euclaise/mathqa_programs huggingface dataset:
Problem: in a flight of 600 km , an aircraft was slowed down due to bad weather . its average speed for the trip was reduced by 200 km / hr and the time of flight increased by 30 minutes . the duration of the flight is
Options: a ) 3 hr . , b ) 5 hr . , c ) 2 hr . , d ) 7 hr . , e ) 1 hr .
Rationale: "e 1 hr . let the duration of the flight be x hours . then , 600 / x - 600 / 0.5 x = 200 - - > 600 / x - 1200 / ( 2 x + 1 ) = 200 - - > x ( 2 x + 1 ) = 3 - - > 2 x ^ 2 + x - 3 = 0 - - > ( 2 x + 3 ) ( x - 1 ) = 0 - - > x = 1 hr ."
Answer: e
Python program:
a = 200 * 30
b = a / 10
c = 600 / b
Problem: money invested at x % , compounded annually , triples in value in approximately every 112 / x years . if $ 2200 is invested at a rate of 8 % , compounded annually , what will be its approximate worth in 28 years ?
Options: a ) $ 3,750 , b ) $ 19,800 , c ) $ 8,100 , d ) $ 15,000 , e ) $ 22,500
Rationale: "x = 8 % 112 / x years = 112 / 8 = 14 years now , money triples every 14 years therefore , in 14 yrs , if $ 2200 triples to $ 6600 , in 28 years , it will again triple to $ 6600 * 3 = $ 19,800 answer b"
Answer: b
Python program:
a = 112 / 8
b = 28 / a
c = 3 ** b
d = 2200 * c
Problem: a rocket soars for 12 seconds at 150 meters per second . it then plummets 600 meters in 3 seconds . what is the average speed of the rocket in meters per second ?
Options: a ) 140 , b ) 150 , c ) 155 , d ) 160 , e ) 175
Rationale: when soaring , the rocket travels a total distance of 1800 m ( 150 m / s for 12 s ) while plummeting the rockets travel distance of 600 m in 3 s the total distance traveled is 2400 m ( 1800 + 600 ) the time taken to travel this distance is 15 s ( 12 + 3 ) average speed = 2400 / 15 = 160 ans : ( option d )
Answer: d
Python program:
a = 12 * 150
b = a + 600 
c = 12 + 3 
d = b / c
Problem: for any integer n greater than 1 , # n denotes the product of all the integers from 1 to n , inclusive . how many prime numbers w are there between # 6 + 2 and # 6 + 6 , inclusive ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: none is the answer . a . because for every k 6 ! + k : : k , because 6 ! : : k , since k is between 2 and 6 . a
Answer: a
Python program:
a = 1 + 1
Problem: a no . when divided by 224 gives a remainder 43 , what remainder will beobtained by dividingthe same no . 17 ?
Options: a ) 2 , b ) 7 , c ) 9 , d ) 11 , e ) 12
Rationale: "224 + 43 = 267 / 17 = 12 ( remainder ) e"
Answer: e
Python program:
a = 224 + 43 
b = a / 17
Problem: 20 beavers , working together in a constant pace , can build a dam in 3 hours . how many hours x will it take 12 beavers that work at the same pace , to build the same dam ?
Options: a ) 2 . , b ) 4 . , c ) x = 5 . , d ) x = 6 . , e ) 8 .
Rationale: "c . 5 hrs if there were 10 beavers it qould have taken double x = 6 hrs . . so closest to that option is 5 ."
Answer: c
Python program:
a = 3 * 20
b = a / 12
Problem: the product of two numbers is 168 and the sum of these two numbers is 26 . what is the largest of these two numbers ?
Options: a ) 22 , b ) 77 , c ) 88 , d ) 12 , e ) 62
Rationale: "let the numbers be x and ( 26 – x ) . therefore , x ( 26 – x ) = 168 x 2 – 26 x + 168 = 0 ( x – 14 ) ( x – 12 ) = 0 x = 14 or x = 12 so , the numbers are 14 and 12 . answer : d"
Answer: d
Python program:
a = 2 * 168
b = 26 - a
c = math.sqrt(b)
d = c ** 2
e = 4 * 168
f = d + e 
g = math.sqrt(f)
Problem: a small company is planning to rent either computer a or computer b to print customer mailing lists . both computer a and computer b must be rented on an hourly basis . the rental fee is based only on the amount of time the computer is turned on . it will cost 40 percent more per hour to rent computer a than to rent computer b . computer b would , however , require 20 hours more than computer a to do the job . if either computer a , or computer b were rented the total cost to rent the computer would be $ 700.00 . what would be the approximate hourly charge to rent computer b ?
Options: a ) $ 9.40 , b ) $ 10.00 , c ) $ 13.20 , d ) $ 17.80 , e ) $ 22.10
Rationale: "pa = price of a pb = price of b ta = time for a to complete the job tb = time for b to complete the job given pa = 1.4 pb ta + 20 = tb pa * ta = pb * tb = 700 1.4 pb * ( tb - 20 ) = pb * tb 1.4 pb tb - pb tb = 1.4 pb * 20 0.4 pbtb = 28 pb tb = 28 / 0.4 = 70 pb = 700 / 70 = 10 b"
Answer: b
Python program:
a = 40 / 100
b = 4 + 3 
c = 40 / 100
d = 20 / 4
e = d / 100
f = c + e 
g = b + f 
h = a + g
Problem: in a survey of 330 employees , 104 of them are uninsured , 54 work part time , and 12.5 percent of employees who are uninsured work part time . if a person is to be randomly selected from those surveyed , what is the probability that the person will neither work part time nor be uninsured ?
Options: a ) 37 / 66 , b ) 8 / 41 , c ) 9 / 348 , d ) 1 / 8 , e ) 41 / 91
Rationale: "- - - - - - - - - ui - - - - - - - - - - - - - - - - nui - - - - - - - total pt - - - - ( 12.5 / 100 ) * 104 = 13 - - - - - - - - - - - - - 54 npt - - - 104 - 13 - - - - - - - - - - - - - - x - - - - - - - - 276 total - - 104 - - - - - - - - - - - - - - - - - - - - - - - - - - - - 330 we have to find not part time and not uninsured . in other words not part time and insured = x / 330 = ( 276 - 104 + 13 ) / 330 = 37 / 66 answer is a ."
Answer: a
Python program:
a = 12 * 5
b = 1 * 100
c = a / b
d = 54 - c
e = d + 104 
f = 330 - e
g = f / 330
Problem: a dishonest dealer professes to sell goods at the cost price but uses a weight of 896 grams per kg , what is his percent ?
Options: a ) 22 % , b ) 25 % , c ) 77 % , d ) 99 % , e ) 11.6 %
Rationale: "896 - - - 104 100 - - - ? = > 11.6 % answer : e"
Answer: e
Python program:
a = 100 / 896
b = 3 + 2 
c = b * 2
d = 100 * c
e = a * d
f = e - 100
Problem: jack has two dice , one has 6 equally probable sides , labeled 1 , 2 , 3 , 4 , 5 , 6 , and the other has 7 equally probable sides , labeled 1 , 2 , 3 , 4 , 5 , 6 , 7 . if jack rolls both dice what is the probability that both of the numbers will be even ?
Options: a ) 3 / 14 , b ) 2 / 7 , c ) 1 / 3 , d ) 1 / 2 , e ) 12 / 21
Rationale: probability that the number on first die is even = 3 / 6 [ because 3 out of 6 faces are even ] probability that the number on second die is even = 3 / 7 [ because 3 out of 7 faces are even ] probability that both dice result in odd numbers = ( 3 / 6 ) * ( 3 / 7 ) = 3 / 14 answer : option a
Answer: a
Python program:
a = 7 * 2
b = 3 / a
Problem: what will be the compound interest on a sum of rs . 26000 after 3 years at the rate of 12 % p . a . ?
Options: a ) s . 10123.22 , b ) s . 10823.20 , c ) s . 10123.20 , d ) s . 10123.29 , e ) s . 10528.13
Rationale: "explanation : amount = [ 26000 * ( 1 + 12 / 100 ) 3 ] = 26000 * 28 / 25 * 28 / 25 * 28 / 25 = rs . 35123.20 c . i . = ( 36528.13 - 26000 ) = rs . 10528.13 answer : e"
Answer: e
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: which number need to add to 859622 to get a no . exactly divisible by 456 ?
Options: a ) 345466 , b ) 465767 , c ) 565676 , d ) 645469 , e ) 859622
Rationale: "dividend = quotient * divisor + reminder 859622 / 456 gives quotient = 1885 and reminder = 62 . so , the next number divisible by 456 is 456 places infront of 456 * 1885 which means 456 – 62 = 394 should be added to 859622 . e"
Answer: e
Python program:
a = 859622 / 456
b = math.floor(a)
c = b + 1 
d = 859622 / 456
e = c - d
f = 456 * e
Problem: a case of 12 rolls of paper towels sells for $ 9 . the cost of one roll sold individually is $ 1 . what is the percent r of savings per roll for the 12 - roll package over the cost of 12 rolls purchased individually ?
Options: a ) 9 % , b ) 11 % , c ) 15 % , d ) 25 % , e ) 90 %
Rationale: "cost of 12 paper towels individually = 1 * 12 = 12 cost of a set of 12 paper towels = 9 cost of one roll = 9 / 12 = 3 / 4 = 0.75 savings per roll = 1 - . 75 = 0.25 % of savings is r = . 25 / 1 * 100 = 25 % d is the answer ."
Answer: d
Python program:
a = 9 / 12
b = a * 100
c = 100 - b
Problem: a cistern is filled by pipe a in 10 hours and the full cistern can be leaked out by an exhaust pipe b in 12 hours . if both the pipes are opened , in what time the cistern is full ?
Options: a ) 50 hrs , b ) 60 hrs , c ) 70 hrs , d ) 80 hrs , e ) 90 hrs
Rationale: "time taken to full the cistern = ( 1 / 10 - 1 / 12 ) hrs = 1 / 60 = 60 hrs answer : b"
Answer: b
Python program:
a = 1 / 10
b = 1 / 12
c = a - b
d = 1 / c
Problem: in a class of 20 students , 2 students did not borrow any books from the library , 8 students each borrowed 1 book , 3 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "the total number of books the students borrowed is 20 * 2 = 40 . the students who borrowed zero , one , or two books borrowed 8 * 1 + 3 * 2 = 14 books . the 7 students who borrowed at least three books borrowed 40 - 14 = 26 books . if 6 of these students borrowed exactly 3 books , then the maximum that one student could have borrowed is 26 - 18 = 8 books . the answer is a ."
Answer: a
Python program:
a = 20 * 2
b = 8 * 1
c = b + 3 
d = c + 2 
e = 20 - d
f = e - 1
g = f * 3
h = 8 * 1
i = 3 * 2
j = h + i 
k = g + j 
l = a - k
Problem: a manufacturer produces a certain men ' s athletic shoe in integer sizes from 8 to 17 . for this particular shoe , each unit increase in size corresponds to a 1 / 4 - inch increase in the length of the shoe . if the largest size of this shoe is 30 % longer than the smallest size , how long , in inches , is the shoe in size 15 ?
Options: a ) 9.25 , b ) 11.75 , c ) 13.25 , d ) 15.75 , e ) 17.25
Rationale: "let x be the length of the size 8 shoe . then 0.3 x = 9 / 4 x = 90 / 12 = 15 / 2 inches the size 15 shoe has a length of 15 / 2 + 7 / 4 = 37 / 4 = 9.25 inches the answer is a ."
Answer: a
Python program:
a = 1 / 4
b = 17 - 8
c = a * b
d = 30 / 100
e = c / d
f = 15 - 8
g = 1 / 4
h = f * g
i = e + h
Problem: what is the measure of the radius of the circle that circumscribes a triangle whose sides measure 11 , 60 and 61 ?
Options: a ) 6.5 , b ) 12.5 , c ) 28 , d ) 30.5 , e ) 40
Rationale: "some of pyhtagron triplets we need to keep it in mind . like { ( 2 , 3,5 ) , ( 5 , 12,13 ) , ( 7 , 24,25 ) , ( 11 , 60,61 ) . so now we know the triangle is an right angle triangle . the circle circumscribes the triangle . the circumraduis of the circle that circumscribes the right angle triangle = hypotanse / 2 = 61 / 2 = 30.5 ans . d"
Answer: d
Python program:
a = triangle_area_three_edges / (
Problem: a man spends 50 % of his income on food , 15 % on children education and 50 % of the remaining on house rent . what percent of his income he is left with ?
Options: a ) 17.5 % , b ) 16 % , c ) 15.4 % , d ) 12.6 % , e ) 13.5 %
Rationale: "let the total income be x then , income left = ( 100 - 50 ) % of x - [ 100 - ( 50 + 15 ) ] % of x = 50 % of 35 % of x = 17.5 % of x answer is a"
Answer: a
Python program:
a = 100 - 50
b = a - 15
c = 100 - 50
d = b * c
e = d / 100
Problem: a car covers a distance of 624 km in 3 hours . find its speed ?
Options: a ) 104 , b ) 277 , c ) 298 , d ) 269 , e ) 208
Rationale: 624 / 3 = 208 kmph answer : e
Answer: e
Python program:
a = 624 / 3
Problem: it was calculated that 50 men could complete a piece of work in 10 days . when work was scheduled to commence , it was found necessary to send 25 men to another project . how much longer will it take to complete the work ?
Options: a ) 20 days . , b ) 15 days . , c ) 22 days . , d ) 30 days . , e ) 18 days .
Rationale: "one day work = 1 / 10 one man ’ s one day work = 1 / ( 10 * 50 ) now : no . of workers = 25 one day work = 25 * 1 / ( 10 * 50 ) the total no . of days required to complete the work = ( 50 * 10 ) / 25 = 20 answer : a"
Answer: a
Python program:
a = 50 / 25
b = 10 * a
Problem: at a supermarket , the ratio of the number of shampoos to the number of soaps is 8 to 5 , and the ratio of the number of drinks to the number of shampoos is 3 to 4 . if the ratio of the soaps to the number of cereals is 9 to 2 , what is the ratio of the number of drinks to the number of cereals ?
Options: a ) 4 : 3 , b ) 15 : 6 , c ) 45 : 16 , d ) 15 : 4 , e ) 27 : 5
Rationale: sh : soaps = 8 : 5 drinks : sh = 3 : 4 = > 6 : 8 drinks : sh : soaps = 6 : 8 : 5 soaps : cer = 9 : 2 = > 9 * 5 : 2 * 5 = 45 : 10 now , drinks : sh : soaps = > 6 * 9 : 8 * 9 : 5 * 9 = 54 : 72 : 45 drinks : sh : soaps : cer = 54 : 72 : 45 : 10 drinks : cer = 54 : 10 = > 27 : 5 e
Answer: e
Python program:
a = 8 + 3 
b = a / 2
Problem: xy = 1 then what is ( 5 ^ ( x + y ) ^ 2 ) / ( 5 ^ ( x - y ) ^ 2 )
Options: a ) 2 , b ) 625 , c ) 8 , d ) 16 , e ) 32
Rationale: "( x + y ) ^ 2 - ( x - y ) ^ 2 ( x + y + x - y ) ( x + y - x + y ) ( 2 x ) ( 2 y ) 4 xy 4 5 ^ 4 = 625 answer b"
Answer: b
Python program:
a = 4 * 1
b = 5 ** a
Problem: gold is 10 times as heavy as water and copper is 5 times as heavy as water . in what ratio should these be mixed to get an alloy 8 times as heavy as water ?
Options: a ) 3 : 2 , b ) 1 : 2 , c ) 3 : 1 , d ) 5 : 2 , e ) 4 : 3
Rationale: "g = 10 w c = 5 w let 1 gm of gold mixed with x gm of copper to get 1 + x gm of the alloy 1 gm gold + x gm copper = x + 1 gm of alloy 10 w + 5 wx = x + 1 * 8 w 10 + 5 x = 8 ( x + 1 ) x = 2 / 3 ratio of gold with copper = 1 : 2 / 3 = 3 : 2 answer is a"
Answer: a
Python program:
a = 8 - 5
b = 10 - 8
c = a / b
Problem: the length of a rectangular floor is more than its breadth by 200 % . if rs . 400 is required to paint the floor at the rate of rs . 3 / sq m , what would be the length of the floor ?
Options: a ) 12 , b ) 18 , c ) 20 , d ) 22 , e ) 24
Rationale: "let the length and the breadth of the floor be l m and b m respectively . l = b + 200 % of b = l + 2 b = 3 b area of the floor = 400 / 3 = 133.33 sq m l b = 133.33 i . e . , l * l / 3 = 133.33 l ^ 2 = 400 > l = 20 . c"
Answer: c
Python program:
a = 400 / 3
b = a / 3
c = math.sqrt(b)
d = c * 3
Problem: a baker charges n dollars for a birthday cake . next week , she intends to earn 320 dollars selling cakes . if she were to reduce the price of the cake by 20 percent , she would have to sell two more cakes to earn the same amount of revenue . how many cakes does she intend to sell next week ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: we ' re told that by selling cakes at n dollars / cake , a baker will make $ 320 . reducing the price by 20 % and selling 2 more cakes will also make her $ 320 . we ' re asked for the original number of cakes that the baker intends to sell . $ 320 is a rather interesting number . based on the answer choices , we ' re almost certainly dealing with integer values for the number of cakes and the price per cake . as such , 6 is probably not going to be part of the solution ( either as 4 and 6 cakes or as 6 and 8 cakes ) . as such , we can avoid answers b and c . . . . let ' s test answer d : 8 cakes if . . . . original cakes = 8 8 ( n ) = $ 320 , so n = $ 40 / cake 20 % off = $ 8 off = 40 - 8 = $ 32 / cake + 2 more cakes = 8 + 2 = 10 cakes 10 ( 32 ) = $ 320 this is an exact match for what we were told , so this must be the answer . final answer : d
Answer: d
Python program:
a = 100 - 20
b = a / 100
c = 320 * b
d = 320 - c
e = 100 - 20
f = e / 100
g = f * 2
h = d / g
i = 320 / h
Problem: a sum of money deposited at c . i . amounts to rs . 1820 in 4 years and to rs . 2402 in 5 years . find the rate percent ?
Options: a ) 30 % , b ) 31 % , c ) 34 % , d ) 19 % , e ) 50 %
Rationale: "1820 - - - 582 100 - - - ? = > 31 % answer : b"
Answer: b
Python program:
a = 2402 - 1820
b = a / 1820
c = b * 100
Problem: an assembly line produces 30 cogs per hour until an initial order of 60 cogs is completed . the speed of the assembly line is then immediately increased so that it can produce 60 cogs per hour until another 60 cogs are produced . what is the overall average output , in cogs per hour , for the assembly line during this whole time ?
Options: a ) 40 , b ) 44 , c ) 48 , d ) 52 , e ) 56
Rationale: "the time to produce the first 60 cogs is 60 / 30 = 2 hours . the time to produce the next 60 cogs is 60 / 60 = 1 hour . the average output is 120 cogs / 3 hours = 40 cogs per hour . the answer is a ."
Answer: a
Python program:
a = 60 * 2
b = 60 / 30
c = b + 1 
d = a / c
Problem: if the cost price of 44 chocolates is equal to the selling price of 24 chocolates , the gain percent is :
Options: a ) 83.55 % , b ) 83.33 % , c ) 80 % , d ) 83.39 % , e ) 84.33 %
Rationale: explanation : solution : let c . p . of each chocolate be re . 1 . then , c . p . of 24 chocolates = rs . 24 ; s . p . of 24 chocolates = rs . 44 . . ' . gain % = 20 * 100 / 24 = 83.33 % answer : b
Answer: b
Python program:
a = 44 - 24
b = 24 / a
c = 100 / b
Problem: 90 percent of your marbles are a solid color . 5 percent of your marbles are solid yellow . what percentage of your marbles are a solid color other than yellow ?
Options: a ) 5 , b ) 15 , c ) 85 , d ) 90 , e ) 95
Rationale: 90 percent are solid colors including solid yellow . 5 percent are solid yellow . 90 % - 5 % = 85 % , so 85 percent are a solid color other than yellow = > ( c )
Answer: c
Python program:
a = 90 - 5
Problem: the length of rectangle is thrice its breadth and its perimeter is 112 m , find the area of the rectangle ?
Options: a ) 432 sq m , b ) 356 sq m , c ) 452 sq m , d ) 588 sq m , e ) 525 sq m
Rationale: "2 ( 3 x + x ) = 112 l = 42 b = 14 lb = 42 * 14 = 588 answer : d"
Answer: d
Python program:
a = 3 * 2
b = 1 * 2
c = a + b 
d = 112 / c
e = d * 3
f = 3 * 2
g = 1 * 2
h = f + g 
i = 112 / h
j = e * i
Problem: in measuring the sides of a rectangle , one side is taken 5 % in excess and the other 4 % in deficit . find the error percent in the area , calculate from the those measurements .
Options: a ) 0.9 % , b ) 0.8 % , c ) 0.3 % , d ) 0.2 % , e ) 0.5 %
Rationale: "explanation : let x and y be the sides of the rectangle then correct area = = error % = answer : b ) 0.8 %"
Answer: b
Python program:
a = 5 - 4
b = 5 * 4
c = b / 100
d = a - c
Problem: we have a rectangular metallic piece of paper that covers exactly the area of a cube . the length of the piece of paper is 144 inches and the width is 72 inches . what is the volume of the cube in cubic feet is 1 feet is 12 inches ?
Options: a ) a 216 , b ) b 196 , c ) c 170 , d ) d 140 , e ) e 121
Rationale: "l = 144 / 12 = 12 ft w = 72 / 12 = 6 ft area of paper = 72 area of cube = 12 * side ^ 2 side of cube = 6 v of cube = 216"
Answer: a
Python program:
a = cube_edge_by_volume + (
Problem: working at constant rate , pump x pumped out half of the water in a flooded basement in 7 hours . the pump y was started and the two pumps , working independently at their respective constant rates , pumped out rest of the water in 3 hours . how many hours would it have taken pump y , operating alone at its own constant rate , to pump out all of the water that was pumped out of the basement ?
Options: a ) a . 10 , b ) b . 12 , c ) c . 34 , d ) d . 18 , e ) e . 24
Rationale: "rate of x = 1 / 8 rate of x + y = 1 / 6 rate of y = 1 / 6 - 1 / 8 = 1 / 24 34 hours c"
Answer: c
Python program:
a = 3 + 7 
b = 1 + a 
c = b + 1 
d = c + 1 
e = d + 1 
f = e + 1 
g = f + 7 
h = g + 1 
i = h + 1 
j = i + 1 
k = j + 1 
l = k + 1 
m = l + 1
Problem: if k is an integer and 0.00010101 x 10 ^ k is greater than 1000 , what is the least possible value of k ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "0.00010101 * 10 ^ k > 1000 we need to move the decimal point to the right 7 places to get 1010.1 this is equivalent to multiplying by 10 ^ 7 . the answer is b ."
Answer: b
Python program:
a = 1000 / 0
b = math.log(a)
c = math.log(10)
d = b / c
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 43 kg , then the weight of b is :
Options: a ) 30 kg , b ) 31 kg , c ) 37 kg , d ) 39 kg , e ) 41 kg
Rationale: "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 = ( 43 x 2 ) = 86 . . . . ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 166 . . . . ( iv ) subtracting ( i ) from ( iv ) , we get : b = 31 . b ' s weight = 31 kg b )"
Answer: b
Python program:
a = 40 * 2
b = 43 * 2
c = a + b 
d = 45 * 3
e = c - d
Problem: a car is purchased on hire - purchase . the cash price is $ 22 000 and the terms are a deposit of 10 % of the price , then the balance to be paid off over 60 equal monthly installments . interest is charged at 12 % p . a . what is the monthly installment ?
Options: a ) $ 503 , b ) $ 504 , c ) $ 515 , d ) $ 528 , e ) $ 537
Rationale: "explanation : cash price = $ 22 000 deposit = 10 % ã — $ 22 000 = $ 2200 loan amount = $ 22000 â ˆ ’ $ 2200 number of payments = 60 = $ 19800 i = p * r * t / 100 i = 11880 total amount = 19800 + 11880 = $ 31680 regular payment = total amount / number of payments = 528 answer : d"
Answer: d
Python program:
a = 22 * 1000
b = 10 / 100
c = 1 - b
d = a * c
e = d / 60
f = 12 / 100
g = f / 12
h = 22 * 1000
i = 10 / 100
j = 1 - i
k = h * j
l = g * k
m = e + l
Problem: 5 is added to a certain number , the sum is multiplied by 2 , the product is divided by 5 and 5 is subtracted from the quotient . the remainder left is half of 44 . what is the number ?
Options: a ) 21 , b ) 20 , c ) 63 , d ) 30 , e ) 45
Rationale: "let number is x . when 5 added to it , = ( x + 5 ) 2 multiplied to sum , = 2 * ( x + 5 ) now , = [ { 2 * ( x + 5 ) } / 5 ] and , = [ { 2 * ( x + 5 ) } / 5 ] - 5 according to question , [ { 2 * ( x + 5 ) } / 5 ] - 5 = half of 44 [ ( 2 x + 10 ) / 5 ) = 22 + 5 2 x + 10 = 27 * 5 2 x - 135 - 10 x = 125 / 2 = 62.5 = 63 so , required number is : 63 . answer : c"
Answer: c
Python program:
a = 44 / 2
b = a + 5 
c = b * 5
d = c / 2
e = d - 5
Problem: the ratio between the sale price and the cost price of an article is 9 : 7 . what is the ratio between the profit and the cost price of that article ?
Options: a ) 2 : 9 , b ) 2 : 7 , c ) 3 : 6 , d ) 2 : 0 , e ) 2 : 1
Rationale: "let c . p . = rs . 7 x and s . p . = rs . 9 x . then , gain = rs . 2 x required ratio = 2 x : 7 x = 2 : 7 answer : b"
Answer: b
Python program:
a = 9 - 7
b = a / 7
Problem: find the number which when multiplied by 15 is increased by 196 .
Options: a ) 14 , b ) 20 , c ) 26 , d ) 28 , e ) 30
Rationale: let the number be x . then , 15 x - x = 196 < = > 14 x = 196 < = > x = 14 . answer : a
Answer: a
Python program:
a = 15 - 1
b = 196 / a
Problem: one night a certain hotel rented 3 / 4 of its rooms . including 2 / 3 of their air conditioned rooms . if 3 / 5 of its rooms were air conditioned , what percent of the rooms that were not rented were air conditioned ?
Options: a ) 20 , b ) 33 1 / 3 , c ) 35 , d ) 40 , e ) 80
Rationale: consider total # of rooms to be 100 ; as 3 / 5 of the rooms are air conditioned then # of rooms that are air conditioned is 3 / 5 * 100 = 60 ; 3 / 4 rooms were rented - - > 1 / 4 * 100 = 25 were not rented ; 2 / 3 of air conditioned rooms were rented - - > 1 / 3 * 60 = 20 air conditioned room were not rented ; 20 / 25 = 4 / 5 = 80 % . answer : e .
Answer: e
Python program:
a = 100 * 3
b = a / 5
c = b / 3
d = 100 * 3
e = d / 4
f = 100 - e
g = c / f
h = g * 100
Problem: two trains of equal length are running on parallel lines in the same direction at 46 km / hr and 36 km / hr . the faster train catches and completely passes the slower train in 72 seconds . what is the length of each train ( in meters ) ?
Options: a ) 70 , b ) 80 , c ) 90 , d ) 100 , e ) 110
Rationale: "the relative speed = 46 - 36 = 10 km / hr = 10 * 5 / 18 = 25 / 9 m / s in 72 seconds , the relative difference in distance traveled is 72 * 25 / 9 = 200 meters this distance is twice the length of each train . the length of each train is 200 / 2 = 100 meters the answer is d ."
Answer: d
Python program:
a = 46 - 36
b = a * 1000
c = b / 3600
d = c * 72
e = d / 2
Problem: 80 + 5 * 12 / ( 180 / 3 ) = ?
Options: a ) 23 , b ) 78 , c ) 27 , d ) 61 , e ) 81
Rationale: "explanation : 80 + 5 * 12 / ( 180 / 3 ) = 80 + 5 * 12 / ( 60 ) = 80 + ( 5 * 12 ) / 60 = 80 + 1 = 81 . answer : e"
Answer: e
Python program:
a = 5 * 12
b = 180 / 3
c = a / b
d = 80 + c