euclaise/mathqa_programs huggingface dataset:
Problem: a chocolate manufacturer produces 400 units of a certain model each month at a cost to the manufacturer of £ 40 per unit and all of the produced units are sold each month . what is the minimum selling price per unit that will ensure that the monthly profit ( revenue from sales minus production costs ) on the sales of these units will be at least £ 40000 ?
Options: a ) 123 , b ) 213 , c ) 440 , d ) 550 , e ) 540
Rationale: 400 ( x - 40 ) ≥ 40000 x - 40 ≥ 400 x ≥ 440 answer : option c
Answer: c
Python program:
a = 400 + 40
Problem: 1,000 ^ 2 + 1,001 ^ 2 + 1,002 ^ 2 + 1,003 ^ 2 + 1,004 ^ 2 + 1,005 ^ 2 + 1,006 ^ 2 =
Options: a ) 6 , 030,053 , b ) 6 , 030,054 , c ) 6 , 030,055 , d ) 6 , 042,091 , e ) 6 , 030,057
Rationale: "interesting problem . i think key is to notice that all the given answer choices differs in last two digits . therefore , our entire focus should be to figure out how the given terms contribute to last two digits of total . 1000 ^ 2 - > 00 1001 ^ 1 - > 01 . . . 1006 ^ 2 - > 36 total - > * 91 answer d ."
Answer: d
Python program:
a = 2 * 3
Problem: ( 112 x 54 ) = ?
Options: a ) 67000 , b ) 70000 , c ) 76500 , d ) 77200 , e ) 85200
Rationale: explanation : ( 112 x 54 ) = 112 x ( 10 / 2 ) 4 = 112 x 10 4 / 2 4 = 1120000 / 16 = 70000 answer is b
Answer: b
Python program:
a = 4 + 1 
b = a ** 4
c = 112 * b
Problem: the circumferences of two circles are 264 meters and 352 meters . find the difference between the areas of the larger and the smaller circles .
Options: a ) 3312 , b ) 2888 , c ) 4312 , d ) 2881 , e ) 1221
Rationale: "let the radii of the smaller and the larger circles be s m and l m respectively . 2 ∏ s = 264 and 2 ∏ l = 352 s = 264 / 2 ∏ and l = 352 / 2 ∏ difference between the areas = ∏ l 2 - ∏ s 2 = ∏ { 1762 / ∏ 2 - 1322 / ∏ 2 } = 1762 / ∏ - 1322 / ∏ = ( 176 - 132 ) ( 176 + 132 ) / ∏ = ( 44 ) ( 308 ) / ( 22 / 7 ) = ( 2 ) ( 308 ) ( 7 ) = 4312 sq m answer : c"
Answer: c
Python program:
a = 2 * math.pi
b = 352 / a
c = circle_area - (
Problem: find avrg speed if a man travels at speed of 15 km / hr up and 28 km / hr dawn at an altitude of 230 m .
Options: a ) 25.8 , b ) 19.5 , c ) 18.0 , d ) 12.2 , e ) 29.8
Rationale: "avg speed = 2 * x * y / ( x + y ) = 2 * 15 * 28 / ( 15 + 28 ) = 19.5 answer : b"
Answer: b
Python program:
a = 2 * 15
b = a * 28
c = 15 + 28 
d = b / c
Problem: an amount at compound interest sums to rs . 17640 / - in 2 years and to rs . 21168 / - in 3 years at the same rate of interest . find the rate percentage ?
Options: a ) 5 % , b ) 7 % , c ) 9 % , d ) 11 % , e ) 20 %
Rationale: "explanation : the difference of two successive amounts must be the simple interest in 1 year on the lower amount of money . s . i = 21168 / - - 17640 / - = rs . 3528 / - rate of interest = ( 3528 / 17640 ) × ( 100 / 1 ) = > 20 % answer : option e"
Answer: e
Python program:
a = 21168 - 17640
b = a / 17640
c = b * 100
Problem: in the above number , a and b represent the tens and units digits , respectively . if the above number is divisible by 25 , what is the greatest possible value of b x a ?
Options: a ) 0 , b ) 15 , c ) 20 , d ) 25 , e ) 35
Rationale: i also was confused when i was looking forabove number : d as far as i understood , 25 is a factor of ab . in other words , the values of b ( units digits can be 5 or 0 . better to have option for 5 in this case to havebigger result ) . now let ' s try 25 x 1 ( a = 2 , b = 5 respectively we have = 10 ) . but we do n ' t have this number in answer choices , move on . ( avoid even multiples of 2,4 , 6,8 etc ( we will have 0 in units thus making our result 0 ) 25 x 3 = 75 ( a = 7 b = 5 respectively . hey ! that ' s 35 . this is the greatest possible value of b x a imo e .
Answer: e
Python program:
a = 3 + 4 
b = 2 + 3 
c = a * b
Problem: a train 100 meters long completely crosses a 300 meters long bridge in 24 seconds . what is the speed of the train is ?
Options: a ) 60 kmph , b ) 76 kmph , c ) 34 kmph , d ) 43 kmph , e ) 40 kmph
Rationale: "s = ( 100 + 300 ) / 24 = 400 / 24 * 18 / 5 = 60 answer : a"
Answer: a
Python program:
a = 100 + 300 
b = a / 1000
c = 24 / 3600
d = b / c
Problem: ( 0.15 ) ( power 3 ) - ( 0.06 ) ( power 3 ) / ( 0.15 ) ( power 2 ) + 0.009 + ( 0.06 ) ( power 2 ) is :
Options: a ) 0.09 , b ) 0.08 , c ) 0.1 , d ) 0.07 , e ) none of them
Rationale: "given expression = ( 0.15 ) ( power 3 ) - ( 0.06 ) ( power 3 ) / ( 0.15 ) ( power 2 ) + ( 0.15 x 0.06 ) + ( 0.06 ) ( power 2 ) = a ( power 3 ) - b ( power 3 ) / a ( power 2 ) + ab + b ( power 2 ) = ( a - b ) = ( 0.15 - 0.06 ) = 0.09 answer is a ."
Answer: a
Python program:
a = 0 ** 15
b = 0 ** 6
c = a - b
d = 0 ** 15
e = d + 0 
f = 0 ** 6
g = e + f 
h = c / g
Problem: if the remainder is 8 when positive integer n is divided by 12 , what is the remainder when n is divided by 6 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "assume x is quotient here , n = 12 x + 8 - - - - - - - - - - ( 1 ) and n = 6 x + ? we can also write equation ( 1 ) as : n = ( 12 x + 6 ) + 2 . ie 6 ( 2 x + 1 ) + 2 ie the first term is perfectly divisible by 6 . so , the remainder left is 2 . so , answer ( c ) is right choice ."
Answer: c
Python program:
a = 12 / 6
Problem: if 9 men do a work in 80 days , in how many days will 20 men do it ?
Options: a ) 18 days , b ) 36 days , c ) 42 days , d ) 48 days , e ) 44 days
Rationale: "9 * 80 = 20 * x x = 36 days answer : b"
Answer: b
Python program:
a = 9 * 80
b = a / 20
Problem: if a 6 cm cube is cut into 1 cm cubes , then what is the percentage increase in the surface area of the resulting cubes ?
Options: a ) 300 % , b ) 400 % , c ) 500 % , d ) 600 % , e ) 750 %
Rationale: "the area a of the large cube is 6 * 6 * 6 = 216 square cm . the area of the 216 small cubes is 216 * 6 = 6 a , an increase of 500 % . the answer is c ."
Answer: c
Python program:
a = surface_cube * (
b = a / surface_cube
c = 100 * b
Problem: if 2994 ÷ 14.5 = 172 , then 29.94 ÷ 1.45 = ?
Options: a ) 17.2 , b ) 18.2 , c ) 19.2 , d ) 15.2 , e ) 16.2
Rationale: "29.94 / 1.45 = 299.4 / 14.5 = ( 2994 / 14.5 ) x 1 / 10 ) [ here , substitute 172 in the place of 2994 / 14.5 ] = 172 / 10 = 17.2 answer is a ."
Answer: a
Python program:
a = 29 / 94
Problem: what is the rate percent when the simple interest on rs . 2000 amount to rs . 500 in 2 years ?
Options: a ) 5 % , b ) 6 % , c ) 12.5 % , d ) 95 % , e ) 1 %
Rationale: "interest for 2 yrs = 500 interest for 1 yr = 250 interest rate = 250 / 2000 x 100 = 12.5 % answer : c"
Answer: c
Python program:
a = 100 * 500
b = 2000 * 2
c = a / b
Problem: a small pool filled only with water will require an additional 400 gallons of water in order to be filled to 80 % of its capacity . if pumping in these additional 400 gallons of water will increase the amount of water in the pool by 30 % , what is the total capacity of the pool in gallons ?
Options: a ) 1000 , b ) 1250 , c ) 1300 , d ) 1600 , e ) 1750
Rationale: "since pumping in additional 400 gallons of water will increase the amount of water in the pool by 30 % , then initially the pool is filled with 1,000 gallons of water . so , we have that 1,000 + 400 = 0.8 * { total } - - > { total } = 1,750 . answer : e ."
Answer: e
Python program:
a = 400 * 100
b = a / 30
c = b + 400 
d = 80 / 100
e = c / d
Problem: a train 90 m long is running at 20 kmph . in how much time will it pass a platform 80 m long ?
Options: a ) 15.6 seconds , b ) 24.6 seconds , c ) 28.6 seconds , d ) 13.6 seconds , e ) 35.6 seconds
Rationale: distance travelled = 90 + 80 m = 170 m speed = 20 * 5 / 8 = 25 / 2 m time = 170 * 2 / 25 = 13.6 seconds answer : d .
Answer: d
Python program:
a = 90 + 80 
b = 20 * const_0_2778
c = a / b
Problem: x varies inversely as square of y . given that y = 2 for x = 1 . the value of x for y = 6 will be equal to :
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 5 , d ) 1 / 9 , e ) 1 / 3
Rationale: "given x = k / y 2 , where k is a constant . now , y = 2 and x = 1 gives k = 4 . x = 4 / y 2 = > x = 4 / 62 , when y = 6 = > x = 4 / 36 = 1 / 9 . answer : d"
Answer: d
Python program:
a = 2 ** 2
b = 1 * a
c = 6 ** 2
d = b / c
Problem: 5 / 4 of all married couples have more than one child . 2 / 5 of all married couples have more than 3 children . what fraction of all married couples have 2 or 3 children ?
Options: a ) 1 / 5 , b ) 1 / 4 , c ) 17 / 20 , d ) 3 / 5 , e ) it can not be determined from the given information .
Rationale: "plug in simple numbers . take 100 couples for example . 5 / 4 of 100 couples have more than one child = 125 couples . 2 / 5 of 100 couples have more than 3 kids = 40 couples . this implies that 40 couples are a subset of 125 couples we need to find couples that have 2 or 3 kids , so essentially , it is 125 - 40 = 85 . fraction will be 85 / 100 = 17 / 20 . option c"
Answer: c
Python program:
a = 5 / 4
b = 2 / 4
c = a - b
Problem: in the first 10 overs of a cricket game , the run rate was only 4.6 . what should be the run rate in the remaining 40 overs to reach the target of 282 runs ?
Options: a ) 4.25 , b ) 5.9 , c ) 6.25 , d ) 7 , e ) 7.5
Rationale: "required run rate = 282 - ( 4.6 x 10 ) = 236 236 / 40 = 5.9 b )"
Answer: b
Python program:
a = 10 * 4
b = 282 - a
c = b / 40
Problem: calculate the dividend from moses ' s stock , if he invested rs . 3000 at 72 to obtain an income of rs . 210 .
Options: a ) 3 , b ) 9 , c ) 3 , d ) 4 , e ) 5.04
Rationale: by investing rs . 3000 , income = rs . 210 by investing rs . 72 , income = 210 ã — 72 / 3000 = 5.04 ie , dividend = 5.04 % answer is e .
Answer: e
Python program:
a = 210 * 72
b = a / 3000
Problem: perimeter of the back wheel = 9 feet , front wheel = 7 feet on a certain distance , the front wheel gets 10 revolutions more than the back wheel . what is the distance ?
Options: a ) 315 , b ) 325 , c ) 335 , d ) 345 , e ) 305
Rationale: for 1 revolution : front wheel goes 7 ft . and back wheel goes 9 feet . let distance is x feet . x / 7 = ( x / 9 ) + 10 or , 2 x / 63 = 10 or , x = ( 10 * 63 ) / 2 therefore , x = 315 answer : a
Answer: a
Python program:
a = 10 * 7
b = 9 - 7
c = a / b
d = 9 * c
Problem: how many positive integers less than 9,000 are there in which the sum of the digits equals 5 ?
Options: a ) 56 , b ) 57 , c ) 58 , d ) 59 , e ) 60
Rationale: "basically , the question asks how many 4 digit numbers ( including those in the form 0 xxx , 00 xx , and 000 x ) have digits which add up to 5 . think about the question this way : we know that there is a total of 5 to be spread among the 4 digits , we just have to determine the number of ways it can be spread . let x represent a sum of 1 , and | represent a seperator between two digits . as a result , we will have 5 x ' s ( digits add up to the 5 ) , and 3 | ' s ( 3 digit seperators ) . so , for example : xx | x | x | x = 2111 | | xxx | xx = 0032 etc . there are 8 c 3 ways to determine where to place the separators . hence , the answer is 8 c 3 = 56 . a"
Answer: a
Python program:
a = 4 + 5 
b = a - 1
c = math.factorial(b)
d = math.factorial(5)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
Problem: a certain airline ' s fleet consisted of 110 type a planes at the beginning of 1980 . at the end of each year , starting with 1980 , the airline retired 3 of the type a planes and acquired 4 new type b plans . how many years did it take before the number of type a planes left in the airline ' s fleet was less than 50 percent of the fleet ?
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19
Rationale: let x be the number of years . 4 x > 110 - 3 x 7 x > 110 x > 15 + 5 / 7 the answer is b .
Answer: b
Python program:
a = 3 + 4 
b = 110 / a
Problem: how many positive integers less than 80 are multiples of 4 but not multiples of 6 ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: "the lcm of 4 and 6 is 12 . if x < 80 and x is divisible by 4 not by 6 - - > x is not divisible by 12 . from 1 - - > 80 , we have 6 numbers which is divisible by 12 : 12 , 24 , 36 , 48 , 60 , 72 . from 1 - - > 80 , we have ( 72 - 4 ) / 4 + 1 = 18 numbers divisible by 4 . therefore , our answer is 18 - 6 = 12 numbers . e"
Answer: e
Python program:
a = 4 + 4 
b = a - 1
c = math.factorial(b)
d = math.factorial(4)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
Problem: two employees x and y are paid a total of rs . 550 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?
Options: a ) rs . 200 , b ) rs . 250 , c ) rs . 300 , d ) rs . 350 , e ) rs . 370
Rationale: "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 550 but x = 120 % of y = 120 y / 100 = 12 y / 10 ∴ 12 y / 10 + y = 550 ⇒ y [ 12 / 10 + 1 ] = 550 ⇒ 22 y / 10 = 550 ⇒ 22 y = 5500 ⇒ y = 5500 / 22 = 500 / 2 = rs . 250 b )"
Answer: b
Python program:
a = 1 + 4 
b = a * 2
c = 550 * b
d = 1 + 4 
e = d * 2
f = e + 1 
g = f * 2
h = c / g
Problem: set a contains all the even numbers between 32 and 80 inclusive . set b contains all the even numbers between 62 and 110 inclusive . what is the difference between the sum of elements of set b and the sum of the elements of set a ?
Options: a ) 450 , b ) 550 , c ) 650 , d ) 750 , e ) 850
Rationale: "each term in set b is 30 more than the corresponding term in set a . the difference of the sums = 25 * 30 = 750 . the answer is d ."
Answer: d
Python program:
a = 62 - 32
b = 80 - 32
c = b / 2
d = c + 1 
e = a * d
Problem: company c produces toy trucks at a cost of $ 5.00 each for the first 100 trucks and $ 3.50 for each additional truck . if 500 toy trucks were produced by company c and sold for $ 9.00 each , what was company c ’ s gross profit ?
Options: a ) $ 2,250 , b ) $ 2,900 , c ) $ 2,600 , d ) $ 3,250 , e ) $ 2,500
Rationale: "cost of 500 trucks : ( 100 * 5 ) + ( 400 * 3.5 ) = 500 + 1400 = $ 1900 revenue : 500 * 9 = $ 4500 profit : 4500 - 1900 = $ 2600 option c is correct"
Answer: c
Python program:
a = 500 * 9
b = 5 * 0
c = a - b
d = 500 - 100
e = d * 3
f = c - e
g = f / 1000
h = math.floor(g)
Problem: p and q invested in a business . the profit earned was divided in the ratio 3 : 5 . if p invested rs 12000 , the amount invested by q is
Options: a ) 30000 , b ) 50000 , c ) 40000 , d ) 20000 , e ) 60000
Rationale: "let the amount invested by q = q 12000 : q = 3 : 5 ⇒ 12000 × 5 = 3 q ⇒ q = ( 12000 × 5 ) / 3 = 30000 answer is a"
Answer: a
Python program:
a = 12000 / 2
b = a * 5
Problem: in a maths test , students were asked to find 5 / 16 of a certain number . one of the students by mistake found 5 / 6 th of that number and his answer was 300 more than the correct answer . find the number .
Options: a ) 125 , b ) 280 , c ) 384 , d ) 400 , e ) 576
Rationale: explanation : let the number be x . 5 * x / 6 = 5 * x / 16 + 300 25 * x / 48 = 300 x = 576 answer e
Answer: e
Python program:
a = 300 * 16
b = a * 6
c = 5 * 16
d = 5 * 6
e = c - d
f = b / e
Problem: seed mixture x is 40 percent ryegrass and 60 percent bluegrass by weight ; seed mixture y is 25 percent ryegrass and 75 percent fescue . if a mixture of x and y contains 30 percent ryegrass , what percent of the weight of this mixture is x ?
Options: a ) 10 % , b ) 33.33 % , c ) 40 % , d ) 50 % , e ) 66.66 %
Rationale: "qnty . ( cheaper ) / qty . ( dearer ) = ( dearer - mean ) / ( mean - cheaper ) thus qy / qx = ( 40 - 30 ) / ( 30 - 25 ) = 2 therefore qy = 2 qx and qy + qx = 100 % ( total ) . hence qx = 33.33 % answer : b"
Answer: b
Python program:
a = 30 - 25
b = 40 / 100
c = 25 / 100
d = b - c
e = a / d
Problem: how many multiples of 2 are there between 1 and 50 , exclusive ?
Options: a ) 21 , b ) 22 , c ) 24 , d ) 26 , e ) 28
Rationale: "24 multiples of 2 between 1 and 50 exclusive . from 2 * 1 upto 2 * 24 , ( 1,2 , 3,4 , . . . , 24 ) . hence , 24 multiples ! correct option is c"
Answer: c
Python program:
a = 50 - 1
b = a / 2
c = b + 1
Problem: a library branch originally contained 18365 volumes , 30 % of which were fiction novels . 1 / 3 of the volumes were transferred to another location and 1 / 3 of the volumes transferred were fiction novels . what percent of the remaining collection was fiction novels ?
Options: a ) 2.5 % , b ) 17.67 % , c ) 28.3 % , d ) 45.2 % , e ) 73.6 %
Rationale: "fiction novels = 5,509 transferred to another location = 6,121 transferred fiction novels = 2,040 non transferred fiction novels = 3,469 percent of the remaining collection was fiction novels = 3469 / ( 18365 - 6121 ) * 100 = > 28.332 . . . % hence answer will be ( c )"
Answer: c
Python program:
a = 30 / 100
b = 1 / 3
c = 1 - b
d = a * c
e = 1 / 3
f = 1 - e
g = d / f
h = g * 100
Problem: a person spent rs . 5,040 from his salary on food and 5,000 on house rent . after that he was left with 20 % of his monthly salary . what is his monthly salary ?
Options: a ) 22,550 , b ) 32,550 , c ) 52,550 , d ) 62,550 , e ) 12,550
Rationale: total money spent on food and house rent = 5,040 + 5,000 = 10,040 which is 100 - 20 = 80 % of his monthly salary ∴ his salary = 10040 x 100 / 80 = 12550 answer : e
Answer: e
Python program:
a = 4 + 1 
b = a * 100
c = b + 20 
d = math.sqrt(100)
e = c / d
Problem: a computer factory produces 5376 computers per month at a constant rate , how many computers are built every 30 minutes assuming that there are 28 days in one month ?
Options: a ) 2.25 . , b ) 3.125 . , c ) 4.5 . , d ) 4.00 . , e ) 6.25 .
Rationale: "number of hours in 28 days = 28 * 24 number of 30 mins in 28 days = 28 * 24 * 2 number of computers built every 30 mins = 5376 / ( 28 * 24 * 2 ) = 4.00 answer d"
Answer: d
Python program:
a = 5376 / 28
b = 28 - 4
c = b * 2
d = a / c
Problem: if the radius of a circle is increased by 40 % then the area is increased by :
Options: a ) 44 % , b ) 120 % , c ) 96 % , d ) 40 % , e ) none of the above
Rationale: "initially a = pi * r 2 now r 2 = 140 / 100 r then area = pi * ( 140 r / 100 ) 2 area = 196 r / 100 that is area increases from 100 to 196 = increase in area = 96 % answer : c"
Answer: c
Python program:
a = 100 / 100
b = 100 / 100
c = 40 / 100
d = b - c
e = d ** 2
f = a - e
g = f * 100
Problem: if a cost college rs 0.70 a companyto produce a program for yhe home coming football game . if rs 15000 was received for addvertisement in the pgm , how many copies rs 0.50 a copy must be sold to make a profit of rs 8000
Options: a ) 15000 , b ) 25000 , c ) 45000 , d ) 32000 , e ) 35000
Rationale: let no . of pages be x while selling with 0.70 paise / page total cost = 0.70 * x while selling with 0.50 paise / page toatal cost = 0.50 * x now according to question - ( 0.70 x - 0.50 x ) + 8000 = 15000 therefore , x = 35000 copies must be sold answer : e
Answer: e
Python program:
a = 15000 - 8000
b = 0 - 7
c = a / b
Problem: if a trader sold two cars each at rs . 325475 and gains 14 % on the first and loses 14 % on the second , then his profit or loss percent on the whole is ?
Options: a ) 1.44 % , b ) 1.74 % , c ) 1.84 % , d ) 1.96 % , e ) 1.24 %
Rationale: "sp of each car is rs . 325475 , he gains 14 % on first car and losses 14 % on second car . in this case , there will be loss and percentage of loss is given by = [ ( profit % ) ( loss % ) ] / 100 = ( 14 ) ( 14 ) / 100 % = 1.96 % answer : d"
Answer: d
Python program:
a = 14 * 14
b = a / 100
Problem: if the wheel is 28 cm then the number of revolutions to cover a distance of 1056 cm is ?
Options: a ) 3 , b ) 5 , c ) 26 , d ) 12 , e ) 6
Rationale: "2 * 22 / 7 * 28 * x = 1056 = > x = 6 answer : e"
Answer: e
Python program:
a = 3 * 100
b = 1 * 10
c = a + b 
d = c + 4 
e = d / 100
f = 2 * e
g = f * 28
h = 1056 / g
Problem: how much more would rs . 30000 fetch , after two years , if it is put at 20 % p . a . compound interest payable half yearly than if is put at 20 % p . a . compound interest payable yearly ?
Options: a ) 482 , b ) 725 , c ) 992 , d ) 837 , e ) 723
Rationale: 30000 ( 11 / 10 ) 4 - 30000 ( 6 / 5 ) 2 = 723 answer : e
Answer: e
Python program:
a = 20 / 100
b = a / 2
c = 1 + b 
d = c ** 4
e = d * 30000
f = 20 / 100
g = f + 1 
h = g ** 2
i = h * 30000
j = e - i
Problem: a survey was sent to 70 customers , 7 of whom responded . then the survey was redesigned and sent to another 63 customers , 9 of whom responded . by approximately what percent did the response rate increase from the original survey to the redesigned survey ?
Options: a ) 2 % , b ) 6 % , c ) 4 % , d ) 28 % , e ) 63 %
Rationale: case 1 : ( 7 / 70 ) = x / 100 x = 10 % case 2 : ( 9 / 63 ) = y / 100 y = 14 % so percent increase is = ( y - x ) = ( 14 - 10 ) % = 4 % answer is c
Answer: c
Python program:
a = 9 / 63
b = 7 / 70
c = a - b
d = c * 100
e = math.floor(d)
Problem: what number should replace the question mark ? 3 , 30 , 11 , 24 , 19 , 18 , - - - ?
Options: a ) 24 , b ) 22 , c ) 27 , d ) 25 , e ) 28
Rationale: "answer : c 3 , 30 , 11 , 24 , 19 , 18 , 27 ? there are two alternate sequences : + 8 and - 6 ."
Answer: c
Python program:
a = 3 + 3 
b = a + 3 
c = b + 3
Problem: a factory producing tennis balls stores them in either big boxes , 25 balls per box , or small boxes , 20 balls per box . if 104 freshly manufactured balls are to be stored , what is the least number of balls that can be left unboxed ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: we have to work with multiples of 20 and 25 . first , we must know the limits of this multiples , so : 105 / 25 = 4 . . . . so the max is 4 105 / 20 = 5 . . . so the max is 5 105 - 100 = 5 answer : e
Answer: e
Python program:
a = 25 - 20
Problem: how many seconds will a train 250 meters long take to cross a platform 200 meters long if the speed of the train is 90 kmph ?
Options: a ) 18 sec , b ) 15 sec , c ) 21 sec , d ) 16 sec , e ) 20 sec
Rationale: "d = 250 + 200 = 450 s = 90 * 5 / 18 = 25 mps t = 450 / 25 = 18 sec a ) 18 sec"
Answer: a
Python program:
a = 200 + 250 
b = 90 * const_0_2778
c = a / b
Problem: if x / y = 7 / 3 , then ( x + y ) / ( x - y ) = ?
Options: a ) 5 , b ) 5 / 2 , c ) - 1 / 6 , d ) - 1 / 5 , e ) - 5
Rationale: "any x and y satisfying x / y = 7 / 3 should give the same value for ( x + y ) / ( x - y ) . say x = 7 and y = 3 , then ( x + y ) / ( x - y ) = ( 7 + 3 ) / ( 7 - 3 ) = 5 / 2 . answer : b ."
Answer: b
Python program:
a = 7 + 3 
b = 7 - 3
c = a / b
Problem: working at their respective constant rates , machine a makes 100 copies in 10 minutes and machine b makes 150 copies in 15 minutes . if these machines work simultaneously at their respective rates for 30 minutes , what is the total number of copies that they will produce ?
Options: a ) 250 , b ) 600 , c ) 675 , d ) 700 , e ) 750
Rationale: "machine a can produce 100 * 30 / 10 = 300 copies and , machine b can produce 150 * 30 / 15 = 300 copies total producing 600 copies . b is the answer"
Answer: b
Python program:
a = 100 / 10
b = 150 / 15
c = a + b 
d = c * 30
Problem: the banker ' s gain on a sum due 3 years hence at 12 % per annum is rs . 360 . the banker ' s discount is :
Options: a ) rs . 1360 , b ) rs . 1000 , c ) rs . 360 , d ) rs . 640 , e ) none of these
Rationale: "explanation : bg = rs . 360 t = 3 years r = 12 % td = ( bg × 100 ) / tr = ( 360 × 100 ) / ( 3 × 12 ) = rs . 1000 bg = bd – td = > bd = bg + td = 360 + 1000 = rs . 1360 answer : option a"
Answer: a
Python program:
a = 360 * 100
b = 12 * 3
c = a / b
d = 360 + c
Problem: calculate the sum of first 19 natural numbers .
Options: a ) 190 , b ) 120 , c ) 150 , d ) 199 , e ) 110
Rationale: solution we know that ( 1 + 2 + 3 + . . . . . + 19 ) = n ( n + 1 ) / 2 therefore ( 1 + 2 + 3 + . . . . + 19 ) = ( 19 × 20 / 2 ) = 190 . answer a
Answer: a
Python program:
a = 19 + 1 
b = 19 / 2
c = a * b
Problem: a is twice as good a workman as b and they took 5 days together to do the work b alone can do it in ?
Options: a ) 15 days , b ) 88 days , c ) 21 days , d ) 11 days , e ) 13 days
Rationale: "wc = 2 : 1 2 x + x = 1 / 5 x = 1 / 15 = > 15 days answer : a"
Answer: a
Python program:
a = 2 + 1 
b = 5 * a
c = b / 2
d = c * 2