euclaise/mathqa_programs huggingface dataset:
Problem: mike drives his new corvette from san francisco to las vegas , a journey of 640 miles . he drives the first half of the trip at an average rate of 80 miles per hour , but has to slow down for the second half of his journey . if the second half of the trip takes him 200 percent longer than the first half , what is his average rate z in miles per hour for the entire trip ?
Options: a ) 26.7 , b ) z = 30.0 , c ) z = 40.0 , d ) z = 53.3 , e ) 60.0
Rationale: "veritas prepofficial solution correct answer : c using the formula : time = distance / rate , we find that mike takes 4 hours to cover the first 320 miles of his trip . since the 2 nd 320 miles take 200 % longer than the first , it takes mike 8 hours longer , or 12 hours . ( note : 200 % longer than the first half is not 200 % of the first half . ) the overall time is 4 hours + 12 hours or 16 hours . since the definition of average rate = total distance traveled / total time of travel , mike ' s average rate = 640 / 16 or 40 miles per hour . answer choice c is correct ."
Answer: c
Python program:
a = 640 / 2
b = a / 80
c = b * 2
d = 640 / 2
e = d / 80
f = c + e 
g = 640 / 2
h = g / 80
i = f + h 
j = 640 / i
Problem: john is going with 10 friends on a trip to sidney for spring break . airfare and hotel costs a total of $ 12100.00 for the group of 11 friends . how much does each person have to pay for their hotel and airfare ?
Options: a ) $ 1010 , b ) $ 1100 , c ) $ 1110 , d ) $ 1101 , e ) $ 1200
Rationale: answer = b the total cost of the trip ( $ 12100.00 ) divided by 11 equals $ 1100.00 .
Answer: b
Python program:
a = 12100 / 11
Problem: a soccer store typically sells replica jerseys at a discount of 30 percent to 50 percent off list price . during the annual summer sale , everything in the store is an additional 20 percent off the original list price . if a replica jersey ' s list price is $ 80 , approximately what r percent of the list price is the lowest possible sale price ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 40 , e ) 50
Rationale: let the list price be 2 x for min sale price , the first discount given should be 50 % , 2 x becomes x here now , during summer sale additional 20 % off is given ie sale price becomes 0.8 x it is given lise price is $ 80 = > 2 x = 80 = > x = 40 and 0.8 x = 32 so lowest sale price is 32 , which r is 40 % of 80 hence , d is the answer
Answer: d
Python program:
a = 80 / 2
Problem: last month , john rejected 0.5 % of the products that he inspected and jane rejected 0.7 percent of the products that she inspected . if total of 0.75 percent of the products produced last month were rejected , what fraction of the products did jane inspect ?
Options: a ) 1 / 6 , b ) 1 / 2 , c ) 5 / 8 , d ) 5 / 4 , e ) 15 / 16
Rationale: x - fraction of products jane inspected ( 1 - x ) - fraction of products john inspected 0.7 ( x ) + 0.5 ( 1 - x ) = 0.75 0.2 x = 0.75 - 0.5 x = 0.25 / 0.2 x = 5 / 4 therefore the answer is d : 5 / 4 .
Answer: d
Python program:
a = 0 - 75
b = 0 - 7
c = a / b
Problem: the area of a square field 3136 sq m , if the length of cost of drawing barbed wire 3 m around the field at the rate of rs . 1.50 per meter . two gates of 1 m width each are to be left for entrance . what is the total cost ?
Options: a ) 978
b ) 789
c ) 999
d ) 778
e ) 787
Rationale: a 2 = 3136 = > a = 56 56 * 4 * 3 = 672 – 6 = 666 * 1.5 = 999 answer : c
Answer: c
Python program:
a = math.sqrt(3136)
b = a * 4
c = 2 * 1
d = b - c
e = d * 1
f = e * 3
Problem: a firm is comprised of partners and associates in a ratio of 2 : 63 . if 50 more associates were hired , the ratio of partners to associates would be 1 : 34 . how many partners are currently in the firm ?
Options: a ) 5 , b ) 10 , c ) 12 , d ) 20 , e ) 25
Rationale: the ratio 1 : 34 = 2 : 68 so the ratio changed from 2 : 63 to 2 : 68 . 68 - 63 = 5 which is 1 / 10 of the increase in 50 associates . the ratio changed from 20 : 630 to 20 : 680 . thus the number of partners is 20 . the answer is d .
Answer: d
Python program:
a = 34 * 2
b = a - 63
c = 50 / b
d = c * 2
Problem: a certain drink of type a is prepared by mixing 4 parts milk with 3 parts fruit juice . another drink of type b is prepared by mixing 4 parts of fruit juice and 3 parts of milk . how many liters of fruit juice must be added to 42 liters of drink a to convert it to drink b ?
Options: a ) 7 , b ) 9 , c ) 12 , d ) 14 , e ) 18
Rationale: in 42 liters of drink a , there are 24 liters of milk and 18 liters of juice . with 24 liters of milk , we need a total of 32 liters of juice to make drink b . we need to add 14 liters of juice . the answer is d .
Answer: d
Python program:
a = 4 + 3 
b = 4 / a
c = b * 42
d = c * 4
e = d / 3
f = 4 + 3 
g = 3 / f
h = g * 42
i = e - h
Problem: the ratio between the number of sheep and the number of horses at the stewar farm is 5 to 7 . if each of horse is fed 230 ounces of horse food per day and the farm needs a total 12880 ounces of horse food per day . what is number sheep in the form ? ?
Options: a ) 18 , b ) 28 , c ) 40 , d ) 56 , e ) 58
Rationale: "et no of sheep and horses are 5 k and 7 k no of horses = 12880 / 230 = 56 now 7 k = 56 and k = 8 no of sheep = ( 5 * 8 ) = 40 answer : c"
Answer: c
Python program:
a = 12880 / 230
b = a / 7
c = b * 5
Problem: working alone , tom finishes cleaning half the house in a third of the time it takes nick to clean the entire house alone . tom alone cleans the entire house in 6 hours . how many hours will it take nick and tom to clean the entire house if they work together ?
Options: a ) 1.5 , b ) 2 , c ) 2.4 , d ) 3 , e ) 3.6
Rationale: answer is 3.6 hours . tom does the complete house in 6 hours while nick does it in 9 hours . 1 / ( 1 / 6 + 1 / 9 ) = 3.6 answer is e
Answer: e
Python program:
a = 6 * 3
b = 3 + 2 
c = a / b
Problem: of the people who responded to a market survey , 360 preferred brand x and the rest preferred brand y . if the respondents indicated a preference for brand x over brand y by ratio of 9 to 1 , how many people responded to the survey ?
Options: a ) 80 , b ) 160 , c ) 240 , d ) 360 , e ) 400
Rationale: "ratio = 9 : 1 = > 9 x respondents preferred brand x and x preferred brand y since , no . of respondents who preferred brand x = 360 = > 9 x = 360 = > x = 40 hence total no . of respondents = 360 + 40 = 400 hence e is the answer ."
Answer: e
Python program:
a = 360 / 9
b = a + 360
Problem: 90 litres of diesel is required to travel 600 km using a 800 cc engine . if the volume of diesel required to cover a distance varies directly as the capacity of the engine , then how many litres of diesel is required to travel 800 km using 1200 cc engine ?
Options: a ) 80 litres , b ) 90 litres , c ) 120 litres , d ) 180 litres , e ) none of these
Rationale: "explanatory answer to cover a distance of 800 kms using a 800 cc engine , the amount of diesel required = 800 / 600 * 90 = 120 litres . however , the vehicle uses a 1200 cc engine and the question states that the amount of diesel required varies directly as the engine capacity . i . e . , for instance , if the capacity of engine doubles , the diesel requirement will double too . therefore , with a 1200 cc engine , quantity of diesel required = 1200 / 800 * 120 = 180 litres . answer d"
Answer: d
Python program:
a = 800 * 600
b = 90 / a
c = 800 * b
d = 1200 * c
Problem: machine – a produces 40 % of the total output and machine - b produces 60 % of the total output . an average of 9 units out of a 1000 goods manufactured by machine - a and one unit of 50 units produced by machine - b prove to be defective . what is the probability that a unit chosen at random from the total daily output of the factory is defective ?
Options: a ) a . 0.156 , b ) b . 0.01506 , c ) c . 0.0156 , d ) d . 0.0001566 , e ) e . 0.00001566
Rationale: let total production be 10000 units . . . . a produces 4000 units and 36 units are defective b produces 6000 units and 120 units are defective so , out of total 10,000 units 156 units are defective . . . so the required probability = 156 / 10000 = > 0.0156 answer will be ( c )
Answer: c
Python program:
a = 1000 * 60
b = a / 40
c = b / 50
d = c + 9 
e = 1000 * 60
f = e / 40
g = f + 1000 
h = d / g
Problem: a 470 m long train is running at a speed of 55 km / hr . it crossed a platform of length 520 m in ?
Options: a ) 41.1 sec , b ) 64.8 sec , c ) 31.8 sec , d ) 50.4 sec , e ) none of the above
Rationale: "speed = 55 km / hr ( to convert km / hr in to m / s ) = 55 x 5 / 18 m / s distance = 470 m + 520 m ( if questions is about train crossing a post you need to consider only the length of train , ) = 990 m time = distance / speed = 990 x 18 / ( 5 x 55 ) = 64.8 sec ans is : b"
Answer: b
Python program:
a = 470 + 520 
b = 55 * const_0_2778
c = a / b
Problem: the ratio between the number of sheep and the number of horses at the stewar farm is 7 to 7 . if each of horse is fed 230 ounces of horse food per day and the farm needs a total 12880 ounces of horse food per day . what is number sheep in the form ? ?
Options: a ) 18 , b ) 28 , c ) 32 , d ) 56 , e ) 58
Rationale: "et no of sheep and horses are 7 k and 7 k no of horses = 12880 / 230 = 56 now 7 k = 56 and k = 8 no of sheep = ( 7 * 8 ) = 56 answer : d"
Answer: d
Python program:
a = 12880 / 230
b = a / 7
c = b * 7
Problem: gold is 10 times as heavy as water and copper is 5 times as heavy as water . in what ratio should these be mixed to get an alloy 9 times as heavy as water ?
Options: a ) 3 : 2 , b ) 1 : 2 , c ) 4 : 1 , d ) 5 : 2 , e ) 4 : 3
Rationale: "g = 10 w c = 5 w let 1 gm of gold mixed with x gm of copper to get 1 + x gm of the alloy 1 gm gold + x gm copper = x + 1 gm of alloy 10 w + 5 wx = x + 1 * 9 w 10 + 5 x = 9 ( x + 1 ) x = 1 / 4 ratio of gold with copper = 1 : 1 / 4 = 4 : 1 answer is c"
Answer: c
Python program:
a = 9 - 5
b = 10 - 9
c = a / b
Problem: veena ranks 73 rd from the top in a class of 182 . what is her rank from the bottom if 22 students have failed the examination ?
Options: a ) 88 , b ) 108 , c ) 110 , d ) 90 , e ) 93
Rationale: "total student = 182 failed = 22 paasd student = 182 - 22 = 160 from bottom her rank is = 160 - 73 + 1 = 88 answer : a"
Answer: a
Python program:
a = 182 - 22
b = 73 - 1
c = a - b
d = c - 4
Problem: what annual installment will discharge a debt of rs . 1176 due in 3 years at 12 % simple interest ?
Options: a ) 315 , b ) 350 , c ) 325 , d ) 335 , e ) none of them
Rationale: "let each installment be rs . x then , ( x + ( ( x * 12 * 1 ) / 100 ) ) + ( x + ( ( x * 12 * 2 ) / 100 ) ) + x = 1176 = ( ( 28 x / 25 ) + ( 31 x / 25 ) + x ) = 1176 ï ƒ › ( 28 x + 31 x + 25 x ) = ( 1176 * 25 ) x = ( 1176 * 25 ) / 84 = rs . 350 . therefore , each installment = rs . 350 . answer is b ."
Answer: b
Python program:
a = 12 / 1176
b = 100 * 0
c = b * 3
Problem: michelle deposited a certain sum of money in a savings account on july 1 st , 2007 . she earns an 12 % interest compounded semiannually . the sum of money in the account on december 31 st , 2009 is approximately what percent of the initial deposit ?
Options: a ) 117 % , b ) 120 % , c ) 121 % , d ) 133 % , e ) 140 %
Rationale: "since michelle earns 12 % interest compounded semiannually , then she earns 6 % interest every 6 months . now , the simple interest earned in 5 periods ( 30 months = 5 * 6 months ) would be 6 % * 5 = 30 % . but , since the interest iscompoundedevery 6 months , then there would be interest earned on interest ( very small amount ) thus the actual interest earned would be a little bit more than 30 % , only answer choice d fits . answer : d"
Answer: d
Python program:
a = 12 / 100
b = a / 2
c = 1 + b 
d = 2 + 3 
e = c ** d
f = e * 100
Problem: if the numerator of a fraction is increased by 50 % and denominator by 20 % , the fraction become 9 / 15 . what was the original fraction ?
Options: a ) 12 / 25 , b ) 13 / 25 , c ) 3 / 5 , d ) 6 / 7 , e ) 7 / 8
Rationale: "explanation : let the fraction be x / y we have 150 x / 120 y = 9 / 15 = x / y = 12 / 25 answer : option a"
Answer: a
Python program:
a = 9 / 15
b = 50 + 100 
c = b / 100
d = 100 - 20
e = d / 100
f = c / e
g = a / f
Problem: every student of a certain school must take one and only one elective course . in last year , 1 / 2 of the students took p . e . as an elective , 1 / 3 of the students took theatre as an elective , and all of the other students took music . in this year , 1 / 3 of the students who took p . e . and 1 / 4 of the students who took theatre left school , other students did not leave , and no fresh student come in . what fraction of all students took p . e . or music ?
Options: a ) 2 / 3 , b ) 1 / 4 , c ) 7 / 9 , d ) 1 / 5 , e ) 8 / 11
Rationale: lets pick smart numbers . total number of students : 12 p . e . ( 1 / 2 ) : 6 theatre ( 1 / 3 ) : 4 music ( 1 / 6 ) : 2 after leaving school p . e . : 4 theatre : 3 music : 2 new total number of students : 9 p . e . and music : 6 answer 2 / 3 or a
Answer: a
Python program:
a = 1 / 2
b = 1 / 3
c = a + b 
d = 1 - c
e = 1 / 3
f = 1 - e
g = 1 / 2
h = f * g
i = d + h 
j = 1 / 2
k = 1 / 3
l = j + k 
m = 1 - l
n = 1 / 3
o = 1 - n
p = 1 / 2
q = o * p
r = m + q 
s = 1 / 4
t = 1 - s
u = 1 / 3
v = t * u
w = r + v 
x = i / w
Problem: what is the compound interest paid on a sum of rs . 1500 for the period of 2 years at 10 % per annum .
Options: a ) 230 , b ) 175 , c ) 225 , d ) 315 , e ) none of these
Rationale: "solution = interest % for 1 st year = 10 interest % for 2 nd year = 10 + 10 % of 10 = 10 + 10 * 10 / 100 = 11 total % of interest = 10 + 11 = 21 total interest = 21 % 1500 = 1500 * ( 21 / 100 ) = 315 answer d"
Answer: d
Python program:
a = 10 / 100
b = 1 + a 
c = b ** 2
d = 1500 * c
e = d - 1500
Problem: if sharon ' s weekly salary increased by 20 percent , she would earn $ 600 per week . if instead , her weekly salary were to increase by 15 percent , how much would she earn per week ?
Options: a ) rs . 575 , b ) rs . 600 , c ) rs . 625 , d ) rs . 485 , e ) rs . 590
Rationale: "soln : - ( 600 / 120 ) 115 = 575 in this case long division does not take much time . ( 5 / 1 ) 115 = rs . 575 answer : a"
Answer: a
Python program:
a = 20 / 100
b = 1 + a 
c = 600 / b
d = 15 / 100
e = 20 / 100
f = 1 + e 
g = 600 / f
h = d * g
i = c + h
Problem: jamshid can paint a fence in 50 percent less time than taimour can when each works alone . when they work together , they can paint the fence in 3 hours . how long would it take taimour to paint the fence alone ?
Options: a ) 6 hours , b ) 9 hours , c ) 14 hours , d ) 24 hours , e ) 32 hours
Rationale: "i believe the answer is b . please see below for explanation . if jamshid can paint a dence in 50 percent less time then taimour we can infer the following rate j = 2 t if working together they can do the job in 8 hours we can infer 1 = 2 t + t * 3 = > 1 / 9 working alone taimour can do the job in 1 = 1 / 9 * hours = > 9 answer b"
Answer: b
Python program:
a = 3 * 3
Problem: a man is walking at the rate of 9 km / hr crosses a bridge in 15 minutes . the length of the bridge is
Options: a ) 1000 meters , b ) 1050 meters , c ) 2200 meters , d ) 2250 meters , e ) none of these
Rationale: "explanation : we need to get the answer in meters . so we will first of change distance from km / hour to meter / sec by multiplying it with 5 / 18 and also change 15 minutes to seconds by multiplying it with 60 . speed = 9 â ˆ — 5 / 18 = 5 / 2 m / sec time = 15 â ˆ — 60 seconds = 900 seconds distance = time â ˆ — speed / distance = 5 / 2 â ˆ — 900 = 2250 meter option d"
Answer: d
Python program:
a = 15 / const_60
b = 9 * a
c = b * 1000
Problem: how many multiples of 4 are there between 1 and 99 ?
Options: a ) 20 , b ) 24 , c ) 26 , d ) 25 , e ) 22
Rationale: "4 multiples are 4 , 8,12 , - - - - - - - - - , 92,96 it should be mentioned whether 1 and 99 are inclusive . the answer is ( 96 - 4 ) / 4 + 1 = 24 answer is b"
Answer: b
Python program:
a = 99 - 1
b = a / 4
c = b + 1
Problem: patrick purchased 80 pencils and sold them at a loss equal to the selling price of 30 pencils . the cost of 80 pencils is how many times the selling price of 80 pencils ?
Options: a ) 0.75 , b ) 0.8 , c ) 1.375 , d ) 1.4 , e ) 1.85
Rationale: say the cost price of 80 pencils was $ 80 ( $ 1 per pencil ) and the selling price of 1 pencil was p . selling at a loss : 80 - 80 p = 30 p - - > p = 8 / 11 . ( cost price ) / ( selling price ) = 1 / ( 8 / 11 ) = 11 / 8 = 1.375 . answer : c .
Answer: c
Python program:
a = 80 + 30 
b = 80 / a
c = 1/(b)
Problem: a shopkeeper sold an article offering a discount of 5 % and earned a profit of 23.5 % . what would have been the percentage of profit earned if no discount was offered ?
Options: a ) 70 % , b ) 60 % , c ) 30 % , d ) 10 % , e ) 20 %
Rationale: "explanation : let c . p . be rs . 100 . then , s . p . = rs . 123.50 let marked price be rs . x . then , 95 / 100 x = 123.50 x = 12350 / 95 = rs . 130 now , s . p . = rs . 130 , c . p . = rs . 100 profit % = 30 % . answer c"
Answer: c
Python program:
a = 100 + 23 
b = a * 100
c = 100 - 5
d = b / c
e = d - 100
Problem: the hiker walking at a constant rate of 7 miles per hour is passed by a cyclist traveling in the same direction along the same path at 28 miles per hour . the cyclist stops to wait for the hiker 5 minutes after passing her , while the hiker continues to walk at her constant rate , how many minutes must the cyclist wait until the hiker catches up ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30
Rationale: "for the 5 minutes the cyclist continues to overtake the hiker , she is going at 21 miles per hour faster than the hiker . once the cyclist stops , the hiker is going at 7 miles per hour while the cyclist is at rest so the amount of time the hiker will take to cover the distance between them is going to be in the ratio of the relative speeds . 21 / 7 * 5 or 15 minutes answer is ( b )"
Answer: b
Python program:
a = 28 - 7
b = 5 / const_60
c = a * b
d = c / 7
e = d * const_60
Problem: find the area of a parallelogram with base 18 cm and height 10 cm ?
Options: a ) 281 , b ) 284 , c ) 288 , d ) 255 , e ) 180
Rationale: "area of a parallelogram = base * height = 18 * 10 = 180 cm 2 answer : e"
Answer: e
Python program:
a = 18 * 10
Problem: the parameter of a square is equal to the perimeter of a rectangle of length 24 cm and breadth 16 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places )
Options: a ) 77.14 cm , b ) 47.14 cm , c ) 84.92 cm , d ) 94.94 cm , e ) 31.42 cm
Rationale: "let the side of the square be a cm . parameter of the rectangle = 2 ( 24 + 16 ) = 80 cm parameter of the square = 80 cm i . e . 4 a = 80 a = 20 diameter of the semicircle = 20 cm circimference of the semicircle = 1 / 2 ( ∏ ) ( 20 ) = 1 / 2 ( 22 / 7 ) ( 20 ) = 440 / 14 = 31.42 cm to two decimal places answer : e"
Answer: e
Python program:
a = square_edge_by_perimeter / (
b = circumface / (
Problem: a man gains 20 % by selling an article for a certain price . if the sells it at double the price , the percentage of profit will be ?
Options: a ) 76 % . , b ) 66 % . , c ) 89 % . , d ) 140 % . , e ) 91 % .
Rationale: "let c . p . = rs . x . then , s . p . = rs . ( 12 % of x ) = rs . 6 x / 5 new s . p . = 2 * 6 x / 5 = rs . 12 x / 5 profit = 12 x / 5 - x = rs . 7 x / 5 profit = 7 x / 5 * 1 / x * 100 = 140 % . answer : d"
Answer: d
Python program:
a = 20 / 100
b = 1 + a 
c = b * 2
d = c - 1
e = d * 100
f = e + 100
Problem: mars travels around the sun at a speed of approximately 15 miles per second . the approximate speed is how many miles per hour ?
Options: a ) 48,000 , b ) 51,000 , c ) 54,000 , d ) 57,000 , e ) 60,000
Rationale: 15 * 3600 = 54,000 the answer is c .
Answer: c
Python program:
a = 15 * 3600
b = a / 1000
c = b - 3
Problem: acme ’ s manufacturing costs for sets of horseshoes include a $ 12450 initial outlay , and $ 20.75 per set . they can sell the sets $ 50 . if profit is revenue from sales minus manufacturing costs , and the company producessells 950 sets of horseshoes , what was their profit ?
Options: a ) $ 15300 , b ) $ 14300 , c ) $ 15337.50 , d ) $ 16300 , e ) $ 15800
Rationale: total manufacturing cost = 12,450 + 950 * 20.75 = 32162.5 total selling cost = 950 * 50 = 47500 profit = 47500 - 32162.50 = 15337.50 answer : c
Answer: c
Python program:
a = 50 - 20
b = 950 * a
c = b - 12450
Problem: the average of 9 numbers is 104 . average of the first 5 of them is 99 and that of the last 5 is 100 . find the 5 th number ?
Options: a ) 46 , b ) 59 , c ) 63 , d ) 75 , e ) 88
Rationale: sum of all the 9 numbers = 9 * 104 = 936 sum of the first 5 of them = 5 * 99 = 495 sum of the last 5 of them = 5 * 100 = 500 so , the 5 th number = 495 + 500 - 936 = 59 . answer : b
Answer: b
Python program:
a = 5 * 100
b = 9 * 104
c = 99 * 5
d = b - c
e = a - d
Problem: the cash realised on selling a 14 % stock is rs . 101.25 , brokerage being 1 / 4 % is
Options: a ) 123 , b ) 106 , c ) 100 , d ) 101 , e ) 240
Rationale: "explanation : cash realised = rs . ( 101.25 - 0.25 ) = rs . 101 . answer : d"
Answer: d
Python program:
a = 1 / 4
b = 101 - 25
Problem: in a 500 m race , the ratio of the speeds of two contestants a and b is 3 : 4 . a has a start of 140 m . then , a wins by :
Options: a ) 60 m , b ) 20 m , c ) 43 m , d ) 20 m , e ) 23 m
Rationale: "to reach the winning post a will have to cover a distance of ( 500 - 140 ) m , i . e . , 360 m . while a covers 3 m , b covers 4 m . while a covers 360 m , b covers 4 x 360 m = 480 m . 3 thus , when a reaches the winning post , b covers 480 m and therefore remains 20 m behind . a wins by 20 m . answer : d"
Answer: d
Python program:
a = 500 - 140
b = a * 4
c = b / 3
d = 500 - c
Problem: tom read a book containing 100 pages by reading the same number of pages each day . if he would have finished the book 10 days earlier by reading 30 pages a day more , how many days did tom spend reading the book ?
Options: a ) 7 , b ) 7.68 , c ) 8 , d ) 9 , e ) 10
Rationale: actually u can set up 2 equation p - - stands for the pages d - - stands for the days 1 ) p * d = 100 ( we want to find the days , sop = 100 / d ) 2 ) ( p + 30 ) ( d - 10 ) = 100 = > pd - 10 p + 30 d - 300 = 100 as the 1 ) stated u can put 1 ) into 2 ) = > 100 - 10 p + 30 d - 300 = 100 = > 30 d - 10 p = 100 put the bold one into it = > 30 d - 10 ( 100 / d ) = 100 the we get the final equation 30 d ^ 2 - 1000 = 100 d ( divide 16 ) = > d ^ 2 - 5 d - 150 = 0 ( d - 15 ) ( d + 10 ) = 0 so d = 7.68 days . ans : ( b )
Answer: b
Python program:
a = 30 * 10
b = a * 4
c = 30 ** 2
d = b + c 
e = math.sqrt(d)
f = e - 30
g = f / 2
Problem: the sum of the squares of three numbers is 241 , while the sum of their products taken two at a time is 100 . their sum is :
Options: a ) 20 , b ) 11 , c ) 21 , d ) 41 , e ) none of these
Rationale: "x ^ + y ^ 2 + z ^ 2 = 241 xy + yz + zx = 100 as we know . . ( x + y + z ) ^ 2 = x ^ 2 + y ^ 2 + z ^ 2 + 2 ( xy + yz + zx ) so ( x + y + z ) ^ 2 = 241 + ( 2 * 100 ) ( x + y + z ) ^ 2 = 441 so x + y + z = 21 answer : c"
Answer: c
Python program:
a = 241 - 100
b = a / 2
c = math.sqrt(b)
d = c * 100
e = 241 - 100
f = e / 2
g = 241 - f
h = math.sqrt(g)
i = d + h
Problem: the speed of a boat in still water is 18 km / hr and the rate of current is 4 km / hr . the distance travelled downstream in 14 minutes is
Options: a ) 1.6 km , b ) 2 km , c ) 5.1 km , d ) 4 km , e ) none of these
Rationale: "explanation : speed downstreams = ( 18 + 4 ) kmph = 22 kmph . distance travelled = ( 22 x 14 / 60 ) km = 5.1 km option c"
Answer: c
Python program:
a = 14 / const_60
b = 18 + 4 
c = a * b
Problem: the present worth of rs . 169 due in 2 years at 4 % per annum compound interest is
Options: a ) rs . 150.50 , b ) rs . 154.75 , c ) rs . 156.25 , d ) rs . 158 , e ) none
Rationale: "solution present worth = rs . [ 169 / ( 1 + 4 / 100 ) ² ] = rs . ( 169 x 25 / 26 x 25 / 26 ) = rs . 156.25 answer c"
Answer: c
Python program:
a = 4 / 100
b = a + 1 
c = b ** 2
d = 169 / c