euclaise/mathqa_programs huggingface dataset:
Problem: the compound interest earned by sunil on a certain amount at the end of two years at the rate of 5 % p . a . was rs . 492 . find the total amount that sunil got back at the end of two years in the form of principal plus interest earned .
Options: a ) rs . 4935 , b ) rs . 4925 , c ) rs . 5390 , d ) rs . 5290 , e ) rs . 5292
Rationale: "let the sum be rs . p p { [ 1 + 5 / 100 ] 2 - 1 } = 492 p ( 5 / 100 ) ( 2 + 5 / 100 ) = 492 [ a 2 - b 2 = ( a - b ) ( a + b ) ] p = 492 / ( 0.05 ) ( 2.05 ) = 4800 . amount = 4800 + 492 = rs . 5292 answer : e"
Answer: e
Python program:
a = 5 / 100
b = 1 + a 
c = b ** 2
d = c - 1
e = 492 / d
f = e + 492
Problem: a train 220 m long is running with a speed of 90 km / hr . in what time will it pass a bus that is running with a speed of 60 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 4.37 , b ) 5.28 , c ) 6.75 , d ) 8 , e ) 3.1
Rationale: "speed of train relative to bus = 90 + 60 = 150 km / hr . = 150 * 5 / 18 = 125 / 3 m / sec . time taken to pass the bus = 220 * 3 / 125 = 5.28 sec . answer : b"
Answer: b
Python program:
a = 90 + 60 
b = a * const_0_2778
c = 220 / b
Problem: a number is doubled and 9 is added . if resultant is trebled , it becomes 57 . what is that number
Options: a ) 5 , b ) 10 , c ) 12 , d ) 14 , e ) 15
Rationale: "explanation : = > 3 ( 2 x + 9 ) = 57 = > 2 x + 9 = 19 = > x = 5 answer : option a"
Answer: a
Python program:
a = 3 * 9
b = 57 - a
c = 3 * 2
d = b / c
Problem: tim and é lan are 30 miles away from one another . they are starting to move towards each other simultaneously , tim at a speed of 10 mph and é lan at a speed of 5 mph . if every hour they double their speeds , what is the distance that tim will pass until he meets é lan ?
Options: a ) 20 miles . , b ) 35 miles . , c ) 45 miles . , d ) 60 miles . , e ) 65 miles .
Rationale: "tim and elan will meet at the same time while their ratio of speed is 2 : 1 respectively . so their individual distance traveled ratio will be same . plugging in the answer choice only answer choice a meet the 2 : 1 ( tim : elan = 20 : 10 ) ratio of maintaining total distance traveled 30 miles so correct answer a"
Answer: a
Python program:
a = 5 + 10 
b = 10 / a
c = b * 30
Problem: 2 pipes can separately fill a tank in 20 hrs and 30 hrs respectively . both the pipes are opened tofill the tank , a leak develops in the tank through which one - third of water supplied by both the pipes goes out . what is the total time taken to fill the tank ?
Options: a ) 10 hrs , b ) 12 hrs , c ) 16 hrs , d ) 18 hrs , e ) 20 hrs
Rationale: "1 / 20 + 1 / 30 = 1 / 12 1 + 1 / 3 = 4 / 3 1 - - - 12 4 / 3 - - - ? 4 / 3 * 12 = 16 hrs c"
Answer: c
Python program:
a = 1 / 3
b = 1 + a 
c = 1/(20)
d = 1/(30)
e = c + d 
f = b / e
Problem: there are 99 people that own pets . 15 people own only dogs , 10 people own only cats , 5 people own only cats and dogs , 3 people own cats , dogs and snakes . how many total snakes are there ?
Options: a ) 2 , b ) 4 , c ) 8 , d ) 69 , e ) 32
Rationale: "lets assign variables to all the areas in venn diagram of three . three different units are dog , cat , snake = total = 99 only dog = d = 15 only cat = c = 10 only snake = s exactly dog and cat = 5 exactly dog and snake = x exactly cat and snake = y all three = 3 so 99 = 15 + 10 + 5 + 3 + x + y + s we need to know total snakes = x + y + s + 3 = 69 answer : d"
Answer: d
Python program:
a = 15 + 10 
b = a + 5 
c = b + 3 
d = 99 - c
e = d + 3
Problem: a certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 9 candidates eligible to fill 2 identical positions in the computer science department . if none of the candidates is eligible for a position in both departments , how many different sets of 3 candidates are there to fill the 3 positions ?
Options: a ) 42 , b ) 70 , c ) 140 , d ) 165 , e ) 252
Rationale: "ans : 252 7 c 1 * 9 c 2 answer e )"
Answer: e
Python program:
a = 9 * 3
b = a * 7
Problem: the simple interest on rs . 8 for 12 months at the rate of 5 paise per rupeeper month is
Options: a ) 1.2 , b ) 4.8 , c ) 4.4 , d ) 3.21 , e ) none
Rationale: "sol . s . i . = rs . [ 8 * 5 / 100 * 12 ] = rs . 4.8 answer b"
Answer: b
Python program:
a = 8 * 12
b = a * 5
c = b / 100
Problem: an athlete runs 360 metres race in 24 seconds . what is his speed ?
Options: a ) 23 , b ) 64.8 , c ) 37 , d ) 30 , e ) 28
Rationale: "speed = distance / time = 360 / 20 = 18 m / s = 18 * 18 / 5 = 64.8 km / hr answer : b"
Answer: b
Python program:
a = 360 / 24
b = a * const_3_6
Problem: two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 4 hours and 36 hours respectively . the ratio of their speeds is ?
Options: a ) 4 : 9 , b ) 4 : 3 , c ) 4 : 5 , d ) 3 : 1 , e ) 4 : 2
Rationale: "let us name the trains a and b . then , ( a ' s speed ) : ( b ' s speed ) = √ b : √ a = √ 36 : √ 4 = 6 : 2 = 3 : 1 answer : d"
Answer: d
Python program:
a = math.sqrt(36)
b = math.sqrt(4)
c = a / b
Problem: a batsman scored 120 runs which included 10 boundaries and 6 sixes . what % of his total score did he make by running between the wickets
Options: a ) 40 % , b ) 50 % , c ) 36.67 % , d ) 70 % , e ) 75 %
Rationale: "number of runs made by running = 120 - ( 10 x 4 + 6 x 6 ) = 120 - ( 76 ) = 44 now , we need to calculate 60 is what percent of 120 . = > 44 / 120 * 100 = 36.67 % c"
Answer: c
Python program:
a = 10 * 6
b = 6 * 10
c = a + b 
d = 120 - c
e = d / 120
f = e * 100
Problem: the sum of the present ages of two persons a and b is 54 . if the age of a is twice that of b , find the sum of their ages 5 years hence ?
Options: a ) 50 , b ) 64 , c ) 70 , d ) 80 , e ) 90
Rationale: "a + b = 54 , a = 2 b 2 b + b = 54 = > b = 18 then a = 36 . 5 years , their ages will be 41 and 23 . sum of their ages = 41 + 23 = 64 . answer : b"
Answer: b
Python program:
a = 54 / 5
b = a * 2
c = b + 5 
d = 54 / 5
e = d + 5 
f = c + e
Problem: if 12 % of x is equal to 6 % of y , then 18 % of x will be equal to how much % of y ?
Options: a ) 7 % , b ) 9 % , c ) 11 % , d ) 12 % , e ) none of these
Rationale: we have , 12 % of x = 6 % of y = > 2 % of x = 1 % of y = > ( 2 x 9 ) % of x = ( 1 x 9 ) % of y thus , 18 % of x = 9 % of y . answer : b
Answer: b
Python program:
a = 6 * 18
b = a / 12
Problem: heinz produces tomato puree by boiling tomato juice . the tomato puree has only 20 % water while the tomato juice has 90 % water . how many liters of tomato puree will be obtained from 80 litres of tomato juice ?
Options: a ) 2.8 liters . , b ) 2.5 liters . , c ) 8.5 liters . , d ) 2.6 liters . , e ) 10 liters .
Rationale: "answer : explanation : in each of the solutions , there is a pure tomato component and some water . so while boiling , water evaporates but tomato not . so we equate tomato part in the both equations . â ‡ ’ â ‡ ’ 10 % ( 80 ) = 80 % ( x ) â ‡ ’ â ‡ ’ x = 10 liters . answer : e"
Answer: e
Python program:
a = 100 - 90
b = a / 100
c = b * 80
d = 100 - 20
e = d / 100
f = c / e
Problem: a technician makes a round - trip to and from a certain service center by the same route . if the technician completes the drive to the center and then completes 30 percent of the drive from the center , what percent of the round - trip has the technician completed ?
Options: a ) 60 , b ) 65 , c ) 55 , d ) 50 , e ) 55
Rationale: round trip means 2 trips i . e . to and fro . he has completed one i . e 50 % completed . then he traveled another 30 % of 50 % i . e 15 % . so he completed 50 + 15 = 65 % of total trip . b
Answer: b
Python program:
a = 100 / 2
b = 100 / 2
c = 30 * b
d = c / 100
e = a + d
Problem: on dividing 127 by a number , the quotient is 9 and the remainder is 1 . find the divisor .
Options: a ) a ) 12 , b ) b ) 14 , c ) c ) 16 , d ) d ) 18 , e ) e ) 22
Rationale: "d = ( d - r ) / q = ( 127 - 1 ) / 9 = 126 / 9 = 14 b )"
Answer: b
Python program:
a = 127 / 9
b = math.floor(a)
Problem: if x + | x | + y = 7 and x + | y | - y = 6 , then x + y =
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 9
Rationale: "if x + | x | + y = 7 and x + | y | - y = 6 , then x + y = can be done in 2.3 mins : there are 4 cases to be tested : 1 ) x is - ve and y is - ve substituting in the equation , we get x - x + y = 7 and x - y - y = 6 solve for x and y we get x = 20 and y = 7 , so x + y = 27 reject 2 ) x is + ve and y is + ve substitute in the equation , we ger x + x + y = 7 and x + y - y = 6 solve for x and y we get x = 6 and y = - 5 , therefore x + y = 1 not on list so reject 3 ) x is - ve and y is + ve substitute , we get x - x = y = 7 and x + y - y = 6 solve fo x and y we get x = 6 and y = 7 , x + y = 13 not on list so reject 4 ) x is + ve and y is - ve substitute , we get x + x = y = 7 and x - y - y = 6 solve for x and y , we get x = 4 and y = - 1 , x + y = 3 , answer choice answer a"
Answer: a
Python program:
a = 6 * 2
Problem: a 300 meter long train crosses a platform in 45 seconds while it crosses a signal pole in 18 seconds . what is the length of the platform ?
Options: a ) 99 , b ) 450 , c ) 350 , d ) 882 , e ) 281
Rationale: "speed = [ 300 / 18 ] m / sec = 50 / 3 m / sec . let the length of the platform be x meters . then , x + 300 / 45 = 50 / 3 3 ( x + 300 ) = 2250 è x = 450 m . answer : b"
Answer: b
Python program:
a = 300 / 18
b = a * 45
c = b - 300
Problem: the ratio between the number of sheep and the number of horses at the stewart farm is 3 to 7 , if each horse is fed 230 ounces of horse food per day and the farm needs a total 12,880 ounces of horse food per day , what is the number of sheep in the farm ?
Options: a ) 24 , b ) 28 , c ) 32 , d ) 56 , e ) 60
Rationale: let the number of sheeps and horses be 3 x and 7 x . now total number of horses = total consumption of horse food / consumption per horse = 12880 / 230 = 56 , which is equal to 7 x . = > x = 8 sheeps = 3 x = 3 * 8 = 24 . hence a
Answer: a
Python program:
a = 4 * 2
b = a * 10
c = 4 * 2
d = c * 100
e = b + d 
f = 12 * 1000
g = e + f 
h = g / 230
i = h / 7
j = i * 3
Problem: one day a car rental agency rented 3 / 4 of its cars , including 4 / 5 of its cars with cd players . if 3 / 5 of its cars have cd players , what percent of the cars that were not rented had cd players ?
Options: a ) 23 / 40 , b ) 17 / 30 , c ) 12 / 25 , d ) 7 / 15 , e ) 3 / 10
Rationale: "the cars with cd players which were not rented is ( 1 / 5 ) ( 3 / 5 ) = 3 / 25 of all the cars . the cars which were not rented is 1 / 4 of all the cars . the percent of non - rented cars which had cd players is ( 3 / 25 ) / ( 1 / 4 ) = 12 / 25 the answer is c ."
Answer: c
Python program:
a = 4 * 4
b = a * 5
c = 4 * b
d = c / 5
e = 4 * 4
f = e * 5
g = 4 * f
h = g / 5
i = h * 4
j = i / 4
k = d - j
l = 4 * 4
m = l * 5
n = 4 * 4
o = n * 5
p = 3 * o
q = p / 4
r = m - q
s = k / r
t = s * 100
Problem: if a ( k ) = ( k + 1 ) ^ 2 , and k = 1 , what is the value of a ( a ( a ( a ( k ) ) ) ) ?
Options: a ) 328359 , b ) 557321 , c ) 258327 , d ) 458329 , e ) 4422
Rationale: a ( a ( a ( a ( 1 ) ) ) ) = a ( a ( a ( 4 ) ) ) = a ( a ( 25 ) ) = a ( 676 ) = 677 ^ 2 = 458329 thus , the answer is d .
Answer: d
Python program:
a = 1 + 1 
b = a ** 2
c = b + 1 
d = c ** 2
e = d + 1 
f = e ** 2
g = f + 1 
h = g ** 2
Problem: from the beginning to the end of 2007 , the price of a stock rose 20 percent . in 2008 , it dropped 25 percent . in 2009 , it rose 20 percent . what percent of the stock ’ s 2007 starting price was the price of the stock at the end of 2009 ?
Options: a ) 80 , b ) 90 , c ) 95 , d ) 100 , e ) 108
Rationale: "assume a value at the beginning of 2007 . as this is a % question , assume p = 100 . at the end of 2007 it becmae = 1.2 * 100 = 120 at the end of 2008 it decreased by 25 % = 120 * . 75 = 90 at the end of 2009 it increased by 20 % = 90 * 1.2 = 108 thus ratio = 108 / 100 = 1.08 ( in % terms = 108 % ) . thus e is the correct answer ."
Answer: e
Python program:
a = 100 + 20 
b = a / 100
c = 100 * b
d = 100 - 25
e = d / 100
f = c * e
g = 100 + 20 
h = g / 100
i = f * h
Problem: a 8 % stock yields 20 % . the market value of the stock is :
Options: a ) rs 48 , b ) rs 45 , c ) rs 40 , d ) rs 50 , e ) rs 55
Rationale: "explanation : for an income of rs . 20 , investment = rs . 100 . for an income of rs 8 , investment = rs . 100 / 20 x 8 = rs 40 market value of rs . 100 stock = rs 40 answer is c"
Answer: c
Python program:
a = 100 / 20
b = a * 8
Problem: the difference between a number and its two fifth is 510 . what is 10 % of that number ?
Options: a ) 12.75 , b ) 50 , c ) 85 , d ) 204 , e ) none
Rationale: "solution let the number be x . then , x - 2 / 5 x = 510 . ‹ = › 3 / 5 x = 510 ‹ = › x = [ 510 x 5 / 3 ] = 850 . therefore 10 % of 850 = 85 . answer c"
Answer: c
Python program:
a = 510 + 4 
b = a ** 4
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 65 % , and the students on the make - up date had an average score of 95 % , what was the average score for the entire class ?
Options: a ) 68 % , b ) 70 % , c ) 72 % , d ) 74 % , e ) 77 %
Rationale: "70 % of the class scored 65 % and 30 % of the class scored 95 % . the difference between 65 % and 95 % is 30 % . the average will be 65 % + 0.3 ( 30 % ) = 74 % . the answer is d ."
Answer: d
Python program:
a = 70 * 65
b = 100 - 70
c = 95 * b
d = a + c 
e = d / 100
Problem: the maximum number of student amoung them 1020 pens and 860 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :
Options: a ) 20 , b ) 40 , c ) 60 , d ) 80 , e ) none of these
Rationale: "solution required number of student = h . c . f of 1020 and 860 = 20 . answer a"
Answer: a
Python program:
a = math.gcd(1020, 860)
Problem: count the numbers between 10 - 99 which yield a remainder of 3 when divided by 9 and also yield a remainder of 2 when divided by 5 ?
Options: a ) two , b ) five , c ) six , d ) four , e ) one
Rationale: answer = a ) two numbers between 10 - 99 giving remainder 3 when divided by 9 = 12 , 21 , 30 , 39 , 48 , 57 , 66 , 75 , 84 , 93 the numbers giving remainder 2 when divided by 5 = 12 , 57 = 2
Answer: a
Python program:
a = 2 * 1
Problem: there were totally 100 men . 80 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 ) 10 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "100 - ( 100 - 80 ) - ( 100 - 75 ) - ( 100 - 85 ) - ( 100 - 70 ) = 100 - 20 - 25 - 15 - 30 = 100 - 90 = 10 answer : a"
Answer: a
Python program:
a = 100 - 80
b = 100 - 75
c = a + b 
d = 100 - 85
e = c + d 
f = 100 - 70
g = e + f 
h = 100 - g
Problem: a boy wanted to calculate his speed on his bike . his starting point was 350 meters from the turning point . he made the round trip 5 times in 30 minutes . what was the boy ' s speed in kilometers per hour ?
Options: a ) 1.75 , b ) 1 , c ) 2.25 , d ) 2.4 , e ) 3.2
Rationale: the distance between the the starting point and the turning point was 350 meters . the boy made the round trip 5 times so that was 10 times he traveled 350 meters . 10 * 350 = 3500 meters or 3.5 km . 30 minutes is half of an hour . divide the 3500 meters in half to put in the right time interval 3500 / 2 = 1750 meters or 1.75 km correct answer is a
Answer: a
Python program:
a = 350 / 1000
b = 5 * a
Problem: if it is assumed that 60 percent of those who receive a questionnaire by mail will respond and 222 responses are needed , what is the minimum number of questionnaires that should be mailed ?
Options: a ) 280 , b ) 370 , c ) 460 , d ) 550 , e ) 640
Rationale: "let x be the minimum number of questionnaires to be mailed . 0.6 x = 222 x = 370 the answer is b ."
Answer: b
Python program:
a = 60 / 100
b = 222 / a
Problem: to deliver an order on time , a company has to make 25 parts a day . after making 25 parts per day for 3 days , the company started to produce 5 more parts per day , and by the last day of work 100 more parts than planned were produced . how many parts the company made ?
Options: a ) 675 , b ) 778 , c ) 654 , d ) 412 , e ) 589
Rationale: "let x be the number of days the company worked . then 25 x is the number of parts they planned to make . at the new production rate they made : 3 ⋅ 25 + ( x − 3 ) ⋅ 30 = 75 + 30 ( x − 3 ) therefore : 25 x = 75 + 30 ( x − 3 ) − 100 25 x = 75 + 30 x − 90 − 100 190 − 75 = 30 x − 25 115 = 5 x x = 23 so the company worked 23 days and they made 23 ⋅ 25 + 100 = 675 pieces . correct answer is a ) 675"
Answer: a
Python program:
a = 25 + 5 
b = a * 3
c = b + 100 
d = 25 * 3
e = c - d
f = e / 5
g = f * 25
h = g + 100
Problem: what annual installment will discharge a debt of rs . 1092 due in 3 years at 12 % simple interest ?
Options: a ) 442 , b ) 441 , c ) 440 , d ) 320 , e ) 532
Rationale: "let the installment be rs . x if he keeps the total amount for 3 years , he have to pay the interest of rs . ( 1092 * 12 * 3 ) / 100 . but he paid rs . x after 1 year . so he need not to pay interest for rs . x for remaining 2 years . i . e he need not to pay rs . ( x * 12 * 2 ) / 100 . and he paid another rs . x after 2 years . so he need not to pay interest for for remaining 1 years . i . e . rs . ( x * 12 * 1 ) / 100 . so the total interest he has to pay is rs . ( ( 1092 * 12 * 3 ) / 100 ) - [ ( ( x * 12 * 2 ) / 100 ) + ( ( x * 12 * 1 ) / 100 ) ] . so , the total amount he has to pay is rs . 1092 + rs . ( ( 1092 * 12 * 3 ) / 100 ) - [ ( ( x * 12 * 2 ) / 100 ) + ( ( x * 12 * 1 ) / 100 ) ] . the total amount he paid = 3 x . ( because he paid rs . x for three times ) 1092 + ( ( 1092 * 12 * 3 ) / 100 ) - [ ( ( x * 12 * 2 ) / 100 ) + ( ( x * 12 * 1 ) / 100 ) ] = 3 x by solving , we will get x = 442 . answer : a"
Answer: a
Python program:
a = 12 / 1092
b = 100 * 0
c = b * 3
Problem: how many integerskgreater than 100 and less than 1100 are there such that if the hundreds and the units digits ofkare reversed , the resulting integer is k + 99 ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: numbers will be like 102 = > 201 = 102 + 99 203 = > 302 = 103 + 99 so the hundereth digit and units digit are consecutive where unit digit is bigger than hundred digit . there will be ninet pairs of such numbers for every pair there will 10 numbers like for 12 = > 102 , 112,132 , 142,152 , 162,172 , 182,192 . total = 9 * 10 = 90 hence e .
Answer: e
Python program:
a = 100 / 10
b = 2 * 4
c = a * b
d = 100 / 10
e = c + d
Problem: sandy walked 20 meters towards south . then sandy turned to her left and walked 20 meters . she then turned to her left and walked 20 meters . she then turned to her right and walked 10 meters . what distance is she from the starting point and in which direction ?
Options: a ) 35 m east , b ) 35 m north , c ) 30 m west , d ) 45 m west , e ) 30 m east
Rationale: "the net distance is 20 + 10 = 30 meters to the east . the answer is e ."
Answer: e
Python program:
a = 20 + 10
Problem: income and expenditure of a person are in the ratio 3 : 2 . if the income of the person is rs . 21000 , then find his savings ?
Options: a ) 6000 , b ) 7000 , c ) 8000 , d ) 9000 , e ) 10000
Rationale: let the income and the expenditure of the person be rs . 3 x and rs . 2 x respectively . income , 3 x = 21000 = > x = 7000 savings = income - expenditure = 3 x - 2 x = x so , savings = rs . 7000 . answer : b
Answer: b
Python program:
a = 2 / 3
b = a * 21000
c = 21000 - b
Problem: in how many ways 4 boys and 3 girls can be seated in a row so that they are alternate .
Options: a ) 144 , b ) 288 , c ) 12 , d ) 256 , e ) none
Rationale: "solution : let the arrangement be , b g b g b g b 4 boys can be seated in 4 ! ways . girl can be seated in 3 ! ways . required number of ways , = 4 ! * 3 ! = 144 . answer : option a"
Answer: a
Python program:
a = math.factorial(4)
b = math.factorial(3)
c = a * b
Problem: the ratio of the radius of two circles is 4 : 3 , and then the ratio of their areas is ?
Options: a ) 1 : 8 , b ) 1 : 6 , c ) 1 : 9 , d ) 16 : 9 , e ) 1 : 2
Rationale: "r 1 : r 2 = 4 : 3 π r 12 : π r 22 r 12 : r 22 = 16 : 9 answer : d"
Answer: d
Python program:
a = circle_area / (
Problem: in a function , every person shakes hand with every other person . if there was a total of 28 handshakes in the function , how many persons were present in the function ?
Options: a ) 8 , b ) 7 , c ) 2 , d ) 6 , e ) 5
Rationale: suppose there are nn persons present in a function and every person shakes hand with every other person . then , total number of handshakes = nc 2 = n ( n − 1 ) / 2 n ( n − 1 ) = 28 × 2 n ( n − 1 ) = 56 n = 8 answer a 8
Answer: a
Python program:
a = 28 - 10
b = a - 10
Problem: 3 * 16 + 3 * 17 + 3 * 20 + 11 = ?
Options: a ) 121 , b ) 129 , c ) 138 , d ) 152 , e ) 170
Rationale: "3 * 16 + 3 * 17 + 3 * 20 + 11 = 48 + 51 + 60 + 11 = 170 the answer is e ."
Answer: e
Python program:
a = 3 * 16
b = 3 * 17
c = a + b 
d = 3 * 20
e = c + d 
f = e + 11
Problem: on the number line , if x is halfway between - 8 and 4 , and if y is halfway between - 4 and 6 , what number is halfway between x and y ?
Options: a ) - 1.5 , b ) - 0.5 , c ) 0.5 , d ) 1.5 , e ) 2.5
Rationale: "x = - 2 and y = 1 . the answer is b ."
Answer: b
Python program:
a = negate + (
Problem: a train speeds past a pole in 15 sec and a platform 120 m long in 25 sec , its length is ?
Options: a ) 100 , b ) 150 , c ) 160 , d ) 170 , e ) 180
Rationale: "let the length of the train be x m and its speed be y m / sec . then , x / y = 15 = > y = x / 15 ( x + 120 ) / 25 = x / 15 = > x = 180 m . answer : option e"
Answer: e
Python program:
a = 2 - 1
b = 120 * a
Problem: a library has an average of 660 visitors on sundays and 240 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is :
Options: a ) 250 , b ) 276 , c ) 280 , d ) 310 , e ) none
Rationale: "since the month begins with sunday , to there will be five sundays in the month average required = ( 660 x 5 + 240 x 25 ) / 30 ) = 310 answer : option d"
Answer: d
Python program:
a = 3 + 4 
b = 30 / a
c = math.floor(b)
d = c + 1 
e = d * 660
f = 3 + 4 
g = 30 / f
h = math.floor(g)
i = h + 1 
j = 30 - i
k = j * 240
l = e + k 
m = l / 30
Problem: mr . riddle invested in fund x and fund y . the total amount she invested , in both funds combined , was $ 200000 . in one year , fund x paid 43 % and fund y paid 28 % . the interest earned in fund y was exactly $ 200 greater than the interest earned in fund x . how much did ms . tom invest in fund x ?
Options: a ) 43 , 870.34 , b ) 56 , 876.45 , c ) 77 , 789.45 , d ) 78 , 450.70 , e ) 87 , 987.34
Rationale: x + y = 200000 0.28 y = 0.43 a + 300 take away decimals first : 28 y + 43 x + 20000 isolate first equation to solve for x ( your goal ) : y = 200000 - y plug in for b : 28 ( 200000 - x ) = 43 x + 30000 5 , 600000 - 28 x = 43 x + 30000 5 , 570000 = 71 x 5 , 570000 / 71 = x 5 , 570000 / 71 = x x = 78 , 450.70 = answer choice d
Answer: d
Python program:
a = 200000 * 28
b = a / 100
c = b - 200
d = c * 100
e = 43 + 28 
f = d / e
g = f / 100
h = 100 - 10
i = g + h
Problem: at the faculty of aerospace engineering , 312 students study random - processing methods , 232 students study scramjet rocket engines and 114 students study them both . if every student in the faculty has to study one of the two subjects , how many students are there in the faculty of aerospace engineering ?
Options: a ) 438 , b ) 436 , c ) 430 , d ) 442 , e ) 444
Rationale: 312 + 232 - 114 ( since 112 is counted twice ) = 430 c is the answer
Answer: c
Python program:
a = 114 / 2
b = 312 - a
c = 114 / 2
d = 232 - c
e = b + d
Problem: two boats are heading towards each other at constant speeds of 5 miles / hr and 25 miles / hr respectively . they begin at a distance 20 miles from each other . how far are they ( in miles ) one minute before they collide ?
Options: a ) 1 / 12 , b ) 5 / 12 , c ) 1 / 6 , d ) 1 / 2 , e ) 1 / 5
Rationale: "the question asks : how far apart will they be 1 minute = 1 / 60 hours before they collide ? since the combined rate of the boats is 5 + 25 = 30 mph then 1 / 60 hours before they collide they ' ll be rate * time = distance - - > 30 * 1 / 60 = 1 / 2 miles apart . answer : d ."
Answer: d
Python program:
a = 25 + 5 
b = a / const_60