euclaise/mathqa_programs huggingface dataset:
Problem: if x ¤ y = ( x + y ) ^ 2 - ( x - y ) ^ 2 . then √ 3 ¤ √ 3 =
Options: a ) 0 , b ) 5 , c ) 12 , d ) 15 , e ) 20
Rationale: "x = √ 3 and y also = √ 3 applying the function ( √ 3 + √ 3 ) ^ 2 - ( √ 3 - √ 3 ) ^ 2 = ( 2 √ 3 ) ^ 2 - 0 = 4 x 3 = 12 . note : alternative approach is the entire function is represented as x ^ 2 - y ^ 2 = ( x + y ) ( x - y ) which can be simplified as ( x + y + x - y ) ( x + y - ( x - y ) ) = ( 2 x ) ( 2 y ) = 4 xy . substituting x = √ 3 and y = √ 3 you get the answer 12 . answer c"
Answer: c
Python program:
a = math.sqrt(3)
b = math.sqrt(3)
c = a + b 
d = c ** 2
Problem: a palindrome is a number that reads the same forward and backward , such as 124 . how many odd , 4 - digit numbers are palindromes ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 60 , e ) 2500
Rationale: "a palindrome is a number that reads the same forward and backward . examples of four digit palindromes are 1221 , 4334 , 2222 etc you basically get to choose the first two digits and you repeat them in opposite order . say , you choose 45 as your first two digits . the next two digits are 54 and the number is 4554 . also , you need only odd palindromes . this means that you need an odd digit at the end i . e . 1 / 3 / 5 / 7 / 9 . this means that you need to start the number with an odd digit . only then will it end with an odd digit . in how many ways can you pick two digits such that the first one is an odd digit ? the first digit can be selected in 5 ways . ( 1 / 3 / 5 / 7 / 9 ) the second digit can be selected in 10 ways . ( 0 / 1 / 2 / 3 . . . 8 / 9 ) total = 5 * 12 = 60 ways d"
Answer: d
Python program:
a = 4 / 2
b = 10 ** a
c = b / 2
Problem: hillary and eddy are climbing to the summit of mt . everest from a base camp 5,000 ft from the summit . when they depart for the summit at 06 : 00 , hillary climbs at a rate of 800 ft / hr with eddy lagging behind at a slower rate of 500 ft / hr . if hillary stops 1000 ft short of the summit and then descends at a rate of 1,000 ft / hr , at what time do hillary and eddy pass each other on her return trip ?
Options: a ) 11.0 , b ) 12.0 , c ) 13.0 , d ) 14.0 , e ) 15.0
Rationale: solution : h stopped 1000 ft before reaching the final point , time taken to reach 4000 ft = 4000 / 800 = 5 hrs . this means she reached there at 11 : 00 . speed difference between them is 800 - 500 = 300 ft / hr so by the time h stops they have 1500 ft of distance so now here we use relative speed formula they both are travelling toward each other with speed of 1000 and 500 total 1500 ft / hr and distance bwn them is 1500 ft so time taken to meet = 1 hr from 11 : 00 means 12 : 00 is the answer . b
Answer: b
Python program:
a = 500 / 100
b = a - 1
c = 800 / 1000
d = b / c
e = 800 / 1000
f = 500 / 1000
g = e - f
h = d * g
i = 500 / 1000
j = i + 1 
k = h / j
l = 500 / 100
m = l - 1
n = 800 / 1000
o = m / n
p = k + o 
q = 6 + p
Problem: a car drives 60 miles on local roads at 20 mph , and 120 miles on the highway at 60 mph , what is the average speed of the entire trip ?
Options: a ) 36 mph , b ) 40 mph , c ) 44 mph , d ) 52 mph , e ) 58 mph
Rationale: "so the answer is plainly a . . . . we have a general relation for speed , time and distance : v ( velocity ) * t ( time ) = d ( distance ) for first part we have d = 60 miles , and v = 20 mph so we can obtain time : 20 * t = 60 or t = 60 / 20 = 3 hours the needed time to cover 60 miles in the same way we should divide 120 to 60 to find the needed time to cover 120 miles , so t = 2 hours so the total time for covering total distance would be 3 + 2 = 5 hours and total distance is 60 + 120 = 180 miles final stage : average speed is total distance divide to total time : 180 / 5 = 36 miles per hour . . . ."
Answer: a
Python program:
a = 60 + 120 
b = 60 / 20
c = 120 / 60
d = b + c 
e = a / d
Problem: how many kg of pure salt must be added to 100 kg of 10 % solution of salt and water to increase it to a 20 % solution ?
Options: a ) 6.7 , b ) 1.3 , c ) 9.6 , d ) 12.5 , e ) 7.9
Rationale: "amount salt in 100 kg solution = 10 * 100 / 100 = 10 kg let x kg of pure salt be added then ( 10 + x ) / ( 100 + x ) = 20 / 100 100 + 10 x = 200 + 2 x 8 x = 100 x = 12.5 answer is d"
Answer: d
Python program:
a = 20 - 10
b = 20 / 100
c = 1 - b
d = a / c
Problem: a train 200 m long passes a man , running at 6 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is ?
Options: a ) 36 , b ) 50 , c ) 78 , d ) 66 , e ) 22
Rationale: "speed of the train relative to man = ( 200 / 10 ) m / sec = 20 m / sec . [ 20 * ( 18 / 5 ) ] km / hr = 72 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 6 ) km / hr . x - 6 = 72 = = > x = 78 km / hr . answer : c"
Answer: c
Python program:
a = 6 * const_0_2778
b = a * 6
c = 200 - b
d = c / 6
e = d / const_0_2778
Problem: a man can row upstream at 20 kmph and downstream at 80 kmph , and then find the speed of the man in still water ?
Options: a ) 32 kmph , b ) 50 kmph , c ) 30 kmph , d ) 45 kmph , e ) 65 kmph
Rationale: "us = 20 ds = 80 m = ( 20 + 80 ) / 2 = 50 answer : b"
Answer: b
Python program:
a = 20 + 80 
b = a / 2
Problem: in a tree , 1 / 5 of the birds are robins while the rest are bluejays . if 1 / 2 of the robins are female and 2 / 5 of the bluejays are female , what fraction of the birds in the tree are male ?
Options: a ) 9 / 25 , b ) 12 / 25 , c ) 17 / 25 , d ) 29 / 50 , e ) 33 / 50
Rationale: "the fraction of birds that are male robins is ( 1 / 2 ) ( 1 / 5 ) = 1 / 10 . the fraction of birds that are male bluejays is ( 3 / 5 ) ( 4 / 5 ) = 12 / 25 . the total fraction of male birds is 1 / 10 + 12 / 25 = 29 / 50 . the answer is d ."
Answer: d
Python program:
a = 1 / 5
b = 2 / 0
c = a * b
d = 2 / 5
e = 1 / 2
f = d * e
g = c + f
Problem: salesperson a ' s compensation for any week is $ 360 plus 6 percent of the portion of a ' s total sales above $ 1,000 for that week . salesperson b ' s compensation for any week is 8 percent of b ' s total sales for that week . for what amount of total weekly sales would both salespeople earn the same compensation ?
Options: a ) $ 21,000 , b ) $ 18,000 , c ) $ 15,000 , d ) $ 4,500 , e ) $ 4,000
Rationale: "360 + 0.06 ( x - 1000 ) = 0.08 x or 360 - 60 = 0.08 x or 300 / 0.02 = x or 15000 = x answer : c"
Answer: c
Python program:
a = 6 / 100
b = a * 1
c = 360 - b
d = 8 / 100
e = 6 / 100
f = d - e
g = c / f
h = 6 / 100
i = h * 1
j = 360 - i
k = 8 / 100
l = 6 / 100
m = k - l
n = j / m
o = g + n 
p = o / 1
Problem: a crate measures 7 feet by 8 feet by 12 feet on the inside . a stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides . what is the radius , in feet , of the pillar with the largest volume that could still fit in the crate ?
Options: a ) 2
b ) 4
c ) 6
d ) 7
e ) 12
Rationale: we can find the radius of all the three cases of cylinders . the only crux to find the answer faster is that : voulme is pi * r ^ 2 * h . the volume is a function of r ^ 2 . so r has to be the highest to find the largest volume . so r = 7 for the surface 8 * 12 face . volume = 343 pi answer d
Answer: d
Python program:
a = 8 * 12
b = a * 7
c = b / 12
d = c / 8
Problem: in a fuel station the service costs $ 2.30 per vehicle and every liter of fuel costs $ 0.70 . assuming that you fill up 4 mini - vans and 2 trucks , what will be the total cost , if a mini - van ' s tank is 65 liters and a truck ' s tank is 120 % bigger and they are all empty ?
Options: a ) $ 396 , b ) $ 400 , c ) $ 404 , d ) $ 408 , e ) $ 412
Rationale: "the service cost of 4 vans and 2 trucks is 6 * 2.30 $ 13.80 the fuel in 4 vans is 4 * 65 = 260 liters the fuel in 2 trucks is 2 * 65 * 2.2 = 286 liters the total fuel ( vans + trucks ) = 546 liters the total fuel cost is 546 * 0.7 = $ 382.20 the total cost is $ 382.20 + $ 13.80 = $ 396 the answer is a ."
Answer: a
Python program:
a = 120 * 65
b = a / 100
c = b + 65 
d = c * 2
e = d * 0
f = 4 * 65
g = f * 0
h = e + g 
i = 4 + 2 
j = 2 * 30
k = h + j
Problem: evaluate : 6502.5 + 650.25 + 65.025 + 6.5025 + 0.65025
Options: a ) 6819.59775 , b ) 6981.59775 , c ) 7224.92775 , d ) 6198.59775 , e ) 6891.59775
Rationale: "6502.5 650.25 65.025 6.5025 + 0.65025 - - - - - - - - - - - - - - - 7224.92775 answer is c ."
Answer: c
Python program:
a = 650 * 25
b = a * 6
c = 6502 - 5
Problem: what is the smallest positive integer k such that the product of 450 x k is a perfect square ?
Options: a ) 3 , b ) 9 , c ) 15 , d ) 25 , e ) 63
Rationale: "a perfect square , is just an integer that can be written as the square of some other integer . for example 16 = 4 ^ 2 , is a perfect square . now , 450 = 3 ^ 2 * 5 ^ 2 * 3 , so if k = 3 then 450 k = ( 3 * 5 * 3 ) ^ 2 , which is a perfect square ( basically the least positive value of k must complete only the power of 7 to even power as powers of other primes are already even ) . answer : a ."
Answer: a
Python program:
a = 3 + 4
Problem: log 3 n + log 5 n what is 3 digit number n that will be whole number
Options: a ) 629 , b ) 729 , c ) 829 , d ) 125 , e ) 727
Rationale: "no of values n can take is 1 5 ^ 3 = 125 answer : d"
Answer: d
Python program:
a = 5 ** 3
Problem: the perimeter of a rectangular yard is completely surrounded by a fence that measures 14 meters . what is the length of the yard if the area of the yard is 6 meters squared ?
Options: a ) 8 , b ) 6 , c ) 2 , d ) 4 , e ) 3
Rationale: "perimeter of rectangular yard = 2 ( l + b ) = 14 - - > l + b = 7 area = l * b = 6 b = 7 - l l ( 7 - l ) = 6 7 l - l ^ 2 = 6 l ^ 2 - 7 l + 6 = 0 upon simplifying we get l = 1 or 6 . only 6 is there in the answer choice . answer : b"
Answer: b
Python program:
a = 4 - 3
Problem: if a and b are positive integers , and a = 4 b + 16 , the greatest common divisor of a and b can not be
Options: a ) 2 , b ) 9 , c ) 4 , d ) 8 , e ) 16
Rationale: "if b is 2 , 4 , 8 , or 16 , then gcd of a and b is 2 , 4 , 8 , and 16 respectively . so , by poe the answer must be b . still : if b is a multiple of 9 , then a is 16 greater than a multiple of 9 , so not a multiple of 9 , so both of them can not be divisive by 9 . answer : b ."
Answer: b
Python program:
a = 16 / 4
b = a + 2
Problem: find large number from below question the difference of two numbers is 1375 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder
Options: a ) 1234 , b ) 1265 , c ) 1350 , d ) 1467 , e ) 1647
Rationale: "let the smaller number be x . then larger number = ( x + 1375 ) . x + 1375 = 6 x + 15 5 x = 1360 x = 272 large number = 272 + 1375 = 1647 e"
Answer: e
Python program:
a = 1375 - 15
b = 6 - 1
c = a / b
d = c * 6
Problem: 3 pumps , working 8 hours a day , can empty a tank in 2 days . how many hours a day must 6 pumps work to empty the tank in 1 day ?
Options: a ) 8 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "3 pumps take 16 hrs total ( 8 hrs a day ) if 1 pump will be working then , it will need 16 * 3 = 48 hrs 1 pump need 48 hrs if i contribute 6 pumps then 48 / 6 = 8 hrs . answer : a"
Answer: a
Python program:
a = 3 * 8
b = a * 2
c = b / 6
Problem: at a garage sale , all of the items were sold at different prices . if the price of a radio sold at the garage sale was both the 18 th highest price and the 25 th lowest price among the prices of the items sold , how many items were sold at the garage sale ?
Options: a ) 41 , b ) 42 , c ) 43 , d ) 44 , e ) 45
Rationale: "there were 17 items sold at a higher price than the radio and 24 items sold at a lower price than the radio . including the radio , there were 17 + 24 + 1 = 42 items sold . the answer is b ."
Answer: b
Python program:
a = 25 + 18 
b = a - 1
Problem: tom , working alone , can paint a room in 6 hours . peter and john , working independently , can paint the same room in 3 hours and 3 hours , respectively . tom starts painting the room and works on his own for one hour . he is then joined by peter and they work together for an hour . finally , john joins them and the three of them work together to finish the room , each one working at his respective rate . what fraction of the whole job was done by peter ?
Options: a ) 1 / 3 , b ) 2 / 5 , c ) 3 / 10 , d ) 7 / 15 , e ) 9 / 25
Rationale: "tom paints 1 / 6 of the room in the first hour . tom and peter paint 1 / 6 + 1 / 3 = 1 / 2 of the room in the next hour for a total of 4 / 6 . the three people then paint the remaining 2 / 6 in a time of ( 2 / 6 ) / ( 5 / 6 ) = 2 / 5 hours peter worked for 7 / 5 hours so he painted 7 / 5 * 1 / 3 = 7 / 15 of the room . the answer is d ."
Answer: d
Python program:
a = 4 * 3
b = a + 1 
c = 4 / b
Problem: if x ^ 2 + 1 / x ^ 2 = 3 , what is the value of x ^ 4 + 1 / x ^ 4 ?
Options: a ) 7 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "important : i notice that if we square x ² , we get x ⁴ , and if we square 1 / x ² , we get 1 / x ⁴ , so let ' s see what happens if we take the equation x ² + 1 / x ² = 3 andsquareboth sides : ( x ² + 1 / x ² ) ² = 9 so , ( x ² + 1 / x ² ) ( x ² + 1 / x ² ) = 9 expand to get : x ⁴ + 1 + 1 + 1 / x ⁴ = 9 simplify : x ⁴ + 1 / x ⁴ = 7 answer : a"
Answer: a
Python program:
a = 2 ** 2
b = a - 2
Problem: find the value of 3.5 x [ ( 3.6 x 0.48 x 2.50 ) / ( 0.12 x 0.09 x 0.5 ) ]
Options: a ) 800 , b ) 500 , c ) 2800 , d ) 1600 , e ) none
Rationale: answer 3.5 x [ ( 3.6 x 0.48 x 2.50 ) / ( 0.12 x 0.09 x 0.5 ) ] = 3.5 x [ ( 36 x 48 x 250 ) / ( 12 x 9 x 5 ) ] = 3.5 x 4 x 4 x 50 = 2800 correct option : c
Answer: c
Python program:
a = 3 * 6
b = a * 2
c = 0 * 12
d = c * 0
e = b / d
f = e * 3
Problem: a and b can do a piece of work in 3 days . with the help of c they finish the work in 2 days . c alone can do that piece of work in ?
Options: a ) 6 days , b ) 5 days , c ) 4 days , d ) 3 days , e ) 2 days
Rationale: "c = 1 / 2 – 1 / 3 = 1 / 6 = > 6 days answer : a"
Answer: a
Python program:
a = 2 / 3
b = 2 - a
c = 1/(b)
Problem: dacid obtained 91 , 65 , 82 , 67 and 85 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 29 , b ) 78 , c ) 39 , d ) 37 , e ) 75
Rationale: "average = ( 91 + 65 + 82 + 67 + 85 ) / 5 = 78 answer : b"
Answer: b
Python program:
a = 91 + 65 
b = a + 82 
c = b + 67 
d = c + 85 
e = 10 / 2
f = d / e
Problem: harkamal purchased 8 kg of grapes at the rate of 80 per kg and 9 kg of mangoes at the rate of 55 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) a ) 1000 , b ) b ) 1055 , c ) c ) 1065 , d ) d ) 1135 , e ) e ) 1080
Rationale: "cost of 8 kg grapes = 80 × 8 = 640 . cost of 9 kg of mangoes = 55 × 9 = 495 . total cost he has to pay = 640 + 495 = 1135 . d )"
Answer: d
Python program:
a = 8 * 80
b = 9 * 55
c = a + b
Problem: the average of 9 observations was 4 , that of the 1 st of 5 being 10 and that of the last 5 being 8 . what was the 5 th observation ?
Options: a ) 54 , b ) 12 , c ) 15 , d ) 17 , e ) 18
Rationale: "explanation : 1 to 9 = 9 * 4 = 36 1 to 5 = 5 * 10 = 50 5 to 9 = 5 * 8 = 40 5 th = 50 + 40 = 90 – 36 = 54 option a"
Answer: a
Python program:
a = 10 * 5
b = 4 * 5
c = a + b 
d = 4 * 9
e = c - d
Problem: 60 percent of movie theatres in town x have 1 screens or less . 20 % of those theatres sell an average of more than $ 300 worth of popcorn per showing . 56 percent of all the movie theatres in town x sell $ 300 or less of popcorn per showing . what percent of all the stores on the street have 4 or more screens and sell an average of more than $ 300 worth of popcorn per day ?
Options: a ) 12 , b ) 18 , c ) 32 , d ) 40 , e ) 44
Rationale: "lets take numbers here . assume that the total number of movie theaters in the town = 100 then number of movie theaters with 3 screens or less = 60 = > number of movie theaters with 4 screens or more = 40 movie theaters with 3 screens or less selling popcorn at more than $ 300 = 20 % of 60 = 12 number of movie theaters selling popcorn at $ 300 or less = 56 = > number of movie theaters selling popcorn at more than $ 300 = 100 - 56 = 44 of these 44 theaters , 12 are those with 3 screens or less therefore 40 ( 44 - 12 ) must be those with four screens or more d is the answer"
Answer: d
Python program:
a = 20 / 300
b = 20 / 300
c = b * 300
d = a * c
Problem: a man can row his boat with the stream at 26 km / h and against the stream in 12 km / h . the man ' s rate is ?
Options: a ) 1 kmph , b ) 4 kmph , c ) 5 kmph , d ) 7 kmph , e ) 8 kmph
Rationale: "ds = 26 us = 12 s = ? s = ( 26 - 12 ) / 2 = 7 kmph answer : d"
Answer: d
Python program:
a = 26 - 12
b = a / 2
Problem: in n is a positive integer less than 200 , and 10 n / 60 is an integer , then n has how many different positive prime factors ?
Options: a ) 2 , b ) 3 , c ) 5 , d ) 6 , e ) 8
Rationale: "( a ) . 10 n / 60 must be an integer . = > 1 n / 6 must be an integer . hence n must be a multiple of 2 * 3 . = > n has 2 different prime integers ."
Answer: a
Python program:
a = 1 + 4 
b = 60 / 2
c = b / 2
d = c / 3
e = a / d
f = e + 2
Problem: a retailer bought a machine at a wholesale price of $ 117 and later on sold it after a 10 % discount of the retail price . if the retailer made a profit equivalent to 20 % of the whole price , what is the retail price of the machine ?
Options: a ) 81 , b ) 100 , c ) 120 , d ) 135 , e ) 159
Rationale: "my solution : wholesale price = 117 retail price , be = x he provides 10 % discount on retail price = x - 10 x / 100 this retail price = 20 % profit on wholesale price x - 10 x / 100 = 117 + 1 / 5 ( 117 ) x = 156 ; answer : e"
Answer: e
Python program:
a = 117 * 20
b = a / 100
c = 117 + b 
d = c * 100
e = 3 * 3
f = e * 10
g = d / f
Problem: what sum of money put at c . i amounts in 2 years to rs . 8000 and in 3 years to rs . 9261 ?
Options: a ) 5969.72 , b ) 8877.72 , c ) 2877.72 , d ) 2678.72 , e ) 1011.72
Rationale: 8000 - - - - 1261 100 - - - - ? = > 15.76 % x * 115.76 / 100 * 115.76 / 100 = 8000 x * 1.34 = 8000 x = 8000 / 1.34 = > 5969.72 answer : a
Answer: a
Python program:
a = 9261 / 8000
b = a - 1
c = b + 1 
d = c ** 2
e = 8000 / d
Problem: carol spends 1 / 4 of her savings on a stereo and 1 / 6 less than she spent on the stereo for a television . what fraction of her savings did she spend on the stereo and television ?
Options: a ) 1 / 4 , b ) 2 / 7 , c ) 5 / 12 , d ) 1 / 2 , e ) 11 / 24
Rationale: "total savings = s amount spent on stereo = ( 1 / 4 ) s amount spent on television = ( 1 - 1 / 6 ) ( 1 / 4 ) s = ( 5 / 6 ) * ( 1 / 4 ) * s = ( 5 / 24 ) s ( stereo + tv ) / total savings = s ( 1 / 4 + 5 / 24 ) / s = 11 / 24 answer : e"
Answer: e
Python program:
a = 1 / 4
Problem: if x and y are both odd prime numbers and x < y , how many distinct positive integer t factors does 2 xy have ?
Options: a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 12
Rationale: since 2 xy prime t factors are x ^ 1 * y ^ 1 * 2 ^ 1 , its total number or factors must be ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 2 ^ 3 = 8 . thus , i think d would be the correct answer .
Answer: d
Python program:
a = 1 + 1 
b = 2 * a
c = 1 + 1 
d = b * c
Problem: how many kg of pure salt must be added to 30 kg of 2 % solution of salt and water to increase it to 10 % solution ?
Options: a ) 3 / 5 , b ) 4 / 3 , c ) 5 / 7 , d ) 2 / 3 , e ) 8 / 3
Rationale: "amount of salt in 30 kg solution = [ ( 20 / 100 ) * 30 ] kg = 0.6 kg let x kg of pure salt be added then , ( 0.6 + x ) / ( 30 + x ) = 10 / 100 60 + 100 x = 300 + 10 x 90 x = 240 x = 8 / 3 . answer is e ."
Answer: e
Python program:
a = 10 - 2
b = 10 / 30
c = 1 - b
d = a / c
Problem: lionel left his house and walked towards walt ' s house , 48 miles away . two hours later , walt left his house and ran towards lionel ' s house . if lionel ' s speed was 3 miles per hour and walt ' s 3 miles per hour , how many miles had lionel walked when he met walt ?
Options: a ) 12 , b ) 16 , c ) 20 , d ) 27 , e ) 28
Rationale: "in the first 2 hours lionel at the rate of 3 miles per hour covered distance = rate * time = 3 * 2 = 6 miles . so , the distance between him and walt was 48 - 6 = 42 miles when walt left his house . now , their combined rate to cover this distance was 3 + 3 = 6 miles per hour , hence they will meet ( they will cover that distance ) in time = distance / rate = 42 / 6 = 7 hours . total time that lionel was walking is 2 + 7 = 9 hours , which means that he covered in that time interval distance = rate * time = 3 * 9 = 27 miles . answer : d ."
Answer: d
Python program:
a = 3 * 3
b = 48 - a
c = 3 + 2 
d = b / c
e = d + 3 
f = 3 * e
Problem: calculate the value of y : 5 y ^ 2 - 8 y + 55 = 59
Options: a ) 7 , b ) 1 , c ) 2 , d ) 9 , e ) 8
Rationale: using the elimination method substitute options for x and find the correct option . answer : c
Answer: c
Python program:
a = 8 ** 2
b = 55 - 59
c = 5 * b
d = c * 4
e = a - d
f = math.sqrt(e)
g = f + 8 
h = 5 * 2
i = g / h
Problem: the average ( arithmetic mean ) of all scores on a certain algebra test was 90 . if the average of the 8 male students ’ grades was 85 , and the average of the female students ’ grades was 92 , how many female students took the test ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 20
Rationale: "total marks of male = m total marks of female = f number of males = 8 number of females = f given : ( m + f ) / ( 8 + f ) = 90 - - - - - - - - - - - - - 1 also given , m / 8 = 85 thus m = 680 - - - - - - - - - 2 also , f / f = 92 thus f = 92 f - - - - - - - - - 3 put 2 and 3 in 1 : we get ( 680 + 92 f ) / ( 8 + f ) = 90 solving this we get f = 20 ans : e"
Answer: e
Python program:
a = 90 * 8
b = 85 * 8
c = a - b
d = 92 - 90
e = c / d
Problem: a pipe can fill a cistern in 55 minutes . find the time in which 1 / 11 part of the cistern will be filled ?
Options: a ) 5 min , b ) 2 min , c ) 3 min , d ) 1 min , e ) 10 min
Rationale: "full cistern filled in = 55 minutes 1 / 11 part filled in = 55 * 1 / 11 = 5 minutes answer is a"
Answer: a
Python program:
a = 1 / 11
b = 55 * a
Problem: if the perimeter of a rectangular garden is 600 m , its length when its breadth is 95 m is ?
Options: a ) 286 m
b ) 899 m
c ) 200 m
d ) 205 m
e ) 187 m
Rationale: 2 ( l + 95 ) = 600 = > l = 205 m answer : d
Answer: d
Python program:
a = 600 / 2
b = a - 95
Problem: two trains of equal are running on parallel lines in the same direction at 46 km / hr and 36 km / hr . the faster train passes the slower train in 72 sec . the length of each train is ?
Options: a ) 50 , b ) 26 , c ) 27 , d ) 28 , e ) 100
Rationale: "let the length of each train be x m . then , distance covered = 2 x m . relative speed = 46 - 36 = 10 km / hr . = 10 * 5 / 18 = 25 / 9 m / sec . 2 x / 72 = 25 / 9 = > x = 100 . answer : e"
Answer: e
Python program:
a = 46 - 36
b = a * 1000
c = b / 3600
d = 72 * c
e = d / 2
Problem: 6 workers should finish a job in 8 days . after 3 days came 4 workers join them . how many days d do they need to finish the same job ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "let rate of one worker be r = > ( 6 * r ) * 8 = 1 ( rate * time = work ) = > r = 1 / 48 = > work remaining after 3 days 1 - ( 3 * 6 ) / 48 = 30 / 48 after 4 ppl joined in ( ( 6 + 4 ) * time ) / 48 = 30 / 48 time d = 3 days to finish the task imo a"
Answer: a
Python program:
a = 6 * 8
b = 3 * 6
c = a - b
d = 6 + 4 
e = c / d
Problem: what is the ratio between perimeters of two squares one having 11 times the diagonal then the other ?
Options: a ) 3 : 8 , b ) 3 : 6 , c ) 3 : 7 , d ) 11 : 1 , e ) 3 : 3
Rationale: "d = 11 d d = d a √ 2 = 11 d a √ 2 = d a = 11 d / √ 2 a = d / √ 2 = > 11 : 1 answer : d"
Answer: d
Python program:
a = 11 / 11
b = 11 / a
Problem: a student has to obtain 40 % of the total marks to pass . he got 150 marks and failed by 50 marks . the maximum marks are ?
Options: a ) 500 , b ) 650 , c ) 400 , d ) 575 , e ) 610
Rationale: "let the maximum marks be x then , 40 % of x = 150 + 50 40 x / 100 = 200 x = 500 answer is a"
Answer: a
Python program:
a = 150 + 50 
b = 40 / 100
c = a / b
Problem: david has $ 1,800 at the beginning of his trip , after spending money , he still has exactly $ 800 less than he spent on the trip . how much money does john still have ?
Options: a ) $ 200 , b ) $ 500 , c ) $ 600 , d ) $ 800 , e ) $ 1,200
Rationale: suppose total money spent = x not spend ( money he still has ) = x - 800 x + x - 800 = 1800 x = 1300 money not spend = 1300 - 800 = 500 answer : b
Answer: b
Python program:
a = 100 * 10
b = a + 800 
c = b + 800 
d = c / 2
e = d - 800