euclaise/mathqa_programs huggingface dataset:
Problem: the area of the house of a hall is 20 m 2 that of a longer wall 10 m 2 and of the shorter wall 8 m 2 , find the edge of the new cube ?
Options: a ) 45 m 3
b ) 40 m 3
c ) 60 m 3
d ) 600 m 3
e ) 300 m 3
Rationale: lb = 20 ; lh = 10 ; fh = 8 ( lbh ) 2 = 20 * 10 * 8 = > lbh = 40 m 3 answer : b
Answer: b
Python program:
a = 20 * 10
b = 2 * a
c = b / 10
Problem: there is a 45 cm line marked at each centimeter and an insect is placed at every centimeter . 9 frogs are trained to jump a constant distance . the first one jumps 2 cm in every leap , the second one jumps 3 cm and so on until the 9 th one jumps 10 cm in every leap and they eat any insect that is available at that spot . if all of them start from start line and finish the entire 45 cm , how many insects were still left after the race was over ?
Options: a ) 0 , b ) 4 , c ) 6 , d ) 7 , e ) 10
Rationale: "only the prime numbers greater than 10 and less than 45 were left . that is 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41 , and 43 . the total is 10 . the answer is e ."
Answer: e
Python program:
a = 10 + 2
Problem: the present population of a town is 4032 . population increase rate is 20 % p . a . find the population of town before 2 years ?
Options: a ) 2500 , b ) 2800 , c ) 3500 , d ) 3600 , e ) 2050
Rationale: "p = 4032 r = 20 % required population of town = p / ( 1 + r / 100 ) ^ t = 4032 / ( 1 + 20 / 100 ) ^ 2 = 4032 / ( 6 / 5 ) ^ 2 = 2800 ( approximately ) answer is b"
Answer: b
Python program:
a = 4032 * 20
b = a / 100
c = 4032 + b
Problem: a cistern has a leak which would empty the cistern in 20 minutes . a tap is turned on which admits 2 liters a minute into the cistern , and it is emptied in 24 minutes . how many liters does the cistern hold ?
Options: a ) 480 , b ) 240 , c ) 289 , d ) 270 , e ) 927
Rationale: "1 / x - 1 / 20 = - 1 / 24 x = 120 120 * 2 = 240 answer : b"
Answer: b
Python program:
a = 24 * 20
Problem: the present population of a town is 10000 . population increase rate is 10 % p . a . find the population of town after 2 years ?
Options: a ) 10000 , b ) 11100 , c ) 15000 , d ) 12100 , e ) 14520
Rationale: "p = 10000 r = 10 % required population of town = p ( 1 + r / 100 ) ^ t = 10000 ( 1 + 10 / 100 ) ^ 2 = 10000 ( 11 / 10 ) ^ 2 = 12100 answer is d"
Answer: d
Python program:
a = 10000 * 10
b = a / 100
c = 10000 + b
Problem: john has taken 4 ( 4 ) tests that have an average of 82 . in order to bring his course grade up to a ‘ b ’ , he will need to have a final average of 86 . what will he need to average on his final two tests to achieve this grade ?
Options: a ) 87 , b ) 90 , c ) 92 , d ) 94 , e ) 97
Rationale: traditional method : total scored till now 82 * 4 = 328 total score to avg 86 in 6 tests = 86 * 6 = 516 total to be scored on 2 tests = 516 - 328 = 188 avg on 2 tests = 188 / 2 = 94 answer : d
Answer: d
Python program:
a = 86 * 2
b = a - 82
Problem: a car started running at a speed of 38 km / hr and the speed of the car was increased by 2 km / hr at the end of every hour . find the total distance covered by the car in the first 10 hours of the journey .
Options: a ) 47 km , b ) 76 km , c ) 25 km , d ) 15 km , e ) 30 km
Rationale: a 47 km the total distance covered by the car in the first 10 hours = 38 + 40 + 42 + 44 + 46 + 48 + 50 + 52 + 54 + 56 = sum of 10 terms in ap whose first term is 30 and last term is 56 = 10 / 2 [ 38 + 56 ] = 470 km .
Answer: a
Python program:
a = 2 * 10
b = 38 + a 
c = b + 38 
d = c / 2
Problem: 3 containers a , b and c are having mixtures of milk and water in the ratio of 1 : 5 and 3 : 5 and 5 : 7 respectively . if the capacities of the containers are in the ratio of all the 3 containers are in the ratio 5 : 4 : 5 , find the ratio of milk to water , if the mixtures of all the 3 containers are mixed together .
Options: a ) 53 : 115 , b ) 55 : 115 , c ) 115 : 55 , d ) 5 : 115 , e ) 115 : 53
Rationale: assume that there are 500400 and 500 liters respectively in the 3 containers . then , we have , 83.33 , 150 and 208.33 liters of milk in each of the three containers . thus , the total milk is 441.66 liters . hence , the amount of water in the mixture is 1400 - 441.66 = 958.33 liters . hence , the ratio of milk to water is 441.66 : 958.33 = > 53 : 115 ( using division by . 3333 ) the calculation thought process should be ( 441 * 2 + 2 ) : ( 958 * 3 + 1 ) = 1325 : 2875 dividing by 25 = > 53 : 115 . answer a 53 : 115
Answer: a
Python program:
a = 1 + 5 
b = 1 / a
c = b * 5
d = 3 + 5 
e = 3 / d
f = e * 4
g = c + f 
h = 5 + 7 
i = 5 / h
j = i * 5
k = g + j 
l = 5 + 4 
m = l + 5 
n = 1 + 5 
o = 1 / n
p = o * 5
q = 3 + 5 
r = 3 / q
s = r * 4
t = p + s 
u = 5 + 7 
v = 5 / u
w = v * 5
x = t + w 
y = m - x
z = k / y
Problem: the length of a rectangle is reduced by 22 % . by what % would the width have to be increased to maintainthe original area ?
Options: a ) 15 % , b ) 20 % , c ) 28 % , d ) 35 % , e ) 40 %
Rationale: "sol . required change = ( 22 * 100 ) / ( 100 - 22 ) = 28 % c"
Answer: c
Python program:
a = 100 - 22
b = a / 100
c = 1 - b
d = 100 - 22
e = d / 100
f = c / e
g = f * 100
Problem: if 5 x = 7 y and xy ≠ 0 , what is the ratio of 1 / 5 * x to 1 / 6 * y ?
Options: a ) 25 / 6 , b ) 42 / 25 , c ) 6 / 5 , d ) 5 / 6 , e ) 25 / 36
Rationale: "5 x = 7 y = > x / y = 7 / 5 1 / 5 * x to 1 / 6 * y = x / y * 6 / 5 = ( 7 / 5 ) * ( 6 / 5 ) = 42 / 25 ans : b"
Answer: b
Python program:
a = 1 / 3
b = 1 / 5
c = a / b
d = 7 / 5
e = c * d
Problem: if 10 litres of an oil of rs . 50 per litres be mixed with 5 litres of another oil of rs . 67 per litre then what is the rate of mixed oil per litre ?
Options: a ) rs . 49.17 , b ) rs . 51.03 , c ) rs . 54.17 , d ) rs . 55.66 , e ) none of the above
Rationale: "50 * 10 = 500 67 * 5 = 335 835 / 15 = 55.66 answer : d"
Answer: d
Python program:
a = 10 * 50
b = 5 * 67
c = a + b 
d = 10 + 5 
e = c / d
Problem: the sum of first 45 natural numbers is :
Options: a ) 1035 , b ) 1040 , c ) 1042 , d ) 1045 , e ) 1050
Rationale: "let sn = ( 1 + 2 + 3 + . . . + 45 ) . this is an a . p . in which a = 1 , d = 1 , n = 45 . sn = n [ 2 a + ( n - 1 ) d ] = 45 x [ 2 x 1 + ( 45 - 1 ) x 1 ] = 45 x 46 = ( 45 x 23 ) 2 2 2 = 45 x ( 20 + 3 ) = 45 x 20 + 45 x 3 = 900 + 135 = 1035 . shorcut method : sn = n ( n + 1 ) = 45 ( 45 + 1 ) = 1035 . 2 2 a"
Answer: a
Python program:
a = 45 + 1 
b = 45 * a
c = b / 2
Problem: there is a 30 % chance sandy will visit china this year , while there is a 60 % chance that she will visit malaysia this year . what is the probability that sandy will visit either china or malaysia this year , but not both ?
Options: a ) 42 % , b ) 48 % , c ) 54 % , d ) 60 % , e ) 66 %
Rationale: p ( china and not malaysia ) = 0.3 * 0.4 = 0.12 p ( malaysia and not china ) = 0.6 * 0.7 = 0.42 total probability = 0.12 + 0.42 = 0.54 = 54 % the answer is c .
Answer: c
Python program:
a = 30 + 60 
b = 5 * 5
c = b * 4
d = a / c
Problem: mike earns $ 14 per hour and phil earns $ 10.5 per hour . approximately how much less , as a percentage , does phil earn than mike per hour ?
Options: a ) 25 % , b ) 32.5 % , c ) 37 % , d ) 37.5 % , e ) 40 %
Rationale: "let it be x % less , then = 14 ( 1 - x / 100 ) = 10.5 1 - x / 100 = 10.5 / 14 x = 350 / 14 x = 25 % answer : a"
Answer: a
Python program:
a = 10 / 5
b = a * 100
Problem: the total price of a basic computer and printer are $ 2500 . if the same printer had been purchased with an enhanced computer whose price was $ 500 more than the price of the basic computer , then the price of the printer would have been 1 / 6 of that total . what was the price of the basic computer ?
Options: a ) 1500 , b ) 1600 , c ) 1750 , d ) 1900 , e ) 2000
Rationale: let the price of basic computer be c and the price of the printer be p : c + p = $ 2,500 . the price of the enhanced computer will be c + 500 and total price for that computer and the printer will be 2,500 + 500 = $ 3,000 . now , we are told that the price of the printer is 1 / 6 of that new total price : p = 1 / 6 * $ 3,000 = $ 500 . plug this value in the first equation : c + 500 = $ 2,500 - - > c = $ 2000 answer : e .
Answer: e
Python program:
a = 2500 + 500 
b = a / 6
c = 2500 - b
Problem: find the average of first 4 multiples of 9 ?
Options: a ) 10 , b ) 12.6 , c ) 22.5 , d ) 31.3 , e ) 40.8
Rationale: "average = ( 9 + 18 + 27 + 36 ) / 4 = 22.5 answer is c"
Answer: c
Python program:
a = 4 + 1 
b = 4 + 1 
c = b + 2 
d = a + c 
e = 9 - 4
f = 9 - 2
g = e + f 
h = d + g 
i = h / 4
Problem: company a ' s workforce consists of 10 percent managers and 90 percent software engineers . company b ' s workforce consists of 30 percent managers , 10 percent software engineers , and 60 percent support staff . the two companies merge , every employee stays with the resulting company , and no new employees are added . if the resulting company í s workforce consists of 25 percent managers , what percent of the workforce originated from company a ?
Options: a ) 10 % , b ) 20 % , c ) 25 % , d ) 50 % , e ) 75 %
Rationale: let say company a has x employes and b has y employees . now they merge and total no of employees = x + y employees . per the question company a ' s workforce consists of 10 percent managers and 90 percent software engineers . company b ' s workforce consists of 30 percent managers , 10 percent software engineers , and 60 percent support staff . we translate it into equation as follows : . 1 x + . 3 y = . 25 ( x + y ) = > x + 3 y = 2.5 ( x + y ) = > . 5 y = 1.5 x = > y = 3 x . now we know total employee = x + y . we need to find % age of x in total ( x + y ) ie x / ( x + y ) x 100 % = > x / ( 3 x + x ) [ substitute y = 3 x ] = > x / 4 x x 100 % = > . 25 x 100 % = > 25 % . answer : c
Answer: c
Python program:
a = 60 / 30
b = a * 25
c = b / 10
d = c + 90 
e = d - 60
f = e - 10
Problem: how many positive integers less than 100 are neither multiples of 5 or 6 .
Options: a ) a ) 30 , b ) b ) 31 , c ) c ) 32 , d ) d ) 33 , e ) e ) 67
Rationale: "to answer this q we require to know 1 ) multiples of 5 till 100 = 100 / 5 = 20 2 ) multiples of 6 till 100 = 100 / 6 = 16.66 = 16 add the two 20 + 16 = 36 ; subtract common terms that are multiple of both 5 and 6 . . lcm of 5 and 6 = 30 multiples of 30 till 100 = 100 / 30 = 3.3 = 3 so total multiples of 2 and 3 = 36 - 3 = 33 ans = 100 - 33 = 67 e"
Answer: e
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 and b walk around a circular track . they start at 9 a . m . from the same point in the opposite directions . a and b walk at a speed of 2 rounds per hour and 3 rounds per hour respectively . how many times shall they cross each other before 12 : 00 p . m . ?
Options: a ) 28 , b ) 27 , c ) 26 , d ) 25 , e ) 20
Rationale: "sol . relative speed = ( 2 + 3 ) = 5 rounds per hour . so , they cross each other 5 times in an hour . hence , they cross each other 20 times before 12 : 00 p . m . answer e"
Answer: e
Python program:
a = 2 + 3 
b = 2 + 3 
c = a + b
Problem: if n is a positive integer and n ^ 3 is a multiple of 550 , what is the least possible value of n ?
Options: a ) 8 , b ) 27 , c ) 81 , d ) 110 , e ) 125
Rationale: "cube of a number entails having 3 copies of the original prime factors . since 550 is a factor of n ^ 3 the least possible value of n is 5 ( 11 ) 2 = 110 the answer is d ."
Answer: d
Python program:
a = 550 / 3
b = math.sqrt(a)
c = b * 3
Problem: two goods trains each 375 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 ) 40 , b ) 45 , c ) 48 , d ) 51 , e ) 36
Rationale: "relative speed = 45 + 30 = 75 km / hr . 75 * 5 / 18 = 125 / 6 m / sec . distance covered = 375 + 375 = 750 m . required time = 750 * 6 / 125 = 36 sec . answer : option e"
Answer: e
Python program:
a = 45 + 30
Problem: if x is invested in a bank at a rate of simple interest of y % p . a . for two years , then the interest earned is 300 . if x is invested at y % p . a . , for two years when the interest is compounded annually , the interest is 307.50 . what is the value of x ?
Options: a ) 8000 , b ) 6000 , c ) 5000 , d ) 4000 , e ) 3000
Rationale: "simple way to solve this question is to use options . from si , we know that x * y = 15,000 . now , put the value of x = 3000 , we will have y = 5 % to calculate ci , now , we know 1 st year amount = 3000 + 5 % of 3000 = 3150 . 2 nd year , amount = 3150 + 5 % of 3150 = 3307.50 . we can see after 2 years interest = 3307.50 - 3000 = 307.50 . hence , it satisfies the question . hence e is the correct answer"
Answer: e
Python program:
a = 300 / 2
b = a ** 2
c = 307 - 50
d = b / c
Problem: a dress on sale in a shop is marked at $ d . during the discount sale its price is reduced by 25 % . staff are allowed a further 20 % reduction on the discounted price . if a staff member buys the dress what will she have to pay in terms of d ?
Options: a ) 0.6 d , b ) 0.7 d , c ) 0.5 d , d ) 0.8 d , e ) 0.9 d
Rationale: "effective discount = a + b + ab / 100 = - 25 - 20 + ( - 25 ) ( - 20 ) / 100 = - 40 sale price = d * ( 1 - 40 / 100 ) sale price = . 6 * d answer ( a )"
Answer: a
Python program:
a = 100 - 25
b = a / 100
c = 100 - 25
d = c / 100
e = 20 / 100
f = d * e
g = b - f
Problem: what is the normal price of an article sold at $ 108 after two successive discounts of 10 % and 20 % ?
Options: a ) $ 130 , b ) $ 140 , c ) $ 150 , d ) $ 160 , e ) $ 170
Rationale: "0.8 * 0.9 * cost price = $ 108 cost price = $ 150 the answer is c ."
Answer: c
Python program:
a = 100 - 10
b = a / 100
c = 100 - 20
d = c / 100
e = b * d
f = 108 / e
Problem: kim has 8 pairs of shoes ; each pair is a different color . if kim randomly selects 2 shoes without replacement from the 16 shoes , what is the probability that she will select 2 shoes of the same color ?
Options: a ) 2 / 5 , b ) 1 / 5 , c ) 1 / 9 , d ) 1 / 10 , e ) 1 / 15
Rationale: "total pairs = 16 c 2 = 120 ; same color pairs = 8 c 1 * 1 c 1 = 8 ; prob = 1 / 15 ans e"
Answer: e
Python program:
a = math.comb(16, 2)
b = 8 / a
Problem: how many factors does 16 ^ 2 have ?
Options: a ) 2 , b ) 8 , c ) 4 , d ) 25 , e ) 26
Rationale: "36 ^ 2 = 6 * 6 * 6 * 6 = 2 ^ 4 * 3 ^ 4 total factors = ( 4 + 1 ) * ( 4 + 1 ) = 2 * 2 = 4 answer c ."
Answer: c
Python program:
a = 10 * 2
b = 16 / a
Problem: there are 14 teams in a certain league and each team plays each of the other teams exactly once . what is the total number of games played ?
Options: a ) 91 , b ) 98 , c ) 105 , d ) 112 , e ) 119
Rationale: "14 c 2 = 91 the answer is a ."
Answer: a
Python program:
a = 14 - 1
b = 14 * a
c = b / 2
Problem: a technology company made a $ 5 million profit on its first $ 15 million in sales and a $ 12 million profit on its next $ 30 million in sales . by what percent did the ratio of profit to sales increase from the first $ 15 million in sales to the next $ 30 million in sales ?
Options: a ) 10 % , b ) 20 % , c ) 30 % , d ) 40 % , e ) 50 %
Rationale: solution : this is a percent increase problem . we will use the formula : percent change = ( new – old ) / old x 100 to calculate the final answer . we first set up the ratios of profits to sales . the first ratio will be for the first 15 million in sales , and the second ratio will be for the next 30 million in sales . because all of the sales are in millions , we do not have to express all the trailing zeros in our ratios . first 15 million profit / sales = 5 / 15 = 1 / 3 next 30 million profit / sales = 12 / 30 = 2 / 5 we can simplify each ratio by multiplying each by the lcm of the two denominators , which is 15 . keep in mind that we are able to do this only because our answer choices are expressed in percents . first 15 million royalties / sales = ( 1 / 3 ) x 15 = 5 next 30 million royalties / sales = ( 2 / 5 ) x 15 = 6 we can plug 5 and 6 into our percent change formula : ( new – old ) / old x 100 [ ( 6 – 5 ) / 5 ] x 100 1 / 5 x 100 , so a 20 % increase . answer b .
Answer: b
Python program:
a = 12 / 30
b = 5 / 15
c = a - b
d = 5 / 15
e = c / d
f = e * 100
Problem: a number is doubled and 9 is added . if the resultant is trebled , it becomes 63 . what is that number ?
Options: a ) 3.5 , b ) 6 , c ) 8 , d ) 7 , e ) 4
Rationale: "let the number be x . then , 3 ( 2 x + 9 ) = 63 2 x = 12 = > x = 6 answer : b"
Answer: b
Python program:
a = 3 * 9
b = 63 - a
c = 3 * 2
d = b / c
Problem: a bag holds 4 red marbles and 3 green marbles . if you removed two randomly selected marbles from the bag , without replacement , what is the probability that both would be red ?
Options: a ) 4 / 14 , b ) 1 / 5 , c ) 3 / 10 , d ) 2 / 5 , e ) 1 / 2
Rationale: "given : 4 r and 3 g marbles required : probability that 2 marbles removed without replacement are both red initially we have to pick one red from a total of 4 red and 3 green marbles after one red has been picked , we need to pick 1 red from a total of 3 red and 3 green marbles . p ( both red ) = ( 4 / 7 ) * ( 3 / 6 ) = 4 / 14 option a"
Answer: a
Python program:
a = math.comb(4, 4)
b = 2 + 0 
c = math.comb(b, 2)
d = a / c
Problem: a train speeds past a pole in 15 seconds and speeds past a platform 100 meters long in 25 seconds . its length in meters is :
Options: a ) 60 m , b ) 70 m , c ) 100 m , d ) 120 m , e ) 150 m
Rationale: "let the length of the train be x metres and its speed be y metres / sec . then x / y = 15 y = x / 15 x + 100 / 25 now , ( x + 100 ) / 25 = x / 15 x = 150 m answer : e"
Answer: e
Python program:
a = 2 - 1
b = 100 * a
Problem: a cab driver 5 days income was $ 300 , $ 150 , $ 750 , $ 400 , $ 500 . then his average income is ?
Options: a ) $ 500 , b ) $ 650 , c ) $ 420 , d ) $ 375 , e ) $ 625
Rationale: "avg = sum of observations / number of observations avg income = ( 300 + 150 + 750 + 400 + 500 ) / 5 = 420 answer is c"
Answer: c
Python program:
a = 300 + 150 
b = a + 750 
c = b + 400 
d = c + 500 
e = d / 5
Problem: if 12401 is divided by any no . then quotient is 76 and remainder is 13 . what is divisor ?
Options: a ) 154 , b ) 124 , c ) 153 , d ) 163 , e ) 183
Rationale: divisor = ( dividend - remainder ) / quotient = ( 12401 - 13 ) / 76 = 12388 / 76 = 163 divisor = 163 answer d
Answer: d
Python program:
a = 12401 - 13
b = a / 76
Problem: in a games hour 4 different types of players came to the ground ? cricket 12 , hokey 17 , football 11 , softball 10 . how many players are present in the ground ?
Options: a ) 70 , b ) 50 , c ) 62 , d ) 49 , e ) 50
Rationale: "total number of players = 12 + 17 + 11 + 10 = 50 answer is b"
Answer: b
Python program:
a = 12 + 17 
b = 11 + 10 
c = a + b
Problem: a trader sells 40 metres of cloth for rs . 8200 at a profit of rs . 55 per metre of cloth . how much profit will the trder earn on 40 metres of cloth ?
Options: a ) rs . 950 , b ) rs . 1500 , c ) rs . 1000 , d ) rs . 2200 , e ) none of these
Rationale: explanation : sp of 1 metre cloth = 8200 / 40 = rs . 205 . cp of 1 metre cloth = rs . 205 – 55 = rs . 150 cp on 40 metres = 150 x 40 = rs . 6000 profit earned on 40 metres cloth = rs . 8200 – rs . 6000 = rs . 2200 . answer : option d
Answer: d
Python program:
a = 55 * 40
Problem: in a neighborhood having 90 households , 11 did not have either a car or a bike . if 20 households had a both a car and a bike and 44 had a car , how many had bike only ?
Options: a ) 30 , b ) 35 , c ) 20 , d ) 18 , e ) 10
Rationale: "{ total } = { car } + { bike } - { both } + { neither } - - > 90 = 44 + { bike } - 20 + 11 - - > { bike } = 55 - - > # those who have bike only is { bike } - { both } = 55 - 20 = 35 . answer : b ."
Answer: b
Python program:
a = 90 - 11
b = a + 20 
c = b - 44
d = c - 20
Problem: what is the units digit of 32 ! + 50 ! + 2 ! + 4 ! ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "for all n greater than 4 , the units digit of n ! is 0 . the sum of the four units digits is 0 + 0 + 2 + 4 = 6 the units digit is 6 . the answer is d ."
Answer: d
Python program:
a = 4 + 3 
b = a + 2
Problem: the amount of an investment will double in approximately 70 / p years , where p is the percent interest , compounded annually . if thelma invests $ 60,000 in a long - term cd that pays 5 percent interest , compounded annually , what will be the approximate total value of the investment when thelma is ready to retire 42 years later ?
Options: a ) $ 280,000 , b ) $ 320,000 , c ) $ 360,000 , d ) $ 480,000 , e ) $ 540,000
Rationale: "the amount of an investment will double in approximately 70 / p years , where p is the percent interest , compounded annually . if thelma invests $ 60,000 in a long - term cd that pays 5 percent interest , compounded annually , what will be the approximate total value of the investment when thelma is ready to retire 42 years later ? the investment gets doubled in 70 / p years . therefore , the investment gets doubled in 70 / 5 = every 14 years . after 42 years , the investment will get doubled 42 / 14 = 3 times . so the amount invested will get doubled thrice . so , 60000 * 2 ^ 3 = 480000 hence , the answer is d ."
Answer: d
Python program:
a = 3600 / 10
Problem: if a and b are multiples of 3 then which are all the multiples of 3 1 ) a / b 2 ) a ^ b 3 ) a + b 4 ) a - b 5 ) a * b
Options: a ) 13 , b ) 12 , 45 , c ) 1 , 25 , d ) all of these , e ) 12 , 35
Rationale: a * b a ^ b a + b a - b are multiples of 3 except a / b answer : e
Answer: e
Python program:
a = 3 * 4
b = 3 * 10
c = 5 + b 
d = a * c
Problem: 75 persons major in physics , 83 major in chemistry , 10 not at major in these subjects u want to find number of students majoring in both subjects
Options: a ) 65 , b ) 66 , c ) 67 , d ) 68 , e ) 69
Rationale: consider the number of total students = n ( t ) = 100 number of persons major in physics = n ( p ) = 75 number of persons major in chemistry = n ( c ) = 83 according to the question ; 10 not at major in these subjects = n ( p ' ∩ c ' ) = 10 n ( p ' ∩ c ' ) = n ( p u c ) ' = 10 n ( p u c ) ' = n ( t ) - n ( p u c ) 10 = 100 - n ( p u c ) n ( p u c ) = 90 n ( p u c ) = n ( p ) + n ( c ) - n ( p ∩ c ) 90 = 75 + 83 - n ( p ∩ c ) n ( p ∩ c ) = 158 - 90 n ( p ∩ c ) = 68 number of students majoring in both subjects will be 68 answer : d
Answer: d
Python program:
a = 75 + 83 
b = 100 - 10
c = a - b
Problem: frank the fencemaker needs to fence in a rectangular yard . he fences in the entire yard , except for one full side of the yard , which equals 40 feet . the yard has an area of 320 square feet . how many feet offence does frank use ?
Options: a ) 14 , b ) 47 , c ) 54 , d ) 56 , e ) 240
Rationale: "area = length x breadth 320 = 40 x breadth so , breadth = 8 units fencing required is - breadth + breadth + length 8 + 8 + 40 = > 56 feet answer must be ( d ) 56"
Answer: d
Python program:
a = 320 / 40
b = 320 / 40
c = a + b 
d = c + 40
Problem: if a is a positive integer , and if the units digit of a ^ 2 is 4 and the units digit of ( a + 1 ) ^ 2 is 9 , what is the units digit of ( a + 2 ) ^ 2 ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "if the units digit of a ^ 2 is 4 , then the units digit of a is either 2 or 8 . if the units digit of ( a + 1 ) ^ 2 is 9 , then the units digit of a + 1 is either 3 or 7 . to satisfy both conditions , the units digit of a must be 2 . then a + 2 has the units digit of 4 , thus the units digit of ( a + 2 ) ^ 2 will be 6 . the answer is d ."
Answer: d
Python program:
a = 4 * 2
b = a + 2 
c = b ** 2
Problem: lagaan is levied on the 60 percent of the cultivated land . the revenue department collected total rs . 3 , 54,000 through the lagaan from the village of mutter . mutter , a very rich farmer , paid only rs . 480 as lagaan . the percentage of total land of mutter over the total taxable land of the village is :
Options: a ) 0.22598 , b ) 0.14544 , c ) 0.25632 , d ) 0.35466 , e ) 0.63435
Rationale: "total land of sukhiya = \ inline \ frac { 480 x } { 0.6 } = 800 x \ therefore cultivated land of village = 354000 x \ therefore required percentage = \ inline \ frac { 800 x } { 354000 } \ times 100 = 0.22598 a"
Answer: a
Python program:
a = 60 / 100
b = 480 / a
c = 3 * 100
d = c * 1000
e = 4 * 10
f = e + 4 
g = f * 1000
h = d + g 
i = b / h
j = i * 100