euclaise/mathqa_programs huggingface dataset:
Problem: in measuring the sides of a rectangle , one side is taken 6 % in excess , and the other 5 % in deficit . find the error percent in the area calculated from these measurements .
Options: a ) 0.11 % , b ) 0.7 % , c ) 0.4 % , d ) 0.6 % , e ) 0.8 %
Rationale: "let x and y be the sides of the rectangle . then , correct area = xy . calculated area = ( 53 / 50 ) x ( 19 / 20 ) y = ( 144 / 143 ) ( xy ) error in measurement = ( 144 / 143 ) xy - xy = ( 1 / 143 ) xy error percentage = [ ( 1 / 143 ) xy ( 1 / xy ) 100 ] % = ( 7 / 10 ) % = 0.7 % . answer is b ."
Answer: b
Python program:
a = 6 - 5
b = 6 * 5
c = b / 100
d = a - c
Problem: a courier charges for packages to a certain destination are 65 cents for the first 250 grams and 10 cents for each additional 100 grams or part thereof . what could be the weight in grams of a package for which the charge is $ 1.95 ?
Options: a ) 980 , b ) 1170 , c ) 1530 , d ) 1720 , e ) 1960
Rationale: "the charge is 65 cents for the first 250 grams . this leaves a charge of $ 1.95 - $ 0.65 = $ 1.30 the charge for the next 1200 grams is $ 1.20 which leaves a charge of $ 0.10 the weight is somewhere between 1450 and 1550 . the answer is c ."
Answer: c
Python program:
a = 65 / 100
b = 1 - 95
c = 10 / 100
d = c / 100
e = d * 250
f = b + e 
g = 10 / 100
h = g / 100
i = f / h
Problem: if the diameter of circle r is 50 % of the diameter of circle s , the area of circle r is what percent of the area of circle s ?
Options: a ) 35 % , b ) 25 % , c ) 20 % , d ) 15 % , e ) 10 %
Rationale: "let diameter of circle r , dr = 50 and diameter of circle s , ds = 100 radius of circle r , rr = 25 radius of circle s , rs = 50 area of circle r / area of circle s = ( pi * rr ^ 2 ) / ( pi * rs ^ 2 ) = ( 25 / 50 ) ^ 2 = ( 5 / 10 ) ^ 2 = 25 % answer : b"
Answer: b
Python program:
a = circle_area * (
b = a / 100
Problem: a can do a piece of work in 9 days . when he had worked for 2 days b joins him . if the complete work was finished in 8 days . in how many days b alone can finish the work ?
Options: a ) 18 , b ) 77 , c ) 66 , d ) 54 , e ) 12
Rationale: "8 / 9 + 6 / x = 1 x = 54 days answer : d"
Answer: d
Python program:
a = 1 / 8
b = 1 / 9
c = 2 * b
d = 1 - c
e = a * d
f = 1 / 9
g = e - f
h = 1/(g)
i = 9 + 8 
j = h - i
Problem: john ' s bank ' s saving amount is decreased 50 % due to loan payment and current balance is rs . 50000 . find the actual balance before deduction ?
Options: a ) 100000 , b ) 8500 , c ) 9000 , d ) 9500 , e ) 10000
Rationale: "50 % decreased 50 % balance = 50000 100 % = 50000 / 50 * 100 = 100000 answer : a"
Answer: a
Python program:
a = 50000 * 50
b = a / 100
c = b + 50000
Problem: a man ' s regular pay is $ 3 per hour up to 40 hours . overtime is twice the payment for regular time . if he was paid $ 192 , how many hours overtime did he work ?
Options: a ) 8 , b ) 5 , c ) 9 , d ) 6 , e ) 12
Rationale: "at $ 3 per hour up to 40 hours , regular pay = $ 3 x 40 = $ 120 if total pay = $ 168 , overtime pay = $ 192 - $ 120 = $ 72 overtime rate ( twice regular ) = 2 x $ 3 = $ 6 per hour = > number of overtime hours = $ 72 / $ 6 = 12 ans is e"
Answer: e
Python program:
a = 3 * 40
b = 192 - a
c = 3 * 2
d = b / c
Problem: if n is a positive integer and the product of all integers from 1 to n , inclusive , is a multiple of 294 , what is the least possible value of n ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "294 = 2 * 3 * 7 * 7 , so n must be at least 14 . the answer is d ."
Answer: d
Python program:
a = 294 / 2
b = a / 3
c = b / 4
d = 10 / 2
e = c / d
Problem: excluding stoppages , the speed of a train is 55 kmph and including stoppages it is 40 kmph . of how many minutes does the train stop per hour ?
Options: a ) 82 , b ) 16 , c ) 12 , d ) 82 , e ) 18
Rationale: "explanation : t = 15 / 55 * 60 = 16 answer : option b"
Answer: b
Python program:
a = 40 / 55
b = const_60 * a
c = const_60 - b
Problem: a train travels 210 km in 3 hours and 270 km in 4 hours . find the average speed of train .
Options: a ) 80 kmph , b ) 69 kmph , c ) 70 kmph , d ) 90 kmph , e ) none of these
Rationale: "as we know that speed = distance / time for average speed = total distance / total time taken thus , total distance = 210 + 270 = 480 km thus , total speed = 7 hrs or , average speed = 480 / 7 or , 69 kmph . answer : b"
Answer: b
Python program:
a = 210 + 270 
b = 3 + 4 
c = a / b
Problem: 15 - 2 + 4 ÷ 1 / 2 × 8 = ?
Options: a ) 272 , b ) 77 , c ) 168 , d ) 56 , e ) 59
Rationale: explanation : 15 - 2 + 4 ÷ 1 / 2 × 8 = 15 - 2 + 4 × 2 × 8 = 15 - 2 + 64 = 77 answer : option b
Answer: b
Python program:
a = 15 - 2
b = 1 / 2
c = 4 / b
d = c * 8
e = a + d
Problem: the difference between the compound interest and simple interest on a certain sum at 20 % per annum for 2 years is $ 500 . find the sum ?
Options: a ) $ 10000 , b ) $ 50000 , c ) $ 15200 , d ) $ 12500 , e ) $ 15000
Rationale: "let the sum be $ x c . i . = x ( 1 + 20 / 100 ) ^ 2 - x = 35 x / 100 s . i . = ( x * 20 * 2 ) / 100 = 2 x / 5 c . i . - s . i . = ( 35 x / 100 ) - ( 2 x / 5 ) = 5 x / 100 5 x / 100 = 500 x = 10000 answer is a"
Answer: a
Python program:
a = 100 * 100
b = a * 500
c = b / 100
Problem: the length of a rectangular garden is three times its width . if the area of the rectangular garden is 432 square meters , then what is the width of the rectangular garden ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "let x be the width of the garden . 3 x ^ 2 = 432 x ^ 2 = 144 x = 12 the answer is e ."
Answer: e
Python program:
a = 432 / 3
b = math.sqrt(a)
Problem: the mean of 50 observations was 39 . it was found later that an observation 48 was wrongly taken as 23 . the corrected new mean is
Options: a ) 35.2 , b ) 36.1 , c ) 36.5 , d ) 39.1 , e ) none
Rationale: "sol . therefore correct sum = ( 39 × 50 + 48 – 23 ) = 1975 . therefore correct mean = 1975 / 50 = 39.5 . answer e"
Answer: e
Python program:
a = 39 * 50
b = 50 - 2
c = b - 23
d = a + c 
e = d / 50
Problem: when positive integer n is divided by 2 , the remainder is 1 . when n is divided by 7 , the remainder is 5 . what is the smallest positive integer p , such that ( n + p ) is a multiple of 10 ?
Options: a ) 1 , b ) 2 , c ) 5 , d ) 19 , e ) 20
Rationale: "when positive integer n is divided by 2 , the remainder is 1 i . e . , n = 2 x + 1 values of n can be one of { 1 , 3 , 5 , 7 , 9 , 11 , 13 , 15 , 17,19 , . . . . . . . . . . . . . . 31 , 33,35 . . . . . . . . . . . . . . . . . . } similarly , when n is divided by 7 , the remainder is 5 . . i . e . , n = 7 y + 5 values of n can be one of { 5 , 12 , 19 , 26 , 33 , 40 , 47 , 54 , 61 . . . . . . . . } combining both the sets we get n = { 19 , 52 , . . . . . . . . . . . } what is the smallest positive integer p , such that ( n + p ) is a multiple of 21 or 21 x in case of n = 5 p = 5 so for min value of p , we take min value of n . c is the answer ."
Answer: c
Python program:
a = 10 - reminder
Problem: how many odd factors does 160 have ?
Options: a ) 2 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: "start with the prime factorization : 160 = 2 * 5 for odd factors , we put aside the factor of two , and look at the other prime factors . set of exponents = { 1 } plus 1 to each = { 2 } product = 2 therefore , there are 2 odd factors of 160 . answer : a ."
Answer: a
Python program:
a = 4 + 2 
b = a + 1 
c = b + 1
Problem: the length of a rectangle is doubled while its width is tripled . what is the % change in area ?
Options: a ) 250 %
b ) 300 %
c ) 500 %
d ) 650 %
e ) 700 %
Rationale: the original area is l * w the new area is 2 l * 3 w = 6 * l * w = l * w + 5 * l * w the area increased by 500 % . the answer is c .
Answer: c
Python program:
a = 2 * 3
b = a - 1
c = b * 10
Problem: there were totally 100 men . 81 are married . 75 have t . v , 85 have radio , 70 have a . c . how many men have t . v , radio , a . c and also married ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "100 - ( 100 - 81 ) - ( 100 - 75 ) - ( 100 - 85 ) - ( 100 - 70 ) = 100 - 19 - 25 - 15 - 30 = 100 - 89 = 11 answer : a"
Answer: a
Python program:
a = 100 - 81
b = 100 - 75
c = a + b 
d = 100 - 85
e = c + d 
f = 100 - 70
g = e + f 
h = 100 - g
Problem: nicky and cristina are running a 400 meter race . since cristina is faster than nicky , she gives him a 12 second head start . if cristina runs at a pace of 5 meters per second and nicky runs at a pace of only 3 meters per second , how many seconds will nicky have run before cristina catches up to him ?
Options: a ) 40 , b ) 25 , c ) 35 , d ) 30 , e ) 50
Rationale: "the distance traveled by both of them is the same at the time of overtaking . 3 ( t + 12 ) = 5 t t = 18 . cristina will catch up nicky in 18 seconds . so in 18 seconds cristina would cover = 18 * 5 = 90 meter . now time taken my nicky to cover 90 meter = 90 / 3 = 30 seconds . d"
Answer: d
Python program:
a = 3 * 12
b = a / 3
c = 3 * 12
d = 5 - 3
e = c / d
f = b + e
Problem: a mixture of 70 liters of wine and water contains 10 % water . how much water must be added to make water 12 ½ % of the total mixture ?
Options: a ) 12 liters , b ) 10 liters , c ) 4 liters , d ) 2 liters , e ) 3 liters
Rationale: "70 * ( 10 / 100 ) = 7 wine water 87 1 / 2 % 12 1 / 2 % 87 1 / 2 % - - - - - - - 63 12 1 / 2 % - - - - - - - ? = > 9 - 7 = 2 answer : d"
Answer: d
Python program:
a = 12 / 100
b = a * 70
c = 10 / 100
d = c * 70
e = b - d
f = 12 / 100
g = 1 - f
h = e / g
Problem: danny and steve are running towards each other , each one from his own house . danny can reach steve ' s house in 35 minutes of running , which is half the time it takes steve to reach danny ' s house . if the two started to run at the same time , how much time longer will it take steve to reach the halfway point between their houses than danny to reach the halfway point between their houses ?
Options: a ) 17.5 minutes . , b ) 35 minutes . , c ) 52.5 minutes . , d ) 70 minutes . , e ) 105 minutes .
Rationale: "danny ' s time is 35 minutes . the time to reach halfway is 17.5 minutes . steve ' s time is 70 minutes . the time to reach halfway is 35 minutes . the time difference is 35 - 17.5 = 17.5 minutes the answer is a ."
Answer: a
Python program:
a = 35 / 2
Problem: a vessel of capacity 2 litre has 20 % of alcohol and another vessel of capacity 6 litre had 40 % alcohol . the total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water . what is the new concentration of mixture ?
Options: a ) 31 % . , b ) 71 % . , c ) 49 % . , d ) 29 % . , e ) 28 % .
Rationale: "20 % of 2 litres = 0.4 litres 40 % of 6 litres = 2.4 litres therefore , total quantity of alcohol is 2.8 litres . this mixture is in a 10 litre vessel . hence , the concentration of alcohol in this 10 litre vessel is 28 % answer : e"
Answer: e
Python program:
a = 20 / 100
b = a * 2
c = 40 / 100
d = c * 6
e = b + d 
f = e / 10
g = f * 100
Problem: in a kilometer race , a beats b by 60 meters or 10 seconds . what time does a take to complete the race ?
Options: a ) 199 sec , b ) 156.7 sec , c ) 726 sec , d ) 127 sec , e ) 128 sec
Rationale: "time taken by b run 1000 meters = ( 1000 * 10 ) / 60 = 166.7 sec . time taken by a = 166.7 - 10 = 156.7 sec . answer : b"
Answer: b
Python program:
a = 1 * 1000
b = 60 / 10
c = a / b
d = c - 10
Problem: the speed at which a man can row a boat in still water is 15 kmph . if he rows downstream , where the speed of current is 3 kmph , what time will he take to cover 120 metres ?
Options: a ) 18 , b ) 24 , c ) 17 , d ) 12 , e ) 13
Rationale: "speed of the boat downstream = 15 + 3 = 18 kmph = 18 * 5 / 18 = 5 m / s hence time taken to cover 120 m = 120 / 5 = 24 seconds . answer : b"
Answer: b
Python program:
a = 15 + 3 
b = a * const_0_2778
c = 120 / b
Problem: when a train moves at an average speed of 100 kmph it reaches its destination on time . when its average speed becomes 80 kmph , then it reaches its destination 20 minutes late . find the length of journey rounded to two decimal places .
Options: a ) 99.33 km , b ) 133.33 km , c ) 125.33 km , d ) 156.66 km , e ) none
Rationale: sol . difference between timings = 20 min = 1 / 3 hr . let the length of journey be x km . then , x / 80 - x / 100 = 1 / 3 â ‡ ” 5 x - 4 x = 133.33 â ‡ ” x = 133.33 km . answer b
Answer: b
Python program:
a = 20 / const_60
b = 100 - 80
c = 100 * 80
d = b / c
e = a / d
Problem: a certain bacteria colony doubles in size every day for 20 days , at which point it reaches the limit of its habitat and can no longer grow . if two bacteria colonies start growing simultaneously , how many days will it take them to reach the habitat ’ s limit ?
Options: a ) 6.33 , b ) 7.5 , c ) 10 , d ) 15 , e ) 19
Rationale: "simultaneous grow = same amount of time in 20 days we should expect to have p ( 2 ) ^ 20 so if we have two things doing the job of getting us there then ; 2 ^ x + 2 ^ x = 20 2 ( 2 ) ^ x = 2 2 ^ ( x + 1 ) = 2 ^ 20 x + 1 = 20 x = 19 ; answer : e"
Answer: e
Python program:
a = 20 / 20
b = 20 - a
Problem: julie put half of her savings in a savings account that pays an annual simple interest and half in a savings account that pays an annual compound interest . after two years she earned $ 120 and $ 126 from the simple interest account and the compound interest account respectively . if the interest rates for both accounts were the same , what was the amount of julie ' s initial savings ?
Options: a ) 600 , b ) 720 , c ) 1080 , d ) 1200 , e ) 1440
Rationale: "$ 120 for 2 years = $ 60 per year . extra $ 6 yearned with the compound interest is the percent yearned on percent . so , $ 6 is yearned on $ 60 , which means that the interest = 10 % . this on the other hand means that half of the savings = 60 * 10 = $ 600 . twice of that = $ 1,200 . answer : d ."
Answer: d
Python program:
a = 126 - 120
b = 2 * a
c = b / 120
d = 120 / c
Problem: find large number from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder ?
Options: a ) 1234 , b ) 1540 , c ) 1650 , d ) 1632 , e ) 1635
Rationale: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 15 5 x = 1350 x = 270 large number = 270 + 1365 = 1635 e"
Answer: e
Python program:
a = 1365 - 15
b = 6 - 1
c = a / b
d = c * 6
Problem: joan and karl each bought a sofa and the sum of their purchases was $ 600 . if twice of what joan paid was $ 90 more than what karl paid , what did joan pay for her sofa ?
Options: a ) $ 190 , b ) $ 210 , c ) $ 230 , d ) $ 250 , e ) $ 270
Rationale: j + k = 600 so k = 600 - j 2 j = k + 90 2 j = ( 600 - j ) + 90 3 j = 690 j = 230 the answer is c .
Answer: c
Python program:
a = 600 + 90 
b = a / 3
Problem: a meeting has to be conducted with 5 managers . find the number of ways in which the managers may be selected from among 8 managers , if there are 2 managers who refuse to attend the meeting together .
Options: a ) 36 , b ) 40 , c ) 45 , d ) 51 , e ) 56
Rationale: "the total number of ways to choose 5 managers is 8 c 5 = 56 we need to subtract the number of groups which include the two managers , which is 6 c 3 = 20 . 56 - 20 = 36 the answer is a ."
Answer: a
Python program:
a = math.comb(8, 5)
b = 8 - 2
c = math.comb(b, 2)
d = a - c
Problem: a reduction of 18 % in the price of oil enables a house wife to obtain 8 kgs more for rs . 1080 , what is the reduced price for kg ?
Options: a ) 72.15 , b ) 27.24 , c ) 24.25 , d ) 28.46 , e ) 20.9
Rationale: "1080 * ( 18 / 100 ) = 194 - - - - 8 ? - - - - 1 = > rs . 24.25 answer : c"
Answer: c
Python program:
a = 1080 * 18
b = a / 100
c = b / 8
Problem: one pipe can fill a tank three times as fast as another pipe . if together the two pipes can fill the tank in 38 minutes , then the slower pipe alone will be able to fill the tank in
Options: a ) 144 mins , b ) 140 mins , c ) 136 mins , d ) 152 minw , e ) none of these
Rationale: "explanation : let the slower pipe alone fill the tank in x minutes then faster will fill in x / 3 minutes . part filled by slower pipe in 1 minute = 1 / x part filled by faster pipe in 1 minute = 3 / x part filled by both in 1 minute = 1 / x + 3 / x = 1 / 38 = > 4 / x = 1 / 38 x = 38 ∗ 4 = 152 mins option d"
Answer: d
Python program:
a = 1 + 4 
b = a * 38
Problem: a satellite is composed of 24 modular units , each of which is equipped with a set of sensors , some of which have been upgraded . each unit contains the same number of non - upgraded sensors . if the number of non - upgraded sensors on one unit is 1 / 6 the total number of upgraded sensors on the entire satellite , what fraction of the sensors on the satellite have been upgraded ?
Options: a ) 5 / 6 , b ) 1 / 5 , c ) 1 / 6 , d ) 1 / 7 , e ) 1 / 24
Rationale: "let x be the number of upgraded sensors on the satellite . the number of non - upgraded sensors per unit is x / 6 . the number of non - upgraded sensors on the whole satellite is 24 ( x / 6 ) = 4 x . the fraction of sensors which have been upgraded is x / ( x + 4 x ) = x / 5 x = 1 / 5 the answer is b ."
Answer: b
Python program:
a = 1 / 6
b = a * 24
c = 24 * b
d = 24 + c 
e = 24 / d
Problem: a copy machine , working at a constant rate , makes 30 copies per minute . a second copy machine , working at a constant rate , makes 55 copies per minute . working together at their respective rates , how many copies do the two machines make in half an hour ?
Options: a ) 90 , b ) 2,700 , c ) 4,500 , d ) 2,550 , e ) 324,000
Rationale: "together the two machines make 30 + 55 = 85 copies per minute . so , in half an hour they will make 85 * 30 = 2,550 copies . answer : d ."
Answer: d
Python program:
a = 30 + 55 
b = a * const_60
c = b / 2
Problem: how many 4 digit numbers are there , if it is known that the first digit is even , the second is odd , the third is prime , the fourth ( units digit ) is divisible by 5 , and the digit 2 can be used only once ?
Options: a ) 20 , b ) 150 , c ) 225 , d ) 300 , e ) 320
Rationale: "4 options for the first digit : 2 , 4 , 6 , 8 ; 5 options for the second digit : 1 , 3 , 5 , 7 , 9 ; 4 options for the third digit : 2 , 3 , 5 , 7 ; 4 options for the fourth digit : 0 , 5 . four digit # possible without the restriction ( about the digit 2 ) : 4 * 5 * 4 * 2 = 160 numbers with two 2 - s , 2 x 2 x 1 * 5 * 1 * 2 = 10 . thus there are 160 - 10 = 150 such numbers . answer : b ."
Answer: b
Python program:
a = 4 + 1 
b = 4 + 1 
c = a * b
d = 4 * 4
e = c * d
f = 4 + 1 
g = 4 + 1 
h = f * g
i = h * 4
j = e - i
Problem: the average salary of the employees in a office is rs . 120 / month . the avg salary of officers is rs . 450 and of non officers is rs 110 . if the no . of officers is 15 , then find the no of nonofficers in the office .
Options: a ) 400 , b ) 420 , c ) 430 , d ) 495 , e ) 510
Rationale: let no . of non - officers be x 15 * 450 + x * 110 = ( x + 15 ) 120 x = 495 d
Answer: d
Python program:
a = 15 * 450
b = 15 * 120
c = a - b
d = 120 - 110
e = c / d
Problem: there are 15 players in a chess group , and each player plays each of the others once . given that each game is played by two players , how many total games will be played ?
Options: a ) 10 , b ) 30 , c ) 105 , d ) 60 , e ) 90
Rationale: 15 players are there . two players play one game with one another . so 15 c 2 = 15 x 14 / 2 = 105 so option c is correct
Answer: c
Python program:
a = 15 - 1
b = 15 * a
c = b / 2
Problem: two heavily loaded sixteen - wheeler transport trucks are 855 kilometers apart , sitting at two rest stops on opposite sides of the same highway . driver a begins heading down the highway driving at an average speed of 90 kilometers per hour . exactly one hour later , driver b starts down the highway toward driver a , maintaining an average speed of 80 kilometers per hour . how many kilometers farther than driver b , will driver a have driven when they meet and pass each other on the highway ?
Options: a ) 90 , b ) 130 , c ) 135 , d ) 320 , e ) 450
Rationale: "i ' ve been reading the website for a while and i ' m always keen to see different approaches so i would like to share one that works for me : short version : truck a travels for an hour . distance remaining = 855 - 90 = 765 k ratio of speeds 9 : 8 - > 765 / 17 = 45 truck a = 90 + 45 * 9 = 495 truck b = 45 * 8 = 360 delta = 135 km answer c"
Answer: c
Python program:
a = 855 - 90
b = 90 + 80 
c = a / b
d = 90 - 80
e = c * d
f = 90 + e
Problem: 5357 x 51 = ?
Options: a ) 273232 , b ) 273243 , c ) 273247 , d ) 273250 , e ) 273207
Rationale: "5357 x 51 = 5357 x ( 50 + 1 ) = 5357 x 50 + 5357 x 1 = 267850 + 5357 = 273207 e )"
Answer: e
Python program:
a = 5357 / 51
b = a * 100
Problem: a person spends 1 / 3 rd of the money with him on clothes , 1 / 5 th of the remaining on food and 1 / 4 th of the remaining on travel . now , he is left with rs 300 . how much did he have with him in the beginning ?
Options: a ) s 200 , b ) s 750 , c ) s 300 , d ) s 450 , e ) s 550
Rationale: "suppose the amount in the beginning was rs ’ x ’ money spent on clothes = rs 1 x / 3 balance = rs 2 x / 3 money spent on food = 1 / 5 of 2 x / 3 = rs 2 x / 15 balance = 2 x / 3 - 2 x / 15 = rs 8 x / 15 money spent on travel = 1 / 4 of 8 x / 15 = rs 2 x / 15 = 8 x / 15 - 2 x / 15 = 6 x / 15 = rs 2 x / 5 therefore 2 x / 5 = 300 = 750 answer : b"
Answer: b
Python program:
a = 1 / 3
b = 1 - a
c = 1 / 3
d = 1 - c
e = d / 5
f = b - e
g = 1 / 3
h = 1 - g
i = 1 / 3
j = 1 - i
k = j / 5
l = h - k
m = l / 4
n = f - m
o = 300 / n
Problem: a student is ranked 16 th from right and 6 th from left . how many students are there in totality ?
Options: a ) 18 , b ) 19 , c ) 20 , d ) 21 , e ) 22
Rationale: "from right 16 , from left 6 total = 16 + 6 - 1 = 21 answer : d"
Answer: d
Python program:
a = 16 + 6 
b = a - 1
Problem: the sum of the first 50 positive even integers is 2550 . what is the sum w of even integers from 102 to 200 inclusive ?
Options: a ) 5100 , b ) 7550 , c ) 10100 , d ) 15500 , e ) 20100
Rationale: "my solution is : first 50 even integers : 2 4 6 8 < . . . > integers from 102 to 200 102 104 106 108 < . . . > we notice that each integer from the second set is 100 more than the respective integer in the first set . since we have 50 even integers from 102 to 200 , then : w = 2550 + ( 100 * 50 ) = 7550 . b"
Answer: b
Python program:
a = 200 + 102 
b = a / 2
c = 200 - 102
d = c / 2
e = d + 1 
f = b * e
Problem: if a number x is 10 % less than another number y and y is 10 % more than 125 , then x is equal to
Options: a ) 143 , b ) 150 , c ) 123.75 , d ) 140.55 , e ) none
Rationale: solution y = 125 + 10 % of 125 = 125 + 12.50 = 137.50 . x = 137.50 - 10 % of 137.50 = 137.50 - 13.75 = 123.75 . answer c
Answer: c
Python program:
a = 10 / 100
b = 1 + a 
c = 125 * b
d = 100 - 10
e = d / 100
f = c * e
Problem: 575.104 x 15.98 ã · 9.001 + 21.25 = ?
Options: a ) 983.578 , b ) 1043.65 , c ) 1033.65 , d ) 656.112 , e ) 456.512
Rationale: "explanation : ? = 575.104 x 15.98 ã · 9.001 + 21.25 â ‰ ˆ ( 575.104 x 16 / 9 ) + 21.25 â ‰ ˆ 1022.40 + 21.25 â ‰ ˆ 1043.65 answer : option b"
Answer: b
Python program:
a = 15 ** 98
b = 575 * 104
Problem: if a car had traveled 30 kmh faster than it actually did , the trip would have lasted 30 minutes less . if the car went exactly 90 km , at what speed did it travel ?
Options: a ) 35 kmh , b ) 45 kmh , c ) 60 kmh , d ) 75 kmh , e ) 90 kmh
Rationale: "time = distance / speed difference in time = 1 / 2 hrs 90 / x - 90 / ( x + 30 ) = 1 / 2 substitute the value of x from the options . - - > x = 60 - - > 90 / 60 - 90 / 90 = 3 / 2 - 1 = 1 / 2 answer : c"
Answer: c
Python program:
a = 90 * 30
b = 2 * a
c = b * 4
d = 30 ** 2
e = c + d 
f = math.sqrt(e)
g = f - 30
h = g / 2
Problem: the length and width of a rectangle are integer values . what is the area of the smallest such rectangle that can be inscribed in a circle whose radius is also an integer
Options: a ) 12
b ) 45
c ) 36
d ) 48
e ) 60
Rationale: if we consider all pythagorean triplets with integral values , we have the following results : - ( 3 , 4,5 ) , ( 6 , 8,10 ) . . . . . . . . the diameter of the circle is 5 in the 1 st case and 10 in the 2 nd . but the question says that radius of the circle is also an integer hence the 1 st triplet will be ruled out . we are left with the 2 nd triplet where radius of the circle = 5 , hence the sides of the rectangle are 6 and 8 making the area = 45 . b
Answer: b
Python program:
a = 4 + rectangle_area