 feet by 25 feet is to be lowered by 6 inches . how many gallons of milk must be removed ? ( 1 cu ft = 7.5 gallons )
Options: a ) 100 , b ) 250 , c ) 750 , d ) 5812.5 , e ) 5835.5
Rationale: "6 inches = 1 / 2 feet ( there are 12 inches in a foot . ) , so 62 * 25 * 1 / 2 = 775 feet ^ 3 of milk must be removed , which equals to 775 * 7.5 = 5812.5 gallons . answer : d ."
Answer: d
Python program:
a = 62 * 25
b = 1 / 2
c = a * b
d = c * 7
Problem: the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 320 resolutions ?
Options: a ) 724 m , b ) 704 m , c ) 287 m , d ) 450.6 m , e ) 927 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 320 resolutions . = 320 * 2 * 22 / 7 * 22.4 = 45056 cm = 450.6 m answer : d"
Answer: d
Python program:
a = 3 + 4 
b = a * 3
c = b + 1 
d = 3 + 4 
e = c / d
f = e * 22
g = f * 2
h = g * 320
i = h / 100
Problem: what is 10 - 8 + 6 - 4 + . . . + ( - 12 ) ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "the expression considers all even numbers between 10 and - 12 with alternate addition and subtraction of the numbers . the numbers to be used are : 10 , 8 , 6 , 4 , 2 , 0 , - 2 , - 4 , - 6 , - 8 , - 10 , and - 12 now , the first term is positive and the next term is subtracted . so , the required expression becomes , 10 - 8 + 6 - 4 + 2 - 0 + ( - 2 ) - ( - 4 ) + ( - 6 ) - ( - 8 ) + ( - 10 ) - ( - 12 ) = 10 - 8 + 6 - 4 + 2 - 0 - 2 + 4 - 6 + 8 - 10 + 12 = 42 - 30 = 12 hence the correct answer choice is c ."
Answer: c
Python program:
a = 6 - 8
Problem: maxwell leaves his home and walks toward brad ' s house at the same time that brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 36 kilometers , maxwell ' s walking speed is 2 km / h , and brad ' s running speed is 4 km / h . what is the distance traveled by maxwell when they meet in the middle ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 9
Rationale: "consider max starts from point a and brad starts from point b and move towards each other . assume they shall meet at point o after time ' t ' . the question asks us to find oa . from the question stem we can make out : - distance oa = 50 km - distance ob = > 2 xt = 36 - 4 xt ( i . e distance = speed x time ) = > 6 t = 36 hence t = 6 oa = 2 x 6 = 12 km answer : c"
Answer: c
Python program:
a = 2 + 4 
b = 36 / a
c = 2 * b
Problem: if 20 % of ( x - y ) = 15 % of ( x + y ) , then what percent of x is y ?
Options: a ) 50.5 % , b ) 44.4 % , c ) 22.2 % , d ) 14.3 % , e ) 25 %
Rationale: "20 % of ( x - y ) = 15 % of ( x + y ) 20 / 100 ( x - y ) = 15 / 100 ( x + y ) 5 x = 35 y required percentage = y / x * 100 = 5 y / 35 y * 100 = 14.28 % answer is d"
Answer: d
Python program:
a = 20 - 15
b = 20 + 15 
c = a / b
d = c * 100
Problem: if a tap could fill entire tank in 18 hrs due to leakage , then in how much time tank can be emptied by leakage if tap can fill entire tank in 12 hrs without leakage ?
Options: a ) 35 hrs , b ) 36 hrs , c ) 37 hrs , d ) 38 hrs , e ) 39 hrs
Rationale: if a tap could fill entire tank in 18 hrs due to leakage , tap can fill entire tank in 12 hrs without leakage . tank emptied in 0 ne hr by leakage = 1 / 12 - 1 / 18 = ( 6 - 4 ) / 72 = 2 / 72 = 1 / 36 . full tank can be emptied in 36 hrs . answer : b
Answer: b
Python program:
a = 1 / 12
b = 1 / 18
c = a - b
d = 1/(c)
Problem: what is the percentage increase in the area of a rectangle , if each of its sides is increased by 20 % ?
Options: a ) 42 % , b ) 43 % , c ) 45 % , d ) 44 % , e ) 46 %
Rationale: let original length = l original breadth = b then original area = lb length is increased by 20 % ⇒ new length = l × 120100 = 1.2 l breadth is increased by 20 % ⇒ new breadth = b × 120100 = 1.2 b new area = 1.2 l × 1.2 b = 1.44 lb increase in area = new area - original area = 1.44 lb − lb = 0.44 lb percentage increase in area = increase in areaoriginal area × 100 = 0.44 lblb × 100 = 44 % answer is d .
Answer: d
Python program:
a = 100 + 20 
b = 100 + 20 
c = a * b
d = 100 * 100
e = c - d
f = e / 100
Problem: the megatek corporation is displaying its distribution of employees by department in a circle graph . the size of each sector of the graph representing a department is proportional to the percentage of total employees in that department . if the section of the circle graph representing the manufacturing department takes up 252 ° of the circle , what percentage of megatek employees are in manufacturing ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 70 %
Rationale: "answer : e 252 ° divided by 360 ° equals 0.7 , therefore the sector is equal to 70 % of the total"
Answer: e
Python program:
a = 3600 / 10
b = 252 / a
c = b * 100
Problem: in a 100 m race , a beats b by 10 m and c by 13 m . in a race of 180 m , b will beat c by :
Options: a ) 3 , b ) 7 , c ) 8 , d ) 6 , e ) 0
Rationale: a : b = 100 : 90 . a : c = 100 : 87 . \ inline \ fn _ jvn { \ color { black } \ therefore \ frac { b } { c } = \ left ( \ frac { b } { a } \ times \ frac { a } { c } \ right ) = \ left ( \ frac { 90 } { 100 } \ times \ frac { 100 } { 87 } \ right ) = \ frac { 30 } { 29 } } when b runs 30 m , c runs 29 m . when b runs 180 m , c runs \ inline \ fn _ jvn { \ color { black } \ left ( \ frac { 29 } { 30 } \ times 180 \ right ) m } = 174 m \ inline \ fn _ jvn { \ color { blue } \ therefore } b beats c by ( 180 - 174 ) m = 6 m . answer : d ) 6 m
Answer: d
Python program:
a = 100 - 13
b = 100 / a
c = 100 - 10
d = c / 100
e = b * d
f = 1/(e)
g = f * 180
h = 180 - g
Problem: the points a ( 0 , 0 ) , b ( 0 , 4 a - 5 ) and c ( 2 a + 3 , 2 a + 6 ) form a triangle . if angle abc = 90 , what is the area of triangle abc ?
Options: a ) 114 , b ) 116 , c ) 118 , d ) 119 , e ) 120
Rationale: "1 / 2 bh = 1 / 2 ( 2 a + 3 ) ( 2 a + 6 ) now 4 a - 5 = 2 a + 6 2 a = 11 therefore , a ( 0,0 ) ; b ( 0,17 ) ; c ( 14,17 ) 1 / 2 * 14 * 17 = 119 answer : d"
Answer: d
Python program:
a = 6 + 2 
b = a / 2
c = b * 4
d = c - 5
e = 6 + 5 
f = e / 5
g = 4 - 5
h = f * g
i = h + 3 
j = d * i
k = j / 5
Problem: jill works as a waitress at the local diner where she earns an hourly wage of $ 4.00 per hour and a standard tip rate of 15 % of the cost of the orders she serves . if she worked 3 8 - hour shifts this week and averaged $ 40 in orders per hour , how much did jill earn this week ?
Options: a ) 280 , b ) 300 , c ) 240 , d ) 350 , e ) 400
Rationale: jill earns 4 dollars / hour and the hourly tip is ( 3 / 20 ) * 40 . jill thus earns 4 * 8 + 8 * 2 * 3 per day ( or 4 ( 8 ) + 6 ( 8 ) = 10 ( 8 ) = 80 ) . jill has worked for 3 days - > 80 * 3 = 240 . this matches answer choice c .
Answer: c
Python program:
a = 15 / 100
b = 3 * 8
c = b * 40
d = a * c
e = 3 * 8
f = e * 4
g = d + f
Problem: if a speaks the truth 85 % of the times , b speaks the truth 60 % of the times . what is the probability that they tell the truth at the same time
Options: a ) 0.49 , b ) 0.48 , c ) 0.41 , d ) 0.482 , e ) 0.51
Rationale: "explanation : probability that a speaks truth is 85 / 100 = 0.85 probability that b speaks truth is 60 / 100 = 0.6 since both a and b are independent of each other so probability of a intersection b is p ( a ) × p ( b ) = 0.85 × 0.6 = 0.51 answer : e"
Answer: e
Python program:
a = 4 * 5
b = a * 5
c = 85 / b
d = 4 * 5
e = d * 5
f = 60 / e
g = c * f
Problem: there are , in a certain league , 14 teams , and each team face another team for a total of 5 times . how many games are played in the season ?
Options: a ) 455 , b ) 525 , c ) 1400 , d ) 180 , e ) 560
Rationale: "by using the formula , t [ n ( n - 1 ) / 2 ] , where t = no . of games between two teams and n = total no . of teams , we get : 455 option a ."
Answer: a
Python program:
a = 14 - 1
b = a * 5
c = 14 / 2
d = b * c
Problem: 10 is added to a certain number , the sum is multiplied by 7 , the product is divided by 5 and 5 is subtracted from the quotient . the remainder left is half of 88 . what is the number ?
Options: a ) 21 , b ) 20 , c ) 25 , d ) 30 , e ) 45
Rationale: "let number is x . when 10 added to it , = ( x + 10 ) 7 multiplied to sum , = 7 * ( x + 10 ) now , = [ { 7 * ( x + 10 ) } / 5 ] and , = [ { 7 * ( x + 10 ) } / 5 ] - 5 according to question , [ { 7 * ( x + 10 ) } / 5 ] - 5 = half of 88 [ ( 7 x + 70 ) / 5 ) = 44 + 5 7 x + 70 = 49 * 5 x + 10 = 7 * 5 x + 10 = 35 x = 35 - 10 x = 25 so , required number is : 25 . answer : c"
Answer: c
Python program:
a = 88 / 2
b = a + 5 
c = b * 5
d = c / 7
e = d - 10