euclaise/mathqa_programs huggingface dataset:
Problem: there are 624 students in a school . the ratio of boys and girls in this school is 3 : 5 . find the total of girls & boys are there in this school ?
Options: a ) 320 , b ) 345 , c ) 375 , d ) 390 , e ) 400
Rationale: "in order to obtain a ratio of boys to girls equal to 3 : 5 , the number of boys has to be written as 3 x and the number of girls as 5 x where x is a common factor to the number of girls and the number of boys . the total number of boys and girls is 624 . hence 3 x + 5 x = 624 solve for x 8 x = 624 x = 78 number of boys 3 x = 3 × 78 = 234 number of girls 5 x = 5 × 78 = 390 d"
Answer: d
Python program:
a = 624 / 5
b = a * 3
Problem: at a loading dock , each worker on the night crew loaded 1 / 2 as many boxes as each worker on the day crew . if the night crew has 4 / 5 as many workers as the day crew , what fraction of all the boxes loaded by the two crews did the day crew load ?
Options: a ) 1 / 2 , b ) 2 / 5 , c ) 3 / 5 , d ) 4 / 5 , e ) 5 / 7
Rationale: "method : x = no . of boxes loaded by day crew . boxes by night crew = 1 / 2 * 4 / 5 x = 2 / 5 x % loaded by day crew = x / ( x + 2 / 5 x ) = 5 / 7 answer e"
Answer: e
Python program:
a = 5 * 2
b = 5 * 2
c = 1 * 4
d = b + c 
e = a / d
Problem: company z has 53 employees . if the number of employees having birthdays on wednesday is more than the number of employees having birthdays on any other day of the week , each of which have same number of birth - days , what is the minimum number of employees having birthdays on wednesday .
Options: a ) 6 , b ) 7 , c ) 8 , d ) 11 , e ) 12
Rationale: "say the number of people having birthdays on wednesday is x and the number of people having birthdays on each of the other 6 days is y . then x + 6 y = 53 . now , plug options for x . d x > y as needed . answer : d ."
Answer: d
Python program:
a = 4 + 3 
b = 53 / a
c = math.floor(b)
d = c + 1 
e = 4 + d
Problem: the average weight of 20 persons sitting in a boat had some value . a new person added to them whose weight was 50 kg only . due to his arrival , the average weight of all the persons decreased by 5 kg . find the average weight of first 20 persons ?
Options: a ) 55 , b ) 56 , c ) 57 , d ) 58 , e ) 59
Rationale: "20 x + 50 = 21 ( x – 5 ) x = 55 answer : a"
Answer: a
Python program:
a = 20 + 1 
b = a * 5
c = b - 50
Problem: if 2 is one solution of the equation x ^ 2 + 3 x + k = 10 , where k is a constant , what is the other solution ?
Options: a ) - 7 , b ) - 4 , c ) - 5 , d ) 1 , e ) 6
Rationale: "the phrase “ 2 is one solution of the equation ” means that one value of x is 2 . thus , we first must plug 2 for x into the given equation to determine the value of k . so we have 2 ^ 2 + ( 3 ) ( 2 ) + k = 10 4 + 6 + k = 10 10 + k = 10 k = 0 next we plug 0 into the given equation for k and then solve for x . x ^ 2 + 3 x = 10 x ^ 2 + 3 x – 10 = 0 ( x + 5 ) ( x - 2 ) = 0 x = - 5 or x = 2 thus , - 5 is the other solution . answer c ."
Answer: c
Python program:
a = 2 ** 2
b = 3 * 2
c = a + b 
d = 10 - c
e = d / 2
Problem: what is the least value of x , so that 2 x 5452 is divisible by 9
Options: a ) 7 , b ) 8 , c ) 9 , d ) 3 , e ) 0
Rationale: "explanation : the sum of the digits of the number is divisible by 9 . then the number is divisible by 9 . 2 + x + 5 + 4 + 5 + 2 = 18 + x least value of x may be ' 0 ' , so that the total 18 + 0 = 18 is divisible by 9 . answer : option e"
Answer: e
Python program:
a = math.lcm(2, 5452)
b = a / 5452
c = b / 4
d = c / 4
Problem: a man bought an article and sold it at a gain of 5 % . if he had bought it at 5 % less and sold it for re 1 less , he would have made a profit of 10 % . the c . p . of the article was
Options: a ) 344 , b ) 218 , c ) 200 , d ) 388 , e ) 211
Rationale: "explanation : let original cost price is x its selling price = ( 105 / 100 ) * x = 21 x / 20 new cost price = ( 95 / 100 ) * x = 19 x / 20 new selling price = ( 110 / 100 ) * ( 19 x / 20 ) = 209 x / 200 [ ( 21 x / 20 ) - ( 209 x / 200 ) ] = 1 = > x = 200 answer : c ) rs 200"
Answer: c
Python program:
a = 5 * 4
b = a * 10
c = b * 1
Problem: the length of a rectangle is twice the breadth . if the area is 128 cm 2 , determine the length and the breadth .
Options: a ) b = 2 , l = 9
b ) b = 8 , l = 16
c ) b = 9 , l = 9
d ) b = 4 , l = 14
e ) b = 3 , l = 9
Rationale: we are given length l = 2 b and l × b = 128 ∴ 2 b × b = 128 2 b ^ 2 = 128 b ^ 2 = 64 b = ± 8 but breadth must be positive , therefore b = 8 cm , and l = 2 b = 16 cm . answer is b .
Answer: b
Python program:
a = 128 / 2
b = math.sqrt(a)
c = b * 2
Problem: in a school with 5 classes , each class has 2 students less than the previous class . how many students are there in the largest class if the total number of students at school is 120 ?
Options: a ) 25 , b ) 26 , c ) 27 , d ) 28 , e ) 29
Rationale: "let x be the number of students in the largest class . then x + ( x - 2 ) + ( x - 4 ) + ( x - 6 ) + ( x - 8 ) = 120 5 x - 20 = 120 5 x = 140 x = 28 the answer is d ."
Answer: d
Python program:
a = 2 + 2 
b = 2 + a 
c = 2 + 2 
d = c + 2 
e = b + d 
f = 2 + 2 
g = f + 2 
h = g + 2 
i = e + h 
j = 120 - i
k = j / 5
l = 2 + 2 
m = l + 2 
n = m + 2 
o = k + n
Problem: rs . 800 amounts to rs . 920 in 3 years at simple interest . if the interest is increased by 3 % , it would amount to how much ?
Options: a ) 288 , b ) 277 , c ) 209 , d ) 992 , e ) 612
Rationale: "( 800 * 3 * 3 ) / 100 = 72 920 + 72 = 992 answer : d"
Answer: d
Python program:
a = 3 / 100
b = 1 + a 
c = b ** 3
d = c * 800
Problem: when positive integer n is divided by positive integer p , the quotient is 18 , with a remainder of 7 . when n is divided by ( p + 2 ) , the quotient is 15 and the remainder is 1 . what is the value of n ?
Options: a ) 151 , b ) 331 , c ) 511 , d ) 691 , e ) 871
Rationale: "use the rule dividend = ( integer quotient ) * ( divisor ) + remainder to translate each sentence . the first sentence becomes n = 18 p + 7 . the second equation becomes n = ( p + 2 ) * 15 + 1 , which simplifies to n = 15 p + 31 . these are ordinary simultaneous equations since they both equal n already , let ’ s set them equal and solve for p . 18 p + 7 = 15 p + 31 3 p + 7 = 31 3 p = 24 p = 8 now that we know p = 8 , we can just plug in . the product 15 * 8 is particularly easy to do , without a calculator , by using the “ doubling and halving ” trick . double 15 to get 30 , and take half of 8 to get 4 — - 15 * 8 = 30 * 4 = 120 . so n = 15 ( 8 ) + 31 = 120 + 31 = 151 n = 151 , answer = a ."
Answer: a
Python program:
a = 15 * 2
b = a + 1 
c = b - 7
d = 18 - 15
e = c / d
f = 18 * e
Problem: car a runs at the speed of 35 km / hr & reaches its destination in 10 hr . car b runs at the speed of 25 km / h & reaches its destination in 6 h . what is the respective ratio of distances covered by car a & car b ?
Options: a ) 7 : 3 , b ) 5 : 7 , c ) 9 : 7 , d ) 3 : 5 , e ) 11 : 6
Rationale: "sol . distance travelled by car a = 36 × 10 = 350 km distance travelled by car b = 25 × 6 = 150 km ratio = 350 / 150 = 7 : 3 a"
Answer: a
Python program:
a = 35 * 10
b = 25 * 6
c = a / b
Problem: the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 12000 and the average salary of the rest is rs . 6000 . how many workers are there in the workshop ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: "explanation : let the number of workers = x given that average salary of all the workers = rs . 8000 then , total salary of all workers = 8000 x given that average salary of 7 technicians is rs . 12000 = > total salary of 7 technicians = 7 × 12000 = 84000 count of the rest of the employees = ( x - 7 ) average salary of the rest of the employees = rs . 6000 total salary of the rest of the employees = ( x - 7 ) ( 6000 ) 8000 x = 84000 + ( x - 7 ) ( 6000 ) = > 8 x = 84 + ( x - 7 ) ( 6 ) = > 8 x = 84 + 6 x - 42 = > 2 x = 42 = > x = 42 / 2 = 21 answer : option a"
Answer: a
Python program:
a = 12000 - 8000
b = 7 * a
c = 8000 - 6000
d = b / c
e = 7 + d
Problem: a 180 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds . what is the length of the other train ?
Options: a ) 320 meter , b ) 225 meter , c ) 230 meter , d ) 235 meter , e ) none of these
Rationale: "explanation : as trains are running in opposite directions so their relative speed will get added so , relative speed = 120 + 80 = 200 kmph = 200 * ( 5 / 18 ) = 500 / 9 m / sec let the length of other train is x meter then x + 180 / 9 = 500 / 9 = > x + 180 = 500 = > x = 320 so the length of the train is 320 meters option a"
Answer: a
Python program:
a = 120 + 80 
b = a * const_0_2778
c = b * 9
d = c - 180
Problem: 40 liters of a mixture is created by mixing liquid p and liquid q in the ratio 5 : 3 . how many liters of liquid q must be added to make the ratio 5 : 6 ?
Options: a ) 5 , b ) 8 , c ) 10 , d ) 12 , e ) 15
Rationale: "let x be the amount of liquid q to be added . ( 3 / 8 ) * 40 + x = ( 6 / 11 ) * ( 40 + x ) 1320 + 88 x = 1920 + 48 x 40 x = 600 x = 15 the answer is e ."
Answer: e
Python program:
a = 5 + 6 
b = 40 * 5
c = 5 + 3 
d = b / c
e = a * d
f = e / 5
g = f * 6
h = 5 + 6 
i = g / h
j = 40 * 3
k = 5 + 3 
l = j / k
m = i - l
Problem: the digital sum of a number is the sum of its digits . for how many of the positive integers 24 - 100 inclusive is the digital sum a multiple of 7 ?
Options: a ) 7 , b ) 11 , c ) 14 , d ) 16 , e ) 20
Rationale: "is there other way than just listing ? 25 34 43 52 59 61 68 70 77 86 95 11 ways . . b"
Answer: b
Python program:
a = 24 - 7
b = a - 2
Problem: a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets $ 500 more than d , what is d ' s share ?
Options: a ) $ 1000 , b ) $ 1200 , c ) $ 1500 , d ) $ 1800 , e ) $ 2000
Rationale: let the shares of a , b , c and d be 5 x , 2 x , 4 x and 3 x respectively . then , 4 x - 3 x = 500 x = $ 500 d ' s share = 3 x = 3 * $ 500 = $ 1500 the answer is c .
Answer: c
Python program:
a = 4 - 3
b = a * 500
c = b * 3
Problem: what is 2 2 / 3 - 1 1 / 4 divided by 1 / 2 - 1 / 5 ?
Options: a ) 17 / 36 , b ) 36 / 17 , c ) 17 / 6 , d ) 17 / 4 , e ) 85 / 18
Rationale: 2 2 / 3 - 1 1 / 4 = 8 / 3 - 5 / 4 = ( 32 - 15 ) / 12 = 17 / 12 1 / 2 - 1 / 5 = ( 5 - 2 ) / 10 = 3 / 10 so 17 / 12 / 3 / 10 = 17 / 12 * 10 / 3 = 85 / 18 answer - e
Answer: e
Python program:
a = 10 * 2
b = a + 2 
c = b / 3
d = 10 + 1 
e = d / 4
f = c - e
Problem: mohit sold an article for $ 24000 . had he offered a discount of 10 % on the selling price , he would have earned a profit of 8 % . what is the cost price of the article ?
Options: a ) 16000 , b ) 20000 , c ) 15000 , d ) 18000 , e ) 17000
Rationale: let the cp be $ x . had he offered 10 % discount , profit = 8 % profit = 8 / 100 x and hence his sp = x + 8 / 100 x = $ 1.08 x = 20000 - 10 / 100 ( 20000 ) = 20000 - 2000 = $ 21600 = > 1.08 x = 21600 = > x = 20000 b
Answer: b
Python program:
a = 24000 * 10
b = a / 100
c = 24000 - b
d = 100 + 8 
e = c / d
f = e * 100
Problem: what is the greatest positive integer x such that 4 ^ x is a factor of 64 ^ 10 ?
Options: a ) 5 , b ) 9 , c ) 10 , d ) 20 , e ) 30
Rationale: "64 ^ 10 = ( 4 ^ 3 ) ^ 10 = 4 ^ 30 answer : e"
Answer: e
Python program:
a = 64 - 10
b = a * 10
Problem: 9.009 / 2.002 =
Options: a ) 4.05 , b ) 4.50045 , c ) 4.501 , d ) 4.5045 , e ) 4.5
Rationale: "9.009 / 2.002 = 9009 / 2002 = 9 ( 1001 ) / 2 ( 1001 ) = 9 / 2 = 4.5 the answer is e ."
Answer: e
Python program:
a = 9 / 9
b = a * 100
Problem: if 45 - [ 28 - { 37 - ( 15 - * ) } ] = 59 , then * is equal to :
Options: a ) - 29 , b ) - 19 , c ) 20 , d ) 29 , e ) 39
Rationale: "45 - [ 28 - { 37 - ( 15 - * ) } ] = 59 = > 45 - [ 28 - { 37 - 15 + * } ] = 59 45 - [ 28 - 37 + 15 - * ] = 59 = > 45 [ 43 - 37 - * ] = 59 45 - [ 6 - * ] = 59 = > 45 - 6 + * = 59 39 + * = 59 = > * = 59 - 39 = 20 answer : c"
Answer: c
Python program:
a = 28 - 37
b = a + 15 
c = 45 - b
d = 59 - c
Problem: a marketing firm determined that , of 200 households surveyed , 80 used neither brand w nor brand b soap , 60 used only brand w soap , and for every household that used both brands of soap , 3 used only brand b soap . how many of the 200 households surveyed used both brands of soap ?
Options: a ) 15 , b ) 20 , c ) 30 , d ) 40 , e ) 45
Rationale: solution for soap w and soap b ( d ) 40
Answer: d
Python program:
a = 200 - 80
b = a - 60
c = 200 - 80
d = c - 60
e = d / 3
f = b - e
Problem: if the wheel is 42 cm then the number of revolutions to cover a distance of 1056 cm is ?
Options: a ) 18 , b ) 4 , c ) 6 , d ) 8 , e ) 19
Rationale: "2 * 22 / 7 * 42 * x = 1056 = > x = 4 answer : b"
Answer: b
Python program:
a = 3 * 100
b = 1 * 10
c = a + b 
d = c + 4 
e = d / 100
f = 2 * e
g = f * 42
h = 1056 / g
Problem: find the total number of prime factors in the expression ( 4 ) 11 x ( 7 ) 5 x ( 11 ) 2 .
Options: a ) 22 , b ) 29 , c ) 19 , d ) 5 , e ) 2
Rationale: "( 4 ) 11 x ( 7 ) 5 x ( 11 ) 2 = ( 2 x 2 ) 11 x ( 7 ) 5 x ( 11 ) 2 = 211 x 211 x 75 x 112 = 222 x 75 x 112 total number of prime factors = ( 22 + 5 + 2 ) = 29 . answer b 29"
Answer: b
Python program:
a = 2 * 11
b = a + 5 
c = b + 2
Problem: the average salary of workers in an industry is rs . 300 the average salary of technicians being rs . 400 and that of non - technicians being rs . 125 . what is the total number of workers ?
Options: a ) 230 , b ) 234 , c ) 250 , d ) 547 , e ) 484
Rationale: 400 125 \ / 300 / \ 175 100 7 : 4 7 - > 150 11 - > ? = > 234 answer : b
Answer: b
Python program:
a = 300 - 125
b = 400 / 300
c = a * b
d = c + 1 
e = math.floor(d)
Problem: if n is a natural number , t hen 6 n ^ 2 + 6 n is always divisible by ?
Options: a ) 6 only , b ) 6 and 12 , c ) 12 only , d ) 18 only , e ) 20 only
Rationale: "6 n ^ 2 + 6 n = 6 n ( n + 1 ) , which is always divisible by 6 and 12 both , since n ( n + 1 ) is always even . answer is b"
Answer: b
Python program:
a = 6 * 100
b = 2 * 6
c = a + b
Problem: a man buys 10 lts of liquid which contains 20 % of the liquid and the rest is water . he then mixes it with 15 lts of another mixture with 30 % of liquid . what is the % of water in the new mixture ?
Options: a ) 74 , b ) 84 , c ) 94 , d ) 49 , e ) 47
Rationale: "20 % in 10 lts is 2 . so water = 10 - 2 = 8 lts . 30 % of 15 lts = 4.5 . so water in 2 nd mixture = 15 - 4.5 = 10.5 lts . now total quantity = 10 + 15 = 25 lts . total water in it will be 8 + 10.5 = 18.5 lts . % of water = ( 100 * 18.5 ) / 25 = 74 answer : a"
Answer: a
Python program:
a = 10 - 20
b = 10 * a
c = 10 - 30
d = 15 * c
e = b + d 
f = 10 + 15 
g = e / f
Problem: a man can buy a new house in 4 years with all of his earnings . but he spend the same amount in household expenses in 8 years and for savings in 12 years . how many time needed for buying the house ?
Options: a ) 12 , b ) 20 , c ) 30 , d ) 15 , e ) 24
Rationale: his savings in 1 year = 1 / 4 - ( 1 / 8 + 1 / 12 ) = 1 / 24 he can buy a new house in 24 years answer : e
Answer: e
Python program:
a = 12 / 4
b = a * 2
c = b * 4
Problem: a man can do a piece of work in 6 days , but with the help of his son , he can finish it in 3 days . in what time can the son do it alone ?
Options: a ) 5 , b ) 5 1 / 2 , c ) 7 1 / 2 , d ) 6 , e ) 9 1 / 2
Rationale: "son ' s 1 day work = 1 / 3 - 1 / 6 = 1 / 6 son alone can do the work in 6 days = 6 days answer is d"
Answer: d
Python program:
a = 6 * 3
b = 6 - 3
c = a / b
Problem: what is the least whole number that should be added to 784839 if it is to be divisible by 10 ?
Options: a ) 3 , b ) 2 , c ) 1 , d ) 5 , e ) 6
Rationale: "a number is divisible by 10 if the last digit is 0 . here , 784839 = 9 , ( last digit is not 0 . 1 must be added to 784839 to make it divisible by 10 c"
Answer: c
Python program:
a = 784839 - 1
b = a + 10 
c = b - 784839
Problem: there are 12 slate rocks , 16 pumice rocks , and 8 granite rocks randomly distributed in a certain field . if 2 rocks are chosen at random and without replacement , what is the probability that both rocks will be slate rocks ?
Options: a ) 3 / 32 , b ) 7 / 64 , c ) 11 / 105 , d ) 15 / 127 , e ) 19 / 134
Rationale: 12 / 36 * 11 / 35 = 11 / 105 the answer is c .
Answer: c
Python program:
a = 12 + 16 
b = a + 8 
c = 12 / b
d = 12 - 1
e = 12 + 16 
f = e + 8 
g = f - 1
h = d / g
i = c * h
Problem: a can do a work in 4 days . b can do the same work in 12 days . if both a & b are working together in how many days they will finish the work ?
Options: a ) 3 , b ) 5 , c ) 4 , d ) 2 , e ) 6
Rationale: a rate = 1 / 4 b rate = 1 / 16 ( a + b ) rate = ( 1 / 4 ) + ( 1 / 12 ) = 1 / 3 a & b finish the work in 3 days correct option is a
Answer: a
Python program:
a = 4 * 12
b = 4 + 12 
c = a / b
Problem: how many positive integers less than 254 are multiple of 4 but not multiples of 6 ?
Options: a ) 20 , b ) 31 , c ) 42 , d ) 43 , e ) 64
Rationale: "252 / 4 = 63 multiples of 4 which are a multiple of 6 will be of the form 2 * 2 * 3 = 12 n where n > 0 240 / 12 = 20 63 - 20 = 43 answer : d"
Answer: d
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: how many 4 - digit numerals begin with a digit that represents a prime and end with a digit that represents a prime number ?
Options: a ) 1600 , b ) 80 , c ) 160 , d ) 180 , e ) 240
Rationale: "prime digits 2 , 3,5 and 7 . three digit numbers _ _ _ 1 st place can be filled in 4 ways 2 nd place can be filled in 10 ways 3 rd place can be filled in 10 ways 3 rd place can be filled in 4 ways total = 4 * 10 * 10 * 4 = 1600 ans : a"
Answer: a
Python program:
a = 100 * 4
b = a + 100
Problem: a courtyard is 28 meter long and 13 meter board is to be paved with bricks of dimensions 22 cm by 12 cm . the total number of bricks required is :
Options: a ) 16000 , b ) 14567 , c ) 13787 , d ) 13456 , e ) none of these
Rationale: explanation : number of bricks = courtyard area / 1 brick area = ( 2800 ã — 1300 / 22 ã — 12 ) = 13787 option c
Answer: c
Python program:
a = 28 * 100
b = 13 * 100
c = a * b
d = 22 * 12
e = c / d
Problem: andy solves problems 80 to 125 inclusive in a math exercise . how many problems does he solve ?
Options: a ) 53 , b ) 52 , c ) 51 , d ) 46 , e ) 49
Rationale: "125 - 80 + 1 = 52 ' d ' is the answer"
Answer: d
Python program:
a = 125 - 80
b = a + 1
Problem: set a of 8 positive integers may have the same element and have 39 . and set b of 8 positive integers must have different elements and have 39 . when m and n are the greatest possible differences between 39 and other elements ’ sums in set a and set b , respectively , m - n = ?
Options: a ) 20 , b ) 23 , c ) 21 , d ) 25 , e ) 26
Rationale: this is maximum - minimum . hence , 39 - ( 1 + 1 + 1 + 1 + 1 + 1 + 1 ) = 32 and 39 - ( 1 + 2 + 3 + 4 + 5 + 6 + 7 ) = 11 . so , 32 - 11 = 21 . the correct answer is c .
Answer: c
Python program:
a = 8 + 2 
b = a + 8 
c = 39 - b
Problem: find the value of 1.5 x [ ( 3.6 x 0.48 x 2.50 ) / ( 0.12 x 0.09 x 0.5 ) ]
Options: a ) 800 , b ) 500 , c ) 900 , d ) 1200 , e ) none
Rationale: "answer 1.5 x [ ( 3.6 x 0.48 x 2.50 ) / ( 0.12 x 0.09 x 0.5 ) ] = 1.5 x [ ( 36 x 48 x 250 ) / ( 12 x 9 x 5 ) ] = 1.5 x 4 x 4 x 50 = 1200 correct option : d"
Answer: d
Python program:
a = 3 * 6
b = a * 2
c = 0 * 12
d = c * 0
e = b / d
f = e * 1
Problem: a shopkeeper sold an article at $ 100 with 20 % profit . then find its cost price ?
Options: a ) $ 120 , b ) $ 100 , c ) $ 91 , d ) $ 83 , e ) $ 69
Rationale: "cost price = selling price * 100 / ( 100 + profit ) c . p . = 100 * 100 / 120 = $ 83 ( approximately ) answer is d"
Answer: d
Python program:
a = 100 + 20 
b = 100 / a
c = 100 * b
Problem: the compound ratio of 1 : 3 , 3 : 2 and 4 : 5 ?
Options: a ) 1 : 9 , b ) 1 : 7 , c ) 1 : 2 , d ) 2 : 5 , e ) 1 : 4
Rationale: "1 / 3 * 3 / 2 * 4 / 5 = 2 / 5 = 2 : 5 answer : d"
Answer: d
Python program:
a = 1 * 3
b = 3 * 2
c = a / b
d = 3 * 4
e = 2 * 5
f = d / e
g = c / f
Problem: a number increased by 10 % gives 550 . the number is
Options: a ) 250 , b ) 500 , c ) 450 , d ) 500 , e ) 520
Rationale: "formula = total = 100 % , increse = ` ` + ' ' decrease = ` ` - ' ' a number means = 100 % that same number increased by 10 % = 110 % 110 % - - - - - - - > 550 ( 110 × 5 = 550 ) 100 % - - - - - - - > 500 ( 100 × 5 = 500 ) b )"
Answer: b
Python program:
a = 10 / 100
b = 1 + a 
c = 550 / b
Problem: by how much does the larger root of the equation 2 z ^ 2 + 5 z = 12 exceed the smaller root ?
Options: a ) 5 / 2 , b ) 10 / 3 , c ) 7 / 2 , d ) 14 / 3 , e ) 11 / 2
Rationale: "for 2 z ^ 2 + 5 z = 12 roots are [ - 5 + sqrt ( 25 + 96 ) ] / 4 or [ - 5 - sqrt ( 25 + 96 ) ] / 4 = 1.5 or - 4 hence larger root 1.5 is 1.5 - ( - 4 ) = 5.5 = 11 / 2 greater than smaller root ( - 4 ) . hence option ( e ) ."
Answer: e
Python program:
a = 5 ** 2
b = 2 * 12
c = b * 4
d = a + c 
e = math.sqrt(d)
f = 5 + e 
g = 2 * 2
h = f / g
i = 5 ** 2
j = 2 * 12
k = j * 4
l = i + k 
m = math.sqrt(l)
n = 5 - m
o = 2 * 2
p = n / o
q = h - p
Problem: . star question : if f ( 1 ) = 4 and f ( x + y ) = f ( x ) + f ( y ) + 7 xy + 4 , then f ( 2 ) + f ( 5 ) = ?
Options: a ) 125 , b ) 977 , c ) 289 , d ) 1077 , e ) 111
Rationale: let x = 1 and y = 1 f ( 1 + 1 ) = f ( 1 ) + f ( 1 ) + 7 x 1 x 1 + 4 ⇒ ⇒ f ( 2 ) = 19 let x = 2 and y = 2 f ( 2 + 2 ) = 19 + 19 + 7 x 2 x 2 + 4 ⇒ ⇒ f ( 4 ) = 70 let x = 1 and y = 4 f ( 1 + 4 ) = 4 + 70 + 28 + 4 = 106 f ( 2 ) + f ( 5 ) = 125 answer : a
Answer: a
Python program:
a = 5 * 5
b = 5 * a
Problem: a man saves 30 % of his monthly salary . if an account of dearness of things he is to increase his monthly expenses by 30 % , he is only able to save rs . 300 per month . what is his monthly salary ?
Options: a ) rs . 4000 , b ) rs . 3750 , c ) rs . 5000 , d ) rs . 5500 , e ) rs . 6500
Rationale: "income = rs . 100 expenditure = rs . 70 savings = rs . 30 present expenditure 70 + 70 * ( 30 / 100 ) = rs . 91 present savings = 100 – 91 = rs . 8 if savings is rs . 8 , salary = rs . 100 if savings is rs . 300 , salary = 100 / 8 * 300 = 3750 answer : b"
Answer: b
Python program:
a = 300 * 100
b = 100 - 30
c = 100 - 30
d = 30 / 100
e = c * d
f = b + e 
g = 100 - f
h = a / g
Problem: the probability that a man will be alive for 10 more yrs is 1 / 3 & the probability that his wife will alive for 10 more yrs is 5 / 8 . the probability that none of them will be alive for 10 more yrs , is
Options: a ) 1 / 8 , b ) 1 / 4 , c ) 2 / 3 , d ) 3 / 4 , e ) 2
Rationale: "sol . required probability = pg . ) x p ( b ) = ( 1 — d x ( 1 — i ) = : x 1 = 1 / 4 ans . ( b )"
Answer: b
Python program:
a = 1 / 3
b = 1 - a
c = 1 / 8
d = 1 - c
e = b * d
Problem: the average ( arithmetic mean ) of 20 , 40 , and 60 is 8 more than the average of 10 , 70 , and what number ?
Options: a ) 16 , b ) 25 , c ) 35 , d ) 45 , e ) 55
Rationale: "a 1 = 120 / 3 = 40 a 2 = a 1 - 8 = 32 sum of second list = 32 * 3 = 96 therefore the number = 96 - 80 = 16 answer : a"
Answer: a
Python program:
a = 20 + 40 
b = a + 60 
c = 8 * 3
d = c + 10 
e = d + 70 
f = b - e