euclaise/mathqa_programs huggingface dataset:
Problem: a machine , working at a constant rate , manufactures 72 staplers in 28 minutes . how many staplers does it make in 1 hr 52 min ?
Options: a ) 268 , b ) 262 , c ) 300 , d ) 288 , e ) 250
Rationale: "change 1 hr 52 min to 112 min . for this , we need to set up a simple proportion of staplers per time 72 / 28 = s / 112 . the absolutely worst thing you could do at this point in the problem is to cross - multiply . that would be a supremely unstrategic move . we can cancel the common factor of 28 in the two denominators . 72 / 28 * 28 = s / 112 * 28 72 / 1 = s / 4 s = 4 * 72 s = 288 the machine would be 288 staplers in 1 hr 52 min . answer : d"
Answer: d
Python program:
a = 1 * const_60
b = a + 52 
c = b / 28
d = c * 72
Problem: wink , inc . follows a certain procedure that requires two tasks to be finished independently in order for a job to be done . on any given day , there is a 1 / 8 probability that task 1 will be completed on time , and a 3 / 5 probability that task 2 will be completed on time . on a certain day , what is the probability that task 1 will be completed on time , but task 2 will not ?
Options: a ) 1 / 20 , b ) 3 / 40 , c ) 13 / 40 , d ) 7 / 20 , e ) 13 / 22
Rationale: "p ( 1 and not 2 ) = 1 / 8 * ( 1 - 3 / 5 ) = 1 / 20 . answer : a ."
Answer: a
Python program:
a = 1 / 8
b = 3 / 1
c = 1 - b
d = a * c
Problem: when a = x + ( 2 / x ) and b = x - ( 2 / x ) , ( 2 ^ a ^ 2 ) / ( 2 ^ b ^ 2 ) = ?
Options: a ) 2 , b ) 256 , c ) 8 , d ) 16 , e ) 32
Rationale: - - > ( 2 ^ a ^ 2 ) / ( 2 ^ b ^ 2 ) = { ( 2 ) ^ ( a ^ 2 - b ^ 2 ) } = 2 ^ ( a - b ) ( a + b ) . since a - b = 4 / x and a + b = 2 x , 2 ^ ( a - b ) ( a + b ) = 2 ^ ( 4 / x ) ( 2 x ) = 2 ^ 8 = 256 answer is b
Answer: b
Python program:
a = 2 * 2
b = 2 * 2
c = a + b 
d = 2 ** c
Problem: if ( 4 - x ) / ( 4 + x ) = x , what is the value of x ^ 2 + 5 x - 4 ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: ( 4 - x ) = x * ( 4 + x ) ( 4 - x ) = 4 x + x ^ 2 0 = x ^ 2 + 5 x - 4 the answer is a .
Answer: a
Python program:
a = 4 * 2
b = a - 4
Problem: walking with 4 / 5 of my usual speed , i miss the bus by 5 minutes . what is my usual time ?
Options: a ) 145 , b ) 5617 , c ) 15 , d ) 20 , e ) 12
Rationale: "speed ratio = 1 : 4 / 5 = 5 : 4 time ratio = 4 : 51 - - - - - - - - 5 4 - - - - - - - - - ? è 20 answer : d"
Answer: d
Python program:
a = 5 / 4
b = 5 / a
c = b * 5
Problem: the average weight of a , b and c is 45 kg . if the average weight of a and b be 40 kg and that of b and c be 45 kg , then the weight of b is :
Options: a ) 31 kg , b ) 32 kg , c ) 33 kg , d ) 35 kg , e ) none of these
Rationale: "explanation : let a , b , c represent their respective weights . then , we have : a + b + c = ( 45 x 3 ) = 135 … . ( i ) a + b = ( 40 x 2 ) = 80 … . ( ii ) b + c = ( 45 x 2 ) = 90 … . ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 170 … . ( iv ) subtracting ( i ) from ( iv ) , we get : b = 35 . b ’ s weight = 35 kg . answer : d"
Answer: d
Python program:
a = 40 * 2
b = 45 * 2
c = a + b 
d = 45 * 3
e = c - d
Problem: evaluate : 35 - 12 * 3 * 2 = ?
Options: a ) 62 , b ) 52 , c ) 32 , d ) 27 , e ) 22
Rationale: "according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 35 - 12 * 3 * 2 = 35 - 8 = 27 correct answer d"
Answer: d
Python program:
a = 12 * 3
b = a * 2
c = 35 - b
Problem: a waiter ' s salary consists of his salary and tips . during one week his tips were 5 / 4 of his salary . what fraction of his income came from tips ?
Options: a ) 4 / 9 , b ) 5 / 4 , c ) 5 / 8 , d ) 5 / 9 , e ) 6 / 9
Rationale: "income = salary ( s ) + tips = s + s * 5 / 4 = s * 9 / 4 tips = s * 5 / 4 fraction of his income came from tips = ( s * 5 / 4 ) / ( s * 9 / 4 ) = 5 / 9 answer : d"
Answer: d
Python program:
a = 5 / 4
b = 5 / 4
c = b + 1 
d = a / c
Problem: in a fort , there are 1200 soldiers . if each soldier consumes 3 kg per day , the provisions available in the fort will last for 30 days . if some more soldiers join , the provisions available will last for 25 days given each soldier consumes 2.5 kg per day . find the number of soldiers joining the fort in that case ?
Options: a ) 273 , b ) 528 , c ) 539 , d ) 538 , e ) 723
Rationale: "assume x soldiers join the fort . 1200 soldiers have provision for 1200 ( days for which provisions last them ) ( rate of consumption of each soldier ) = 1200 ( 30 ) ( 3 ) kg also provisions available for ( 1200 + x ) soldiers is ( 1200 + x ) ( 25 ) ( 2.5 ) kg as the same provisions are available = > 1200 ( 30 ) ( 3 ) = ( 1200 + x ) ( 25 ) ( 2.5 ) x = [ 1200 ( 30 ) ( 3 ) ] / [ ( 25 ) ( 2.5 ) ] - 1200 x = 528 answer : option b"
Answer: b
Python program:
a = 1200 * 3
b = a * 30
c = b / 25
d = c / 2
e = d - 1200
Problem: 19 people went to a hotel for combine dinner party 13 of them spent rs . 79 each on their dinner and rest spent 4 more than the average expenditure of all the 19 . what was the total money spent by them .
Options: a ) 1628.4 , b ) 1534 , c ) 1492 , d ) 1496 , e ) none of these
Rationale: solution : let average expenditure of 19 people be x . then , 19 x = 13 * 79 + 6 * ( x + 4 ) ; or , 19 x = 13 * 79 + 6 x + 24 ; or , x = 80.84 ; so , total money spent = 80.84 * 19 = rs . 1536.07 . answer : option e
Answer: e
Python program:
a = 13 * 79
b = 19 - 13
c = b * 4
d = a + c 
e = 19 - 13
f = 19 - e
g = d / f
h = g * 19
Problem: in a competitive examination in state a , 6 % candidates got selected from the total appeared candidates . state b had an equal number of candidates appeared and 7 % candidates got selected with 81 more candidates got selected than a . what was the number of candidates appeared from each state ?
Options: a ) 7000 , b ) 8100 , c ) 6000 , d ) 5000 , e ) 4000
Rationale: state a and state b had an equal number of candidates appeared . in state a , 6 % candidates got selected from the total appeared candidates in state b , 7 % candidates got selected from the total appeared candidates but in state b , 81 more candidates got selected than state a from these , it is clear that 1 % of the total appeared candidates in state b = 81 = > total appeared candidates in state b = 81 x 100 = 8100 = > total appeared candidates in state a = total appeared candidates in state b = 8100
Answer: b
Python program:
a = 7 - 6
b = a / 100
c = 81 / b
Problem: find the compound ratio of ( 3 : 2 ) , ( 4 : 3 ) and ( 1 : 4 ) is
Options: a ) 1 : 2 , b ) 2 : 3 , c ) 3 : 4 , d ) 4 : 5 , e ) 3 : 2
Rationale: "required ratio = 3 / 2 * 4 / 3 * 1 / 4 = 1 / 2 = 1 : 2 answer is a"
Answer: a
Python program:
a = 3 / 4
b = 4 / 0
c = 4 / 2
d = b * c
e = a * d
Problem: a ( 5 , w ^ 2 ) is the ( x , y ) coordinate of point located on the parabola y = x ^ 2 + 11 . what is the value of w ?
Options: a ) 3 . , b ) 4 . , c ) 5 . , d ) 6 . , e ) 9 .
Rationale: "y = x ^ 2 + 11 w ^ 2 = 5 ^ 2 + 11 w ^ 2 = 36 w = 6 answer d"
Answer: d
Python program:
a = 5 ** 2
b = a - 11
c = 11 / 5
d = b ** c
Problem: how many positive integers less than 5,000 are evenly divisible by neither 16 nor 21 ?
Options: a ) 4,514 , b ) 4,475 , c ) 4,521 , d ) 4,428 , e ) 4,349
Rationale: "integers less than 5000 divisible by 16 5000 / 16 = 333 . something , so 333 integers less than 5000 divisible by 21 5000 / 21 = 238 . # # , so 238 we have double counted some , so take lcm of 16 and 21 = 105 and divide by 5000 , we get 47 . so all numbers divisible by 16 and 21 = 333 + 238 - 47 = 524 now subtract that from 4999 . 4999 - 524 = 4514 answer a ."
Answer: a
Python program:
a = 4 + 16 
b = a - 1
c = math.factorial(b)
d = math.factorial(16)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
Problem: a girl walks at a speed of 5 kmph . how much time does he take to walk a distance of 30 km ?
Options: a ) 10 hrs , b ) 2 hrs , c ) 3 hrs , d ) 5 hrs , e ) 6 hrs
Rationale: time = distance / speed = 30 / 5 = 6 hours . answer is e
Answer: e
Python program:
a = 30 / 5
Problem: a man â € ™ s current age is ( 2 / 5 ) of the age of his father . after 10 years , he will be ( 1 / 2 ) of the age of his father . what is the age of father at now ?
Options: a ) 40 , b ) 45 , c ) 38 , d ) 50 , e ) 39
Rationale: "let , father â € ™ s current age is a years . then , man â € ™ s current age = [ ( 2 / 5 ) a ] years . therefore , [ ( 2 / 5 ) a + 10 ] = ( 1 / 2 ) ( a + 10 ) 2 ( 2 a + 50 ) = 5 ( a + 10 ) a = 50 d"
Answer: d
Python program:
a = 1 / 2
b = 10 * a
c = 10 - b
d = 1 / 2
e = 2 / 5
f = d - e
g = c / f
Problem: when positive integer n is divided by 5 , the remainder is 1 . when n is divided by 7 , the remainder is 3 . what is the smallest positive integer k such that k + n is a multiple of 34 ?
Options: a ) 3 , b ) 4 , c ) 12 , d ) 32 , e ) 35
Rationale: "n = 5 p + 1 = 6,11 , 16,21 , 26,31 n = 7 q + 3 = 3 , 10,17 , 24,31 = > n = 34 m + 31 to get this , we need to take lcm of co - efficients of p and q and first common number in series . so we need to add 3 more to make it 34 m + 34 answer - a"
Answer: a
Python program:
a = 34 - reminder
Problem: a cricketer whose bowling average is 12.4 runs per wicket takes 5 wickets for 26 runs and thereby decreases his average by 0.4 . the number of wickets taken by him till the last match was :
Options: a ) 64 , b ) 72 , c ) 80 , d ) 85 , e ) none of the above
Rationale: "let the number of wickets taken till the last match be x . then , 12.4 x + 26 / x + 5 = 12 ⇒ 12.4 x + 26 = 12 x + 60 ⇒ 0.4 x = 34 ⇒ x = 34 ⁄ 0.4 = 340 ⁄ 4 = 85 . answer d"
Answer: d
Python program:
a = 12 - 4
b = 5 * a
c = b - 26
d = c / 0
Problem: working together , tim and tom can type 12 pages in one hour . if they would be able to type 14 pages in one hour if tom increases his typing speed by 25 % , what is the ratio of tom ' s normal typing speed to that of tim ?
Options: a ) 2 / 1 , b ) 1 / 2 , c ) 1 / 3 , d ) 4 / 1 , e ) 1 / 4
Rationale: "lets say tim types x pages an hour and tom types y pages an hour . we know that x + y = 12 tom increase speed by 25 % means he will type 1.25 y pages an hour . so we get x + 1.25 y = 14 we need to know the ratio of tom ' s speed to tim ' s speed . this is going to be proportional to the number of pages each can type in an hour , hence ( y / x ) . subtracting both : 0.25 y = 2 so y = 8 . . . so x = 4 ( y / x ) = 8 / 4 = 2 / 1 answer is ( a )"
Answer: a
Python program:
a = 14 - 12
b = 100 * 1
c = 25 / b
d = a / c
e = 14 - 12
f = 100 * 1
g = 25 / f
h = e / g
i = 12 - h
j = d / i
Problem: in a bus left side are 15 seats available , 3 few seats in right side because in rear exit door . each seat hold 3 people . in addition , there is a seat back can sit 9 people all together . how many people can sit in a bus ?
Options: a ) 52 , b ) 49 , c ) 95 , d ) 90 , e ) 66
Rationale: "right side = 15 seat left side = 15 - 3 ( 3 few seat in right side ) = 12 seat total = 15 + 12 = 27 people can seat in 27 seat = 27 * 3 = 81 people can seat in last seat = 9 total people can seat = 81 + 9 = 90 answer : d"
Answer: d
Python program:
a = 15 - 3
b = 15 + a 
c = b * 3
d = c + 9
Problem: the average of temperatures at noontime from monday to friday is 25 ; the lowest one is 15 , what is the possible maximum range of the temperatures ?
Options: a ) 20 , b ) 25 , c ) 50 , d ) 45 , e ) 75
Rationale: average = 25 , sum of temperatures = 25 * 5 = 125 as the min temperature is 15 , max would be 125 - 4 * 15 = 65 - - > the range = 65 ( max ) - 15 ( min ) = 50 answer : c
Answer: c
Python program:
a = 2 + 3 
b = 25 * a
c = 15 * 4
d = b - c
e = d - 15
Problem: what will be the compound interest on a sum of rs . 27,000 after 3 years at the rate of 12 % p . a . ?
Options: a ) s . 10123.77 , b ) s . 10123.21 , c ) s . 10933.05 , d ) s . 10123.28 , e ) s . 10123.21
Rationale: "amount = [ 27000 * ( 1 + 12 / 100 ) 3 ] = 27000 * 28 / 25 * 28 / 25 * 28 / 25 = rs . 37933.0 c . i . = ( 37933.056 - 27000 ) = rs . 10933.05 answer : c"
Answer: c
Python program:
a = 4 * 100
b = a * 100
c = 12 / 100
d = 1 + c 
e = d ** 3
f = b * e
g = 4 * 100
h = g * 100
i = f - h
Problem: a merchant marks goods up by 75 % and then offers a discount on the marked price . the profit that the merchant makes after offering the discount is 22.5 % . what % discount did the merchant offer ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 40 %
Rationale: let p be the original price of the goods and let x be the rate after the markup . ( 1.75 p ) * x = 1.225 p x = 1.225 / 1.75 = 0.7 which is a discount of 30 % . the answer is c .
Answer: c
Python program:
a = 75 / 100
b = 1 + a 
c = b - 1
d = 22 / 5
e = c - d
f = 75 / 100
g = 1 + f 
h = e / g
i = h * 100
Problem: a , b and c rents a pasture for rs . 1130 . a put in 12 horses for 8 months , b 16 horses for 9 months and 18 horses for 6 months . how much should c pay ?
Options: a ) 270 , b ) 199 , c ) 351 , d ) 156 , e ) 122
Rationale: "12 * 8 : 16 * 9 = 18 * 6 8 : 12 : 9 9 / 29 * 1130 = 351 answer : c"
Answer: c
Python program:
a = 12 * 8
b = 16 * 9
c = a + b 
d = 18 * 6
e = c + d 
f = 1130 / e
g = 16 * 9
h = f * g
Problem: how many multiples of 2 are there between 1 and 54 , exclusive ?
Options: a ) 21 , b ) 22 , c ) 24 , d ) 26 , e ) 28
Rationale: "26 multiples of 2 between 1 and 54 exclusive . from 2 * 1 upto 2 * 26 , ( 1,2 , 3,4 , . . . , 26 ) . hence , 26 multiples ! correct option is d"
Answer: d
Python program:
a = 54 - 1
b = a / 2
c = b + 1
Problem: at what rate percent per annum will a sum of money double in 2 years .
Options: a ) 34 % , b ) 50 % , c ) 11.5 % , d ) 20 % , e ) 21.5 %
Rationale: "let principal = p , then , s . i . = p and time = 8 years rate = [ ( 100 x p ) / ( p x 2 ) ] % = 50 % per annum . answer : b"
Answer: b
Python program:
a = 100 / 2
Problem: the sum of 2 consecutive numbers is definitely :
Options: a ) positive . , b ) divisible by 2 . , c ) divisible by 3 . , d ) divisible by 4 . , e ) divisible by 5 .
Rationale: "if 1 st term is x : x + ( x + 1 ) = 2 x + 1 - - - > positive if 2 nd term is x : ( x - 1 ) + x = 2 x - 1 - - - > positive a"
Answer: a
Python program:
a = 2 - 10
b = a - 2
c = b / 4
d = c + 2 
e = d + 2 
f = e ** 2
g = 2 - 10
h = g - 2
i = h / 4
j = i + 2 
k = j + 2 
l = k + 2 
m = l ** 2
n = f + m 
o = 2 - 10
p = o - 2
q = p / 4
r = q ** 2
s = 2 - 10
t = s - 2
u = t / 4
v = u + 2 
w = v ** 2
x = r + w 
y = n + x
Problem: four concentric circles r given . the radius of 1 st circle is x . next is 2 x , then 3 x and 4 x . given that area b / w 2 nd and 1 st is a and 4 th and 3 rd circles being b . find ratio of a to b
Options: a ) 2 : 7
b ) 1 : 7
c ) 3 : 5
d ) 3 : 7
e ) 3 : 4
Rationale: area of first circle = pi * ( x ) ^ 2 = pi * x ^ 2 area of second circle = pi * ( 2 x ) ^ 2 = 4 * pi * x ^ 2 area of third circle = pi * ( 3 x ) ^ 2 = 9 * pi * x ^ 2 area of fourth circle = pi * ( 4 x ) ^ 2 = 16 * pi * x ^ 2 area b / w 1 st and 2 nd circles = 3 * pi * x ^ 2 area b / w 3 rd and 4 th circles = 7 * pi * x ^ 2 so ratio = 3 : 7 answer : d
Answer: d
Python program:
a = 3 + 4 
b = 3 / a
Problem: a grocery shop has a sale of rs . 6335 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6500 ?
Options: a ) 4857 , b ) 4184 , c ) 4012 , d ) 5091 , e ) 5291
Rationale: "let the sale in the sixth month = x then ( 6335 + 6927 + 6855 + 7230 + 6562 + x ) / 6 = 6500 = > 6335 + 6927 + 6855 + 7230 + 6562 + x = 6 × 6500 = > 33909 + x = 39000 = > x = 39000 − 33909 = 5091 answer : d"
Answer: d
Python program:
a = 5 + 1 
b = 6500 * a
c = 6335 + 6927 
d = 6855 + c 
e = d + 7230 
f = e + 6562 
g = b - f
Problem: two numbers have a h . c . f of 9 and a product of two numbers is 1800 . find the l . c . m of the two numbers ?
Options: a ) 200 , b ) 150 , c ) 160 , d ) 170 , e ) 180
Rationale: "l . c . m of two numbers is given by ( product of the two numbers ) / ( h . c . f of the two numbers ) = 1800 / 9 = 200 . answer : a"
Answer: a
Python program:
a = 1800 / 9
Problem: in a market , a dozen eggs cost as much as a pound of rice , and a half - liter of kerosene costs as much as 4 eggs . if the cost of each pound of rice is $ 0.33 , then how many cents does a liter of kerosene cost ? [ one dollar has 100 cents . ]
Options: a ) 0.22 , b ) 0.44 , c ) 0.55 , d ) 22 , e ) 55
Rationale: a dozen eggs cost as much as a pound of rice - - > 12 eggs = 1 pound of rice = 33 cents ; a half - liter of kerosene costs as much as 8 eggs - - > 4 eggs = 1 / 2 liters of kerosene . how many cents does a liter of kerosene cost - - > 1 liter of kerosene = 8 eggs = 8 / 12 * 33 = 22 cents . answer : d .
Answer: d
Python program:
a = 1 / 2
b = 4 / a
c = b / 12
d = 0 * 33
e = c * d
Problem: the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 14000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 28
Rationale: "solution let the toatl number of workers be x . then 8000 x = ( 14000 x 7 ) + 6000 ( x - 7 ) x = 28 . answer e"
Answer: e
Python program:
a = 14000 - 8000
b = 7 * a
c = 8000 - 6000
d = b / c
e = 7 + d
Problem: a man buys rs . 48 shares paying 9 % dividend . the man wants to have an interest of 12 % on his money . the market value of each share is :
Options: a ) s . 12 , b ) s . 15 , c ) s . 18 , d ) s . 21 , e ) s . 36
Rationale: "dividend on rs . 48 = rs . 9 / 100 x 48 = rs . 4.32 . rs . 12 is an income on rs . 100 . rs . 4.32 is an income on rs . 100 / 12 x 4.32 = rs . 36 . answer : option e"
Answer: e
Python program:
a = 100 / 12
b = 9 / 100
c = b * 48
d = a * c
Problem: a can do a piece of work in 20 days . when he had worked for 2 days b joins him . if the complete work was finished in 8 days . in how many days b alone can finish the work ?
Options: a ) 18 , b ) 77 , c ) 66 , d ) 55 , e ) 10
Rationale: "8 / 20 + 6 / x = 1 x = 10 days answer : e"
Answer: e
Python program:
a = 1 / 8
b = 1 / 20
c = 2 * b
d = 1 - c
e = a * d
f = 1 / 20
g = e - f
h = 1/(g)
i = 20 + 8 
j = h - i
Problem: the ratio of three numbers is 3 : 4 : 5 and the sum of their squares is 1250 . the sum of the numbers is :
Options: a ) 30 , b ) 50 , c ) 60 , d ) 70 , e ) 80
Rationale: "let the numbers be 3 x , 4 x and 5 x then , 9 x 2 + 16 x 2 + 25 x 2 = 1250 50 x 2 = 1250 x = 5 sum of numbers = 3 x + 4 x + 5 x = 12 x = 60 answer c 60"
Answer: c
Python program:
a = 5 ** 4
b = 3 ** 4
c = 4 ** 4
d = b + c 
e = a + d 
f = 1250 / e
g = math.sqrt(f)
Problem: elena ’ s bread recipe calls for 8 ounces of butter for each 14 cups of flour used . she needs to make 4 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 ) 56
Rationale: "solving through algebra route : 8 b + 14 f = x amount if we multiply this equation with 4 we get : 32 b + 56 f = 4 x therefore , we got 32 ounces of butter and 4 x amount of quantity when we use 56 ounces of floor . ans : e"
Answer: e
Python program:
a = 14 * 4
Problem: solution a is 20 % salt and solution b is 80 % salt . if you have 30 ounces of solution a and 60 ounces of solution b , in what ratio could you mix solution a with solution b to produce 50 ounces of a 50 % salt solution ?
Options: a ) 6 : 4 , b ) 6 : 14 , c ) 4 : 4 , d ) 4 : 6 , e ) 3 : 7
Rationale: "let : x = ounces taken from solution a ( 20 % salt ) y = ounces taken from solution b ( 80 % salt ) to prepare 50 ounce 50 % salt . first equation is simple : x + y = 50 to get another equation so as to be able to solve , compute salt contents . 20 % of x + 80 % of y = 50 % of 50 or x / 5 + 4 / 5 * y = 25 or x + 4 y = 125 solve two equations to get : x = 25 y = 25 so solutions has to mix in 1 : 1 oops 4 : 4 answer : c"
Answer: c
Python program:
a = 80 / 100
b = 50 * a
c = 50 / 100
d = 50 * c
e = b - d
f = 80 / 100
g = 20 / 100
h = f - g
i = e / h
j = 80 / 100
k = 50 * j
l = 50 / 100
m = 50 * l
n = k - m
o = 80 / 100
p = 20 / 100
q = o - p
r = n / q
s = 50 - r
t = i / s
Problem: a man can row at 6 kmph in still water . if the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back , how far is the place ?
Options: a ) 2.4 km , b ) 2.6 km , c ) 2.9 km , d ) 4.4 km , e ) 5.6 km
Rationale: "explanation : speed in still water = 6 kmph speed of the current = 1 kmph speed downstream = ( 6 + 1 ) = 7 kmph speed upstream = ( 6 - 1 ) = 5 kmph let the required distance be x km total time taken = 1 hour â ‡ ’ x / 7 + x / 5 = 1 â ‡ ’ 5 x + 7 x = 35 â ‡ ’ 12 x = 35 â ‡ ’ x = 2.9 km answer : option c"
Answer: c
Python program:
a = 6 - 1
b = a * 3
c = b / 6
Problem: 5 kilograms of oranges contained 95 % of water . if the next day the concentration of water decreased by 5 % , what was the new weight of the oranges , in kilograms ?
Options: a ) 30 , b ) 25 , c ) 15 , d ) 10 , e ) 5
Rationale: five kilograms of oranges contained 95 % of water . if the next day the concentration of water decreased by 5 % , what was the new weight of the oranges , in kilograms ? ( a ) 30 ( b ) 25 ( c ) 15 ( d ) 10 ( e ) 5 if b is the answer , then the question means that the concentration of water the newt day became 90 % . out of 5 kilograms 95 % , or 4.75 kilograms was water and 0.25 kilograms was non - water . the next day , after some water evaporated , oranges became 90 % water and 10 % of non - water , so the next day 0.25 kilograms of non - water composed 10 % of oranges , which means that the new weight of the oranges was x * 0.10 = 0.25 - - > x = 25 kilograms . answer : b .
Answer: b
Python program:
a = 5 * 5
Problem: the mean of 20 values was 150 . it was detected on rechecking that one value 160 was wrongly copied as 135 for the computation of the mean . find the correct mean .
Options: a ) 151 , b ) 149 , c ) 151.25 , d ) 148 , e ) none of the above
Rationale: corrected mean = 150 × 20 − 135 + 160 / 20 = 3000 − 135 + 160 / 20 = 3025 / 20 = 151.25 answer c
Answer: c
Python program:
a = 20 * 150
b = 160 - 135
c = a + b 
d = c / 20
Problem: the present population of a town is 200 . population increase rate is 10 % p . a . find the population of town after 1 years ?
Options: a ) 100 , b ) 120 , c ) 200 , d ) 220 , e ) 250
Rationale: "p = 200 r = 10 % required population of town = p * ( 1 + r / 100 ) ^ t = 200 * ( 1 + 10 / 100 ) = 200 * ( 11 / 10 ) = 220 ( approximately ) answer is d"
Answer: d
Python program:
a = 200 * 10
b = a / 100
c = 200 + b
Problem: at a certain resort , each of the 39 food service employees is trained to work in a minimum of 1 restaurant and a maximum of 3 restaurants . the 3 restaurants are the family buffet , the dining room , and the snack bar . exactly 19 employees are trained to work in the family buffet , 18 are trained to work in the dining room , and 12 are trained to work in the snack bar . if 2 employees are trained to work in exactly 2 restaurants , how many employees are trained to work in all 3 restaurants ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "39 = 19 + 18 + 12 - 2 - 2 x 2 x = 19 + 18 + 12 - 2 - 39 = 45 - 37 = 8 x = 4 c"
Answer: c
Python program:
a = 19 + 18 
b = a + 12 
c = b - 2
d = c - 39
e = d / 2
Problem: if n is a prime number greater than 7 , what is the remainder when n ^ 2 is divided by 12 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5
Rationale: "there are several algebraic ways to solve this question , but the easiest way is as follows : since we can not have two correct answers just pick a prime greater than 7 , square it and see what would be the remainder upon division of it by 12 . n = 11 - - > n ^ 2 = 121 - - > remainder upon division 121 by 12 is 1 . answer : b ."
Answer: b
Python program:
a = 7 + 2 
b = a ** 2
c = 12 * 4
d = b - c
Problem: if sushi rows 27 km upstream and 81 km down steam taking 9 hours each , then the speed of the stream
Options: a ) 12 kmph , b ) 13 kmph , c ) 22 kmph , d ) 20 kmph , e ) 15 kmph
Rationale: speed upstream = 27 / 9 = 3 kmph speed down stream = 81 / 3 = 27 kmph speed of stream = ½ ( 27 - 3 ) = 12 kmph answer : a
Answer: a
Python program:
a = 81 / 9
b = 27 / 9
c = a + b