euclaise/mathqa_programs huggingface dataset:
Problem: a bottle contains a certain solution . in the bottled solution , the ratio of water to soap is 3 : 4 , and the ratio of soap to salt is four times this ratio . the solution is poured into an open container , and after some time , the ratio of water to soap in the open container is halved by water evaporation . at that time , what is the ratio of water to salt in the solution ?
Options: a ) 3 : 8 , b ) 3 : 9 , c ) 3 : 4 , d ) 3 : 12 , e ) 4 : 12
Rationale: "water : soap = 3 : 4 soap : salt = 12 : 16 = > for 12 soap , salt = 16 = > for 4 soap , salt = ( 16 / 12 ) * 4 = 16 / 12 = 64 / 12 = 18 / 3 = 6 / 1 so , water : soap : salt = 3 : 4 : 6 = 3 : 4 : 6 after open container , water : soap : salt = 1.5 : 4 : 6 so , water : salt = 1.5 : 6 = 3 : 12 answer : d"
Answer: d
Python program:
a = 4 * 3
b = a * 3
c = 4 * 4
d = c * 4
e = b / d
Problem: in a group of people , if 30 people were made to stand in each column , 16 columns could be formed . if 12 people were made to stand in a column , how many columns could be formed ?
Options: a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 60
Rationale: "16 * 30 = 12 * n n = 40 the answer is c ."
Answer: c
Python program:
a = 12 / 16
b = 30 / a
Problem: if x is a positive integer with fewer than 3 digits , what is the probability q that x * ( x + 1 ) is a multiple of either 4 or 5 ?
Options: a ) 4 / 99 , b ) 2 / 25 , c ) 8 / 99 , d ) 49 / 100 , e ) 86 / 99
Rationale: interesting question ! also one that we should be able to answer very quickly be keeping an eye on our best friends , the answer choices . we know that x belongs to the set { 1 , 2 , 3 , . . . , 99 } . we want to know the probability q that x ( x + 1 ) is a multiple of either 4 or 5 . when will this happen ? if either x or ( x + 1 ) is a multiple of 4 or 5 . since 4 * 5 is 20 , let ' s look at the first 20 numbers to get a rough idea of how often this happens . out of the numbers from 1 to 20 : 4 , 5 , 6 , 8 , 9 , 10 , 11 , 12 , 13 , 15 , 16 , 17 , 20 so , 14 out of the first 20 numbers match our criteria . since : probability = ( # of desired outcomes ) / ( total # of possibilities ) , we guesstimate the answer to be 14 / 20 . since ( e ) is the only answer greater than 1 / 2 , we go with ( e ) .
Answer: e
Python program:
a = 100 / 4
b = a * 2
c = 100 / 5
d = c * 2
e = b + d 
f = e - 4
g = 100 - 1
h = f / g
Problem: by weight , liquid x makes up 0.8 percent of solution a and 1.8 percent of solution b . if 200 grams of solution a are mixed with 700 grams of solution b , then liquid x accounts for what percent of the weight of the resulting solution ?
Options: a ) 1.42 % , b ) 1.9 % , c ) 10 % , d ) 15 % , e ) 19 %
Rationale: "i think there is a typo in question . it should have been ` ` by weight liquid ' x ' makes up . . . . . ` ` weight of liquid x = 0.8 % of weight of a + 1.8 % of weight of b when 200 gms of a and 700 gms of b is mixed : weight of liquid x = ( 0.8 * 200 ) / 100 + ( 1.8 * 700 ) / 100 = 14.2 gms % of liquid x in resultant mixture = ( 14.2 / 1000 ) * 100 = 1.42 % a"
Answer: a
Python program:
a = 200 * 0
b = 700 * 1
c = a + b 
d = c / 1000
Problem: the s . i . on a certain sum of money for 3 years at 5 % per annum is half the c . i . on rs . 4000 for 2 years at 10 % per annum . the sum placed on s . i . is ?
Options: a ) 2197 , b ) 2800 , c ) 1750 , d ) 2267 , e ) 1262
Rationale: "explanation : c . i . = [ 4000 * ( 1 + 10 / 100 ) 2 - 4000 ] = ( 4000 * 11 / 10 * 11 / 10 - 4000 ) = rs . 840 . sum = ( 420 * 100 ) / ( 3 * 5 ) = rs . 2800 answer : b"
Answer: b
Python program:
a = 10 / 100
b = 1 + a 
c = b ** 2
d = 4000 * c
e = d - 4000
f = e / 2
g = 5 / 100
h = 3 * g
i = f / h
Problem: two train each 500 m long , are running in opposite directions on parallel tracks . if their speeds are 45 km / hr and 30 km / hr respectively , the time taken by the slower train to pass the driver of the faster one is
Options: a ) 50 sec , b ) 58 sec , c ) 24 sec , d ) 22 sec , e ) 21 sec
Rationale: "explanation : relative speed = 45 + 30 = 75 km / hr = 750 / 36 m / s = 125 / 6 m / s we are calculating the time taken by the slower train to pass the driver of the faster one . hence the distance = length of the smaller train = 500 m time = distance / speed = 500 / ( 125 / 6 ) = 24 sec answer : option c"
Answer: c
Python program:
a = 45 + 30 
b = a * const_0_2778
c = 500 / b
Problem: if a fraction is multiplied by itself and then divided by the reciprocal of the same fraction , the result is 18 26 / 27 . find the fraction .
Options: a ) 8 / 27 , b ) 1 1 / 3 , c ) 2 2 / 3 , d ) 3 / 3 , e ) none of these
Rationale: answer if the required fraction be p according to the question ( p x p ) / ( 1 / p ) = 1826 / 27 ⇒ p 3 = 512 / 27 ∴ p = 8 / 3 = 2 2 / 3 correct option : c
Answer: c
Python program:
a = 26 / 27
b = a + 18 
c = 1 / 3
d = b ** c
e = d * 3
f = 26 / 27
g = f + 18 
h = 1 / 3
i = g ** h
j = e - i
k = j + 2
Problem: two trains of length 100 meters and 200 meters are 630 meters apart . they are moving towards each other on parallel tracks , at speeds of 90 km / h and 72 km / h . after how many seconds will the trains meet ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: the speeds are 90000 / 3600 = 25 m / s and 72000 / 3600 = 20 m / s the relative speed is 45 m / s . time = 630 / 45 = 14 seconds the answer is b .
Answer: b
Python program:
a = 90 + 72 
b = a * const_0_2778
c = 630 / b
Problem: a can do a job in 15 days and b can do it in 30 days . a and b working together will finish twice the amount of work in days ?
Options: a ) 20 , b ) 22 1 / 2 , c ) 22 1 / 0 , d ) 22 1 / 9 , e ) 22 1 / 1
Rationale: "1 / 15 + 1 / 30 = 3 / 30 = 1 / 10 10 = 10 * 2 = 20 days answer : a"
Answer: a
Python program:
a = 1 / 15
b = 1 / 30
c = a + b
Problem: find the value of y from ( 12 ) ^ 3 x 6 ^ 4 ÷ 432 = y ?
Options: a ) 2450 , b ) 2560 , c ) 2650 , d ) 3500 , e ) 5184
Rationale: "given exp . = ( 12 ) 3 x 64 = ( 12 ) 3 x 64 = ( 12 ) 2 x 62 = ( 72 ) 2 = 5184 432 12 x 62 e"
Answer: e
Python program:
a = 12 ** 3
b = 6 ** 4
c = a * b
d = c / 432
Problem: in a graduating class , 40 percent of the students are male . in this class , 60 percent of the male students and 40 percent of the female students are 25 years old or older . if one student in the class is randomly selected , approximately what is the probability that he or she will be less than 25 years old ?
Options: a ) 0.4 , b ) 0.44 , c ) 0.48 , d ) 0.52 , e ) 0.56
Rationale: "let x be the total number of students . the number students who are younger than 25 is 0.4 * 0.4 x + 0.6 * 0.6 x = 0.52 x the answer is d ."
Answer: d
Python program:
a = 40 / 100
b = 60 / 100
c = a * b
d = 40 / 100
e = 40 / 100
f = 1 - e
g = d * f
h = c + g 
i = 1 - h
Problem: at a tanning salon , customers are charged $ 10 for their first visit in a calendar month and $ 8 for each visit after that in the same calendar month . in the last calendar month , 100 customers visited the salon , of which 30 made a second visit , and 10 made a third visit . all other customers made only one visit . if those visits were the only source of revenue for the salon , what was the revenue for the last calendar month at the salon ?
Options: a ) $ 1220 , b ) $ 1240 , c ) $ 1300 , d ) $ 1340 , e ) $ 1880
Rationale: i get b . this question seems too straightforward for 600 + . am i missing something ? 100 first - time visits - - > 100 ( 10 ) = $ 1000 30 + 10 = 40 subsequent visits - - > 40 ( 8 ) = $ 320 total revenue : 1000 + 320 = $ 1320 the answer is b .
Answer: b
Python program:
a = 10 + 8 
b = a * 30
c = 100 - 30
d = c * 10
e = b + d
Problem: audrey 4 hours to complete a certain job . ferris can do the same job in 3 hours . audrey and ferris decided to collaborate on the job , working at their respective rates . while audrey worked continuously , ferris took 1 breaks of equal length . if the two completed the job together in 2 hours , how many minutes long was each of ferris ’ breaks ?
Options: a ) 5 , b ) 30 , c ) 15 , d ) 20 , e ) 25
Rationale: "audery and ferris collective work rate : 1 / 4 + 1 / 3 = 7 / 12 collective work time = 12 / 7 = 1.7 hrs job was actually done in = 2 ( includes breaks ) breaks = actual time taken - collective work time = 2 - 1.7 = . 3 hrs = 1 / 2 so ferrais took 1 breaks = . 3 / 1 = . 3 hrs = 30 m so answer is b ) 30 mins"
Answer: b
Python program:
a = 1 * 10
b = 2 * a
c = 3 / 2
d = 1 * 10
e = c * d
f = b - e
g = f / 1
Problem: sahil purchased a machine at rs 11000 , then got it repaired at rs 5000 , then gave its transportation charges rs 1000 . then he sold it with 50 % of profit . at what price he actually sold it .
Options: a ) rs . 22500 , b ) rs . 25500 , c ) rs . 26000 , d ) rs . 28000 , e ) none of these
Rationale: "explanation : question seems a bit tricky , but it is very simple . just calculate all cost price , then get 150 % of cp . c . p . = 11000 + 5000 + 1000 = 17000 150 % of 17000 = 150 / 100 * 17000 = 25500 option b"
Answer: b
Python program:
a = 11000 + 5000 
b = a + 1000 
c = 11000 + 5000 
d = c + 1000 
e = d / 100
f = e * 50
g = b + f
Problem: a boat can travel with a speed of 16 km / hr in still water . if the speed of the stream is 4 km / hr , find the time taken by the boat to go 60 km downstream .
Options: a ) 2 hours . , b ) 3 hours . , c ) 4 hours . , d ) 5 hours . , e ) 6 hours .
Rationale: "speed downstream = ( 16 + 4 ) km / hr = 20 km / hr . time taken to travel 60 km downstream = 60 / 20 = 3 hours . answer : b"
Answer: b
Python program:
a = 16 + 4 
b = 60 / a
Problem: walking 5 / 4 of his usual rate , a boy reaches his school 4 min early . find his usual time to reach the school ?
Options: a ) 22 , b ) 99 , c ) 27 , d ) 28 , e ) 20
Rationale: "speed ratio = 1 : 5 / 4 = 4 : 5 time ratio = 5 : 4 1 - - - - - - - - 5 4 - - - - - - - - - ? 20 m . answer : e"
Answer: e
Python program:
a = 4 * 5
Problem: an engineer designed a ball so that when it was dropped , it rose with each bounce exactly one - half as high as it had fallen . the engineer dropped the ball from a 16 - meter platform and caught it after it had traveled 46.5 meters . how many times did the ball bounce ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "going down = 16 m going up = 8 - - > total = 24 going down = 8 - - > total = 32 going up = 4 - - > total = 36 going down = 4 - - > total = 40 going up = 2 - - > total = 42 going down = 2 - - > total = 44 going up = 1 - - > total = 45 going down = 1 - - > total = 46 going up = 0.5 - - > total = 46.5 ( caught ) no of going downs = 5 . . answer : a"
Answer: a
Python program:
a = 16 / 2
b = a / 2
Problem: 6000 - 5000 ÷ 20.00 = ?
Options: a ) 900 , b ) 500 , c ) 5750 , d ) 5000 , e ) none
Rationale: "answer given expression = 6000 - 5000 ÷ 20.00 = 6000 - 250 = 5750 correct option : c"
Answer: c
Python program:
a = 6000 / 100
b = a * 5000
c = 1 / 3
d = 6000 / 100
e = d * 5000
f = c * e
g = b - f
Problem: mahesh can do a piece of work in 50 days . he works at it for 20 days and then rajesh finished it in 30 days . how long will y take to complete the work ?
Options: a ) 45 , b ) 25 , c ) 37 , d ) 41 , e ) 50
Rationale: "work done by mahesh in 50 days = 20 * 1 / 50 = 2 / 5 remaining work = 1 - 2 / 5 = 3 / 5 3 / 5 work is done by rajesh in 30 days whole work will be done by rajesh is 30 * 5 / 3 = 50 days answer is e"
Answer: e
Python program:
a = 1 / 50
b = 20 * a
c = 1 - b
d = c / 30
e = 1 / d
Problem: the area of a square is 4096 sq cm . find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square .
Options: a ) 5 : 78
b ) 5 : 11
c ) 5 : 12
d ) 5 : 19
e ) 5 : 16
Rationale: let the length and the breadth of the rectangle be l cm and b cm respectively . let the side of the square be a cm . a 2 = 4096 = 212 a = ( 212 ) 1 / 2 = 26 = 64 l = 2 a and b = a - 24 b : l = a - 24 : 2 a = 40 : 128 = 5 : 16 answer : e
Answer: e
Python program:
a = math.sqrt(4096)
b = a - 24
c = math.sqrt(4096)
d = c * 2
e = b / d
Problem: if x < y < z and y - x > 1 , where x is an even integer and y and z are odd integers , what is the least possible value of z - x ?
Options: a ) 6 , b ) 3 , c ) 8 , d ) 9 , e ) 10
Rationale: "we have : 1 ) x < y < z 2 ) y - x > 1 3 ) x = 2 k ( x is an even number ) 4 ) y = 2 n + 1 ( y is an odd number ) 5 ) z = 2 p + 1 ( z is an odd number ) 6 ) z - x = ? least value z - x = 2 p + 1 - 2 k = 2 p - 2 k + 1 = 2 ( p - k ) + 1 - that means that z - x must be an odd number . we are asked to find the least value , so we have to pick the least numbers since y is odd and x is even , y - x must be odd . since y - x > 1 , the least value for y - x must be 3 , the least value for x must be 2 , and , thus , the least possible value for y must be 3 ( y - 2 = 1 , y = 3 ) 2 < 3 < z , since z is odd , the least possible value for z is 5 z - x = 5 - 2 = 3 answer b"
Answer: b
Python program:
a = 1 + 2 
b = a + 2
Problem: a 12 % stock yielding 8 % is quoted at ?
Options: a ) 165 , b ) 170 , c ) 175 , d ) 150 , e ) 185
Rationale: "assume that face value = rs . 100 as it is not given to earn rs . 8 , money invested = rs . 100 to earn rs . 12 , money invested = 100 × 12 / 8 = rs . 150 ie , market value of the stock = rs . 150 answer is d ."
Answer: d
Python program:
a = 100 / 8
b = a * 12
Problem: the toll for crossing a certain bridge is $ 0.75 each crossing . drivers who frequently use the bridge may instead purchase a sticker each month for $ 13.00 and then pay only $ 0.10 each crossing during that month . if a particular driver will cross the bridge twice on each of x days next month and will not cross the bridge on any other day , what is the least value of x for which this driver can save money by using the sticker ?
Options: a ) 12 , b ) 15 , c ) 16 , d ) 28 , e ) 29
Rationale: "option # 1 : $ 0.75 / crossing . . . . cross twice a day = $ 1.5 / day option # 2 : $ 0.30 / crossing . . . . cross twice a day = $ 0.6 / day + $ 13 one time charge . if we go down the list of possible answers , you can quickly see that 14 days will not be worth purchasing the sticker . 1.5 x 14 ( 21 ) is cheaper than 0.6 x 14 + 13 ( 21.4 ) . . . it ' s pretty close so let ' s see if one more day will make it worth it . . . if we raise the number of days to 15 , the sticker option looks like a better deal . . . 1.5 x 15 ( 22.5 ) vs 0.6 x 15 + 13 ( 22 ) . answer : a"
Answer: a
Python program:
a = 0 - 75
b = a * 2
c = 13 / 0
d = c * 2
e = d / 10
f = e * 2
g = 0 - 75
h = g * 2
i = 13 / 0
j = i * 2
k = f + j
Problem: 9 people are planning to share equally the cost of a rental van . if one person withdraws from the arrangement and the others share equally the cost of the rental van , then the share of each of the remaining people will increase by . . . ?
Options: a ) 1 / 9 , b ) 1 / 8 , c ) 1 / 7 , d ) 7 / 8 , e ) 8 / 7
Rationale: let p = total cost of the rental van . the original share per person is p / 9 . the new share per person is p / 8 . p / 8 = p / 9 * 9 / 8 = ( 1 + 1 / 8 ) * original share the answer is b .
Answer: b
Python program:
a = 9 - 1
b = 1 / a
c = 1 / 9
d = b - c
e = 1 / 9
f = d / e
Problem: what will be the percentage increase in the area of the cube ' s surface if each of the cube ' s edges grows by 50 % ?
Options: a ) 125 % , b ) 150 % , c ) 100 % , d ) 90 % , e ) 85 %
Rationale: "the question is very easy . my logic is the following : a surface = 6 * a ^ 2 after 50 % increase a surface = 6 * ( ( 1.5 a ) ^ 2 ) = 6 * 2.25 * a ^ 2 the increase in the surface area = ( 6 * 2.25 * a ^ 2 - 6 * a ^ 2 ) / 6 * a ^ 2 = ( 6 * a ^ 2 ( 2.25 - 1 ) ) / ( 6 * a ^ 2 ) = 2.25 - 1 = 1.25 = 125 % answer : a"
Answer: a
Python program:
a = 50 / 100
b = 1 + a 
c = b ** 2
d = c - 1
e = d * 100
Problem: there is a 5 % chance that tigers will not win at all during the whole season . there is a 5 % chance that federer will not play at all in the whole season . what is the greatest possible probability that the tigers will win and federer will play during the season ?
Options: a ) 55 % , b ) 60 % , c ) 70 % , d ) 72 % , e ) 95 %
Rationale: "there is a 5 % chance that tigers will not win at all during the whole season we can infer that there is 95 % chance tigers will win . similarly there is a 5 % chance that federer will not play at all in the whole season we can also infer that there is 95 % chance that federer will play . answer e"
Answer: e
Python program:
a = 2 * 5
b = 2 * 5
c = a * b
d = 5 / c
e = 1 - d
f = 2 * 5
g = 2 * 5
h = f * g
i = 5 / h
j = 1 - i
k = e * j
Problem: at a florist shop on a certain day , all corsages sold for either $ 25 or $ 40 . if 8 of the corsages that sold for $ 30 had instead sold for $ 20 , then the store ' s revenue from corsages that day would have been reduced by 40 percent . what was the store ' s actual revenue from corsages that day ?
Options: a ) $ 200 , b ) $ 400 , c ) $ 600 , d ) $ 800 , e ) $ 300
Rationale: "i am doing it elaborately , hope it will help you . let , no . of corsages @ $ 25 = x , no . of corsages @ $ 40 = y and revenue = r so , 25 x + 40 y = r . . . . . . . . . ( 1 ) now , given the situation , 25 ( x + 8 ) + 40 ( y - 8 ) = r - . 4 r = > 25 x + 200 + 40 y - 320 = . 6 r = > 25 x + 40 y = . 8 r + 120 . . . . . . . . . . . . ( 2 ) so , r = . 6 r + 120 = > r = 300 the answer is e ."
Answer: e
Python program:
a = 25 * 8
b = 40 * 8
c = a - b
d = negate / (
e = 40 / 100
f = d - e
Problem: in an election between two candidates , the first candidate got 60 % of the votes and the second candidate got 480 votes . what was the total number of votes ?
Options: a ) 900 , b ) 1200 , c ) 1500 , d ) 1800 , e ) 2100
Rationale: "let v be the total number of votes . 0.4 v = 480 v = 1200 the answer is b ."
Answer: b
Python program:
a = 480 * 100
b = 100 - 60
c = a / b
Problem: a jogger running at 9 km / hr along side a railway track is 260 m ahead of the engine of a 120 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?
Options: a ) 67 sec , b ) 89 sec , c ) 38 sec , d ) 87 sec , e ) 45 sec
Rationale: "speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 260 + 120 = 380 m . time taken = 380 / 10 = 38 sec . answer : c"
Answer: c
Python program:
a = 260 + 120 
b = 45 - 9
c = 10 / 2
d = 45 - 9
e = d / 2
f = c / e
g = b * f
h = a / g
Problem: pipe a that can fill a tank in an hour and pipe b that can fill the tank in 15 are opened simultaneously when the tank is empty . pipe b is shut 15 minutes before the tank overflows . when will the tank overflow ?
Options: a ) 40 mins , b ) 35 mins , c ) 30 mins , d ) 32 mins , e ) 36 mins
Rationale: the last 15 minutes only pipe a was open . since it needs 1 hour to fill the tank , then in 15 minutes it fills 1 / 4 th of the tank , thus 3 / 4 of the tank is filled with both pipes open . the combined rate of two pipes is 1 + 4 = 5 tanks / hour , therefore to fill 3 / 4 th of the tank they need ( time ) = ( work ) / ( rate ) = ( 3 / 4 ) / 5 = 3 / 20 hours = 15 minutes . total time = 15 + 15 = 30 minutes . answer : c
Answer: c
Python program:
a = 3 / 4
b = a / 3
c = b * const_60
d = c + 15
Problem: john has exactly 31 pens , and each pen is either bule , black , or red . if he has 5 more black pens than red pens , and twice as many blue pens as black pens , how many blue pens does john has ?
Options: a ) 15 , b ) 18 , c ) 20 , d ) 22 , e ) 17
Rationale: x = the number of blue pens y = the number of black pens z = the number of red pens from the first sentence we have equation # 1 : x + y + z = 31 . . . he has 5 more black pens than red pens . . . equation # 2 : y = 5 + z . . . twice as many blue pens as black pens . . . equation # 3 : x = 2 y solve equation # 1 for z : z = y - 5 now , we can replace both x and z with y in equation # 1 2 y + y + ( y - 5 ) = 31 4 y - 5 = 31 4 y = 36 y = 9 there are 9 black pens . this is 5 more than the number of red pens , so z = 4 . hence the answer is . x = 18 , and just for check 18 + 9 + 4 = 31 . answer = 18 , ( b )
Answer: b
Python program:
a = 31 + 5 
b = a / 4
c = b * 2
Problem: what is the average ( arithmetic mean ) of the numbers 5 , 6 , 7 , 7 , 8 , and 9 ?
Options: a ) 4.2 , b ) 6.5 , c ) 6 , d ) 7 , e ) 8
Rationale: "{ 5 , 6 , 7 , 7 , 8 , 9 } = { 7 - 2,7 - 1 , 7 , 7,7 + 1,7 + 2 } - - > the average = 7 . answer : d ."
Answer: d
Python program:
a = 5 + 7 
b = 7 - 6
c = b / 5
d = c + 1 
e = a * d
f = e / 2
g = 7 - 5
h = g / 5
i = h + 1 
j = f / i
Problem: the average monthly salary of 20 employees in an organisation is rs . 1500 . if the manager ' s salary is added , then the average salary increases by rs . 500 . what is the manager ' s monthly salary ?
Options: a ) rs . 16003 , b ) rs . 16029 , c ) rs . 1288 , d ) rs . 16108 , e ) rs . 12000
Rationale: "explanation : manager ' s monthly salary rs . ( 2000 * 21 - 1500 * 20 ) = rs . 12000 . answer : e"
Answer: e
Python program:
a = 1500 + 500 
b = 20 + 1 
c = a * b
d = 1500 * 20
e = c - d
Problem: a rectangular tiled patio is composed of 50 square tiles . the rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles . after the change in layout , the patio will still have 50 tiles , and it will still be rectangular . how many rows are in the tile patio before the change in layout ?
Options: a ) 5 , b ) 6 , c ) 10 , d ) 13 , e ) 28
Rationale: "r * c = 50 and ( 6 + 4 ) ( 7 - 2 ) = 50 - - > r = 6 and c = 7 . answer : b ."
Answer: b
Python program:
a = negate + ( 
b = 4 ** 2
c = 50 * 2
d = 4 * c
e = b + d 
f = math.sqrt(e)
g = a / f
h = 50 / g
Problem: the tax on a commodity is diminished by 20 % but its consumption is increased by 15 % . find the decrease percent in the revenue derived from it ?
Options: a ) 12 % , b ) 14 % , c ) 16 % , d ) 20 % , e ) 8 %
Rationale: "explanation : 100 * 100 = 10000 80 * 115 = 9200 10000 - - - - - - - 800 100 - - - - - - - ? = 8 % e )"
Answer: e
Python program:
a = 100 + 15 
b = 100 - 20
c = a * b
d = c / 100
e = 100 - d
Problem: the number of stamps that kaye and alberto had were in the ration of 5 : 3 respectively . after kaye gave alberto 15 of her stamps , the ration of the number of kaye had to the number of alberto had was 4 : 3 . as a result of the gift , kaye had how many more stamps than alberto ?
Options: a ) 20 , b ) 30 , c ) 70 , d ) 60 , e ) 90
Rationale: "c k 1 = 5 x a 1 = 3 x k 2 = 5 x - 15 a 2 = 3 x + 15 k 2 / a 2 = 7 / 5 ( 5 x - 15 ) / ( 3 x + 15 ) = 4 / 3 3 * ( 5 x - 15 ) = 4 * ( 3 x + 15 ) 15 x - 45 = 12 x + 60 3 x = 105 x = 35 k 2 = 5 * 35 - 15 = 160 a 2 = 3 * 35 + 15 = 90 k 2 - a 2 = 70 answer : c"
Answer: c
Python program:
a = 5 + 3 
b = 4 + 3 
c = math.lcm(a, b)
d = 4 + 3 
e = c / d
f = 4 * e
Problem: find the area of a parallelogram with base 24 cm and height 10 cm ?
Options: a ) 240 cm 2 , b ) 384 cm 2 , c ) 279 cm 2 , d ) 200 cm 2 , e ) 297 cm 2
Rationale: "area of a parallelogram = base * height = 24 * 10 = 240 cm 2 answer : a"
Answer: a
Python program:
a = 24 * 10
Problem: beginning in town a , biker bob rides his bike 8 miles west , 5 miles north , 4 miles east , and then 15 miles north , to town b . how far apart are town a and town b ? ( ignore the curvature of the earth . )
Options: a ) 25 miles , b ) 20.4 miles , c ) 30 miles , d ) 32 miles , e ) 33 miles
Rationale: "using pythagoras we have one side i , e total distance traveled in north direction = 15 + 5 = 20 m other being the base ie distance traveled west - distance traveled eat = 8 - 4 = 4 m now this third side or the distance between town a and town b = 20 ^ 2 + 4 ^ 2 = sq root 416 = 20.4 miles answer : b"
Answer: b
Python program:
a = 5 + 15 
b = a ** 2
c = 4 ** 2
d = b + c 
e = math.sqrt(d)
Problem: a rectangular field is to be fenced on three sides leaving a side of 40 feet uncovered . if the area of the field is 680 sq . ft , how many feet of fencing will be required ?
Options: a ) 44 ft , b ) 88 ft , c ) 74 ft , d ) 11 ft , e ) 66 ft
Rationale: "given that length and area , so we can find the breadth . length x breadth = area 40 x breadth = 680 breadth = 17 feet area to be fenced = 2 b + l = 2 ( 17 ) + 40 = 74 feet answer : c ) 74 ft"
Answer: c
Python program:
a = 680 / 40
b = a * 2
c = b + 40