euclaise/mathqa_programs huggingface dataset:
Problem: in an election , candidate a got 70 % of the total valid votes . if 15 % of the total votes were declared invalid and the total numbers of votes is 560000 , find the number of valid vote polled in favor of candidate ?
Options: a ) 355600 , b ) 355800 , c ) 356500 , d ) 356800 , e ) 333200
Rationale: total number of invalid votes = 15 % of 560000 = 15 / 100 × 560000 = 8400000 / 100 = 84000 total number of valid votes 560000 – 84000 = 476000 percentage of votes polled in favour of candidate a = 70 % therefore , the number of valid votes polled in favour of candidate a = 70 % of 476000 = 70 / 100 × 476000 = 33320000 / 100 = 333200 e )
Answer: e
Python program:
a = 15 / 100
b = 1 - a
c = 560000 * b
d = 70 / 100
e = c * d
Problem: a telephone company needs to create a set of 3 - digit area codes . the company is entitled to use only digits 2 , 4 and 5 , which can be repeated . if the product of the digits in the area code must be odd , how many different codes can be created ?
Options: a ) 20 , b ) 22 , c ) 24 , d ) 1 , e ) 30
Rationale: "total # of codes possible is 3 * 3 * 3 = 27 . oit of those 27 codes only the product of 555 will be odd , the remaining 26 will have either 2 or 4 in them , which ensures that their product will be even . therefore the number of codes where the product of the digits is even = ( total ) - ( restriction ) = 27 - 26 = 1 . answer : d ."
Answer: d
Python program:
a = 3 ** 3
b = a - 1
Problem: if a * b denotes the greatest common divisor of a and b , then ( ( 12 * 16 ) * ( 30 * 24 ) ) = ?
Options: a ) 24 , b ) 12 , c ) 6 , d ) 4 , e ) 2
Rationale: "the greatest common divisor of 12 and 16 is 4 . hence 12 * 16 = 4 ( note that * here denotes the function not multiplication ) . the greatest common divisor of 30 and 24 is 6 . hence 30 * 24 = 6 . hence ( ( 12 * 16 ) * ( 30 * 24 ) ) = 4 * 6 . the greatest common divisor of 4 and 6 is 2 . answer ; e ."
Answer: e
Python program:
a = 30 / 3
b = a / 3
Problem: a certain number of horses and an equal number of men are going somewhere . half of the owners are on their horses ' back while the remaining ones are walking along leading their horses . if the number of legs walking on the ground is 60 , how many horses are there ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "legs 12 * 4 = 48 now half on their horses so remaining on the walk so 6 men 6 men has 12 legs so , 12 + 48 = 60 legs walking answer : b"
Answer: b
Python program:
a = 2 / 2
b = 4 + a 
c = 60 / b
Problem: in a certain parking lot , 2 % of the cars are towed for parking illegally . however 90 % of the cars which are parked illegally are not towed . what percentage of cars in the parking lot are parked illegally ?
Options: a ) 10 % , b ) 12 % , c ) 16 % , d ) 18 % , e ) 20 %
Rationale: "let x be the number of cars and let y be the number of cars parked illegally . 2 % * x = 10 % * y y / x = 1 / 5 = 20 % the answer is e ."
Answer: e
Python program:
a = 90 / 100
b = 1 - a
c = 2 / 100
d = b / c
Problem: a certain sky blue paint contains 10 percent blue pigment and 90 percent red pigment by weight . a certain green paint contains 70 percent blue pigment and 30 percent yellow pigment . when these paints are mixed to produce a brown paint , the brown paint contains 40 percent blue pigment . if the brown paint weighs 10 grams , then the red pigment contributes how many grams of that weight ?
Options: a ) 1.5 , b ) 2.5 , c ) 3.5 , d ) 4.5 , e ) 5.5
Rationale: 10 grams of combined mixture and 40 % blue pigment means that the mixtures were mixed 50 % each . thus 5 grams a piece . out of the 5 grams of the dark blue paint , 60 % is red . therefore , 5 * . 9 = 4.5 grams of red pigment
Answer: d
Python program:
a = 100 * 2
b = 90 / a
c = b * 10
Problem: alok ordered 16 chapatis , 5 plates of rice , 7 plates of mixed vegetable and 6 ice - cream cups . the cost of each chapati is rs . 6 , that of each plate of rice is rs . 45 and that of mixed vegetable is rs . 70 . the amount that alok paid the cashier was rs . 985 . find the cost of each ice - cream cup ?
Options: a ) 25 , b ) 76 , c ) 29 , d ) 12 , e ) 20
Rationale: explanation : let the cost of each ice - cream cup be rs . x 16 ( 6 ) + 5 ( 45 ) + 7 ( 70 ) + 6 ( x ) = 985 96 + 225 + 490 + 6 x = 985 6 x = 174 = > x = 29 . answer : c
Answer: c
Python program:
a = 16 * 6
b = 985 - a
c = 5 * 45
d = b - c
e = 7 * 70
f = d - e
g = f / 6
Problem: excluding stoppages , the speed of a bus is 65 kmph and including stoppages , it is 48 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 70 min , b ) 15 min , c ) 20.4 min , d ) 15.6 min , e ) 40 min
Rationale: "d 15.6 min due to stoppages , it covers 17 km less . time taken to cover 17 km = ( 17 / 65 x 60 ) min = 15.6 min"
Answer: d
Python program:
a = 65 - 48
b = a / 65
c = const_60 * b
Problem: a and b ’ s salaries together amount to rs . 2,000 . a spends 95 % of his salary and b spends 85 % of his . if now their savings are the same , what is b ’ s salary ?
Options: a ) 777 , b ) 500 , c ) 789 , d ) 776 , e ) 881
Rationale: "( 5 / 100 ) a = ( 15 / 100 ) b a = 3 b a + b = 2000 4 b = 2000 = > b = 500 answer b"
Answer: b
Python program:
a = 2 + 3 
b = 4 * a
c = 2 * b
d = c * 100
e = 85 / 100
f = 1 - e
g = d * f
h = 95 / 100
i = 1 - h
j = 85 / 100
k = 1 - j
l = i + k 
m = g / l
Problem: the inner circumference of a circular race track , 14 m wide is 440 m . find the radius of the outer circle .
Options: a ) 84 , b ) 12 , c ) 67 , d ) 28 , e ) 21
Rationale: "explanation : let inner radius be r meters . { \ color { black } then , 2 \ pi r = 440 \ rightarrow r = 440 \ times \ frac { 7 } { 22 } \ times \ frac { 1 } { 2 } = 70 m } radius of outer circle = 70 + 14 = 84 m answer : a ) 84 m"
Answer: a
Python program:
a = 440 / math.pi
b = a / 2
c = 14 + b
Problem: the length of the rectangular field is double its width . inside the field there is square shaped pond 8 m long . if the area of the pond is 1 / 8 of the area of the field . what is the length of the field ?
Options: a ) 73 , b ) 32 , c ) 34 , d ) 43 , e ) 42
Rationale: "explanation : a / 8 = 8 * 8 = > a = 8 * 8 * 8 x * 2 x = 8 * 8 * 8 x = 16 = > 2 x = 32 answer : option b"
Answer: b
Python program:
a = square_area * (
b = a / 8
c = 1/(2)
d = math.sqrt(b)
Problem: two goods train each 500 m long , are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one .
Options: a ) 12 sec , b ) 24 sec , c ) 48 sec , d ) 60 sec , e ) 65 sec
Rationale: "explanation : relative speed = = ( 45 + 30 ) km / hr = 75 x 5 / 18 m / sec = 125 / 6 m / sec we have to find the time taken by the slower train to pass the driver of the faster train and not the complete train . so , distance covered = length of the slower train . therefore , distance covered = 500 m . required time = 500 x 6 / 125 = 24 sec . answer is b"
Answer: b
Python program:
a = 45 + 30 
b = 1000 * a
c = b / 3600
d = 500 / c
e = d * 2
Problem: the age of somu is one - third his father ' s . 5 years back he was one - fifth of his father ' s age . what is his persent age ?
Options: a ) 11 , b ) 13 , c ) 14 , d ) 12 , e ) 10
Rationale: "explanation : let somu ' s age be x and that of his father be 3 x . so , x - 5 = 3 x - 5 / 5 = x = 10 answer : option e"
Answer: e
Python program:
a = 4 + 1 
b = a * 5
c = b - 5
d = 4 + 1 
e = d - 3
f = c / e
Problem: a charitable association sold an average of 66 raffle tickets per member . among the female members , the average was 70 raffle tickets . the male to female ratio of the association is 1 : 2 . what was the average number w of tickets sold by the male members of the association
Options: a ) 50 , b ) 56 , c ) 58 , d ) 62 , e ) 66
Rationale: "given that , total average w sold is 66 , male / female = 1 / 2 and female average is 70 . average of male members isx . ( 70 * f + x * m ) / ( m + f ) = 66 - > solving this equation after substituting 2 m = f , x = 58 . ans c ."
Answer: c
Python program:
a = 1 + 2 
b = 66 * a
c = 70 * 2
d = b - c
Problem: amit and ananthu can do a work in 15 days and 90 days respectively . amit started the work and left after 3 days . ananthu took over and completed the work . in how many days was the total work completed ?
Options: a ) 68 days , b ) 70 days , c ) 73 days , d ) 75 days , e ) 77 days
Rationale: "amit ’ s one day ’ s work = 1 / 15 amit ’ s 3 day ’ s work = 1 / 15 * 3 = 1 / 5 work left = 1 - 1 / 5 = 4 / 5 ananthu ’ s one day ’ s work = 1 / 90 ananthu can do work in = 4 / 5 * 90 = 72 days so total days = 72 + 3 = 75 days answer : d"
Answer: d
Python program:
a = 1/(15)
b = a * 3
c = 1 - b
d = 1/(90)
e = c / d
f = e + 3
Problem: city x has a population 6 times as great as the population of city y , which has a population twice as great as the population of city z . what is the ratio of the population of city x to the population of city z ?
Options: a ) 1 : 8 , b ) 1 : 4 , c ) 2 : 1 , d ) 4 : 1 , e ) 12 : 1
Rationale: "x = 6 y , y = 2 * z x : y , y : z 6 : 1 , 2 : 1 12 : 2 , 2 : 1 so , x : z = 12 : 1 ( e )"
Answer: e
Python program:
a = 6 * 2
Problem: a and b can do a work in 2 days , b and c in 4 days and c and a in 6 days . in how many days will the work be completed , if all three of them work together ?
Options: a ) 10 / 12 , b ) 16 / 28 , c ) 24 / 11 , d ) 42 / 16 , e ) 18 / 12
Rationale: one day work of a and b = 1 / 2 one day work of b and c = 1 / 4 one day work of c and a = 1 / 6 2 ( a + b + c ) = 1 / 2 + 1 / 4 + 1 / 6 . 2 ( a + b + c ) = 11 / 12 ( a + b + c ) = 11 / 24 number of days required = 24 / 11 days . answer : c
Answer: c
Python program:
a = 1/(2)
b = 1/(4)
c = a + b 
d = 1/(6)
e = c + d 
f = e / 2
g = 1 / f
Problem: what is the sum of all the multiples of 7 between 30 and 100 ?
Options: a ) 692 , b ) 700 , c ) 677 , d ) 654 , e ) 665
Rationale: "you first have to know all the multiples of 7 between 30 and 100 . they are 35 , 42 , 49 , 56 , 63 , 70 , 77 , 84 , 91 , and 98 . if you add all these numbers together , you get 665 . final answer : e"
Answer: e
Python program:
a = 12 + 2 
b = a + 1 
c = 12 + 2 
d = 2 + 4 
e = d + 4 
f = 10 - 1
g = e + f 
h = 2 + 4 
i = h + 4 
j = g + i 
k = 10 + 2 
l = j + k 
m = c + l 
n = b + m 
o = 12 + 2 
p = o + 1 
q = p + 1 
r = n + q 
s = r + 7 
t = 2 + 4 
u = s + t
Problem: if { x } is the product of all even integers from 1 to x inclusive , what is the greatest prime factor of { 20 } + { 24 } ?
Options: a ) 23 , b ) 25 , c ) 11 , d ) 5 , e ) 2
Rationale: "soln : { 24 } + { 20 } = 24 * { 20 } + { 20 } = 25 * { 20 } answer : b"
Answer: b
Python program:
a = 20 + 24 
b = a / 2
c = 1 * 2
d = b + c
Problem: the maximum number of students among them 1001 pens and 910 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils ?
Options: a ) 87 , b ) 91 , c ) 100 , d ) 96 , e ) 101
Rationale: "number of pens = 1001 number of pencils = 910 required number of students = h . c . f . of 1001 and 910 = 91 answer is b"
Answer: b
Python program:
a = math.gcd(1001, 910)
Problem: how many even integers n , such that 20 < = n < = 250 are of the form 3 k + 4 , where k is any natural number ?
Options: a ) 33 , b ) 36 , c ) 39 , d ) 42 , e ) 45
Rationale: "the first number is 22 = 16 + 6 ( 1 ) . we can continue adding 6 to make a list : 22 , 28 , 34 , . . . the last number is 250 = 16 + 6 ( 39 ) there are 39 numbers in the list . the answer is c ."
Answer: c
Python program:
a = 250 - 2
b = 20 + 2 
c = a - b
d = 2 + 4 
e = c / d
f = e + 1
Problem: a trader sells 85 meters of cloth for $ 8925 at the profit of $ 15 per metre of cloth . what is the cost price of one metre of cloth ?
Options: a ) $ 69 , b ) $ 78 , c ) $ 90 , d ) $ 86 , e ) $ 77
Rationale: c $ 90 sp of 1 m of cloth = 8925 / 85 = $ 105 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = $ 105 - $ 15 = $ 90 .
Answer: c
Python program:
a = 8925 / 85
b = a - 15
Problem: a fruit - salad mixture consists of apples , peaches , and grapes in the ratio 12 : 8 : 7 , respectively , by weight . if 54 pounds of the mixture is prepared , the mixture includes how many more pounds of apples than grapes ?
Options: a ) 15 , b ) 10 , c ) 9 , d ) 6 , e ) 4
Rationale: "we can first set up our ratio using variable multipliers . we are given that a fruit - salad mixture consists of apples , peaches , and grapes , in the ratio of 6 : 5 : 2 , respectively , by weight . thus , we can say : apples : peaches : grapes = 12 x : 8 x : 7 x we are given that 54 pounds of the mixture is prepared so we can set up the following question and determine a value for x : 12 x + 8 x + 7 x = 54 27 x = 54 x = 2 now we can determine the number of pounds of apples and of grapes . pounds of grapes = ( 7 ) ( 2 ) = 14 pounds of apples = ( 12 ) ( 2 ) = 24 thus we know that there are 24 - 14 = 10 more pounds of apples than grapes . answer is b ."
Answer: b
Python program:
a = 12 * 2
b = 7 * 2
c = a - b
Problem: of the six - digit positive integers that have no digits equal to zero , how many have two digits that are equal to each other and the remaining digit different from the other two ?
Options: a ) 2443200 , b ) 3643200 , c ) 5443200 , d ) 1443200 , e ) 2163200
Rationale: "of the six - digit positive integers that have no digits equal to zero , how many have two digits that are equal to each other and the remaining digit different from the other two ? a . 24 b . 36 c . 72 d . 144 e . 216 choosing the digit for p - 9 ways ; choosing the digit for q - 8 ways ; choosing the digit for r - 7 ways ; choosing the digit for s - 6 ways ; choosing the digit for t - 5 ways ; # of permutations of 3 digits in ppqrst - 6 ! / 2 ! total : 9 * 8 * 7 * 6 * 5 * 6 ! / 2 ! = 5443200 . answer : c ."
Answer: c
Python program:
a = 10 - 1
b = 10 - 2
c = a * b
d = c * 1
Problem: two employees x and y are paid a total of rs . 330 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?
Options: a ) s . 150 , b ) s . 200 , c ) s . 250 , d ) s . 350 , e ) s . 400
Rationale: "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 330 but x = 120 % of y = 120 y / 100 = 12 y / 10 â ˆ ´ 12 y / 10 + y = 330 â ‡ ’ y [ 12 / 10 + 1 ] = 330 â ‡ ’ 22 y / 10 = 330 â ‡ ’ 22 y = 3300 â ‡ ’ y = 3300 / 22 = 300 / 2 = rs . 150 a )"
Answer: a
Python program:
a = 1 + 4 
b = a * 2
c = 330 * b
d = 1 + 4 
e = d * 2
f = e + 1 
g = f * 2
h = c / g
Problem: if the price of a certain computer increased 30 percent from d dollars to 338 dollars , then 2 d =
Options: a ) 540 , b ) 520 , c ) 619 , d ) 649 , e ) 700
Rationale: "before price increase price = d after 30 % price increase price = d + ( 30 / 100 ) * d = 1.3 d = 338 ( given ) i . e . d = 338 / 1.3 = $ 260 i . e . 2 d = 2 * 260 = 520 answer : option b"
Answer: b
Python program:
a = 100 + 30 
b = a / 100
c = 338 / b
d = c * 2
Problem: simple interest on a certain sum of money for 2 years at 16 % per annum is one fourth the compound interest on rs . 4000 for 2 years at 8 % per annum . the sum placed on simple interest is
Options: a ) rs . 4000 , b ) rs . 665.6 , c ) rs . 520 , d ) rs . 166.4 , e ) none
Rationale: "solution c . i . = rs [ 4000 x ( 1 + 8 / 100 ) â ² - 4000 ] rs . ( 4000 x 108 / 100 x 108 / 100 - 4000 ) = rs . 665.6 . sum = rs . [ 166.4 x 100 / 2 x 16 ] = rs . 520 . answer c"
Answer: c
Python program:
a = 4000 * 8
b = a / 100
c = 4000 * 8
d = c / 100
e = 4000 + d 
f = e * 8
g = f / 100
h = b + g 
i = h / 2
j = i / 2
k = j * 100
l = k / 16
Problem: each digit 1 through 5 is used exactly once to create a 5 - digit integer . if the 1 and the 5 can not be adjacent digits in the integer , how many 5 - digit integers are possible ?
Options: a ) 48 , b ) 66 , c ) 76 , d ) 78 , e ) none of these
Rationale: "number of arrangements using 5 distinct digits = 5 ! number of arrangements in which 1 and 5 are adjacent - consider 1 and 5 together as one group . now you have 4 numbers / groups to arrange which can be done in 4 ! ways . in each of these arrangements , 1 and 5 can be arranged as 15 or 51 . number of arrangements in which 3 and 4 are not adjacent = 5 ! - 2 * 4 ! = 72 answer : e"
Answer: e
Python program:
a = 5 * 5
b = a * 1
c = b * 2
d = 5 * 1
e = d * 2
f = e * 2
g = c - f
Problem: a pupil ' s marks were wrongly entered as 79 instead of 45 . due to that the average marks for the class got increased by half . the number of pupils in the class is :
Options: a ) 30 , b ) 80 , c ) 20 , d ) 68 , e ) 26
Rationale: "let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 . x / 2 = ( 79 - 45 ) = > x / 2 = 34 = > x = 68 . answer : d"
Answer: d
Python program:
a = 79 - 45
b = a * 2
Problem: in a can , there is a mixture of milk and water in the ratio 2 : 5 . if it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 4 : 5 . find the capacity of the can ?
Options: a ) 40 , b ) 44 , c ) 48 , d ) 50 , e ) 8
Rationale: "let the capacity of the can be t litres . quantity of milk in the mixture before adding milk = 2 / 7 ( t - 8 ) after adding milk , quantity of milk in the mixture = 4 / 9 t . 4 t / 9 - 8 = 2 / 7 ( t - 8 ) 2 t = 72 - 56 = > t = 8 . answer : e"
Answer: e
Python program:
a = 4 / 5
b = a * 5
c = b - 2
d = 8 / c
e = 5 * d
f = 4 / 5
g = f * 5
h = g - 2
i = 8 / h
j = e + i 
k = j + 8
Problem: 90 % of the population of a village is 45000 . the total population of the village is ?
Options: a ) 26799 , b ) 24000 , c ) 50000 , d ) 29973 , e ) 12312
Rationale: "x * ( 90 / 100 ) = 45000 x = 500 * 100 x = 50000 answer : c"
Answer: c
Python program:
a = 100 / 90
b = a * 45000
Problem: total 52 matches are conducted in knockout match type . how many players will be participated in that tournament ?
Options: a ) 60 , b ) 51 , c ) 53 , d ) 56 , e ) 50
Rationale: "51 players answer : b"
Answer: b
Python program:
a = 52 + 1
Problem: the ratio between the number of sheep and the number of horses at the stewart farm is 1 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 ) 18 , b ) 28 , c ) 32 , d ) 56 , e ) 8
Rationale: "let the number of sheeps and horses be 1 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 = 1 x = 1 * 8 = 8 . hence e"
Answer: e
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 * 1
Problem: there are 12 teams in a soccer league and each team plays each of the other teams once . how many games will be played in total ?
Options: a ) 58 , b ) 62 , c ) 66 , d ) 70 , e ) 74
Rationale: 12 c 2 = 66 the answer is c .
Answer: c
Python program:
a = math.factorial(12)
b = 12 - 2
c = math.factorial(b)
d = math.factorial(2)
e = c * d
f = a / e
Problem: the length of a rectangle is increased by 45 % and its breadth is decreased by 20 % . what is the effect on its area ?
Options: a ) 1288 , b ) 1299 , c ) 1000 , d ) 10000 , e ) 11600
Rationale: "100 * 100 = 10000 145 * 80 = 11600 answer : e"
Answer: e
Python program:
a = 45 + 100 
b = 100 - 20
c = a * b
Problem: michael cashed a check for $ 1270 and received only $ 10 and $ 50 bills in return . during the course of a day , he used 15 bills and then lost the rest of the money . if the number of $ 10 bills used was either one more or one less than the number of $ 50 bills used , what is the minimum possible amount of money that was lost ?
Options: a ) $ 830 , b ) $ 800 , c ) $ 770 , d ) $ 730 , e ) $ 700
Rationale: 1 . 15 bills spent 2 . number of $ 10 bills is one more or one less than number of $ 50 bills . so , 2 choices 1 . 7 * 10 + 8 * 50 = $ 470 2 . 8 * 10 + 7 * 50 = $ 430 least money lost implies most money spent . i . e $ 470 therefore , lost money = 1270 - 470 = 800 . answer b
Answer: b
Python program:
a = 15 / 2
b = math.floor(a)
c = 15 - b
d = 50 * c
e = 15 / 2
f = math.floor(e)
g = f * 10
h = d + g 
i = 1270 - h
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 $ 180 , how many hours overtime did he work ?
Options: a ) 8 , b ) 5 , c ) 9 , d ) 6 , e ) 10
Rationale: "at $ 3 per hour up to 40 hours , regular pay = $ 3 x 40 = $ 120 if total pay = $ 168 , overtime pay = $ 180 - $ 120 = $ 60 overtime rate ( twice regular ) = 2 x $ 3 = $ 6 per hour = > number of overtime hours = $ 60 / $ 6 = 10 ans is e"
Answer: e
Python program:
a = 3 * 40
b = 180 - a
c = 3 * 2
d = b / c
Problem: if a farmer sells 5 of his goats , his stock of feed will last for 4 more days than planned , but if he buys 10 more goats , he will run out of feed 3 days earlier than planned . if no goats are sold or bought , the farmer will be exactly on schedule . how many goats does the farmer have ?
Options: a ) 12 , b ) 20 , c ) 48 , d ) 55 , e ) 60
Rationale: say farmer has n goat and he is good for d days . : - we have 3 equations given in question : - ( n - 5 ) * d + 4 = ( n + 10 ) * ( d - 3 ) = n * d solving these : ( you can solve 1 st and 3 rd and 2 nd and 3 rd together ) we get : 10 d - 3 n = 30 4 n - 5 d = 20 = > n = 20 ans b it is !
Answer: b
Python program:
a = 3 * 4
b = a - 10
c = b * 10
Problem: cole drove from home to work at an average speed of 30 kmh . he then returned home at an average speed of 90 kmh . if the round trip took a total of 2 hours , how many minutes did it take cole to drive to work ?
Options: a ) 66 , b ) 70 , c ) 72 , d ) 75 , e ) 90
Rationale: "let the distance one way be x time from home to work = x / 30 time from work to home = x / 90 total time = 2 hrs ( x / 30 ) + ( x / 90 ) = 2 solving for x , we get x = 45 time from home to work in minutes = ( 45 ) * 60 / 30 = 90 minutes ans = e"
Answer: e
Python program:
a = 90 * 2
b = 30 + 90 
c = a / b
d = c * const_60
Problem: when tom works alone he chops 3 lb . salad in 2 minutes , and when tammy works alone she chops 2 lb . salad in 3 minutes . they start working together , and after some time finish chopping 65 lb . of salad . of those 80 lb . , the salad quantity chopped by tammy is what percent lesser than the quantifying chopped by tom ?
Options: a ) 44 % , b ) 100 % , c ) 15 % , d ) 125 % , e ) 400 %
Rationale: "tom chops 4 lbs in 6 minutes tammy chops 9 lbs in 6 minutes so in the same amount of time , tammy chops 125 % more than tom , since 9 is 125 % greater than 4 . so 125 % is the answer . note that the actual time does n ' t matter . if you multiply the time each work by x , you ' ll multiply the work each does by x , and 9 x is still 125 % greater than 4 x . 125 % lesser than tom ans : d"
Answer: d
Python program:
a = 2 / 3
b = 2 / 0
c = a - b
d = 3 / 2
e = c / d
f = e * 100
Problem: what is the smallest integer y for which 27 ^ y > 3 ^ 24 ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 12
Rationale: "27 ^ y > 3 ^ 24 converting into the same bases : 27 ^ y > 27 ^ 8 therefore for the equation to hold true , y > 8 or y = 9 option c"
Answer: c
Python program:
a = 24 / 3
b = math.floor(a)
c = b + 1
Problem: a and b together can do a piece of work in 4 days . if a alone can do the same work in 20 days , then b alone can do the same work in ?
Options: a ) 0.35 days , b ) 0.45 days , c ) 0.55 days , d ) 0.25 days , e ) 0.2 days
Rationale: "b = 1 / 4 – 1 / 20 = 0.2 days answer : e"
Answer: e
Python program:
a = 1/(4)
b = 1/(20)
c = a - b
d = 1/(c)
Problem: a bell curve ( normal distribution ) has a mean of − 1 and a standard deviation of 1 / 8 . how many integer values z are within 3 standard deviations of the mean ?
Options: a ) 0 , b ) 1 , c ) 3 , d ) 6 , e ) 7
Rationale: got the question correctly - - the second item - - [ highlight ] bthe list of elements in the set is required . [ / highlight ] is not required . with the new information , there is only one integer value ( - 1 ) that is between ( - 1.375 , - 0.625 ) i . e . , falls within the three 3 sd range . b
Answer: b
Python program:
a = 1 - 1