euclaise/mathqa_programs huggingface dataset:
Problem: a new tower has just been built at the verbico military hospital ; the number of beds available for patients at the hospital is now 2 times the number available before the new tower was built . currently , 1 / 3 of the hospital ' s original beds , as well as 1 / 5 of the beds in the new tower , are occupied . for the purposes of renovating the hospital ' s original wing , all of the patients in the hospital ' s original beds must be transferred to beds in the new tower . if patients are neither admitted nor discharged during the transfer , what fraction of the beds in the new tower will be unoccupied once the transfer is complete ?
Options: a ) 11 / 30 , b ) 29 / 60 , c ) 17 / 30 , d ) 19 / 30 , e ) 7 / 15
Rationale: i think e - 7 / 15 is the correct answer . here goes : lets assume originally the number of beds = x after the new tower , the total combined no of beds = 2 x so old = x , new = x now 1 / 3 of x are occupied and 1 / 5 of x are occupied which simplifies to ( 1 / 5 ) x we are shifting 1 / 3 of x to the new ward so there will now be : 1 / 3 of x plus 1 / 5 of x occupied in the new ward . add them up to get 8 / 15 of x there are x beds in new tower so ratio is : ( 8 / 15 ) x / x = 8 / 15 of x subtract that from 15 / 15 of x and you get the number of un - occupied beds to total capacity of new towerb = 7 / 15 . e
Answer: e
Python program:
a = 2 * 3
b = a + 1 
c = 1 / 3
d = 1 / 5
e = c * d
f = b * e
Problem: cricket match is conducted in us . the run rate of a cricket game was only 3.2 in first 10 over . what should be the run rate in the remaining 40 overs to reach the target of 222 runs ?
Options: a ) 6 , b ) 6.25 , c ) 7.25 , d ) 7.5 , e ) 4.75
Rationale: "required run rate = 222 - ( 3.2 x 10 ) = 190 = 4.75 40 40 e"
Answer: e
Python program:
a = 3 * 2
b = 222 - a
c = b / 40
Problem: if the sum of a number and its square is 342 , what is the number ?
Options: a ) 16 , b ) 77 , c ) 25 , d ) 87 , e ) 18
Rationale: "explanation : let the integer be x . then , x + x 2 = 342 x 2 + x - 342 = 0 ( x + 19 ) ( x – 18 ) = 0 x = 18 answer : e"
Answer: e
Python program:
a = math.sqrt(342)
b = math.floor(a)
Problem: the arithmetic mean and standard deviation of a certain normal distribution are 16.2 and 2.3 , respectively . what value is exactly 2 standard deviations less than the mean ?
Options: a ) 10.5 , b ) 11 , c ) 11.6 , d ) 12 , e ) 12.5
Rationale: "mean = 16.2 two standard deviations is 2.3 + 2.3 = 4.6 there could be two calues for this . mean + two standard deviations = 20.8 mean - two standard deviations = 11.6 answer choice has 11.6 and so c is the answer ."
Answer: c
Python program:
a = 2 * 2
b = 16 - 2
Problem: p and q started a business investing rs . 85,000 and rs . 25,000 respectively . in what ratio the profit earned after 2 years be divided between p and q respectively ?
Options: a ) 17 : 6 , b ) 17 : 0 , c ) 17 : 4 , d ) 17 : 2 , e ) 17 : 5
Rationale: "p : q = 85000 : 25000 = 17 : 5 . answer : e"
Answer: e
Python program:
a = 2 + 3 
b = a + 3 
c = 2 + 3 
d = c * 2
e = b * d
f = 2 + 3 
g = e + f 
h = 2 + 3 
i = h * 2
j = 3 * i
k = 2 + 3 
l = j + k 
m = g / l
Problem: a shopkeeper has 280 kg of apples . he sells 40 % of these at 10 % profit and remaining 60 % at 30 % profit . find his % profit on total .
Options: a ) 22 % , b ) 25 % , c ) 26 % , d ) 28 % , e ) 35 %
Rationale: if the total quantity was 100 then 40 x 10 % + 60 x 30 % = 22 this profit will remain same for any total quantity unless the % of products remains the same . hence ' a ' is the answer
Answer: a
Python program:
a = 280 * 40
b = a / 100
c = 100 + 10 
d = c / 100
e = b * d
f = 280 * 60
g = f / 100
h = 100 + 30 
i = h / 100
j = g * i
k = e + j 
l = k - 280
m = l * 100
n = m / 280
Problem: the simple interest on a sum of money will be rs . 600 after 10 years . if the principal is trebled after 5 years , what will be the total interest at the end of the tenth year ?
Options: a ) rs . 600 , b ) rs . 900 , c ) 1200 rupees , d ) rs . 1500 , e ) none
Rationale: solution 22.22 let the sum be rs . x . now , s . i . = rs . 600 , t = 10 years . rate = % = ( 100 x 600 / x x 10 ) % = ( 6000 / x ) % s . i . for first 5 years = rs . ( x x 5 x 6000 / x x 100 ) = rs . 300 . s . i . for first 5 years = rs . ( 3 x x 5 x 6000 / x x 100 ) = rs . 900 . ∴ total interest = rs . 1200 . answer c
Answer: c
Python program:
a = 600 / 10
b = a * 5
c = b * 3
d = 600 / 10
e = d * 5
f = c + e
Problem: we define that k @ j is the product of j number from k in increasing order for positive integers k , j . for example , 6 @ 4 = 6 * 7 * 8 * 9 . if a = 2020 and b = 2120 , what is the value w of the ratio a / b ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 2 / 3 , d ) 1 / 4 , e ) 1 / 5
Rationale: "w - > a / b = 20 * 21 * … … * 39 / 21 * 22 * … . * 39 * 40 = 20 / 40 = 1 / 2 . therefore , the answer is a ."
Answer: a
Python program:
a = 2020 / 2020
b = 2020 / 2020
c = 2020 / 2020
d = b + c 
e = a / d
Problem: out of 3 consecutive odd numbers 8 times the first number is equal to addition of thrice the third number and adding 5 to twice the second . what is the first number ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: description : = > 8 x = 2 ( x + 2 ) + 5 + 3 ( x + 4 ) = > 3 x = 21 , x = 7 = > x + 4 = 11 x = 11 - 4 = 7 answer c
Answer: c
Python program:
a = 2 * 2
b = 3 * 4
c = a + b 
d = c + 5 
e = 3 + 2 
f = 8 - e
g = d / f
Problem: a train running at the speed of 60 km / hr crosses a pole in 30 sec . what is the length of the train ?
Options: a ) 535 m , b ) 178 m , c ) 186 m , d ) 168 m , e ) 500 m
Rationale: "speed = 60 * 5 / 18 = 50 / 3 m / sec length of the train = speed * time = 50 / 3 * 30 = 500 m answer : e"
Answer: e
Python program:
a = 60 * 1000
b = a / 3600
c = b * 30
Problem: a , b , c , d and e are 5 consecutive points on a straight line . if bc = 3 cd , de = 8 , ab = 5 and ac = 11 , what is the length of ae ?
Options: a ) 15 , b ) 17 , c ) 19 , d ) 21 , e ) 23
Rationale: "ac = 11 and ab = 5 , so bc = 6 . bc = 3 cd so cd = 2 . the length of ae is ab + bc + cd + de = 5 + 6 + 2 + 8 = 21 the answer is d ."
Answer: d
Python program:
a = 11 - 5
b = a / 3
c = 11 + b 
d = c + 8
Problem: what is the smallest number which when increased by 3 is divisible by 9 , 35 , 25 and 21 ?
Options: a ) 1572 , b ) 1782 , c ) 1992 , d ) 2122 , e ) 2342
Rationale: "when increased by 3 , the number must include at least 3 ^ 2 * 5 ^ 2 * 7 = 1575 the answer is a ."
Answer: a
Python program:
a = math.lcm(9, 35)
b = math.lcm(25, 21)
c = math.lcm(a, b)
d = c + 3
Problem: if | r + s | = | r - s | , then r * s must be equal to :
Options: a ) - 2 , b ) 2 , c ) 0 , d ) - 3 , e ) 3
Rationale: solution 1 : distance perspective | r - s | = | r + s | = = > the distance of r and s is equal to the distance of r and - s . < = = = = = = = ( - s ) = = = = = = = 0 = = = = = = = ( s ) = = = = = = > only 0 is the value that has a distance equal to s and - s . solution 2 : | r - s | = | r + s | ( square both ) r ^ 2 - 2 rs + s ^ 2 = r ^ 2 + 2 rs + s ^ 2 4 rs = 0 rs = 0 answer : c
Answer: c
Python program:
a = 10 - 10
Problem: 8 cups of milk are to be poured into a 4 - cup bottle and a 8 - cup bottle . if each bottle is to be filled to the same fraction of its capacity , how many cups of milk should be poured into the 8 - cup bottle ?
Options: a ) 16 / 3 , b ) 7 / 3 , c ) 5 / 2 , d ) 4 / 3 , e ) 3
Rationale: let x be the # of cups going into the 8 cup bottle . so . . . . x / 8 = ( ( 8 - x ) / 4 ) 64 - 8 x = 4 x 64 = 12 x x = 16 / 3 . answer : a
Answer: a
Python program:
a = 4 + 8 
b = 8 / a
c = b * 8
Problem: there are some people in party , 1 / 3 rd left the party . then 2 / 5 th of the remaining left the party , then 2 / 3 rd of the remaining left the party . at last 6 were remaining . how many people were in total ?
Options: a ) 45 , b ) 27 , c ) 28 , d ) 26 , e ) 91
Rationale: sol : 45 if x persons were there in total , then x × ( 1 – 1 / 3 ) × ( 1 – 2 / 5 ) × ( 1 – 2 / 3 ) = 6 x × 2 / 3 × 3 / 5 × 1 / 3 = 6 x = 6 × 5 × 3 / 2 = 45 answer : a
Answer: a
Python program:
a = 1 / 3
b = 1 - a
c = 2 / 5
d = 1 - c
e = b * d
f = 2 / 3
g = 1 - f
h = e * g
i = 6 / h
Problem: in what ratio must tea at rs . 62 per kg be mixed with tea at rs . 72 per kg so that the mixture must be worth rs . 67 per kg ?
Options: a ) 3 : 1 , b ) 3 : 2 , c ) 4 : 3 , d ) 5 : 3 , e ) 1 : 1
Rationale: "required ratio = 500 : 500 = 3 : 1 answer e"
Answer: e
Python program:
a = 72 - 67
b = 67 - 62
c = a / b
Problem: a 8 % stock yielding 10 % is quoted at :
Options: a ) 80 , b ) 110 , c ) 112 , d ) 120 , e ) 160
Rationale: "solution to earn rs . 10 , money invested = rs . 100 . to earn rs . 8 , money invested = rs . ( 100 / 10 x 8 ) = rs . 80 . â ˆ ´ market value of rs . 100 stock = rs . 80 answer a"
Answer: a
Python program:
a = 100 / 10
b = a * 8
Problem: if it is assumed that 50 percent of those who receive a questionnaire by mail will respond and 300 responses are needed , what is the minimum number of questionnaires that should be mailed ?
Options: a ) 400 , b ) 420 , c ) 480 , d ) 500 , e ) 600
Rationale: "minimum no of mail to be sent for getting 300 responses at 50 % = 300 / 0.5 = 600 option e"
Answer: e
Python program:
a = 50 / 100
b = 300 / a
Problem: the average age of 15 students of a class is 15 years . out of these , the average age of 7 students is 14 years and that of the other 7 students is 16 years . the age of the 15 th student is
Options: a ) 9 years , b ) 11 years , c ) 15 years , d ) 21 years , e ) 25 years
Rationale: "solution age of the 15 th student = [ 15 x 15 - ( 14 x 7 + 16 x 7 ) ] = ( 225 - 210 ) = 15 years . answer c"
Answer: c
Python program:
a = 15 * 15
b = 7 * 14
c = 7 * 16
d = b + c 
e = a - d
Problem: car a travels at 3 times the average speed of car b . car a started to travel at 12 : 00 o ' clock , car b started to travel at 16 : 00 o ' clock . what is the speed of car b ( in km / h ) if the total distance that both cars traveled until 18 : 00 was 1000 km ?
Options: a ) 10 . , b ) 25 . , c ) 30 . , d ) 38 , e ) 50 .
Rationale: total distance - 1000 km time ratio a : b - 3 : 1 speed ratio a : b - 3 : 1 so distance ( speed * time ) ratio will be - 3 * 3 : 1 * 1 - 9 : 1 so total distance traveled by b - 100 km time taken by b ( 18 : 00 - 16 : 00 = 2 ) - 2 hours speed of b - 50 kmph answer : e
Answer: e
Python program:
a = 18 - 12
b = a * 3
c = 18 - 16
d = b + c 
e = 1000 / d
Problem: there are 6 books on a shelf , of which 2 are paperbacks and 4 are hardbacks . how many possible selections of 4 books from this shelf include at least one paperback ?
Options: a ) a ) 40 , b ) b ) 14 , c ) c ) 50 , d ) d ) 55 , e ) e ) 60
Rationale: "approach 1 at - least 1 paper back = total - no paper back 6 c 4 - 4 c 4 = 14 approach 2 at - least 1 paper back = 1 paper back , 3 hard back or 2 paper back 2 hard back = 2 c 1 * 4 c 3 + 2 c 2 * 4 c 2 = 14 answer is b"
Answer: b
Python program:
a = math.comb(6, 4)
b = math.comb(4, 4)
c = a - b
Problem: alok ordered 16 chapatis , 5 plates of rice , 7 plates of mixed vegetable and 6 ice - cream cups . the cost of each chapati is rs . 6 , that of each plate of rice is rs . 45 and that of mixed vegetable is rs . 70 . the amount that alok paid the cashier was rs . 931 . find the cost of each ice - cream cup ?
Options: a ) 25 , b ) 76 , c ) 29 , d ) 12 , e ) 20
Rationale: "explanation : let the cost of each ice - cream cup be rs . x 16 ( 6 ) + 5 ( 45 ) + 7 ( 70 ) + 6 ( x ) = 931 96 + 225 + 490 + 6 x = 931 6 x = 120 = > x = 20 . answer : e"
Answer: e
Python program:
a = 16 * 6
b = 931 - a
c = 5 * 45
d = b - c
e = 7 * 70
f = d - e
g = f / 6
Problem: the average weight of 10 men is increased by 2 ½ kg when one of the men who weighs 68 kg is replaced by a new man . what is the weight of the new man ?
Options: a ) 80 kg , b ) 93 kg , c ) 70 kg , d ) 75 kg , e ) 85 kg
Rationale: "since the average has increased by 1.5 kg , the weight of the man who stepped in must be equal to 68 + 10 x 2.5 68 + 25 = 93 kg ans : ' b '"
Answer: b
Python program:
a = 1 / 2
b = 2 + a 
c = 10 * b
d = 68 + c
Problem: in a certain company , a third of the workers do not have a retirement plan . 20 % of the workers who do not have a retirement plan are women , and 40 % of the workers who do have a retirement plan are men . if 176 of the workers of that company are men , how many of the workers are women ?
Options: a ) 80 , b ) 95 , c ) 105 , d ) 120 , e ) 154
Rationale: "set up equation : x = total number of workers 176 = 0,4 * 2 / 3 * x + 0,8 * 1 / 3 * x 176 = 16 / 30 x x = 330 330 - 176 = 154 answer e"
Answer: e
Python program:
a = 1 / 3
b = 1 / 3
c = 20 / 100
d = b * c
e = a - d
f = 1 / 3
g = 1 - f
h = 40 / 100
i = g * h
j = e + i 
k = 176 / j
l = 1 / 3
m = 20 / 100
n = l * m
o = 1 / 3
p = 1 - o
q = 1 / 3
r = 1 - q
s = 40 / 100
t = r * s
u = p - t
v = n + u 
w = k * v
Problem: elena ’ s bread recipe calls for 3 ounces of butter for each 4 cups of flour used . she needs to make 6 times the original recipe . if 12 ounces of butter is used , then how many cups of flour are needed ?
Options: a ) 1 , b ) 4 , c ) 9 , d ) 13 , e ) 24
Rationale: "solving through algebra route : 3 b + 4 f = x amount if we multiply this equation with 6 we get : 18 b + 24 f = 6 x therefore , we got 18 ounces of butter and 6 x amount of quantity when we use 24 ounces of floor . ans : e"
Answer: e
Python program:
a = 4 * 6
Problem: in how many w ways can 5 people from a group of 6 people be seated around a circular table
Options: a ) 56
b ) 80
c ) 100
d ) 120
e ) 144
Rationale: w = 6 c 5 * ( 5 - 1 ) ! ( select 5 out of 6 and arrange them in circular manner ) = 6 * 4 ! = 6 * 24 = 144 answer - e
Answer: e
Python program:
a = math.factorial(6)
b = a / 5
Problem: suganya and suriya are partners in a business . suganya invests rs . 35,000 for 8 months and suriya invests rs . 42,000 for 10 months . out of a profit of rs . 30,570 . suganya ' s share is
Options: a ) rs . 9471 , b ) rs . 12,628 , c ) rs . 262.8 , d ) rs . 241.7 , e ) none
Rationale: solution ratio of their shares = ( 35000 ã — 8 ) : ( 42000 ã — 10 ) = 128 : 125 suganya ' s share = rs . ( 30570 ã — 2 / 253 ) = rs . 241.7 . answer d
Answer: d
Python program:
a = const_0_25 * 100
b = a * 10
Problem: a space shuttle orbits the earth at about 9 kilometers per second . this speed is equal to how many kilometers per hour ?
Options: a ) 480 , b ) 2,880 , c ) 4,800 , d ) 28,800 , e ) 32,400
Rationale: "seconds in 1 hours : 60 s in 1 min 60 min in 1 hr 60 * 60 = 3600 sec in 1 hr 9 * 3600 = 32,400 answer : e"
Answer: e
Python program:
a = 9 * 3600
Problem: 7 liters of a 22 percent solution of alcohol in water are mixed with 3 liters of an 11 percent alcohol in water solution . what is the percentage of alcohol in the new solution ?
Options: a ) 17.5 % , b ) 17.8 % , c ) 18.1 % , d ) 18.4 % , e ) 18.7 %
Rationale: "the total amount of alcohol is 0.22 ( 7 ) + 0.11 ( 3 ) = 1.87 liters . the percentage is 1.87 / 10 = 18.7 / 100 which is 18.7 % the answer is e ."
Answer: e
Python program:
a = 22 / 100
b = 7 * a
c = 11 / 100
d = 22 / 100
e = 7 * d
f = c * e
g = b + f 
h = 7 + 2 
i = g / h
j = i * 100
Problem: a cricketer scored 136 runs which included 12 boundaries and 2 sixes . what percent of his total score did he make by running between the wickets .
Options: a ) 46.2 % , b ) 54.54 % , c ) 55.88 % , d ) 70 % , e ) none of these
Rationale: "explanation : number of runs made by running = 136 - ( 12 x 4 + 2 x 6 ) = 136 - ( 60 ) = 76 now , we need to calculate 72 is what percent of 136 . = > 76 / 136 * 100 = 55.88 % answer : c"
Answer: c
Python program:
a = 12 * 4
b = 2 * 3
c = 2 * b
d = a + c 
e = 136 - d
f = e / 136
g = f * 100
Problem: by investing in 1623 % stock at 64 , one earns rs . 1700 . the investment made is
Options: a ) s . 9600 , b ) s . 7500 , c ) s . 5640 , d ) s . 6528 , e ) s . 6760
Rationale: "explanation : market value = rs . 64 face value is not given and hence take it as rs . 100 16 2 / 3 % of the face value = 50 / 3 ie , to earn 50 / 3 , investment = rs . 64 hence , to earn rs . 1700 , investment needed = 64 × 3 × 1700 / 50 = 6528 answer : option d"
Answer: d
Python program:
a = 4 * 2
b = 4 * 2
c = a * b
d = c * 3
e = 100 / 2
f = d / e
g = 4 * 100
h = 1700 - g
i = f * h
Problem: for any integer k greater than 1 , the symbol k * denotes the product of all integers between 1 and k , inclusive . if k * is a multiple of 945 what is the least possible value of k ?
Options: a ) 5 , b ) 7 , c ) 9 , d ) 11 , e ) 13
Rationale: "945 = 3 * 3 * 3 * 5 * 7 thus k must include numbers at least up to the number 9 so that there are at least three appearances of 3 ( that is : 3 , 6 , and 9 ) . the answer is c ."
Answer: c
Python program:
a = 945 / 3
b = a / 3
c = 1 + 4 
d = b / c
Problem: if ( 18 ^ a ) * 9 ^ ( 3 a – 1 ) = ( 2 ^ 2 ) ( 3 ^ b ) and a and b are positive integers , what is the value of a ?
Options: a ) 22 , b ) 11 , c ) 9 , d ) 6 , e ) 2
Rationale: "( 18 ^ a ) * 9 ^ ( 3 a – 1 ) = ( 2 ^ 2 ) ( 3 ^ b ) = 2 ^ a . 9 ^ a . 9 ^ ( 3 a – 1 ) = ( 2 ^ 2 ) ( 3 ^ b ) just compare powers of 2 from both sides answer = 2 = e"
Answer: e
Python program:
a = 3 * 1
Problem: there are 6 people in the elevator . their average weight is 160 lbs . another person enters the elevator , and increases the average weight to 151 lbs . what is the weight of the 7 th person .
Options: a ) 97 , b ) 168 , c ) 189 , d ) 190 , e ) 200
Rationale: "solution average of 7 people after the last one enters = 151 . â ˆ ´ required weight = ( 7 x 151 ) - ( 6 x 160 ) = 1057 - 960 = 97 . answer a"
Answer: a
Python program:
a = 151 * 7
b = 6 * 160
c = a - b
Problem: what least fraction should be added to 1 / ( 2 × 3 ) + 1 / ( 3 × 4 ) + 1 / ( 4 × 5 ) + . . . . . . . + 1 / ( 21 × 22 ) so that the result is unity ?
Options: a ) 5 / 11 , b ) 6 / 11 , c ) 4 / 11 , d ) 7 / 11 , e ) 8 / 11
Rationale: explanation : given expression = 1 / ( 2 × 3 ) + 1 / ( 3 × 4 ) + 1 / ( 4 × 5 ) + . . . . . . + 1 / ( 21 × 22 ) = ( 1 / 2 - 1 / 3 ) + ( 1 / 3 - 1 / 4 ) + ( 1 / 4 - 1 / 5 ) + . . . . . . . . . . = ( 1 / 21 - 1 / 22 ) = 1 / 2 - 1 / 22 = 10 / 22 = 5 / 11 thus , least fraction to be added = 1 - 5 / 11 = 6 / 11 answer : option b
Answer: b
Python program:
a = 3 * 2
b = 3 * 2
c = 2 + 3 
d = b + c 
e = a / d
Problem: how many positive integers less than 160 are there such that they are multiples of 13 or multiples of 12 but not both ?
Options: a ) 18 , b ) 19 , c ) 20 , d ) 23 , e ) 25
Rationale: "for 13 : 13 . . . 160 = 13 * 12 for 12 : 12 . . . 156 = 12 * 13 but there is one integer 13 * 12 . so n = ( 12 - 1 ) + ( 13 - 1 ) = 23 d"
Answer: d
Python program:
a = 4 + 13 
b = a - 1
c = math.factorial(b)
d = math.factorial(13)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
Problem: 24 * 22 = ? / 8
Options: a ) 4224 , b ) 2224 , c ) 5374 , d ) 2434 , e ) 4254
Rationale: "a 4224 ? / 8 = 24 * 22 ? = 24 * 22 * 8 ? = 4224"
Answer: a
Python program:
a = 24 * 22
Problem: how many 5 - digit numbers that do not contain the digits 4 or 7 are there ?
Options: a ) 44648 , b ) 27844 , c ) 28642 , d ) 16864 , e ) 32458
Rationale: we can have 7 digits ( 1 , 2,3 , 5,6 , 8,9 ) for the first place ( ten thousand ' s place ) . and similarly 8 digits for thousand ' s , hundred ' s , tenth ' s and unit digit . ( 0,1 , 2,3 , 5,6 , 8,9 ) so in total 7 * 8 * 8 * 8 * 8 = 28672 hence c
Answer: c
Python program:
a = 4 * 2
b = 5 - 1
c = a ** b
d = c * 7
Problem: evaluate 75 % of 450 + 45 % of 750
Options: a ) 632 , b ) 642 , c ) 652 , d ) 675 , e ) 572
Rationale: "explanation : = ( 75 / 100 ) * 450 + ( 45 / 100 ) * 750 = 675 option e"
Answer: e
Python program:
a = 450 / 75
b = 75 / a
Problem: how many positive integers i less than 20 are either a multiple of 2 , an odd multiple of 9 , or the sum of a positive multiple of 2 and a positive multiple of 9 ?
Options: a ) 19 , b ) 18 , c ) 17 , d ) 16 , e ) 15
Rationale: we ' re asked to deal with the positive integers less than 20 . there are only 19 numbers in that group ( 1 to 19 , inclusive ) . we ' re asked to find all of the numbers that fit one ( or more ) of the given descriptions . looking at the answer choices , we have every value form 15 to 19 , inclusive , so most ( if not all ) of the numbers from 1 to 19 fit one ( or more ) of the descriptions . how long would it take you to find the ones that do n ' t fit . . . . . ? the first several should be pretty easy to find - the prompt wants us to focus on multiples of 2 and 9 ( and sums of those multiples ) . so what odd numbers are less than 9 ? 1 , 3 , 5 , 7 none of these values fit the given descriptions . that ' s 4 out of 19 that we know for sure do not fit . 19 - 4 = 15 = e
Answer: e
Python program:
a = 9 + 1 
b = 2 + 3 
c = a + b
Problem: a train passes a station platform in 33 sec and a man standing on the platform in 20 sec . if the speed of the train is 54 km / hr . what is the length of the platform ?
Options: a ) 228 , b ) 240 , c ) 887 , d ) 195 , e ) 1811
Rationale: "speed = 54 * 5 / 18 = 15 m / sec . length of the train = 15 * 20 = 300 m . let the length of the platform be x m . then , ( x + 300 ) / 33 = 15 = > x = 195 m . answer : d"
Answer: d
Python program:
a = 54 * const_0_2778
b = 20 * a
Problem: the weights of 3 bags are in the ratio 4 : 5 : 6 . if the sum of the weights of the heaviest and the lightest bag is 45 kg more than the weight of the third bag , what is the weight of the lightest bag ?
Options: a ) 45 kg , b ) 38 kg , c ) 66 kg , d ) 36 kg , e ) of these
Rationale: let the weights of the three boys be 4 k , 5 k and 6 k respectively . 4 k + 6 k = 5 k + 45 = > 5 k = 45 = > k = 9 therefore the weight of the lightest boy = 4 k = 4 ( 9 ) = 36 kg . answer : d
Answer: d
Python program:
a = 4 + 6 
b = a - 5
c = 45 / b
d = c * 4
Problem: the area of a circular field is 13.86 hectares . find the cost of fencing it at the rate of rs . 4.70 per metre .
Options: a ) 2399 , b ) 6204 , c ) 2999 , d ) 5808 , e ) 2888
Rationale: "explanation : area = ( 13.86 x 10000 ) sq . m = 138600 sq . m circumference = cost of fencing = rs . ( 1320 x 4.70 ) = rs . 6204 . answer : b ) 6204"
Answer: b
Python program:
a = 13 / 86
b = math.sqrt(a)
c = b * 100
d = circumface * (
Problem: if x / 4 + 24 / x = 5 , what are the values of 4 x - 7 ?
Options: a ) 8 and 9 , b ) 8 and 24 , c ) 25 and 41 , d ) 12 and 29 , e ) 17 and 29
Rationale: i got the same thing c is the answer 25 or 41
Answer: c
Python program:
a = 24 - 4
b = 24 - 4
c = b ** 4
d = 24 * 4
e = 4 * d
f = c - e
g = math.sqrt(f)
h = a + g 
i = h - 7
j = i * 10
k = 24 - 4
l = 24 - 4
m = l ** 4
n = 24 * 4
o = 4 * n
p = m - o
q = math.sqrt(p)
r = k - q
s = r - 7
t = j + s
Problem: a room is 6 meters 72 centimeters in length and 4 meters 32 centimeters in width . find the least number of square tiles of equal size required to cover the entire floor of the room .
Options: a ) 107 , b ) 126 , c ) 117 , d ) 136 , e ) 147
Rationale: let us calculate both the length and width of the room in centimeters . length = 6 meters and 72 centimeters = 672 cm width = 4 meters and 32 centimeters = 432 cm as we want the least number of square tiles required , it means the length of each square tile should be as large as possible . further , the length of each square tile should be a factor of both the length and width of the room . hence , the length of each square tile will be equal to the hcf of the length and width of the room = hcf of 672 and 432 = 48 thus , the number of square tiles required = ( 672 x 432 ) / ( 48 x 48 ) = 14 x 9 = 126 answer : b
Answer: b
Python program:
a = 6 * 100
b = a + 72 
c = 4 * 100
d = c + 32 
e = b * d
f = 6 * 100
g = f + 72 
h = 4 * 100
i = h + 32 
j = math.gcd(g, i)
k = 6 * 100
l = k + 72 
m = 4 * 100
n = m + 32 
o = math.gcd(l, n)
p = j * o
q = e / p