euclaise/mathqa_programs huggingface dataset:
Problem: in the xy - plane , a triangle has vertices ( 0,0 ) , ( 4,0 ) and ( 4,8 ) . if a point ( a , b ) is selected at random from the triangular region , what is the probability that a - b > 0 ?
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 4 / 5
Rationale: "the area of the right triangle is ( 1 / 2 ) * 4 * 8 = 16 . only the points ( a , b ) below the line y = x satisfy a - b > 0 . the part of the triangle which is below the line y = x has an area of ( 1 / 2 ) ( 4 ) ( 4 ) = 8 . p ( a - b > 0 ) = 8 / 16 = 1 / 2 the answer is c ."
Answer: c
Python program:
a = 0 + 0 
b = 4 / a
Problem: the speed of a boat in still water is 15 km / hr and the rate of current is 3 km / hr the distance travelled downstream in 12 minutes is :
Options: a ) 2 km , b ) 2.6 km , c ) 3.6 km , d ) 4 km , e ) none
Rationale: sol . speed downstream = ( 15 + 3 ) kmph = 18 kmph . distance travelled = [ 18 * 12 / 60 ] km = 3.6 km . answer c
Answer: c
Python program:
a = 12 / const_60
b = 15 + 3 
c = a * b
Problem: two cubes each with side b are joined to form a cuboids . what is the surface area of this cuboids ?
Options: a ) 12 b ^ 2
b ) 10 b ^ 2
c ) 6 b ^ 2
d ) 4 b ^ 2
e ) 2 b ^ 2
Rationale: l = 2 b ; b = b ; h = b ; surface area = 2 * ( lb + bh + hl ) = 2 * ( 2 b ^ 2 + b ^ 2 + 2 b ^ 2 ) = 10 b ^ 2 answer : b
Answer: b
Python program:
a = 1 * 2
b = a * 2
c = 1 * 1
d = b + c 
e = d * 2
Problem: bob is attempting to feed his pets . he feeds his pets as follows : - no dog receives more food than any other dog - no cat receives any less food than any other cat - the cats , as a group , receive exactly as much food as a single dog if bob has 7 dogs and 4 cats , approximately what percentage of the food bag does a cat receive ?
Options: a ) 25.0 % , b ) 8.3 % , c ) 3.1 % , d ) 2.7 % , e ) 1.0 %
Rationale: c . each cat gets 1 / 4 as much food as a dog . a dog gets 1 / 8 of the food . 1 / 4 of 1 / 8 is 1 / 32 , which is about 3.1 % , so the answer is c .
Answer: c
Python program:
a = 7 * 4
b = a + 4 
c = 1 / b
d = c * 100
Problem: in the xy - coordinate plane , the graph of y = - x ^ 2 + 9 intersects line l at ( p , 5 ) and ( t , 7 ) . what is the least possible value of the slope of line l ?
Options: a ) 6 , b ) 2 , c ) - 2 , d ) 1 , e ) - 10
Rationale: "we need to find out the value of p and l to get to the slope . line l and graph y intersect at point ( p , 5 ) . hence , x = p and y = 5 should sactisfy the graph . soliving 5 = - p 2 + 9 p 2 = 4 p = + or - 2 simillarly point ( t , 7 ) should satisfy the equation . hence x = t and y = 7 . - 7 = - t 2 + 9 t = + or - 4 considering p = - 2 and t = 4 , the least slope is ( 7 - 5 ) / ( 4 - 2 ) = 1 imo option d is correct answer ."
Answer: d
Python program:
a = 7 - 5
b = 9 + 7 
c = math.sqrt(b)
d = 5 + 9 
e = math.sqrt(d)
f = c - e
g = a / f
Problem: what is the least number of square tiles required to pave the floor of a room 11 m 50 cm long and 1 m 50 cm broad ?
Options: a ) 724 , b ) 804 , c ) 69 , d ) 844 , e ) none
Rationale: "solution length of largest tile = h . c . f . of 1150 cm & 150 cm = 50 cm . area of each tile = ( 50 x 50 ) cm 2 ∴ required number of tiles = [ 1150 x 150 / 50 x 50 ] = 69 . answer c"
Answer: c
Python program:
a = 1 * 100
b = a + 50 
c = 11 * 100
d = b * c
e = 50 ** 2
f = d / e
Problem: in a cricket match , 5 batsmen a , b , c , d and e scored an average of 36 runs . d scored 5 more than e ; e scored 8 fewer than a ; b scored as many as d and e combined ; and b and c scored 107 between them . how many runs did e score ?
Options: a ) 62 , b ) 45 , c ) 28 , d ) 20 , e ) 25
Rationale: explanation : total runs scored = ( 36 x 5 ) = 180 . let the runs scored by e be x . then , runs scored by d = x + 5 ; runs scored by a = x + 8 ; runs scored by b = x + x + 5 = 2 x + 5 ; runs scored by c = ( 107 - b ) = 107 - ( 2 x + 5 ) = 102 - 2 x . so , total runs = ( x + 8 ) + ( 2 x + 5 ) + ( 102 - 2 x ) + ( x + 5 ) + x = 3 x + 120 . therefore 3 x + 120 = 180 3 x = 60 x = 20 . answer : option d
Answer: d
Python program:
a = 36 * 5
b = 2 * 5
c = b + 3 
d = c + 107 
e = a - d
f = e / 3
Problem: a property decreases in value every year at the rate of 6 1 / 4 % of its value at the beginning of the year its value at the end of 3 years was rs . 21093 . find its value at the beginning of the first year ?
Options: a ) 25600.24 , b ) 25600.27 , c ) 25600.28 , d ) 25600.21 , e ) 25600.29
Rationale: 6 1 / 4 % = 1 / 16 x * 15 / 16 * 15 / 16 * 15 / 16 = 21093 x = 25600.24 answer : a
Answer: a
Python program:
a = 1 / 4
b = a + 6 
c = b / 100
d = 1 - c
e = d ** 3
f = 21093 / e
Problem: the speed at which a man can row a boat in still water is 24 kmph . if he rows downstream , where the speed of current is 8 kmph , what time will he take to cover 40 metres ?
Options: a ) 4.49 seconds , b ) 8.89 seconds , c ) 26 seconds , d ) 12 seconds , e ) 16 seconds
Rationale: "speed of the boat downstream = 24 + 8 = 32 kmph = 32 * 5 / 18 = 8.89 m / s hence time taken to cover 40 m = 40 / 8.89 = 4.49 seconds . answer : a"
Answer: a
Python program:
a = 24 + 8 
b = a * const_0_2778
c = 40 / b
Problem: a manufacturing company has 15 % cobalt , 25 % led and 60 % of copper . if 5 kg of led is used in a mixture how much copper we need to use
Options: a ) 12 kg , b ) 13 kg , c ) 22 kg , d ) 14 kg , e ) 15 kg
Rationale: 25 % = 5 kg 100 % = 20 kg 60 % of 20 kg = 12 kg 12 kg answer : a
Answer: a
Python program:
a = 60 / 100
b = 5 * 4
c = a * b
Problem: in a simultaneous throw of pair of dice . find the probability of getting the total more than 7 ?
Options: a ) 12 / 5 , b ) 5 / 12 , c ) 6 / 4 , d ) 2 / 3 , e ) 4 / 7
Rationale: "here n ( s ) = ( 6 * 6 ) = 36 let e = event of getting a total more than 7 = { ( 2,6 ) , ( 3,5 ) , ( 3,6 ) , ( 4,4 ) , ( 4,5 ) , ( 4,6 ) , ( 5,3 ) , ( 5,4 ) , ( 5,5 ) , ( 5,6 ) , ( 6,2 ) , ( 6,3 ) , ( 6,4 ) , ( 6,5 ) , ( 6,6 ) } p ( e ) = n ( e ) / n ( s ) = 15 / 36 = 5 / 12 option b"
Answer: b
Python program:
a = 7 + 4 
b = a + 4 
c = 4 + 2 
d = 4 + 2 
e = c * d
f = b / e
Problem: the smallest number which when diminished by 15 , is divisible 10 , 15 , 25 , 30 and 35 is :
Options: a ) 1008 , b ) 1055 , c ) 1022 , d ) 1032 , e ) 1048
Rationale: "required number = ( l . c . m . of 10 , 15 , 25 , 30 , 35 ) + 15 = 1050 + 15 = 1055 answer : option b"
Answer: b
Python program:
a = 3 ** 2
b = 2 ** 0
c = a * b
d = 3 + 4 
e = c * d
f = e + 15
Problem: the length of the longest tape in cm which can be used to measure exactly , the length 7 m ; 3 m 85 cm ; and 12 m 95 cm is :
Options: a ) 37 , b ) 35 , c ) 34 , d ) 36 , e ) 38
Rationale: "the three lengths in cm are 700 , 385 & 1295 . hcf of 700 , 385 & 1295 is 35 . hence , the answer is 35 cm . answer : b"
Answer: b
Python program:
a = math.sqrt(85)
Problem: two pipes can fill a tank in 12 minutes and 15 minutes . an outlet pipe can empty the tank in 10 minutes . if all the pipes are opened when the tank is empty , then how many minutes will it take to fill the tank ?
Options: a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 28
Rationale: "let v be the volume of the tank . the rate per minute at which the tank is filled is : v / 12 + v / 15 - v / 10 = 3 v / 60 = v / 20 per minute the tank will be filled in 20 minutes . the answer is a ."
Answer: a
Python program:
a = 1 / 12
b = 1 / 15
c = a + b 
d = 1 / 10
e = c - d
Problem: an article with cost price of 192 is sold at 25 % profit . what is the selling price ?
Options: a ) 198 , b ) 200 , c ) 204 , d ) 240 , e ) 210
Rationale: "sp = 1.25 * 192 = 240 answer : d"
Answer: d
Python program:
a = 25 / 100
b = 192 * a
c = 192 + b
Problem: two pipes a and b can fill a tank in 50 hour and 75 hours respectively . if both the pipes are opened simultaneously , how much time will be taken to fill the tank ?
Options: a ) 15 hrs , b ) 20 hrs , c ) 25 hrs , d ) 30 hrs , e ) 32 hrs
Rationale: part filled by a in 1 hour = 1 / 50 part filled by b in 1 hour = 1 / 75 part filled by a + b in 1 hour = 1 / 50 + 1 / 75 = 1 / 30 both the pipes will together will fill the tank in 30 hours . answer is d
Answer: d
Python program:
a = 1 / 50
b = 1 / 75
c = a + b 
d = 1 / c
Problem: how many integers from 0 to 50 inclusive have a remainder of 3 when divided by 7 ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "the numbers should be of the form 7 c + 3 . the minimum is 3 when c = 0 . the maximum is 45 when c = 6 . there are 7 such numbers . the answer is c ."
Answer: c
Python program:
a = 50 / 10
Problem: addison high school ’ s senior class has 160 boys and 200 girls . if 75 % of the boys attended the college and 40 % of the girls did not attend the college , what percentage of the total class attended college ?
Options: a ) 35 , b ) 64 , c ) 66.67 , d ) 60 , e ) 84
Rationale: number of boys attending the college : 0.75 * 160 = 120 number of girls not attending the college : 0.40 * 200 = 80 number of girls attending the college : 200 - 80 = 120 total attending = 120 + 120 = 240 total people = 160 + 200 = 360 % of people attending = 240 / 360 = 66.67 % . c is the correct answer
Answer: c
Python program:
a = 75 / 100
b = a * 160
c = 40 / 100
d = 1 - c
e = d * 200
f = b + e 
g = 160 + 200 
h = f / g
i = h * 100
Problem: if x dollars is invested at 10 percent for one year and y dollars is invested at 8 percent for one year , the annual income from the 10 percent investment will exceed the annual income from the 8 percent investment by $ 92 . if $ 2,000 is the total amount invested , how much is invested at 8 percent ?
Options: a ) $ 600 , b ) $ 700 , c ) $ 800 , d ) $ 900 , e ) $ 1000
Rationale: 0.1 x = 0.08 ( 2000 - x ) + 92 0.18 x = 252 x = 1400 then the amount invested at 8 % is $ 2000 - $ 1400 = $ 600 the answer is a .
Answer: a
Python program:
a = 100 * 10
b = a * 2
c = 10 * 8
d = c * 2
e = d + 92 
f = 10 / 100
g = 8 / 100
h = f + g 
i = e / h
j = b - i
Problem: there is a 30 % increase in the price of an article in the first year , a 20 % decrease in the second year and a 10 % increase in the next year . if the final price of the article is rs . 3432 , then what was the price of the article initially ?
Options: a ) rs . 2000 , b ) rs . 4000 , c ) rs . 3000 , d ) rs . 5000 , e ) rs . 6000
Rationale: "let the price of the article , four years age be rs . 100 in the 1 st year , price of the article = 100 + 30 = rs . 130 . in the 2 nd year , price = 130 - 20 % of 130 = 130 - 26 = rs . 104 . in the 3 rd year , price = 104 + 10 % of 104 = 104 + 10.4 = rs . 114.40 . but present price of the article is rs . 3432 for 114.4 - - - > 100 ; 2288 - - - > ? required price = ( 3432 * 100 ) / 114.4 = 30 * 100 = rs . 3000 . answer : c"
Answer: c
Python program:
a = 30 - 20
b = a + 10 
c = b / 100
d = 1 + c 
e = 3432 / d
Problem: the balance of a trader weighs 10 % less than it should . still the trader marks up his goods to get an overall profit of 40 % . what is the mark up on the cost price ?
Options: a ) 40 % , b ) 8 % , c ) 25 % , d ) 16.66 % , e ) 26 %
Rationale: "the most natural way to deal with ' weights ' questions is by assuming values . say the trader ' s balance shows 100 gms . it is actually 90 gms because it weighs 10 % less . say , the cost price is $ 90 ( $ 1 / gm ) . since he gets a profit of 40 % , the selling price must be 90 + ( 40 / 100 ) * 90 = $ 126 since the cost price is actually supposed to be $ 100 ( for 100 gms ) and the selling price is $ 126 , the mark up is simply 26 % . ans : e"
Answer: e
Python program:
a = 4 * 10
b = 40 / 100
c = a * b
d = 4 * 10
e = c + d 
f = e - 100
Problem: jaclyn buys $ 60 000 worth of debentures in a company . she earns 9.5 % p . a . simple interest , paid to her quarterly ( that is , every 3 months ) . if the agreed period of the debenture was 18 months : calculate the amount of interest jaclyn will earn for each quarter
Options: a ) 1187.5 , b ) 1234 , c ) 1289 , d ) 1425 , e ) none of these
Rationale: "explanation : i = ( p x r x t ) / 100 = 60000 * 9.5 / 100 * ( 18 / 12 ) ^ 1 / 6 = 1425 answer : d"
Answer: d
Python program:
a = 100 * 100
b = a * 9
c = b / 100
d = c / 4
Problem: danny obtained 76 , 65 , 82 , 67 and 75 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) a ) 87 , b ) b ) 99 , c ) c ) 68 , d ) d ) 82 , e ) e ) 73
Rationale: average = ( 76 + 65 + 82 + 67 + 75 ) / 5 = 365 / 5 = 73 . answer : e
Answer: e
Python program:
a = 76 + 65 
b = a + 82 
c = b + 67 
d = c + 75 
e = 10 / 2
f = d / e
Problem: in the land of oz only one or two - letter words are used . the local language has 69 different letters . the parliament decided to forbid the use of the seventh letter . how many words have the people of oz lost because of the prohibition ?
Options: a ) 65 , b ) 66 , c ) 67 , d ) 131 , e ) 138
Rationale: "the answer to the question is indeed e . the problem with above solutions is that they do not consider words like aa , bb , . . . the number of 1 letter words ( x ) that can be made from 69 letters is 69 ; the number of 2 letter words ( xx ) that can be made from 69 letters is 69 * 69 , since each x can take 69 values . total : 69 + 69 * 69 . similarly : the number of 1 letter words ( x ) that can be made from 68 letters is 68 ; the number of 2 letter words ( xx ) that can be made from 68 letters is 68 * 68 , since each x can take 68 values . total : 68 + 68 * 68 . the difference is ( 69 + 69 * 69 ) - ( 68 + 68 * 68 ) = 138 . answer : e ."
Answer: e
Python program:
a = 1 + 69 
b = a + 69
Problem: a candidate got 35 % of the votes and lost to the rival by 2400 votes . how many votes were cast ?
Options: a ) 7700 , b ) 8000 , c ) 8300 , d ) 8600 , e ) 8900
Rationale: "35 % - - - - - - - - - - - l 65 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 30 % = 2400 10 % = 800 100 % of the votes = 8000 answer : b"
Answer: b
Python program:
a = 35 / 100
b = 1 - a
c = 35 / 100
d = b - c
e = 2400 / d
Problem: a bag contains 9 green and 8 white balls . if two balls are drawn simultaneously , the probability that both are of the same colour is
Options: a ) 8 / 17 , b ) 2 / 5 , c ) 3 / 5 , d ) 11 / 15 , e ) 7 / 15
Rationale: "drawing two balls of same color from nine green balls can be done in 9 c ₂ ways . similarly from eight white balls two can be drawn in ⁸ c ₂ ways . p = 9 c ₂ / ¹ ⁵ c ₂ + ⁸ c ₂ / ¹ ⁵ c ₂ = 8 / 17 answer : a"
Answer: a
Python program:
a = 9 + 8 
b = 8 / a
c = 8 - 1
d = 9 + 8 
e = d - 1
f = c / e
g = b * f
h = 9 + 8 
i = 9 / h
j = 9 - 1
k = 9 + 8 
l = k - 1
m = j / l
n = i * m
o = g + n
Problem: speed of a boat in standing water is 8 kmph and speed of the stream is 0.5 kmph . a man can rows to a place at a distance of 105 km and comes back to the starting point . the total time taken by him is ?
Options: a ) 27.35 hours , b ) 26.35 hours , c ) 25.35 hours , d ) 24.35 hours , e ) 23.35 hours
Rationale: "speed upstream = 7.5 kmph speed downstream = 8.5 kmph total time taken = 105 / 7.5 + 105 / 8.5 = 26.35 hours answer is b"
Answer: b
Python program:
a = 8 + 0 
b = 8 - 0
c = a + b 
d = c * 105
e = 8 + 0 
f = 105 / e
g = 8 - 0
h = 105 / g
i = f + h 
j = 8 + 0 
k = 8 - 0
l = j + k 
m = i - l
n = m * const_60
o = d + n
Problem: a , b and c started a business with a total investment of rs . 90000 . a invests rs . 6000 more than b and b invests rs . 3000 less than c . if the total profit at the end of a year is rs . 8640 , find a ' s share .
Options: a ) rs . 3168 , b ) rs . 2520 , c ) rs . 2880 , d ) rs . 3360 , e ) none of these
Rationale: "explanation : let c ' s investment = rs . x b ' s investment = rs . ( x - 3000 ) a ' s investment = rs . ( x - 3000 + 6000 ) = rs . ( x + 3000 ) now , ( a + b + c ) ' s investment = rs . 90000 = > x + ( x - 3000 ) + ( x + 3000 ) = 90000 = > 3 x = 90000 = > x = 30000 hence , a ' s investment = rs . 33000 b ' s investment = rs . 27000 c ' s investment = rs . 30000 ratio of the capitals of a , b and c = 33000 : 27000 : 30000 = 11 : 9 : 10 a ' s share = rs . [ ( 11 / 30 ) ã — 8640 ] = rs . 3168 answer : option a"
Answer: a
Python program:
a = 6000 + 3000 
b = 90000 - a
c = b / 3
d = c + 6000 
e = d / 90000
f = 8640 * e
Problem: on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.40 per glass on the first day , what was the price per glass on the second day ?
Options: a ) $ 0.15 , b ) $ 0.26 , c ) $ 0.30 , d ) $ 0.40 , e ) $ 0.45
Rationale: on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.4 = 3 * x - - > x = $ 0.26 . answer : b .
Answer: b
Python program:
a = 1 + 1 
b = a * 0
c = 1 + 2 
d = b / c
Problem: the largest four - digit number which is a perfect cube , is
Options: a ) 8000
b ) 9261
c ) 9999
d ) none of these
e ) can not be determined
Rationale: solution clearly , 9261 is a perfect cube satisfying the given property . answer b
Answer: b
Python program:
a = 10 * 2
b = a + 1 
c = b ** 3
Problem: a number when divided by 6 leaves a remainder 3 . when the square of the same number is divided by 6 , the remainder is
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "sol . let x = 6 q + 3 . then x 2 = ( 6 q + 3 ) 2 = 36 q 2 + 36 q + 9 = 6 ( 6 q 2 + 6 q + 1 ) + 3 . so , when x 2 is divided by 6 , remainder = 3 . answer d"
Answer: d
Python program:
a = 6 * 3
b = a / 6
Problem: the contents of a certain box consist of 40 apples and 30 oranges . how many oranges must be added to the box so that exactly 40 % of the pieces of fruit in the box will be apples ?
Options: a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 30
Rationale: "apple = ( apple + orange + x ) * 0.4 40 = ( 30 + 40 + x ) * 0.4 x = 30 answer : e"
Answer: e
Python program:
a = 40 + 30 
b = 40 / 100
c = 40 / b
d = a - c
Problem: two numbers are in the ratio 5 : 8 and thier h . c . f is 4 . find the numbers .
Options: a ) 25 and 40 , b ) 20 and 32 , c ) 30 and 48 , d ) 15 and 24 , e ) 16 and 25
Rationale: explanation : let two numbers 5 x , 8 x their h . c . f = 4 therefore h . c . f is 4 i . e , x in this case . therefore the numbers are 5 x 4 = 20 8 x 4 = 32 answer : option b
Answer: b
Python program:
a = 5 * 4
b = a * 100
c = 8 * 4
d = b + c
Problem: a ' s speed is 20 / 13 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that b beats a by 60 % of the length of the race ?
Options: a ) 44 % , b ) 48 % , c ) 52 % , d ) 42 % , e ) 74 %
Rationale: "first calculate the distance , b has covered with his speed in the time , in which a reached 40 % of the race . then add the remaining distance as head start for b to win the race . its best to apply ratios concept here . since a ' s speed is 20 / 13 of b , therefore , b ' s speed is 13 / 20 of a distance covered by b = speed x time = ( 13 / 20 ) x ( 0.4 ) = 0.26 ( which means b would have covered 0.26 of the race length during the time in which a has covered 0.4 of the race length . therefore to win , b needs a headstart of ( 1 - 0.26 = ) 0.74 of the race length . so the answer is e"
Answer: e
Python program:
a = 100 - 60
b = a / 100
c = 13 / 20
d = b * c
e = 1 - d
f = e * 100
Problem: a contract is to be completed in 46 days sad 117 men were said to work 8 hours a day . after 33 days , ( 4 / 7 ) of the work is completed . how many additional men may be employed so that the work may be completed in time , each man now working 9 hours a day ?
Options: a ) 91 , b ) 87 , c ) 85 , d ) 81 , e ) none of them
Rationale: remaining work = ( 1 - ( 4 / 7 ) = ( 3 / 7 ) remaining period = ( 46 - 33 ) days = 13 days let the total men working at it be x . less work , less men ( direct proportion ) less days , more men ( indirect proportion ) more hours per day , less men ( indirect proportion ) work ( 4 / 7 ) : ( 3 / 7 ) days 13 : 33 } : : 117 : x hrs / day 9 : 8 therefore ( 4 / 7 ) x 13 x 9 x x = ( 3 / 7 ) x 33 x 8 x 117 or x = ( 3 x 33 x 8 x 117 ) / ( 4 x 13 x 9 ) = 198 additional men to be employed = ( 198 - 117 ) = 81 . answer is d .
Answer: d
Python program:
a = 4 / 7
b = 1 - a
c = b * 33
d = c * 8
e = d * 117
f = 4 / 7
g = 46 - 33
h = f * g
i = h * 9
j = e / i
k = j - 117
Problem: a person borrows 1000000 for 7 years at 3 % p . a . simple interest . he immediately lends it to another person at 5 % p . a . for 7 years . find his gain in the transaction per year .
Options: a ) 20068 , b ) 20050 , c ) 20000 , d ) 25000 , e ) 28000
Rationale: "gain in 7 years = [ ( 1000000 ã — 5 ã — 7 / 100 ) â ˆ ’ ( 1000000 ã — 7 ã — 3 / 100 ) ] = ( 350000 â € “ 210000 ) = 140000 â ˆ ´ gain in 1 year = ( 140000 / 7 ) = 20000 answer c"
Answer: c
Python program:
a = 1 / 100
b = 1000000 * a
Problem: 12 : 21 : : 31 : ?
Options: a ) 13 , b ) 14 , c ) 30 , d ) 31 , e ) 40
Rationale: "ans 13 reverse of 31 answer : a"
Answer: a
Python program:
a = 12 / 21
b = 31 * a
Problem: if ( n + 2 ) ! / n ! = 72 , n = ?
Options: a ) 7 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: ( n + 2 ) ! / n ! = 72 rewrite as : [ ( n + 2 ) ( n + 1 ) ( n ) ( n - 1 ) ( n - 2 ) . . . . ( 3 ) ( 2 ) ( 1 ) ] / [ ( n ) ( n - 1 ) ( n - 2 ) . . . . ( 3 ) ( 2 ) ( 1 ) ] = 132 cancel out terms : ( n + 2 ) ( n + 1 ) = 72 from here , we might just test the answer choices . since ( 9 ) ( 8 ) = 72 , we can see that n = 7 a
Answer: a
Python program:
a = 4 + 4 
b = a - 1
Problem: a room 5 m 55 cm long and 3 m 74 cm broad is to be paved with square tiles . find the least number of square tiles required to cover the floor
Options: a ) 176 , b ) 170 , c ) 160 , d ) 179 , e ) 174
Rationale: "let x and y be the sides of the rectangle . then , correct area = xy . area of the room = ( 544 x 374 ) cm 2 . size of largest square tile = h . c . f . of 544 cm and 374 cm = 34 cm . area of 1 tile = ( 34 x 34 ) cm 2 . number of tiles required = ( 544 * 374 ) / ( 34 * 34 ) = 176 answer a 176"
Answer: a
Python program:
a = 5 * 100
b = a + 55 
c = 3 * 100
d = c + 74 
e = b * d
f = 2 * 4
g = f + 2 
h = 55 - g
i = 2 * 4
j = i + 2 
k = 55 - j
l = h * k
m = e / l
Problem: the ages of two persons differ by 16 years . if 6 years agao , the elder one be 3 times as old as the younger one , find their present ages .
Options: a ) 20 years . , b ) 30 years . , c ) 40 years . , d ) 50 years . , e ) 60 years .
Rationale: "sol . let the age of the younger person be x years . then , age of the elder perosn = ( x + 16 ) years . ∴ 3 ( x - 6 ) = ( x + 16 - 6 ) ⇔ 3 x - 18 = x + 10 ⇔ 2 x = 28 ⇔ x = 14 hence , their present ages are 14 years and 30 years . answer b"
Answer: b
Python program:
a = 16 * 6
b = 6 - 1
c = a / b
d = c + 6 
e = d - 16
Problem: working at a constant rate , p can finish a job in 4 hours . q , also working at a constant rate , can finish the same job in 15 hours . if they work together for 3 hours , how many more minutes will it take p to finish the job , working alone at his constant rate ?
Options: a ) 5 , b ) 8 , c ) 10 , d ) 12 , e ) 15
Rationale: "each hour they complete 1 / 4 + 1 / 15 = 19 / 60 of the job . in 3 hours , they complete 3 ( 19 / 60 ) = 19 / 20 of the job . the time for p to finish is ( 1 / 20 ) / ( 1 / 4 ) = ( 1 / 5 ) hour = 12 minutes the answer is d ."
Answer: d
Python program:
a = 1/(4)
b = 1/(15)
c = a + b 
d = c * 3
e = 1 - d
f = 1/(4)
g = e / f
h = g * const_60