euclaise/mathqa_programs huggingface dataset:
Problem: a palindrome is a word or a number that reads the same forward and backward . for example , 2442 and 111 are palindromes . if 5 - digit palindromes are formed using one or more of the digits 1 , 2 , 3 , 4 , 5 , 6 , and 7 , how many palindromes are possible ?
Options: a ) 35 , b ) 49 , c ) 105 , d ) 255 , e ) 343
Rationale: "there are 7 choices for each of the first three digits . the number of possible palindromes is 7 ^ 3 = 343 . the answer is e ."
Answer: e
Python program:
a = 5 ** 3
Problem: a money lender finds that due to a fall in the annual rate of interest from 8 % to 7 3 / 4 % his yearly income diminishes by rs . 63.50 , his capital is ?
Options: a ) 24,602 , b ) 28,888 , c ) 24,600 , d ) 24,628 , e ) 24,400
Rationale: "let the capital be rs . x . then , ( x * 8 * 1 ) / 100 - ( x * 31 / 4 * 1 / 100 ) = 63.50 32 x - 31 x = 6350 * 4 x = 25,400 . answer : e"
Answer: e
Python program:
a = 4 / 4
b = 63 / 50
Problem: in a certificate by mistake a candidate gave his height as 25 % more than actual height . in the interview panel , he clarified that his height was 5 feet 5 nches . find the % correction made by the candidate from his stated height to his actual height ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 35 , e ) 43
Rationale: "his height was = 5 feet 5 inch = 5 + 60 = 65 inch . required % correction = 65 * ( 1.25 - 1 ) * 100 = 20 b"
Answer: b
Python program:
a = const_0_25 + const_0_25 
b = 25 + a 
c = b - 5
d = const_0_25 + const_0_25 
e = 25 + d 
f = e - 5
g = 100 + f 
h = c / g
i = h * 100
Problem: a train of length l is traveling at a constant velocity and passes a pole in t seconds . if the same train travelling at the same velocity passes a platform in 6 t seconds , then what is the length of the platform ?
Options: a ) l , b ) 3 l , c ) 5 l , d ) 7 l , e ) 9 l
Rationale: "the train passes a pole in t seconds , so velocity v = l / t ( l + p ) / v = 6 t ( l + p ) / ( l / t ) = 6 t p = 5 l the answer is c ."
Answer: c
Python program:
a = 6 - 1
Problem: a bus 15 m long is running with a speed of 40 km / hr . in what time will it pass a man who is skateboarding at 8 km / hr in the direction opposite to that in which the car is going ?
Options: a ) 1.125 , b ) 1.5 , c ) 1.75 , d ) 1.25 , e ) 1
Rationale: speed of bus relative to man = 40 + 8 = 48 km / hr . = 48 * 5 / 18 = 40 / 3 m / sec . time taken to pass the man = 5 * 3 / 40 = 1.125 sec . answer : a
Answer: a
Python program:
a = 15 * 3600
b = 40 + 8 
c = a / b
d = c / 1000
Problem: the end of a blade on an airplane propeller is 10 feet from the center . if the propeller spins at the rate of 660 revolutions per second , how many miles will the tip of the blade travel in one minute ? ( 1 mile = 5,280 feet )
Options: a ) 150 π , b ) 240 π , c ) 300 π , d ) 480 π , e ) 1,200 π
Rationale: distance traveled in 1 revolution = 2 π r = 2 π 10 / 5280 revolutions in one second = 660 revolutions in 60 seconds ( one minute ) = 660 * 60 total distance traveled = total revolutions * distance traveled in one revolution 660 * 60 * 2 π 10 / 5280 = 150 π a is the answer
Answer: a
Python program:
a = 2 * 100
b = 2 + 3 
c = b * 1000
d = a + c 
e = 10 / d
f = e * 2
g = 2 * 10
h = 2 + g 
i = 3 + 4 
j = h / i
k = f * j
l = k * 660
m = l * const_60
Problem: victor gets 92 % marks in examinations . if these are 368 marks , find the maximum marks .
Options: a ) 334 , b ) 500 , c ) 400 , d ) 288 , e ) 271
Rationale: "let the maximum marks be m then 92 % of m = 368 ⇒ 92 / 100 × m = 368 ⇒ m = ( 368 × 100 ) / 92 ⇒ m = 36800 / 92 ⇒ m = 400 therefore , maximum marks in the examinations are 400 . answer : c"
Answer: c
Python program:
a = 92 / 100
b = 368 / a
Problem: a train running at the speed of 300 km / hr crosses a pole in 15 seconds . what is the length of the train ?
Options: a ) 1200 m , b ) 1250 m , c ) 1300 m , d ) 1350 m , e ) 1450 m
Rationale: "speed = ( 300 * 5 / 18 ) m / sec = ( 250 / 3 ) m / sec length of the train = ( speed x time ) = ( 250 / 3 * 15 ) m = 1250 m . answer : b"
Answer: b
Python program:
a = 300 * 1000
b = a / 3600
c = b * 15
Problem: a starts business with rs . 3500 and after 6 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b â € ™ s contribution in the capital ?
Options: a ) 24887 , b ) 20778 , c ) 23788 , d ) 10500 , e ) 2811
Rationale: "explanation : a invested rs . 3500 for 12 months . let b joined with investment x . and he invested for 12 - 6 = 6 months . so there profit ratio = ( 3500 ã — 12 ) : ( 6 x ) = 2 : 3 â ‡ ’ x = 10500 answer : d"
Answer: d
Python program:
a = 3500 * 12
b = a * 3
c = 12 - 6
d = c * 2
e = b / d
Problem: the population of a village is 10000 . it increases annually at the rate of 20 % p . a . what will be its population after 2 years ?
Options: a ) 10000 , b ) 12000 , c ) 13000 , d ) 14000 , e ) 14400
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 10000 × 120 / 100 × 120 / 100 = 14400 e"
Answer: e
Python program:
a = 20 / 100
b = 1 + a 
c = b ** 2
d = 10000 * c
Problem: in a class of 30 students , 5 students did not borrow any books from the library , 12 students each borrowed 1 book , 8 students each borrowed 2 books , and the rest of the students each borrowed at least 3 books . if the average ( arithmetic mean ) number of books borrowed per student was 2 , what is the maximum number of books that any single student could have borrowed ?
Options: a ) 5 , b ) 8 , c ) 15 , d ) 18 , e ) 20
Rationale: the average number of books per student was 2 means that total of 2 * 30 = 60 books were borrowed ; 5 + 12 + 8 = 25 students borrowed total of 5 * 0 + 12 * 1 + 8 * 2 = 28 books ; so 60 - 28 = 32 books are left to distribute among 30 - 25 = 5 students , these 5 arethe rest who borrowed at least 3 books ; tomaximizethe number of books one student from above 5 could have borrowed we shouldminimizethe number of books other 4 students from 5 could have borrowed . minimum these 4 students could have borrowed is 3 books per student , so total number of books they could have borrowed is 4 * 3 = 12 books . so the 5 th student could have borrowed is 32 - 12 = 20 books . answer : e .
Answer: e
Python program:
a = 30 * 2
b = 8 * 2
c = 12 + b 
d = 5 * 3
e = c + d 
f = a - e
g = f + 3
Problem: two carpenters , working in the same pace , can build 2 desks in two hours and a half . how many desks can 4 carpenters build in 3 hours ?
Options: a ) 2.4 . , b ) 3.6 . , c ) 4.8 . , d ) 5.5 . , e ) 6.4
Rationale: "w = 2 desks t = 2.5 hrs rate of 2 carpenters = 2 × r rate = work done / time 2 xr = 2 / 2.5 r = 1 / 2.5 = 2 / 5 ( this is the rate of each carpenter ) work done by 4 carpenters in 3 hrs = 4 × rate of each carpenter x time = 4 × 2 / 5 × 3 = 4.8 desks c is the correct answer ."
Answer: c
Python program:
a = 3 / 2
b = 2 / a
c = b / 2
d = c * 4
e = d * 3
Problem: mr . kutty has only hens and sheep . if the total number of their heads is 38 and the total number of legs is 100 then what is the ratio between the numbers of hens and sheep ?
Options: a ) 2 : 1 , b ) 1 : 2 , c ) 6 : 13 , d ) 13 : 6 , e ) none of these
Rationale: let the total number of hens and sheep be x and y respectively . i . e . , x + y = 38 and 2 x + 4 y = 100 ∴ ratio = 13 : 6 answer d
Answer: d
Python program:
a = 38 * 2
b = 100 - a
c = b / 2
d = 38 - c
e = 38 * 2
f = 100 - e
g = f / 2
h = d / g
Problem: a boat covers a certain distance downstream in 1 hour , while it comes back in 1.30 hours . if the speed of the stream be 3 kmph , what is the speed of the boat in still water ?
Options: a ) 10 , b ) 13 , c ) 11 , d ) 08 , e ) 15
Rationale: "let the speed of the water in still water = x given that speed of the stream = 3 kmph speed downstream = ( x + 3 ) kmph speed upstream = ( x − 3 ) kmph he travels a certain distance downstream in 1 hour and come back in 1 1 ⁄ 2 hour . i . e . , distance travelled downstream in 1 hour = distance travelled upstream in 1 1 ⁄ 2 hour since distance = speed × time , we have ( x + 3 ) × 1 = ( x − 3 ) 3 / 2 ⇒ 2 ( x + 3 ) = 3 ( x − 3 ) ⇒ 2 x + 6 = 3 x − 9 ⇒ x = 6 + 9 = 15 kmph answer is e ."
Answer: e
Python program:
a = 3 / 2
b = a * 3
c = b + 3 
d = 3 / 2
e = d - 1
f = c / e
Problem: if x is a positive number and 1 / 4 the square root of x is equal to 3 x , then x =
Options: a ) 1 / 16 , b ) 12 , c ) 1 / 12 , d ) 144 , e ) 1 / 144
Rationale: "1 / 4 of sqrt ( x ) = 3 x , which means that sqrt ( x ) = 12 x or x = 144 x ^ 2 - > divide by x 1 = 144 x x = 1 / 144 e ."
Answer: e
Python program:
a = 4 * 3
b = 4 ** a
Problem: a library has an average of 510 visitors on sundays and 240 on other day . the average number of visitors in a month of 15 days starting with sunday is
Options: a ) 280 , b ) 285 , c ) 290 , d ) 295 , e ) 570
Rationale: "explanation : as the month begin with sunday , so there will be five sundays in the month . so result will be : = ( 510 × 5 + 240 × 25 / 15 ) = ( 8550 / 15 ) = 570 answer : option e"
Answer: e
Python program:
a = 3 + 4 
b = 15 / a
c = math.floor(b)
d = c + 1 
e = d * 510
f = 3 + 4 
g = 15 / f
h = math.floor(g)
i = h + 1 
j = 15 - i
k = j * 240
l = e + k 
m = l / 15
Problem: if 35 percent of 400 is 20 percent of x , then x =
Options: a ) 200 , b ) 350 , c ) 700 , d ) 900 , e ) 1,400
Rationale: "5 / 100 ( 400 ) = 2 / 10 ( x ) x = 700 . . answer : c"
Answer: c
Python program:
a = 35 * 400
b = a / 20
Problem: the side of a rhombus is 26 m and length of one of its diagonals is 20 m . the area of the rhombus is ?
Options: a ) 488
b ) 429
c ) 418
d ) 480
e ) 410
Rationale: 262 – 102 = 242 d 1 = 20 d 2 = 48 1 / 2 * 20 * 48 = 480 answer : d
Answer: d
Python program:
a = 2 * 26
b = a ** 2
c = 20 ** 2
d = b - c
e = math.sqrt(d)
f = 20 * e
g = f / 2
Problem: 80 370 ? 1550 2440 3530
Options: a ) 900 , b ) 840 , c ) 750 , d ) 860 , e ) 960
Rationale: "10 ^ 2 - 20 = 80 20 ^ 2 - 30 = 370 30 ^ 2 - 40 = 860 40 ^ 2 - 50 = 1550 50 ^ 2 - 60 = 2440 60 ^ 2 - 70 = 3530 . answer : d"
Answer: d
Python program:
a = 370 / 1550
b = 80 + a 
c = b * 2440
d = c / 100
Problem: how many liters of water must be evaporated from 50 liters of a 3 - percent sugar solution to get a 4 - percent solution ?
Options: a ) 35 , b ) 33 1 / 3 , c ) 21 , d ) 16 2 / 3 , e ) 15
Rationale: "how many liters of water must be evaporated from 50 liters of a 3 - percent sugar solution to get a 4 - percent solution ? 3 % of a 50 liter solution is 1.5 l . so you are trying to determine how many liters must a solution be for the 1.5 l to represent 4 % of the solution . set up an inequality and solve for x : 1.5 / x = 1 / 4 x = 6 since you need a 15 l solution , you must evaporate 21 of the original 50 l solution to get a 4 % solution . answer is c ."
Answer: c
Python program:
a = 50 / 100
b = a * 4
c = 50 - b
Problem: three coins are tossed . find the probability of at least 1 head and 1 tail ?
Options: a ) 1 / 2 , b ) 1 / 4 , c ) 3 / 4 , d ) 7 / 8 , e ) 1 / 8
Rationale: "n ( s ) = 2 ^ 3 = 8 . . . . ( 3 coins tossed ) let e is the event of getting at least 1 head and 1 tail n ( e ) = tth , htt , tht , hht , hth , thh = 6 p ( e ) = n ( e ) / n ( s ) = 6 / 8 = 3 / 4 ans - c"
Answer: c
Python program:
a = 1 / 1
b = 1 / 1
c = a * b
d = 4 * c
Problem: 10 chess players take part in a tournament . every player plays twice with each of his opponents . how many games are to be played ?
Options: a ) 90 , b ) 98 , c ) 35 , d ) 99 , e ) 80
Rationale: "though 2 * ( 10 c 2 ) is the correct approcah to do this , but for people like me who find perm , comb n prob a nightmare , an easy approach can be used . the first guy has to play 2 matches with the rest of 9 , so he ' ll play 18 matches . similarly , second guy has to play with the rest of 8 as his 2 games with the first guy are already played . so he plays 16 matches . this continues like this and the total matches are 18 + 16 + 14 . . . + 2 18 + 16 + . . . + 2 = 2 ( 9 + 8 + . . . + 1 ) = 2 ( ( 9 * 10 ) / 2 ) = 9 * 10 = 90 . answer : a"
Answer: a
Python program:
a = 10 - 1
b = 10 * a
Problem: john is building a rectangular fence around a garden . the length will be 5 feet shorter than its width . if the total area of the garden is 176 square feet , what is the length of the diagonal ( in feet ) ?
Options: a ) between 18 and 19
b ) between 19 and 20
c ) between 20 and 21
d ) between 21 and 22
e ) between 22 and 23
Rationale: to solve this , we first need to set up an equation for the area of the garden . if x is the width , then we have x ( x - 5 ) = 176 . by putting the equation in standard form , we get x ^ 2 - 5 x - 176 = 0 . by using the quadratic formula , we get roots of - 11 and 16 . we know that x is the width , and x - 5 is the length , so by using the roots , we get 16 as the width ( x ) , and 11 as the length ( x - 5 ) . once we have this , we can use the pythagorean theorem to solve for the diagonal . plugging in the length and width , we will get d ^ 2 = 16 ^ 2 + 11 ^ 2 = 256 + 121 = 377 the square root of 377 is less than 20 , since 20 ^ 2 = 400 . going down a number , we can compute 19 ^ 2 = 361 < 377 . therefore , the length of the diagonal must be between 19 and 20 . the correct answer is b .
Answer: b
Python program:
a = 10 + 1 
b = a ** 2
c = 5 + 1 
d = 10 + c 
e = d ** 2
f = b + e 
g = math.sqrt(f)
Problem: divide $ 450 among a , b in the ratio 1 : 4 . how many $ that a get ?
Options: a ) $ 90 , b ) $ 500 , c ) $ 150 , d ) $ 250 , e ) $ 600
Rationale: "sum of ratio terms = 1 + 4 = 5 a = 450 * 1 / 5 = $ 90 answer is a"
Answer: a
Python program:
a = 450 / 1
Problem: 88 % of 370 + 24 % of 210 - ? = 118
Options: a ) 256 , b ) 258 , c ) 268 , d ) 358 , e ) none of these
Rationale: "let 88 % of 370 + 240 % of 210 - x = 118 then , x = ( 88 / 100 * 370 ) + ( 24 / 100 * 210 ) - 118 - 325.60 + 50.40 - 118 = 376 - 118 = 258 correct option : b"
Answer: b
Python program:
a = 88 * 370
b = a / 24
Problem: a train passes a platform in 22 seconds . the same train passes a man standing on the platform in 20 seconds . if the speed of the train is 54 km / hr , the length of the platform is
Options: a ) 40 , b ) 50 , c ) 60 , d ) 30 , e ) 20
Rationale: "speed of the train = 54 km / hr = ( 54 × 10 ) / 36 m / s = 15 m / s length of the train = speed × time taken to cross the man = 15 × 20 = 300 m let the length of the platform = l time taken to cross the platform = ( 300 + l ) / 15 = > ( 300 + l ) / 15 = 12 = > 300 + l = 15 × 22 = 330 = > l = 330 - 300 = 30 meter answer is d ."
Answer: d
Python program:
a = const_0_2778 * 54
b = 22 - 20
c = a * b
Problem: in an election only two candidates contested . a candidate secured 70 % of the valid votes and won by a majority of 184 votes . find the total number of valid votes ?
Options: a ) 430 , b ) 438 , c ) 436 , d ) 434 , e ) 460
Rationale: "let the total number of valid votes be x . 70 % of x = 70 / 100 * x = 7 x / 10 number of votes secured by the other candidate = x - 7 x / 100 = 3 x / 10 given , 7 x / 10 - 3 x / 10 = 184 = > 4 x / 10 = 184 = > 4 x = 1840 = > x = 460 . answer : e"
Answer: e
Python program:
a = 100 - 70
b = 70 - a
c = b / 100
d = 184 / c
Problem: a , b , k start from the same place and travel in the same direction at speeds of 30 km / hr , 40 km / hr , 60 km / hr respectively . b starts four hours after a . if b and k overtake a at the same instant , how many hours after a did k start ?
Options: a ) 3 , b ) 4.5 , c ) 8 , d ) d ) 5.5 , e ) e ) 5
Rationale: "the table you made does n ' t make sense to me . all three meet at the same point means the distance they cover is the same . we know their rates are 30 , 40 and 60 . say the time taken by b is t hrs . then a takes 4 + t hrs . and we need to find the time taken by k . distance covered by a = distance covered by b 30 * ( 4 + t ) = 40 * t t = 12 hrs distance covered by b = distance covered by k 40 * t = 60 * time taken by k time taken by k = 40 * 12 / 60 = 8 hrs time taken by a = 4 + t = 4 + 12 = 16 hrs time taken by k = 8 hrs so k starts 16 - 8 = 8 hrs after a . ( answer c )"
Answer: c
Python program:
a = 40 - 30
Problem: a and b together can complete work in 5 days . a alone starts working and leaves it after working for 3 days completing only half of the work . in how many days it can be completed if the remaining job is undertaken by b ?
Options: a ) 4 , b ) 8 , c ) 15 , d ) 6 , e ) 7
Rationale: "explanation : ( a + b ) one day work = 1 / 5 now a does half of the work in 3 days so a can complete the whole work in 6 days a ’ s one day work = 1 / 6 b ’ s one day work = 1 / 5 - 1 / 6 = 1 / 30 b alone can complete the work in 30 days so half of the work in 15 days answer : option c"
Answer: c
Python program:
a = 3 / 5
b = 5 * a
Problem: a rectangular plot measuring 15 meters by 50 meters is to be enclosed by wire fencing . if the poles of the fence are kept 5 meters apart . how many poles will be needed ?
Options: a ) 46 m , b ) 26 m , c ) 26 m , d ) 56 m , e ) 25 m
Rationale: "perimeter of the plot = 2 ( 15 + 50 ) = 130 m no of poles = 130 / 5 = 26 m answer : b"
Answer: b
Python program:
a = 15 + 50 
b = a * 2
c = b / 5
Problem: if a train , travelling at a speed of 270 kmph , crosses a pole in 5 sec , then the length of train is ?
Options: a ) 281 m , b ) 325 m , c ) 117 m , d ) 375 m , e ) 350 m
Rationale: "d d = 270 * 5 / 18 * 5 = 375 m"
Answer: d
Python program:
a = 270 * const_0_2778
b = a * 5
Problem: a certain car uses one gallon of gasoline every 36 miles when it travels on highway , and one gallon of gasoline every 20 miles when it travels in the city . when a car travels 4 miles on highway and 4 additional miles in the city , it uses what percent more gasoline than if it travels 8 miles on the highway ?
Options: a ) 15 % , b ) 20 % , c ) 22.5 % , d ) 25 % , e ) 40 %
Rationale: "4 miles on the highway = 4 / 36 gallons ; 4 miles in the city = 4 / 20 gallons ; total = 4 / 36 + 4 / 20 = 14 / 45 gallons . 8 miles on the highway = 8 / 30 gallons . the % change = ( 14 / 45 - 8 / 36 ) / ( 8 / 36 ) = 0.40 . answer : e ."
Answer: e
Python program:
a = 1 / 20
b = a * 4
c = 1 / 36
d = 4 * c
e = b + d 
f = 1 / 36
g = 8 * f
h = e - g
i = 1 / 36
j = 8 * i
k = h / j
l = k * 100
Problem: the calendar of the year 2060 can be used again in the year ?
Options: a ) 2081 , b ) 2083 , c ) 2088 , d ) 1971 , e ) 1973
Rationale: "explanation : given year 2060 when divided by 4 , leaves a remainder 0 . note : when remainder is 0 , 28 is added to the given year to get the result . so , 2060 + 28 = 2088 answer : c"
Answer: c
Python program:
a = 4 * 4
b = a - 2
c = b * 2
d = c + 2060
Problem: mixture a is 40 percent alcohol , and mixture b is 80 percent alcohol . if the two are poured together to create a 4 - gallon mixture that contains 50 percent alcohol , approximately how many gallons of mixture a are in the mixture ?
Options: a ) 1.5 , b ) 1.7 , c ) 2.3 , d ) 2.5 , e ) 2.4
Rationale: "( 80 - 50 ) / ( 50 - 40 ) = qa / qb 30 / 10 = qa / qb 3 / 1 = qa / qb qa = ( 3 / 5 ) * 4 = 12 / 5 = 2.4 approx answer : e"
Answer: e
Python program:
a = 40 * 80
b = a / 80
c = b / 2
Problem: the length of each side of square a is increased by 100 percent to make square b . if the length of the side of square b is increased by 75 percent to make square c , by what percent is the area of square c greater than the sum of the areas of squares a and b ?
Options: a ) 75 % , b ) 80 % , c ) 145 % , d ) 150 % , e ) 180 %
Rationale: "let length of each side of square a be 10 area of a = 10 ^ 2 = 100 since , length of each side of square a is increased by 100 percent to make square b length of each side of square b = 2 * 10 = 20 area of b = 20 ^ 2 = 400 since , length of the side of square b is increased by 75 percent to make square c length of each side of square c = 1.75 * 20 = 35 area of c = 35 ^ 2 = 1225 difference in areas of c and cummulative areas of a and b = 1225 - ( 400 + 100 ) = 725 percent is the area of square c greater than the sum of the areas of squares a and b = ( 725 / 500 ) * 100 % = 145 % answer c"
Answer: c
Python program:
a = 100 / 100
b = 1 + a 
c = 100 / 100
d = 1 + c 
e = d * 75
f = e / 100
g = b + f 
h = square_area - (
i = h - 1
j = i / 4
k = 100 / 100
l = 1 + k 
m = 1 + square_area 
n = j * m
Problem: the temperature of a certain cup of coffee 15 minutes after it was poured was 120 degrees fahrenheit . if the temperature f of the coffee t minutes after it was poured can be determined by the formula f = 120 * 2 ^ ( - at ) + 60 , where f is in degrees fahrenheit and a is a constant . then the temperature of the coffee 30 minutes after it was poured was how many degrees fahrenheit ?
Options: a ) 65 , b ) 75 , c ) 80 , d ) 85 , e ) 90
Rationale: "first , we have to find a . we know that after t = 15 minutes the temperature f = 120 degrees . hence : 120 = 120 * ( 2 ^ - 15 a ) + 60 60 = 120 * ( 2 ^ - 15 a ) 60 / 120 = 2 ^ - 15 a 1 / 2 = 2 ^ - 15 a 2 ^ - 1 = 2 ^ - 15 a - 1 = - 15 a 1 / 15 = a now we need to find f after t = 30 minutes : f = 120 * ( 2 ^ - 1 / 15 * 30 ) + 60 f = 120 * ( 2 ^ - 2 ) + 60 f = 120 * ( 1 / 2 ^ 2 ) + 60 f = 120 * 1 / 4 + 60 f = 30 + 60 = 90 answer e !"
Answer: e
Python program:
a = 60 / 15
b = 1 - 2
c = a * b
d = 2 ** c
e = d * 120
f = e + 60
Problem: p and q are the only two applicants qualified for a short - term research project that pays 480 dollars in total . candidate p has more experience and , if hired , would be paid 50 percent more per hour than candidate q would be paid . candidate q , if hired , would require 10 hours more than candidate p to do the job . candidate p ’ s hourly wage is how many dollars greater than candidate q ’ s hourly wage ?
Options: a ) $ 5 , b ) $ 8 , c ) $ 11 , d ) $ 14 , e ) $ 17
Rationale: "let q ' s hourly wage be x , then p ' s hourly wage is 1.5 x let t be the number of hours that q needs , then p needs t - 10 hours to do the job . since they both are paid an equal total amount of $ 480 : x * t = 1.5 x * ( t - 10 ) t = 30 hours and q ' s hourly wage is 480 / 30 = $ 16 p ' s hourly wage is 480 / ( t - 10 ) = $ 24 which is $ 8 per hour more . the answer is b ."
Answer: b
Python program:
a = 3 / 2
b = a - 1
c = 10 / b
d = 480 / c
e = 3 / 2
f = e - 1
g = 10 / f
h = g + 10 
i = 480 / h
j = d - i
Problem: what profit percent is made by selling an article at a certain price , if by selling at 1 / 3 rd of that price , there would be a loss of 20 % ?
Options: a ) 140 % , b ) 29 % , c ) 70 % , d ) 27 % , e ) 28 %
Rationale: "sp 2 = 1 / 3 sp 1 cp = 100 sp 2 = 80 1 / 3 sp 1 = 80 sp 1 = 240 100 - - - 240 = > 140 % answer : a"
Answer: a
Python program:
a = 100 - 20
b = 1 / 3
c = a / b
d = c - 100
Problem: a certain company had a total annual expenditure of 1.89 ∗ 10 ^ 7 on employee salaries last year . if the company employed 420 people , what was the average employee salary ?
Options: a ) $ 20,000 , b ) $ 25,000 , c ) $ 35,000 , d ) $ 40,000 , e ) $ 45,000
Rationale: "given : total annual expenditure of 1.89 ∗ 10 ^ 7 on employee salaries total employees = 420 observe that 420 * 4 = 1890 therefore try to bring the numerator in terms of 1890 average salary = ( 1890 * 10 ^ 4 ) / 420 = 4.5 * 10 ^ 4 = 45,000 option e"
Answer: e
Python program:
a = 10 * 7
b = 1 * 89
c = b / 420
d = c * 100
Problem: the timing of a college is from 12 p . m to 4.00 p . m . five lectures are held in the given duration and a break of 5 minutes after each lecture is given to the students . find the duration of each lecture .
Options: a ) 52 minutes , b ) 45 minutes , c ) 30 minutes , d ) 48 minutes , e ) 44 minutes
Rationale: "explanation : total time a student spends in college = 4 hours 00 minutes = 240 minutes as there are 5 lectures , the number of breaks between lectures is 4 . total time of the break = 20 minutes hence , the duration of each lecture is = ( 240 â € “ 20 ) / 5 = 44 minutes answer e"
Answer: e
Python program:
a = 4 * 0
b = a / 5