euclaise/mathqa_programs huggingface dataset:
Problem: a pupil ' s marks were wrongly entered as 73 instead of 63 . due to the average marks for the class got increased by half . the number of pupils in the class is ?
Options: a ) 18 , b ) 82 , c ) 20 , d ) 27 , e ) 29
Rationale: "let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 x / 2 = ( 73 - 63 ) = > x / 2 = 10 = > x = 20 . answer : c"
Answer: c
Python program:
a = 73 - 63
b = a * 2
Problem: in the coordinate plane , one of the vertices of a square is the point ( - 3 , - 4 ) . if the diagonals of that square intersect at point ( 4 , 2 ) , what is the area of that square ?
Options: a ) 196 , b ) 125 , c ) 140 , d ) 128 , e ) 134
Rationale: "one point ( - 3 - 4 ) , intersection ( 4,2 ) so the distance from the first point - 3 - 4 = - 7 is the midpoint of the square - - > whole side 14 , 14 * 14 = 196 a"
Answer: a
Python program:
a = 3 * 4
b = 3 * 4
c = a * b
Problem: a sports equipment store sold ping pong rackets for a total of $ 588 . if the average ( arithmetic mean ) price of a pair of rackets is $ 9.8 , how many pairs were sold ?
Options: a ) 50 , b ) 60 , c ) 490 , d ) 500 , e ) 980
Rationale: "average price for a pair of rackets = $ 9.8 total cost = $ 9.8 * x = $ 588 x = 60 pairs were sold . answer : b"
Answer: b
Python program:
a = 588 / 9
Problem: if a is a positive integer , and if the units digit of a ^ 2 is 1 and the units digit of ( a + 1 ) ^ 2 is 4 , what is the units digit of ( a + 2 ) ^ 2 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "if the units digit of a ^ 2 is 1 , then the units digit of a is either 1 or 9 . if the units digit of ( a + 1 ) ^ 2 is 4 , then the units digit of a + 1 is either 2 or 8 . to satisfy both conditions , the units digit of a must be 1 . then a + 2 has the units digit of 3 , thus the units digit of ( a + 2 ) ^ 2 will be 9 . the answer is e ."
Answer: e
Python program:
a = 1 * 2
b = a + 2 
c = b ** 2
Problem: the difference between simple interest and compound interest on $ 1200 for one year at 10 % per annum reckoned half - yearly is :
Options: a ) $ 5 , b ) $ 8 , c ) $ 9 , d ) $ 3 , e ) $ 7
Rationale: "s . i = $ [ ( 1200 * 10 * 1 ) / 100 ] = $ 120 . c . i = $ [ 1200 * ( 1 + ( 5 / 100 ) ^ 2 ) - 1200 ] = $ 123 . difference = $ ( 123 - 120 ) = $ 3 . answer ( d )"
Answer: d
Python program:
a = 10 / 2
b = a / 100
c = b + 1 
d = c ** 2
e = d * 1200
f = e - 1200
g = 1200 * 10
h = g / 100
i = f - h
Problem: a train 110 meters long takes 6 seconds to cross a man walking at 5 kmph in the direction opposite to that of the train . find the speed of the train .
Options: a ) 45 kmph , b ) 50 kmph , c ) 55 kmph , d ) 61 kmph , e ) 70 kmph
Rationale: explanation : let the speed of the train be x kmph . speed of the train relative to man = ( x + 5 ) kmph = ( x + 5 ) × 5 / 18 m / sec . therefore 110 / ( ( x + 5 ) × 5 / 18 ) = 6 < = > 30 ( x + 5 ) = 1980 < = > x = 61 speed of the train is 61 kmph . answer : option d
Answer: d
Python program:
a = 6 * const_0_2778
b = 110 / a
c = b - 5
Problem: the price of a bushel of corn is currently $ 3.20 , and the price of a peck of wheat is $ 5.80 . the price of corn is increasing at a constant rate of 5 x 5 x cents per day while the price of wheat is decreasing at a constant rate of 2 √ ∗ x − x 2 ∗ x − x cents per day . what is the approximate price when a bushel of corn costs the same amount as a peck of wheat ?
Options: a ) $ 4.50 , b ) $ 5.10 , c ) $ 5.30 , d ) $ 5.50 , e ) $ 5.60
Rationale: "let yy be the # of days when these two bushels will have the same price . first let ' s simplify the formula given for the rate of decrease of the price of wheat : 2 √ ∗ x − x = 1.41 x − x = 0.41 x 2 ∗ x − x = 1.41 x − x = 0.41 x , this means that the price of wheat decreases by 0.41 x 0.41 x cents per day , in yy days it ' ll decrease by 0.41 xy 0.41 xy cents ; as price of corn increases 5 x 5 x cents per day , in yy days it ' ll will increase by 5 xy 5 xy cents ; set the equation : 320 + 5 xy = 580 − 0.41 xy 320 + 5 xy = 580 − 0.41 xy , solve for xyxy - - > xy = 48 xy = 48 ; the cost of a bushel of corn in yy days ( the # of days when these two bushels will have the same price ) will be 320 + 5 xy = 320 + 5 ∗ 48 = 560320 + 5 xy = 320 + 5 ∗ 48 = 560 or $ 5.6 . answer : e ."
Answer: e
Python program:
a = 5 - 80
b = math.sqrt(5)
c = b - 2
d = 5 + c 
e = a / d
f = e * 5
g = 3 + 20
Problem: find a positive number which when increased by 17 is equal to 60 times the reciprocal of the number
Options: a ) 17 , b ) 15 , c ) 12 , d ) 8 , e ) 3
Rationale: "f the number is x , then , x + 17 = 60 / x x 2 + 17 x - 60 = 0 ( x + 20 ) ( x - 3 ) = 0 x = 3 , - 20 , so x = 3 ( as 3 is positive ) answer : e"
Answer: e
Python program:
a = math.gcd(60, 17)
b = 2 + a
Problem: the length of a rectangular garden is three times its width . if the area of the rectangular garden is 588 square meters , then what is the width of the rectangular garden ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: "let x be the width of the garden . 3 x ^ 2 = 588 x ^ 2 = 196 x = 14 the answer is c ."
Answer: c
Python program:
a = 588 / 3
b = math.sqrt(a)
Problem: a train 360 m long is running at a speed of 72 km / hr . in what time will it pass a bridge 140 m long ?
Options: a ) 40 sec , b ) 29 sec , c ) 25 sec , d ) 27 sec , e ) 34 sec
Rationale: "speed = 72 * 5 / 18 = 20 m / sec total distance covered = 360 + 140 = 500 m required time = 500 * 1 / 20 = 25 sec answer : c"
Answer: c
Python program:
a = 72 - 140
b = a * const_0_2778
c = 360 / b
Problem: if 20 typists can type 48 letters in 20 minutes , then how many letters will 30 typists working at the same rate complete in 1 hour ?
Options: a ) 63 , b ) 72 , c ) 144 , d ) 216 , e ) 400
Rationale: "20 typists can type 48 letters , so 30 typists can type = 48 * 30 / 20 48 * 30 / 20 letters can be typed in 20 mins . in 60 mins typist can type = 48 * 30 * 60 / 20 * 20 = 216 d is the answer"
Answer: d
Python program:
a = 48 * 3
b = a / 20
c = b * 30
Problem: a car traveling at a certain constant speed takes 15 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 60 kilometers per hour . at what speed , in kilometers per hour , is the car traveling ?
Options: a ) 48 , b ) 50 , c ) 52 , d ) 54 , e ) 56
Rationale: "60 * t = 1 km = > t = 1 / 60 km / h v * ( t + 15 / 3600 ) = 1 v ( 1 / 60 + 15 / 3600 ) = 1 v ( 75 / 3600 ) = 1 v = 48 km / h the answer is a ."
Answer: a
Python program:
a = 1 / 60
b = 3600 * a
c = b + 15 
d = c / 3600
e = 1 / d
Problem: p and q started a business investing rs . 96,000 and rs . 28,000 respectively . in what ratio the profit earned after 2 years be divided between p and q respectively ?
Options: a ) 17 : 6 , b ) 24 : 7 , c ) 25 : 6 , d ) 21 : 3 , e ) 17 : 4
Rationale: "p : q = 96000 : 28000 = 24 : 7 answer : b"
Answer: b
Python program:
a = 2 + 3 
b = a + 3 
c = 2 + 3 
d = c * 2
e = b * d
f = 2 + 3 
g = e + f 
h = 2 + 3 
i = h * 2
j = 3 * i
k = 2 + 3 
l = j + k 
m = g / l
Problem: a train 90 m long running at 56 kmph crosses a platform in 18 sec . what is the length of the platform ?
Options: a ) 190 , b ) 200 , c ) 180 , d ) 881 , e ) 271
Rationale: "d = 56 * 5 / 18 = 25 = 280 – 90 = 190 answer : a"
Answer: a
Python program:
a = 56 * const_0_2778
b = 18 * a
c = b - 90
Problem: a card is drawn from a pack of 52 cards . the probability of ge ƫ ng a queen of club or a king of heart is
Options: a ) 1 / 13 , b ) 2 / 13 , c ) 1 / 26 , d ) 1 / 52 , e ) none of these
Rationale: "explanation : total number of cases = 52 favourable cases = 2 probability = 2 / 56 = 1 / 26 answer : c"
Answer: c
Python program:
a = 4 * 4
b = 52 - a
c = b / 52
Problem: this topic is locked . if you want to discuss this question please re - post it in the respective forum . matt and peter can do together a piece of work in 20 days . after they have worked together for 12 days matt stops and peter completes the remaining work in 14 days . in how many days peter complete the work separately .
Options: a ) 26 days , b ) 27 days , c ) 23 days , d ) 35 days , e ) 24 days
Rationale: together they complete the job in 20 days means they complete 12 / 20 of the job after 12 days . peter completes the remaining ( 8 / 20 ) of the job in 14 days which means that the whole job ( 1 ) can be completed in x days . < = > 8 / 20 - > 14 < = > x = 14 / ( 8 / 20 ) = 35 thus the answer is d .
Answer: d
Python program:
a = 1 / 2
b = a * 14
c = 14 * 2
d = b + c
Problem: we bought a total of 80 books at the store . math books cost $ 4 and history books cost $ 5 . the total price was $ 373 . how many math books did we buy ?
Options: a ) 23 , b ) 27 , c ) 31 , d ) 35 , e ) 39
Rationale: "m + h = 80 h = 80 - m 4 m + 5 h = 373 4 m + 5 * ( 80 - m ) = 373 m = 27 the answer is b ."
Answer: b
Python program:
a = 80 * 4
b = 373 - a
c = 80 - b
Problem: if a , b , c , d , e and f are integers and ( ab + cdef ) < 0 , then what is the maximum number s of integers that can be negative ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "minimuum should be 1 maximum should be 4 : 1 out of a or b to make the multiplication negative 3 out of c , d , e or f to make the multiplication negative . negative + negative < 0 answer : c maximum will be 5 . . you dont require both the multiplicatin to be negative for entire equation to be negative . . . any one a or b can be negative to make ab negative and it can still be more ( away from 0 ) than the multiplication of 4 other - ve numbers . . . actually by writing minimum required as 1 out of 6 , you are actually meaning s = 5 out of 6 also possible as you will see 5 or 1 will give you same equation . . ans d"
Answer: d
Python program:
a = 10 / 2
b = a + 0
Problem: a monkey ascends a greased pole 14 metres high . he ascends 2 metres in first minute and slips down 1 metre in the alternate minute . in which minute , he reaches the top ?
Options: a ) 25 th , b ) 22 nd , c ) 23 rd , d ) 24 th , e ) none of these
Rationale: "in 2 minutes , he ascends = 1 metre â ˆ ´ 12 metres , he ascends in 24 minutes . â ˆ ´ he reaches the top in 25 th minute . answer a"
Answer: a
Python program:
a = 2 * 14
b = a - 1
Problem: due to a reduction of 25 / 4 % in the price of sugar , a man is able to buy 1 kg more for rs . 120 . find the original rate of sugar .
Options: a ) 7 , b ) 8 , c ) 8.5 , d ) 9 , e ) 9.5
Rationale: rate reduced by 6.25 % , so amount rs 120 reduced by = ( 6.25 / 100 ) * 120 = 7.5 so in rs 7.5 extra sugar obtained is 1 kg i . e . new rate is rs . 7.5 per kg thus original rate = [ 7.5 / ( 100 – 6.25 ) ] / 100 = 7.5 / 0.9375 = rs . 8 answer : option b
Answer: b
Python program:
a = 25 / 4
b = a / 100
c = b * 120
d = 25 / 4
e = 100 - d
f = e / 100
g = c / f
Problem: on a test average ( arithmetic mean ) test score for 9 students is 80 . what must be 10 th student ' s score that average score for 10 students to be 82 ?
Options: a ) 100 , b ) 90 , c ) 80 , d ) 70 , e ) 60
Rationale: "( 9 * 80 + x ) / 10 = 82 x = ( 10 * 82 ) - ( 9 * 80 ) x = 820 - 720 total score required 820 - 720 = 100 correct answer is a"
Answer: a
Python program:
a = 82 * 10
b = 9 * 80
c = a - b
Problem: a man can row 4 kmph in still water . when the river is running at 1.8 kmph , it takes him 1 hour to row to a place and black . what is the total distance traveled by the man ?
Options: a ) 7.13 , b ) 6.19 , c ) 4.12 , d ) 3.19 , e ) 4.21
Rationale: "m = 4 s = 1.8 ds = 5.8 us = 2.2 x / 5.8 + x / 2.2 = 1 x = 1.59 d = 1.59 * 2 = 3.19 answer : b"
Answer: b
Python program:
a = 4 + 1 
b = 4 - 1
c = a * b
d = 4 + 1 
e = 4 - 1
f = d + e 
g = c / f
h = g * 2
Problem: the annual interest rate earned by an investment increased by 5 percent from last year to this year . if the annual interest rate earned by the investment this year was 26.25 percent , what was the annual interest rate last year ?
Options: a ) 25 % , b ) 24 % , c ) 23 % , d ) 22 % , e ) 21 %
Rationale: "let i = interest rate i ( this year ) = i ( last year ) + 0.05 i ( last year ) = 1.05 i ( last year ) 26.25 = 1.05 x i ( last year ) i ( last year ) = 26.25 / 1.05 = 2625 / 105 = 25 % answer : a"
Answer: a
Python program:
a = 26 * 25
b = 26 + 25 
c = a / b
Problem: a certain farmer pays $ 30 per acre per month to rent farmland . how much does the farmer pay per month to rent a rectangular plot of farmland that is 360 feet by 1210 feet ? ( 43,560 square feet = 1 acre )
Options: a ) $ 5,330
b ) $ 3,360
c ) $ 1,350
d ) $ 300
e ) $ 150
Rationale: basically the question an error . 1 acre = 43,560 square feet and if it is then the answer is 300 ( d )
Answer: d
Python program:
a = 360 * 1210
b = 360 * 1210
c = b / 10
d = a / c
e = 30 * d
Problem: how many multiples of 7 are there between 21 and 343 , inclusive ?
Options: a ) 48 , b ) 47 , c ) 46 , d ) 45 , e ) 44
Rationale: "7 * 3 = 21 7 * 49 = 343 total multiples = ( 49 - 3 ) + 1 = 47 include 21 and 343 = 47 answer is b"
Answer: b
Python program:
a = 343 - 21
b = a / 7
c = b + 1
Problem: in an office in singapore there are 60 % female employees . 50 % of all the male employees are computer literate . if there are total 62 % employees computer literate out of total 1600 employees , then the no . of female employees who are computer literate ?
Options: a ) 690 , b ) 674 , c ) 672 , d ) 960 , e ) none
Rationale: "solution : total employees , = 1600 female employees , 60 % of 1600 . = ( 60 * 1600 ) / 100 = 960 . then male employees , = 640 50 % of male are computer literate , = 320 male computer literate . 62 % of total employees are computer literate , = ( 62 * 1600 ) / 100 = 992 computer literate . thus , female computer literate = 992 - 320 = 672 . answer : option c"
Answer: c
Python program:
a = 62 / 100
b = 60 / 100
c = 1 - b
d = 50 / 100
e = c * d
f = a - e
g = f * 1600
Problem: shop offered 20 % offer for every shirt , smith bought a shirt at rs . 560 . and what was the shop ' s original selling price ?
Options: a ) 500 , b ) 550 , c ) 600 , d ) 700 , e ) 750
Rationale: "sp * ( 80 / 100 ) = 560 sp = 70 * 100 = > cp = 700 answer : d"
Answer: d
Python program:
a = 20 / 100
b = 1 - a
c = 560 / b
Problem: the present worth of $ 3600 due in 2 years at 20 % per annum compound interest is ?
Options: a ) $ 1200 , b ) $ 1850 , c ) $ 2010 , d ) $ 3200 , e ) $ 2500
Rationale: present worth = 3600 / ( 1 + 20 / 100 ) ^ 2 = 3600 * 5 / 6 * 5 / 6 = $ 2500 answer is e
Answer: e
Python program:
a = 20 / 100
b = a + 1 
c = b ** 2
d = 3600 / c
Problem: if the wheel is 19 cm then the number of revolutions to cover a distance of 1156 cm is ?
Options: a ) 11 , b ) 14 , c ) 18 , d ) 10 , e ) 19
Rationale: 2 * 22 / 7 * 19 * x = 1156 = > x = 9.7 answer : d
Answer: d
Python program:
a = 3 * 100
b = 1 * 10
c = a + b 
d = c + 4 
e = d / 100
f = 2 * e
g = f * 19
h = 1156 / g
Problem: harkamal purchased 8 kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 60 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) a ) 1055 , b ) b ) 1075 , c ) c ) 1065 , d ) d ) 1070 , e ) e ) 1100
Rationale: cost of 8 kg grapes = 70 × 8 = 560 . cost of 9 kg of mangoes = 60 × 9 = 540 . total cost he has to pay = 560 + 540 = 1100 . e )
Answer: e
Python program:
a = 8 * 70
b = 9 * 60
c = a + b
Problem: the commuter rail between scottsdale and sherbourne is 200 km of track , and one train makes a round trip in 5 hours . if harsha boards the train at the forest grove station , which is located one fifth of the track ' s length out from scottsdale , how long will it take her to get to sherbourne ?
Options: a ) . 5 hours , b ) 1 hour , c ) 1.5 hours , d ) 2 hours , e ) 2.5 hours
Rationale: distance between scottsdale and sherbourne = 200 km time for a one - way trip between scottsdale and sherbourne : 5 / 2 = 2.5 hours distance between forest grove and scottsdale : 200 / 5 = 40 km distance between forest grove and sherbourne : 40 x 4 = 160 km time between scottsdale and forest grove : 2.5 / 5 = . 5 hours time between forest grove and sherborne : . 5 x 4 = 2 hours .
Answer: d
Python program:
a = 200 / 5
b = 5 / 2
c = a * b
d = 200 / c
Problem: excluding stoppages , the speed of a train is 45 kmph and including stoppages it is 35 kmph . of how many minutes does the train stop per hour ?
Options: a ) 73 , b ) 83 , c ) 12 , d ) 13 , e ) 28
Rationale: "explanation : t = 10 / 45 * 60 = 13 answer : option d"
Answer: d
Python program:
a = 35 / 45
b = const_60 * a
c = const_60 - b
Problem: if the price of a certain bond on may 1 st was 2 / 3 the price of the bond on june 1 st and the price of the bond on july 1 st was 25 % greater than the price of the bond on may 1 st . then the price of the bond on june 1 st st was what percent of the average ( arithmetic mean ) price of the bond on may 1 st and july 1 st ?
Options: a ) 50 % , b ) 75 % , c ) 120 % , d ) 133 1 / 3 % , e ) 150 %
Rationale: "the price on june 1 st = 12 ( assume ) ; the price on may 1 st = 2 / 3 * 12 = 8 ; the price on july 1 st = 8 * 1.25 = 10 . the average price of the bond on may 1 st and july 1 st = ( 8 + 10 ) / 2 = 9 . the price of the bond on june 1 st ( 12 ) is 4 / 3 times ( 134 % ) the average price of the bond on may 1 st and july 1 st . answer : d ."
Answer: d
Python program:
a = 25 * const_0_33
b = 100 + const_0_33 
c = a + b
Problem: to asphalt 1 km road , 30 men spent 12 days working 8 hours per day . how many days , 20 men will spend to asphalt a road of 2 km working 10 hours a day ?
Options: a ) 28.8 , b ) 30 , c ) 32 , d ) 34 , e ) 36
Rationale: "man - hours required to asphalt 1 km road = 30 * 12 * 8 = 2880 man - hours required to asphalt 2 km road = 2880 * 2 = 5760 man - hours available per day = 20 * 10 = 200 therefore number of days = 5760 / 200 = 28.8 days ans = a"
Answer: a
Python program:
a = 30 * 12
b = a * 8
c = b * 2
d = 20 * 10
e = c / d
Problem: two good train each 900 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 ) 12.2 sec , b ) 24.9 sec , c ) 86.4 sec , d ) 60.2 sec , e ) none
Rationale: "sol . relative speed = ( 45 + 30 ) km / hr = ( 75 x 5 / 18 ) m / sec = ( 125 / 6 ) m / sec . distance covered = ( 900 + 900 ) m = 1000 m . required time = ( 1800 x 6 / 125 ) sec = 86.4 sec . answer c"
Answer: c
Python program:
a = 45 + 30 
b = a * const_0_2778
c = 1/(b)
d = 900 * c
e = d * 2
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 e 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 e 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: uncle bruce is baking chocolate chip cookies . he has 72 ounces of dough ( with no chocolate ) and 50 ounces of chocolate . how much chocolate is left over if he uses all the dough but only wants the cookies to consist of 40 % chocolate ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 2 , e ) 10
Rationale: "first , you must find the total weight of the mixture given that 80 % of it will be dough . 60 % * total = 72 = > ( 6 / 10 ) total = 72 = > total = 720 / 6 = > total = 120 oz , from there , you must find 10 % of the total 40 oz of the mixture . 40 % * total = > ( 4 / 10 ) ( 120 ) = 48 oz choclate used , not forgetting that the question asks how much chocolate is left over we must subtract the chocolate used from the initial chocolate . 50 - 48 oz = 2 oz chocolate left over . answer : d"
Answer: d
Python program:
a = 40 / 100
b = a * 40
Problem: 107 ã — 107 + 93 ã — 93 = ?
Options: a ) 20198 , b ) 20098 , c ) 20000 , d ) 20088 , e ) 20085
Rationale: "explanation : ( a + b ) 2 + ( a â ˆ ’ b ) 2 = 2 ( a 2 + b 2 ) ( reference : basic algebraic formulas ) 1072 + 932 = ( 100 + 7 ) 2 + ( 100 â ˆ ’ 7 ) 2 = 2 ( 1002 + 72 ) = 2 ( 10000 + 49 ) = 20098 . answer : option b"
Answer: b
Python program:
a = 107 ** 2
b = a - 107
c = 93 ** 2
d = c - 93
e = b + d
Problem: how many integers from 100 to 800 , inclusive , remains the value unchanged when the digits were reversed ?
Options: a ) 50 , b ) 60 , c ) 80 , d ) 70 , e ) 90
Rationale: "question is asking for palindrome first digit possibilities - 1 through 7 = 7 8 is not possible here because it would result in a number greater than 8 ( i . e 808 , 818 . . ) second digit possibilities - 0 though 9 = 10 third digit is same as first digit = > total possible number meeting the given conditions = 7 * 10 = 70 answer is d ."
Answer: d
Python program:
a = 800 / 10
Problem: a part - time employee whose hourly wage was increased by 50 percent decided to reduce the number of hours worked per week so that the employee ' s total weekly income would remain unchanged . by what percent should the number of hours worked be reduced ?
Options: a ) 9 , b ) 13 , c ) 17 , d ) 20 , e ) 33.33
Rationale: "let original hourly wage be x and let the no of hours worked be y total wage will be = x * y after the increment the wage will be = 1.5 x now we need to find number of hours worked so that x * y = 1.5 x * z i . e z = 1 / 1.5 y = 2 / 3 y % decrease = ( y - 2 / 3 y ) / y * 100 = 100 / 3 = 33.33 % . thus my answer is e ."
Answer: e
Python program:
a = 50 + 100 
b = a / 100
c = b * 50
d = 1 / c
e = d * 100
Problem: pascal has 96 miles remaining to complete his cycling trip . if he reduced his current speed by 4 miles per hour , the remainder of the trip would take him 16 hours longer than it would if he increased his speed by 50 % . what is his current speed w ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 16
Rationale: "let the current speed be x miles per hour . time taken if speed is 50 % faster ( i . e . 3 x / 2 = 1.5 x ) = 96 / 1.5 x time taken if speed is reduced by 4 miles / hr ( i . e . ( x - 4 ) ) = 96 / ( x - 4 ) as per question , 96 / ( x - 4 ) - 96 / 1.5 x = 16 solving this w we get x = 8 . b ."
Answer: b
Python program:
a = 96 / 16
b = 96 / 16
c = 50 / 100
d = 1 + c 
e = b / d
f = e * 4
g = f * 4
h = 96 / 16
i = h ** 2
j = g + i 
k = math.sqrt(j)
l = a + k 
m = l / 2
Problem: 653 ã — 1001 = ?
Options: a ) 649011 , b ) 540041 , c ) 654321 , d ) 653001 , e ) 643001
Rationale: "653 ã — ( 1000 + 1 ) 653000 + 1 653001 answer d"
Answer: d
Python program:
a = 653 / 1001
b = a * 100
Problem: pascal has 96 miles remaining to complete his cycling trip . if he reduced his current speed by 4 miles per hour , the remainder of the trip would take him 16 hours longer than it would if he increased his speed by 50 % . what is his current speed x ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 16
Rationale: "let the current speed be x miles per hour . time taken if speed is 50 % faster ( i . e . 3 x / 2 = 1.5 x ) = 96 / 1.5 x time taken if speed is reduced by 4 miles / hr ( i . e . ( x - 4 ) ) = 96 / ( x - 4 ) as per question , 96 / ( x - 4 ) - 96 / 1.5 x = 16 solving this x we get x = 8 . b ."
Answer: b
Python program:
a = 96 / 16
b = 96 / 16
c = 50 / 100
d = 1 + c 
e = b / d
f = e * 4
g = f * 4
h = 96 / 16
i = h ** 2
j = g + i 
k = math.sqrt(j)
l = a + k 
m = l / 2
Problem: at a certain college , 50 percent of the total number of students are freshmen . if 40 percent of the fresh - men are enrolled in the school of liberal arts and , of these , 20 percent are psychology majors , what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts ?
Options: a ) 14 % , b ) 4 % , c ) 15 % , d ) 5 % , e ) 25 %
Rationale: "let ' s say there is a total of 100 students at this college . 50 percent of the total number of students are freshmen . # of freshmen = 50 % of 100 = 50 40 percent of the fresh - men are enrolled in the school of liberal arts . . . number of liberal arts freshmen = 40 % of 50 = 20 . . . and , of these , 20 percent are psychology majors . . . number of liberal arts freshmen who are psychology majors = 20 % of 20 = 4 what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts ? 4 / 100 = 4 % answer : b"
Answer: b
Python program:
a = 50 * 40
b = a / 100
c = b * 20
d = c / 100