euclaise/mathqa_programs huggingface dataset:
Problem: right triangle pqr is to be constructed in the xy - plane so that the right angle is at p and pr is parallel to the x - axis . the x - and y - coordinates of p , q and r are to be integers that satisfy the inequalities - 4 < = x < = 5 and 6 < = y < = 16 . how many different triangles with these properties could be constructed ?
Options: a ) 110 , b ) 1100 , c ) 9900 , d ) 10000 , e ) 12100
Rationale: "we know that p , q , r can only lie on a grid 10 x 11 let ' s start by fixing p ' x - coordinate : we have 10 possible places for it then we choose x - coordinate for r : since pr | | x - axis , r ' s x - coordinate can not coincide with p ' s x - coord , so we have only 9 possible choices left . then , we fix p ' s ( and r ' s too ) y - coordinate : 11 possible choices . finally , after we fixed p and r , q ' s x - coordinate must be the same as p ' s ( because p is the right angle and pr | | x - axis ) , so the only choice is for y - coordinate , and we have 10 possible choices left . so , total number of different triangles : 10 * 9 * 11 * 10 = 9,900 answer : c"
Answer: c
Python program:
a = 10 - 1
b = 6 + 4 
c = 16 - 5
d = b * c
e = a * d
f = e * 10
Problem: sand is poured into a box so that the box is being filled at the rate of 3 cubic feet per hour . if the empty rectangular box is 5 feet long , 4 feet wide , and 3 feet deep , approximately how many hours does it take to fill the box ?
Options: a ) 14 , b ) 16 , c ) 18 , d ) 20 , e ) 22
Rationale: "the volume the box is : length * width * depth = 5 * 4 * 3 = 60 cubic feet . 60 cubic feet / 3 cubic feet per hour = 20 hours . it will take 20 hours to fill the box . the answer is d ."
Answer: d
Python program:
a = 5 * 4
b = a * 3
c = b / 3
Problem: jack and christina are standing 270 feet apart on a level surface . their dog , lindy , is standing next to christina . at the same time , they all begin moving toward each other . jack walks in a straight line toward christina at a constant speed of 4 feet per second and christina walks in a straight line toward jack at a constant speed of 5 feet per second . lindy runs at a constant speed of 8 feet per second from christina to jack , back to christina , back to jack , and so forth . what is the total distance , in feet , that lindy has traveled when the three meet at one place ?
Options: a ) 150 , b ) 180 , c ) 210 , d ) 240 , e ) 270
Rationale: "the relative speed of jack and christina is 4 + 5 = 9 feet per second . the distance between them is 210 feet , hence they will meet in ( time ) = ( distance ) / ( relative speed ) = 270 / 7 = 30 seconds . for all this time lindy was running back and forth , so it covered ( distance ) = ( speed ) * ( time ) = 8 * 30 = 240 feet . answer : d ."
Answer: d
Python program:
a = 4 + 5 
b = 270 / a
c = b * 8
Problem: how many liters of water must be added to 20 liters of milk and water containing 10 % water to make it 50 % water ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "by rule of alligation : 50 % - 10 % = 40 % 100 % - 50 % = 50 % quantity of pure water : quantity of the mixture = 4 : 5 there are 20 liters of mixture , so we need to add 16 liters of pure water . the answer is d ."
Answer: d
Python program:
a = 20 / 10
b = 50 / 10
c = a * b
Problem: man 1 alone can do a piece of work in 6 days and man 2 alone in 8 days . man 1 and man 2 undertook to do it for rs . 3200 . with the help of man 3 , they completed the work in 3 days . how much is to be paid to man 3 ?
Options: a ) 400 , b ) 200 , c ) 100 , d ) 150 , e ) 500
Rationale: man 3 1 day work = 1 / 3 - ( 1 / 6 + 1 / 8 ) = 1 / 3 - 7 / 24 = 1 / 24 man 1 : man 2 : man 3 = 1 / 6 : 1 / 8 : 1 / 24 = = > 4 : 3 : 1 man 3 share = 3 * 1 / 24 * 3200 = rs 400 answer a
Answer: a
Python program:
a = 1 / 3
b = 1 / 6
c = 1 / 8
d = b + c 
e = a - d
f = 1/(e)
g = 3 / f
h = 3200 * g
Problem: in arun ' s opinion , his weight is greater than 65 kg but leas than 72 kg . his brother does not agree with arun and he thinks that arun ' s weight is greater than 60 kg but less than 70 kg . his mother ' s view is that his weight can not be greater than 68 kg . if all of them are correct in their estimation , what is the average of diferent probable weights of arun ?
Options: a ) 16.5 kg , b ) 66.5 kg , c ) 26.5 kg , d ) 56.5 kg , e ) 86.5 kg
Rationale: "let arun ' s weight be x kg . according to arun , 65 < x < 72 . according to arun ' s brother , 60 < x < 70 . according to arun ' s mother , x < 68 . the values satisfying all the above conditions are 66 and 67 . required average = ( 66 + 67 ) / 2 = 66.5 kg answer : b"
Answer: b
Python program:
a = 65 + 1 
b = 68 + a 
c = b / 2
Problem: shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $ 500 as interest . he invested the remaining in a bond that paid compound interest , interest being compounded annually , for the same 2 years at the same rate of interest and received $ 555 as interest . what was the value of his total savings before investing in these two bonds ?
Options: a ) 2,000 , b ) 2,500 , c ) 4,000 , d ) 5,000 , e ) 6,000
Rationale: "so , we know that shawn received 20 % of the amount he invested in a year . we also know that in one year shawn received $ 250 , thus 0.2 x = $ 250 - - > x = $ 1,250 . since , he invested equal sums in his 2 bonds , then his total savings before investing was 2 * $ 1,250 = $ 2,500 . answer : b"
Answer: b
Python program:
a = 500 / 2
b = 500 / 2
c = a * b
d = 555 - 500
e = c / d
f = e * 2
Problem: ramesh purchased a refrigerator for rs . 15500 after getting a discount of 20 % on the labelled price . he spent rs . 125 on transport and rs . 250 on installation . at what price should it be sold so that the profit earned would be 10 % if no discount was offered ?
Options: a ) 34778 , b ) 26888 , c ) 2899 , d ) 17600 , e ) 21725
Rationale: "price at which the tv set is bought = rs . 15,500 discount offered = 20 % marked price = 15500 * 100 / 80 = rs . 19375 the total amount spent on transport and installation = 125 + 250 = rs . 375 \ total price of tv set = 19375 + 375 = rs . 19750 the price at which the tv should be sold to get a profit of 10 % if no discount was offered = 19750 * 110 / 100 = rs . 21725 answer : e"
Answer: e
Python program:
a = 100 + 10 
b = 15500 * 100
c = 100 - 20
d = b / c
e = 125 + 250 
f = d + e 
g = a * f
h = g / 100
Problem: how many numbers from 10 to 1000000 are exactly divisible by 9 ?
Options: a ) 900 , b ) 8000 , c ) 1100 , d ) 111110 , e ) 14
Rationale: "10 / 9 = 1 and 1000000 / 9 = 111111 = = > 111111 - 1 = 111110 . answer : d"
Answer: d
Python program:
a = 1000000 / 9
b = math.floor(a)
c = b * 9
d = 10 / 9
e = math.floor(d)
f = e + 1 
g = f * 9
h = c - g
i = h / 9
j = i + 1
Problem: a train running at the speed of 60 km / hr crosses a pole in 9 seconds . find the length of the train ?
Options: a ) 150 , b ) 872 , c ) 287 , d ) 288 , e ) 212
Rationale: "speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 9 = 150 meter answer : a"
Answer: a
Python program:
a = 60 * 1000
b = a / 3600
c = b * 9
Problem: a rectangular plot measuring 30 meters by 50 meters is to be enclosed by wire fencing . if the poles of the fence are kept 5 meters apart . how many poles will be needed ?
Options: a ) 46 m , b ) 66 m , c ) 26 m , d ) 56 m , e ) 32 m
Rationale: "perimeter of the plot = 2 ( 30 + 50 ) = 160 m no of poles = 160 / 5 = 32 m answer : e"
Answer: e
Python program:
a = 30 + 50 
b = a * 2
c = b / 5
Problem: a certain list consists of 21 different numbers . if n is in the list and n is 4 times the average ( arithmetic mean ) of the other 20 numbers in the list , then n is what fraction of the sum of the 21 numbers in the list ?
Options: a ) 1 / 20 , b ) 1 / 6 , c ) 1 / 5 , d ) 4 / 21 , e ) 5 / 21
Rationale: "series : a 1 , a 2 . . . . a 20 , n sum of a 1 + a 2 + . . . + a 20 = 20 * x ( x = average ) so , n = 4 * x hence , a 1 + a 2 + . . + a 20 + n = 24 x so , the fraction asked = 4 x / 24 x = 1 / 6 ; answer : b ."
Answer: b
Python program:
a = 1 * 1
b = 20 / 4
c = b + 21 
d = c / 4
e = d * 2
f = e - 4
g = f - 3
h = a / g
Problem: a batsman in his 12 th innings makes a score of 80 and thereby increases his average by 2 runs . what is his average after the 12 th innings if he had never been ‘ not out ’ ?
Options: a ) 42 , b ) 43 , c ) 44 , d ) 45 , e ) 58
Rationale: "let ‘ x ’ be the average score after 12 th innings ⇒ 12 x = 11 × ( x – 2 ) + 80 ∴ x = 58 answer e"
Answer: e
Python program:
a = 12 * 2
b = 80 - a
c = b + 2
Problem: what is the compound interest on rs . 4500 at 5 % p . a . compounded half - yearly for 3 1 / 2 years .
Options: a ) rs . 859.09 , b ) rs . 349.09 , c ) rs . 449.09 , d ) rs . 749.09 , e ) rs . 849.09
Rationale: "compound interest : a = p ( 1 + r / n ) nt a = 5 , 349.09 c . i . > > 5 , 349.09 - 4500 > > rs . 849.09 answer : e"
Answer: e
Python program:
a = 5 / 2
b = a + 100 
c = b / 100
d = 3 * 2
e = c ** d
f = e - 1
g = 4500 * f
Problem: danny can divide his herd into 5 equal parts and also to 6 equal parts , but not to 9 equal parts . what could be the number of cows danny has in his herd ?
Options: a ) 120 , b ) 155 , c ) 180 , d ) 336 , e ) 456
Rationale: danny can divide his herd into 5 equal parts and also to 6 equal parts = > no of cows = multiple of 5 and 6 = multiple of 30 . only option a and c qualify . now 2 nd condition : but not to 9 equal parts : so it should not be a multiple of 9 . answer : a
Answer: a
Python program:
a = 5 * 4
b = 100 + a
Problem: a and b can do a work in 8 days , b and c can do it in 12 days ; a , b and c together can finish it in 6 days . a and c together will do it in ?
Options: a ) 8 days , b ) 10 days , c ) 12 days , d ) 7 days , e ) 5 days
Rationale: "a + b + c 1 day work = 1 / 6 a + b 1 day work = 1 / 8 b + c 1 day work = 1 / 12 a + c 1 day work = 2 * 1 / 6 - 1 / 8 + 1 / 12 = 1 / 3 - 5 / 24 = 3 / 24 = 1 / 8 a and c together will do the work in 8 days . answer is a"
Answer: a
Python program:
a = 1 / 12
b = 1 / 8
c = 1 / 6
d = b - c
e = a - d
f = 1 / 8
g = 1 / 6
h = f - g
i = e + h 
j = 1/(i)
Problem: how much is 90 % of 40 is greater than 4 / 5 of 25 ?
Options: a ) 29 , b ) 776 , c ) 66 , d ) 16 , e ) 99
Rationale: "( 90 / 100 ) * 40 – ( 4 / 5 ) * 25 36 - 20 = 16 answer : d"
Answer: d
Python program:
a = 90 / 100
b = 40 * a
c = 4 / 5
d = c * 25
e = b - d
Problem: a grocer is storing soap boxes in cartons that measure 25 inches by 42 inches by 60 inches . if the measurement of each soap box is 7 inches by 6 inches by 6 inches , then what is the maximum number of soap boxes that can be placed in each carton ?
Options: a ) 210 , b ) 252 , c ) 250 , d ) 300 , e ) 420
Rationale: "however the process of dividing the volume of box by the volume of a soap seems flawed but it does work in this case due to the numbers dimensions of the box = 25 * 42 * 60 dimensions of the soap = 6 * 6 * 7 placing the 7 inch side along 42 inch side we get 6 soaps in a line and in a similar way 5 along 25 and 6 along 60 we get = 5 x 5 x 10 = 250 so the question is why this particular arrangement , in order to maximize number of soaps we need to minimize the space wasted and this is the only config where we dont waste any space so we can expect the maximum number the answer is ( c )"
Answer: c
Python program:
a = 25 * 42
b = a * 60
c = 7 * 6
d = c * 6
e = b / d
Problem: suresh and ramesh started a business investing rs . 24,000 and rs . 40,000 respectively . out of total profit of rs . 19,000 , what is ramesh ' s share ?
Options: a ) s . 7375 , b ) s . 8379 , c ) s . 9875 , d ) s . 10875 , e ) s . 11875
Rationale: explanation : ratio of suresh and ramesh ' s share = 24,000 : 40,000 = 3 : 5 ramesh ' s share = rs . ( 19000 x 5 / 8 ) = rs . 11875 answer : e
Answer: e
Python program:
a = 2 + 3 
b = 2 * a
c = 4 * b
d = 2 + 3 
e = 2 * d
f = 100 * e
g = c * f
h = 3 * 4
i = h * 2
j = 2 + 3 
k = i - j
l = 2 + 3 
m = 2 * l
n = 100 * m
o = k * n
p = 3 * 4
q = p * 2
r = 2 + 3 
s = 2 * r
t = 100 * s
u = q * t
v = 2 + 3 
w = 2 * v
x = 4 * w
y = 2 + 3 
z = 2 * y
A = 100 * z
B = x * A
C = u + B 
D = o / C
E = g * D
Problem: if difference between compound interest and simple interest on a sum at 5 % p . a . for 2 years is rs . 60 , then what is the sum ?
Options: a ) rs . 8000 , b ) rs . 4000 , c ) rs . 5000 , d ) rs . 6000 , e ) rs . 24000
Rationale: "c . i - s . i = 60 si = ( x * 2 * 5 ) / 100 = x / 10 ci = { x * ( 1 + 5 / 100 ) ^ 2 - x } = 41 x / 400 ci - si = 41 x / 400 - x / 10 = 60 x = 24000 answer : e"
Answer: e
Python program:
a = 5 / 100
b = 5 / 100
c = a * b
d = 60 / c
Problem: salesperson a ' s compensation for any week is $ 360 plus 6 percent of the portion of a ' s total sales above $ 1000 for that week . salesperson b ' s compensation for any week is 10 percent of a ' s total sales for that week . for what amount of total weekly sales would both salepeople earn the same compensation ?
Options: a ) $ 21,000 , b ) $ 18,000 , c ) $ 15,00 , d ) $ 4,500 , e ) $ 15,000
Rationale: sometime , setting up an equation is an easy way to go with : 360 + 0.06 ( x - 1000 ) = 0.1 x x = 15,000 ans : e
Answer: e
Python program:
a = 6 / 100
b = a * 1000
c = 360 - b
d = 10 / 100
e = 6 / 100
f = d - e
g = c / f
h = g * 2
i = h / 1000
Problem: if 1 / 2 of the air in a tank is removed with each stroke of a vacuum pump , what fraction of the original amount of air has been removed after 3 strokes ?
Options: a ) 15 / 16 , b ) 7 / 8 , c ) 1 / 4 , d ) 1 / 8 , e ) 1 / 16
Rationale: "left after 1 st stroke = 1 / 2 left after 2 nd stroke = 1 / 2 * 1 / 2 = 1 / 4 left after 3 rd stroke = 1 / 2 * 1 / 4 = 1 / 8 so removed = 1 - 1 / 8 = 7 / 8 = b"
Answer: b
Python program:
a = 1 / 2
b = 1 / 2
c = b / 2
d = a + c 
e = 1 / 2
f = e / 2
g = f / 2
h = d + g 
i = 1 / 2
j = i / 2
k = j / 2
l = k / 2
m = h + l 
n = 1 / 2
o = n / 2
p = o / 2
q = p / 2
r = q / 2
s = m + r
Problem: if it is assumed that 60 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 60 % = 300 / 0.6 = 500 option d"
Answer: d
Python program:
a = 60 / 100
b = 300 / a
Problem: a person crosses a 1000 m long street in 10 minutes . what is his speed in km per hour ?
Options: a ) 7.1 , b ) 8.2 , c ) 4.6 , d ) 6.0 , e ) 12.8
Rationale: "distance = 1000 meter time = 10 minutes = 10 x 60 seconds = 600 seconds speed = distance / time = 1000 / 600 = 1.67 m / s = 1.67 ã — 18 / 5 km / hr = 6.0 km / hr answer : d"
Answer: d
Python program:
a = 1000 / 1000
b = 10 * const_60
c = b / 3600
d = a / c
Problem: how long does a train 110 m long travelling at 60 kmph takes to cross a bridge of 170 m in length ?
Options: a ) 15.8 sec , b ) 14.9 sec , c ) 12.4 sec , d ) 16.8 sec , e ) 11.8 sec
Rationale: "d 16.8 sec d = 110 + 170 = 280 m s = 60 * 5 / 18 = 50 / 3 t = 280 * 3 / 50 = 16.8 sec"
Answer: d
Python program:
a = 110 + 170 
b = 60 * const_0_2778
c = a / b
Problem: two trains from opposite directions are to cross each other . the length of two trains are 100 meter and 200 meter respectively . the speed of first train is 100 km / hour and second train 200 km / hour . in how much time will they cross each other ?
Options: a ) 2 second , b ) 3.6 second , c ) 5 second , d ) 5.5 second , e ) 6 second
Rationale: the crossing moment starts when the head of first compartment of two trains meet or touch . the process of crossing each other continues till 100 + 200 meter = 300 meter is covered . the speed will be 100 km / hour + 200 km / hour = 300 km / hour . 300 x 1000 meter covered in 3600 seconds . so , 300 meter covered in 3.6 seconds . answer : b .
Answer: b
Python program:
a = 100 + 200 
b = 100 + 200 
c = b * 1000
d = c / 3600
e = a / d
Problem: let n be the greatest number that will divide 1305 , 4665 and 6905 , leaving the same remainder in each case . then sum of the digits in n is :
Options: a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 10
Rationale: "explanation : n = h . c . f . of ( 4665 - 1305 ) , ( 6905 - 4665 ) and ( 6905 - 1305 ) = h . c . f . of 3360 , 2240 and 5600 = 1120 . sum of digits in n = ( 1 + 1 + 2 + 0 ) = 4 answer is a"
Answer: a
Python program:
a = 1 + 1 
b = a + 2
Problem: in a garden , there are 10 rows and 12 columns of mango trees . the distance between the two trees is 2 metres and a distance of five metre is left from all sides of the boundary of the garden . what is the length of the garden ?
Options: a ) 32 , b ) 24 , c ) 26 , d ) 28 , e ) 30
Rationale: between the 12 mango trees , there are 11 gaps and each gap has 2 meter length also , 5 meter is left from all sides of the boundary of the garden . hence , length of the garden = ( 11 ã — 2 ) + 5 + 5 = 32 meter answer is a .
Answer: a
Python program:
a = 12 - 1
b = a * 2
c = 10 / 2
d = b + c 
e = 10 / 2
f = d + e
Problem: 15.06 * 0.000001 = ?
Options: a ) 15060000 , b ) 0.001506 , c ) 0.01506 , d ) 1.506 e - 05 , e ) none of these
Rationale: "explanation : clearly after decimal 8 digits should be there . option d"
Answer: d
Python program:
a = 15 / 6
b = a * 100
Problem: darcy lives 1.5 miles from work . she can walk to work at a constant rate of 3 miles per hour , or she can ride the train to work at a constant rate of 20 miles per hour . if she rides the train , there is an additional x minutes spent walking to the nearest train station , waiting for the train , and walking from the final train station to her work . if it takes darcy a total of 2 more minutes to commute to work by walking than it takes her to commute to work by riding the train , what is the value of x ?
Options: a ) 10.5 , b ) 15 , c ) 25.5 , d ) 30 , e ) 23.5
Rationale: "the time it takes darcy to walk to work is ( 1.5 / 3 ) * 60 = 30 minutes the time it takes darcy to take the train is ( 1.5 / 20 ) * 60 + x = 4.5 + x minutes it takes 15 minutes longer to walk , so 30 = 4.5 + x + 2 x = 23.5 minutes answer : e"
Answer: e
Python program:
a = const_60 / 2
b = a - 2
c = 20 / 1
d = const_60 / c
e = b - d
Problem: a driver would have reduced the time it took to drive from home to the store by 1 / 4 if the average speed had been increased by 12 miles per hour . what was the actual average speed , in miles per hour , when the driver drove from home to the store ?
Options: a ) 24 , b ) 28 , c ) 32 , d ) 36 , e ) 40
Rationale: "since the distance remains the same ( we ' re just changing the rate and time ) , any increase in rate or time is met with a decrease in the other term . decreasing the time by 1 / 4 would give us : d = ( r ) ( t ) = ( 3 t / 4 ) ( x * r ) x = 4 / 3 since ( 3 t / 4 ) ( 4 r / 3 ) = ( r ) ( t ) = d 4 r / 3 = r + 12 r / 3 = 12 r = 36 the answer is d ."
Answer: d
Python program:
a = 1 / 4
b = 1 - a
c = b * 12
d = 1 / 4
e = 1 - d
f = 1 - e
g = c / f
Problem: a certain company expects quarterly earnings of $ 0.80 per share of stock , half of which will be distributed as dividends to shareholders while the rest will be used for research and development . if earnings are greater than expected , shareholders will receive an additional $ 0.04 per share for each additional $ 0.10 of per share earnings . if quarterly earnings are $ 1.10 per share , what will be the dividend paid to a person who owns 300 shares of the company ' s stock ?
Options: a ) $ 92 , b ) $ 96 , c ) $ 156 , d ) $ 120 , e ) $ 240
Rationale: "eps actual > eps expected . each gets and additional . 12 per share . thus . 52 * 300 - - > $ 156 answer is c"
Answer: c
Python program:
a = 0 / 80
b = 1 - 10
c = b * 10
d = c * 0
e = a + d 
f = e * 300
Problem: can you find the smallest non fractional number such that if the number gets divided by 6 , we get the remainder of 1 ; if the number gets divided by 7 , we get the remainder of 2 if the number gets divided by 8 , we get the remainder of 3 ; if the number gets divided by 9 , we get the remainder of 4 .
Options: a ) 1006 , b ) 1230 , c ) 1010 , d ) 1200 , e ) 1300
Rationale: a . 1006 as we know lcm of the numbers 6 7 8 & 9 is 1008 so if i divide 1008 by any of the four number , it gives remainder as 0 . now to get reminder as desired , is should be 2 short of 1006 . ( 3 - 1,4 - 2,5 - 3,6 - 4 ) ans : option a
Answer: a
Python program:
a = 6 - 1
b = a ** 4
Problem: which is less than 3 ?
Options: a ) 3 , b ) 0.3 , c ) 33 , d ) 3 / 1 , e ) 13
Rationale: "0.3 less than 3 . answer : b"
Answer: b
Python program:
a = 3 / 4
b = a / 3
c = b / 4
d = c / 3
e = d / 2
f = e / 2
Problem: the difference of two numbers is 1360 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder . what is the smaller number ?
Options: a ) 240 , b ) 270 , c ) 295 , d ) 360 , e ) 269
Rationale: "let the smaller number be x . then larger number = ( x + 1360 ) . x + 1360 = 6 x + 15 5 x = 1345 x = 269 smaller number = 270 . answer e"
Answer: e
Python program:
a = 1360 + 15 
b = 6 - 1
c = a / b
Problem: the average of 10 numbers is 23 . if each number is increased by 2 , what will the new average be ?
Options: a ) 36 , b ) 25 , c ) 72 , d ) 29 , e ) 22
Rationale: "sum of the 10 numbers = 230 if each number is increased by 2 , the total increase = 2 * 10 = 20 the new sum = 230 + 20 = 250 the new average = 250 / 10 = 25 . answer : b"
Answer: b
Python program:
a = 23 * 2
Problem: on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.50 per glass on the first day , what was the price per glass on the second day ?
Options: a ) $ 0.15 , b ) $ 0.20 , c ) $ 0.33 , d ) $ 0.40 , e ) $ 0.45
Rationale: "on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.5 = 3 * x - - > x = $ 0.33 . answer : c ."
Answer: c
Python program:
a = 1 + 1 
b = a * 0
c = 1 + 2 
d = b / c
Problem: a polling company surveyed a certain country , and it found that 35 % of that country ’ s registered voters had an unfavorable impression of both of that state ’ s major political parties and that 20 % had a favorable impression only of party t . if one registered voter has a favorable impression of both parties for every two registered voters who have a favorable impression only of party b , then what percentage of the country ’ s registered voters have a favorable impression of both parties ( assuming that respondents to the poll were given a choice between favorable and unfavorable impressions only ) ?
Options: a ) 15 , b ) 20 , c ) 30 , d ) 35 , e ) 45
Rationale: "s = 100 not ( t and b ) = 35 only t = 20 ( t and b ) / b = 1 / 2 let ( t and b ) = x only b = 2 x so now , 20 + 35 + x + 2 x = 100 x = 15 a ans"
Answer: a
Python program:
a = 35 + 20 
b = 100 - a
c = b / 3
Problem: rs . 1500 is divided into two parts such that if one part is invested at 6 % and the other at 5 % the whole annual interest from both the sum is rs . 85 . how much was lent at 5 % ?
Options: a ) 399 , b ) 700 , c ) 288 , d ) 500 , e ) 211
Rationale: "( x * 5 * 1 ) / 100 + [ ( 1500 - x ) * 6 * 1 ] / 100 = 85 5 x / 100 + 90 – 6 x / 100 = 85 x / 100 = 5 = > x = 500 answer : d"
Answer: d
Python program:
a = 5 + 6 
b = a * 100
Problem: excluding stoppages , the speed of a train is 30 kmph and including stoppages it is 21 kmph . of how many minutes does the train stop per hour ?
Options: a ) 16 , b ) 17 , c ) 12 , d ) 15 , e ) 18
Rationale: "t = 9 / 30 * 60 = 18 answer : e"
Answer: e
Python program:
a = 21 / 30
b = const_60 * a
c = const_60 - b