euclaise/mathqa_programs huggingface dataset:
Problem: a woman invested $ 1,000 , part at 5 % and the rest at 6 % . her total investment with interest at the end of the year was $ 1,052 . how much did she invest at 5 % ?
Options: a ) $ 500 , b ) $ 600 , c ) $ 700 , d ) $ 800 , e ) $ 950
Rationale: "et x be the portion invested at 5 % and let ( 1 - x ) be the rest which is invested at 6 % the question states that the return after 1 year is ( 1052 / 1000 ) - 1 = 0.052 = 5.2 % we want to find the dollar amount invested in x using our defined variables , put together the equation and solve for x ( the percentage of 1000 invested at 5 % ) 0.05 x + 0.06 ( 1 - x ) = 0.052 ( 0.05 ) x + 0.06 - ( 0.06 ) x = 0.052 - 0.01 x = - 0.008 x = - 0.008 / - 0.01 = 8 / 10 = 80 % so x = 80 % of the 1000 which is 800 answer : d"
Answer: d
Python program:
a = 5 * 2
b = a * 100
c = 5 * 2
d = c * 100
e = 5 * 2
f = e * 5
g = f + 4 
h = d + g 
i = 5 * 2
j = i * 100
k = h - j
l = k * 100
m = 5 * 2
n = m * 100
o = 5 * n
p = l - o
q = b - p
Problem: one ball will drop from a certain height . the height it will reach after rebounding from the floor is 50 percent of the previous height . the total travel is 260 cm when it touches the floor on third time . what is the value of the original height ?
Options: a ) 80 cm , b ) 90 cm , c ) 104 cm , d ) 120 cm , e ) 130 cm
Rationale: when ball comes down , then i have indicated the distance covered in green when ball goes up , then i have indicated the distance covered in red distance travelled uptil the ball touches the floor 3 rd time : h + 0.5 h + 0.5 h + 0.5 * 0.5 h + 0.5 * 0.5 h h + 2 * 0.5 * h + 2 * 0.25 * h = h ( 1 + 2 * 0.5 + 2 * 0.25 ) = h ( 1 + 1 + 0.5 ) = 260 2.5 h = 260 h = 104 . c is the answer .
Answer: c
Python program:
a = 50 / 100
b = 2 + a 
c = 260 / b
Problem: 16.02 ã — 0.00001 = ?
Options: a ) 0.1602 , b ) 0.001602 , c ) 1.6021 , d ) 0.01602 , e ) none of these
Rationale: "16.02 ã — 0.00001 = 0.0001602 the answer is e ."
Answer: e
Python program:
a = 16 / 2
b = a * 100
Problem: a distributor sells a product through an online store , which take a commission of 20 % of the price set by the distributor . the distributor obtains the product from a producer at the price of $ 17 per item . what is the price that the buyer observers online if the distributor wants to maintain a 20 % profit on the cost of the item ?
Options: a ) $ 22.50 , b ) $ 23.50 , c ) $ 24.50 , d ) $ 25.50 , e ) $ 26.50
Rationale: "let x be the price that buyers see online . the distributor wants to receive 1.2 ( original price ) which should be 80 % of x . 1.2 ( 17 ) = 0.8 x x = 1.2 ( 17 ) / 0.8 = 1.5 ( 17 ) = $ 25.50 the answer is d ."
Answer: d
Python program:
a = 20 / 100
b = a * 17
c = b + 17 
d = 100 - 20
e = d / 100
f = c / e
Problem: when working alone , painter w can paint a room in 2 hours , and working alone , painter x can paint the same room in a hours . when the two painters work together and independently , they can paint the room in 3 / 4 of an hour . what is the value of a ?
Options: a ) 3 / 4 , b ) 1 [ 1 / 5 ] , c ) 1 [ 2 / 5 ] , d ) 1 [ 3 / 4 ] , e ) 2
Rationale: "rate * time = work let painter w ' s rate be w and painter x ' s rate be x r * t = work w * 2 = 1 ( if the work done is same throughout the question then the work done can be taken as 1 ) = > w = 1 / 2 x * a = 1 = > x = 1 / a when they both work together then their rates get added up combined rate = ( w + x ) r * t = work ( w + x ) * 3 / 4 = 1 = > w + x = 4 / 3 = > 1 / 2 + 1 / a = 4 / 3 = > 1 / a = ( 8 - 3 ) / 6 = 5 / 6 = > a = 6 / 5 = 1 [ 1 / 5 ] answer b"
Answer: b
Python program:
a = 4 - 2
b = 2 + 3 
c = 1 / b
d = a + c
Problem: the total age of a and b is 10 years more than the total age of b and c . c is how many years younger than a ?
Options: a ) 12 , b ) 10 , c ) c is elder than a , d ) data inadequate , e ) none
Rationale: "solution [ ( a + b ) - ( b + c ) ] = 10 â € ¹ = â € º a - c = 10 . answer b"
Answer: b
Python program:
a = 10 * 1
Problem: a new tower has just been built at the verbico military hospital ; the number of beds available for patients at the hospital is now 5 times the number available before the new tower was built . currently , 1 / 3 of the hospital ' s original beds , as well as 1 / 5 of the beds in the new tower , are occupied . for the purposes of renovating the hospital ' s original wing , all of the patients in the hospital ' s original beds must be transferred to beds in the new tower . if patients are neither admitted nor discharged during the transfer , what fraction of the beds in the new tower will be unoccupied once the transfer is complete ?
Options: a ) 11 / 30 , b ) 43 / 60 , c ) 17 / 30 , d ) 19 / 30 , e ) 11 / 15
Rationale: "i think b - 43 / 60 is the correct answer . here goes : lets assume originally the number of beds = x after the new tower , the total combined no of beds = 5 x so old = x , new = 4 x now 1 / 3 of x are occupied and 1 / 5 of 4 x are occupied which simplifies to ( 4 / 5 ) x we are shifting 1 / 3 of x to the new ward so there will now be : 1 / 3 of x plus 4 / 5 of x occupied in the new ward . add them up to get 17 / 15 of x there are 4 x beds in new tower so ratio is : ( 17 / 15 ) x / 4 x = 17 / 60 of x subtract that from 60 / 60 of x and you get the number of un - occupied beds to total capacity of new tower = 43 / 60 . b"
Answer: b
Python program:
a = 5 * 3
b = a + 1 
c = 1 / 3
d = 1 / 5
e = c * d
f = b * e
Problem: what is the probability of having 53 fridays in an ordinary year
Options: a ) 1 / 5 , b ) 1 / 6 , c ) 1 / 7 , d ) 1 / 8 , e ) 1 / 9
Rationale: "1 / 7 because 53 friday in ordinary year then 53 * 7 = 371 ( 53 / 371 = 1 / 7 ) answer : c"
Answer: c
Python program:
a = 3 + 3 
b = math.comb(a, 3)
c = 2 / b
Problem: how many integerskgreater than 100 and less than 900 are there such that if the hundreds and the units digits ofkare reversed , the resulting integer is k + 99 ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "numbers will be like 102 = > 201 = 102 + 99 203 = > 302 = 103 + 99 so the hundereth digit and units digit are consecutive where unit digit is bigger than hundred digit . there will be seven pairs of such numbers for every pair there will 10 numbers like for 12 = > 102 , 112,132 , 142,152 , 162,172 , 182,192 . total = 7 * 10 = 70 hence c ."
Answer: c
Python program:
a = 100 / 10
b = 2 * 4
c = a * b
d = 100 / 10
e = c + d
Problem: how many halves are there in 9 - fourth ?
Options: a ) 8 , b ) 4.5 , c ) 3.2 , d ) 7 , e ) 3
Rationale: divide 9 / 4 by 1 / 2 = 9 / 4 ÷ 1 / 2 = 9 / 4 * 2 / 1 = 18 / 4 = 4.5 . answer is b .
Answer: b
Python program:
a = 9 / 4
b = 1 / 2
c = a / b
Problem: what is the population standard deviation for the numbers : 75 , 83 , 96 , 100 , 121 and 125 ?
Options: a ) 18.2 , b ) 20 , c ) 25 , d ) 26 , e ) 28
Rationale: 1 . firstly find the mean : mean = ( 75 + 83 + 96 + 100 + 121 + 125 ) ÷ 6 = 600 ÷ 6 = 100 2 . next find the variance . to calculate the variance , take each difference , square it , and then average the result : ( 75 - 100 ) 2 + ( 83 - 100 ) 2 + ( 96 - 100 ) 2 + ( 100 - 100 ) 2 + ( 121 - 100 ) 2 + ( 125 - 100 ) 2 = ( - 25 ) 2 + ( - 17 ) 2 + ( - 4 ) 2 + ( 0 ) 2 + ( 21 ) 2 + ( 25 ) 2 = 625 + 289 + 16 + 0 + 441 + 625 = 1996 so the variance = 1996 ÷ 6 = 332.66 . . . 3 . the standard deviation is just the square root of the variance = √ ( 332.66 . . . ) = 18.2 correct to 1 decimal places answer is a
Answer: a
Python program:
a = 121 + 125 
b = a - 100
c = b - 96
d = 83 / 3
e = c - d
f = e - 4
Problem: 63 small identical cubes are used to form a large cube . how many more cubes are needed to add one top layer of small cube all over the surface of the large cube ?
Options: a ) 64 , b ) 128 , c ) 152 , d ) 216 , e ) 153
Rationale: "63 small cube will make a large cube with 4 cubes in each line i . e . adding one layer will require one cube at each end and hence new cube will have 6 cubes in each line . total number of small cubes in new cube = 6 ^ 3 = 216 extra cube required = 216 - 63 = 153 hence , e is the answer ."
Answer: e
Python program:
a = cube_edge_by_volume + ( 
b = volume_cube - (
Problem: there are two tanks a & b with same capacity of 20 litres . if the water inflow rate ( speed ) in tank a is 2 litres per hour & in tank b is 4 litres per hour . how much longer tank a takes to fill than tank b ?
Options: a ) 4 hours , b ) 5 hours , c ) 3 hours , d ) 2 hours , e ) 1 hour
Rationale: time taken for tank a to fill = 20 / 2 = 10 hours time taken for tank b to fill = 20 / 4 = 5 hours so tank a takes 5 more hours to fill answer : b
Answer: b
Python program:
a = 20 / 2
b = 20 / 4
c = a - b
Problem: while calculating the edge of a square , a worker makes an error of 2 % in excess . what % error does he make in calculating area ? ( % )
Options: a ) 4.09
b ) 4.0
c ) 4.04
d ) 4.02
e ) 4.01
Rationale: explanation : given error = 2 % while measuring the side of a square . if the correct value of the side of square is 100 , the measured value : = > 100 + 2 % * 100 = 100 + 2 = 102 the area of square with edge 100 = side * side = > 100 * 100 = > 10000 the area of square with side 102 = 102 * 102 = 10404 error in area calculation = 10404 - 1000 = 404 % error = ( 404 / 10000 ) * 100 = 4.04 % answer : c
Answer: c
Python program:
a = 100 + 2 
b = square_area - (
c = b / square_area
Problem: how many positive integers less than 200 are there such that they are multiples of 13 or multiples of 12 ?
Options: a ) 28 , b ) 29 , c ) 30 , d ) 31 , e ) 32
Rationale: "total multiples of 13 : 15 ( first multiple : 13 , last multiple : 195 ) total multiples of 12 : 16 ( first multiple : 12 , last multiple : 192 ) multiple of 12 and 13 : 1 ( 156 ) 15 + 16 - 1 = 30 answer : c"
Answer: c
Python program:
a = 4 + 13 
b = a - 1
c = math.factorial(b)
d = math.factorial(13)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
Problem: if a / b = 1 / 2 , b / c = 5 , c / d = 2 / 3 , d / e = 1 / 6 and e / f = 2 / 3 , then what is the value of abc / def ?
Options: a ) 50 / 729 , b ) 20 / 456 , c ) 45 / 752 , d ) 13 / 452 , e ) 45 / 741
Rationale: "say a = 2 . then : a / b = 1 / 2 - - > b = 4 ; b / c = 5 - - > c = 4 / 5 ; c / d = 2 / 3 - - > d = 6 / 5 ; d / e = 1 / 6 - - > e = 36 / 5 ; e / f = 2 / 3 - - > f = 54 / 2 . abc / def = ( 2 * 4 * 4 / 5 ) / ( 6 / 5 * 36 / 5 * 54 / 5 ) = 50 / 729 . answer : a ."
Answer: a
Python program:
a = 2 * 2
b = 2 * 2
c = 5 * b
d = a / c
Problem: a salesperson received a commission of 3 percent of the sale price for each of the first 100 machines that she sold and 4 percent of the sale price for each machine that she sold after the first 100 . if the sale price of each machine was $ 10,000 and the salesperson received a $ 40,000 commission , how many machines did she sell ?
Options: a ) 90 , b ) 103 , c ) 105 , d ) 115 , e ) 125
Rationale: "first 100 machines = 3 % commission = 0.03 * 100 * 10000 = 30000 commission from sale of next machines = 40000 - 30000 = 10000 so 25 more machines . . total = 125 machines imo e . . ."
Answer: e
Python program:
a = 4 + 3 
b = 3 * 2
c = a * b
d = c * 100
e = 4 + 1 
f = e * 2
g = d * f
h = 100 * 100
i = 3 / 100
j = h * i
k = j * 100
l = g - k
m = 100 * 100
n = 4 / 100
o = m * n
p = l / o
q = 100 + p
Problem: find the average of all the numbers between 6 and 30 which are divisible by 4 .
Options: a ) 15 , b ) 18 , c ) 20 , d ) 22 , e ) none
Rationale: "sol . average = ( 8 + 12 + 16 + 20 + 24 + 28 / 6 ) = 108 / 6 = 18 answer b"
Answer: b
Python program:
a = 6 + 4 
b = 30 - 4
c = a + b 
d = c / 2
Problem: in a renowned city , the average birth rate is 8 people every two seconds and the death rate is 6 people every two seconds . estimate the size of the population net increase that occurs in one day .
Options: a ) 32,300 , b ) 172,800 , c ) 468,830 , d ) 86,400 , e ) 259,200
Rationale: "every 2 seconds , 2 persons are added ( 8 - 6 ) . every second 1 persons are added . in a day 24 hrs = 24 * 60 minutes = 24 * 60 * 60 = 86400 seconds . 86400 * 1 = 86400 option d"
Answer: d
Python program:
a = 8 - 6
b = a * 3600
c = b * 12
Problem: in 1970 there were 8,902 women stockbrokers in the united states . by 1978 the number had increased to 24,947 . approximately what was the percent increase ?
Options: a ) 45 % , b ) 125 % , c ) 145 % , d ) 150 % , e ) 180 %
Rationale: "the percent increase is ( 24947 - 8902 ) / 8902 = 16045 / 8902 = 1.80 so the approximate answer is e"
Answer: e
Python program:
a = 24 - 947
b = a / 8
Problem: in may , the groundskeeper at spring lake golf club built a circular green with an area of 70 π square feet . in august , the groundskeeper doubled the distance from the center of the green to the edge of the green . what is the total area of the renovated green ?
Options: a ) 1000 π , b ) 400 π , c ) 280 π , d ) 200 π , e ) 20 π
Rationale: "area = π r ^ 2 , so doubling the radius results in an area that is 4 times the original area . 4 ( 70 π ) = 280 π the answer is c ."
Answer: c
Python program:
a = math.sqrt(70)
b = a * 2
c = b ** 2
d = c * math.pi
Problem: find the cost of fencing around a circular field of diameter 30 m at the rate of rs . 5 a meter ?
Options: a ) 288 , b ) 132 , c ) 772 , d ) 592 , e ) 471.25
Rationale: "2 * 22 / 7 * 15 = 94.25 94.25 * 5 = rs . 471.25 answer : e"
Answer: e
Python program:
a = 30 / 2
b = circumface * (
Problem: if x # y is defined to equal x ^ 2 / y for all x and y , then ( - 1 # 2 ) # - 3 =
Options: a ) 1 / 12 , b ) 1 / 3 , c ) 1 / 2 , d ) - 1 / 12 , e ) - 4 / 3
Rationale: ( - 1 ) ^ 2 / 2 = 1 / 2 ( - 1 / 2 ) ^ 2 / - 3 = - 1 / 12 so d is my answer
Answer: d
Python program:
a = negate ** (
b = a / 2
c = b ** 2
d = c / 2
Problem: 39 persons can repair a road in 12 days , working 5 hours a day . in how many days will 15 persons , working 6 hours a day , complete the work ?
Options: a ) 10 , b ) 13 , c ) 14 , d ) 26 , e ) 16
Rationale: "let the required number of days be x . less persons , more days ( indirect proportion ) more working hours per day , less days ( indirect proportion ) persons 15 : 39 : : 12 : x working hours / day 6 : 5 15 x 6 x x = 39 x 5 x 12 x = ( 39 x 5 x 12 ) / ( 15 x 6 ) x = 26 . answer : d"
Answer: d
Python program:
a = 39 * 12
b = a * 5
c = 15 * 6
d = b / c
Problem: the circumference of the front wheel of a cart is 30 ft long and that of the back wheel is 40 ft long . what is the distance traveled by the cart , when the front wheel has done five more revolutions than the rear wheel ?
Options: a ) 20 ft , b ) 25 ft , c ) 600 ft , d ) 900 ft , e ) 1000 ft
Rationale: "point to note : both the wheels would have traveled the same distance . now consider , no . of revolutions made by back wheel as x , which implies that the number of revolutions made by the front wheel is ( x + 5 ) . equating the distance traveled by front wheel to back wheel : ( x + 5 ) * 30 = x * 40 . ( formula for calculating the distance traveled by each wheel is : # of revolutions * circumference . ) solving this eqn . gives x = 15 . sub x = 15 either in ( x + 5 ) * 30 or in x * 40 to get the distance , which is 600 . so the correct choice is c ."
Answer: c
Python program:
a = 10 / 2
b = 30 * a
c = b / 3
d = 10 / 2
e = c + d 
f = 30 * e
Problem: a leak in the bottom of a tank can empty the full tank in 6 hours . an inlet pipe fills water at the rate of 4.5 liters per minute . when the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours . the capacity of the tank is ?
Options: a ) 5729 , b ) 5760 , c ) 2889 , d ) 6480 , e ) 2799
Rationale: "1 / x - 1 / 6 = - 1 / 8 x = 24 hrs 24 * 60 * 4.5 = 6480 . answer : d"
Answer: d
Python program:
a = 8 * const_60
b = 4 * 5
c = 8 * const_60
d = 6 * const_60
e = c / d
f = e - 1
g = b / f
Problem: a and b invests rs . 10000 each , a investing for 8 months and b investing for all the 12 months in the year . if the total profit at the end of the year is rs . 5000 , find their shares ?
Options: a ) 2000,8000 , b ) 2000,4000 , c ) 2000,3000 , d ) 1000,3000 , e ) 4000,3000
Rationale: "the ratio of their profits a : b = 8 : 12 = 2 : 3 share of a in the total profit = 2 / 5 * 5000 = rs . 2000 share of b in the total profit = 3 / 5 * 5000 = rs . 3000 answer : c"
Answer: c
Python program:
a = 10000 * 1
b = a / 3
Problem: a circular path of 12 m radius has marginal walk 2 m wide all round it . find the cost of leveling the walk at 50 p per m 2 ?
Options: a ) rs . 49 , b ) rs . 40 , c ) rs . 81.72 , d ) rs . 42 , e ) rs . 43
Rationale: "explanation : π ( 14 ^ 2 - 12 ^ 2 ) = 22 / 7 * 52 = 163.43 163.43 * 1 / 2 = rs . 81.72 answer : option c"
Answer: c
Python program:
a = 12 + 2 
b = circle_area - (
c = 50 * b
Problem: last year sandy saved 6 % of her annual salary . this year , she made 10 % more money than last year , and she saved 8 % of her salary . the amount saved this year was what percent of the amount she saved last year ?
Options: a ) 132 % , b ) 147 % , c ) 158 % , d ) 176 % , e ) 188 %
Rationale: "let last year ' s salary be x . last year , sandy save 0.06 x this year , sandy saved 0.08 * 1.1 x = 0.088 x 0.088 x / 0.06 x = 88 / 60 = 1.47 = 147 % the answer is b ."
Answer: b
Python program:
a = 8 / 100
b = 100 + 10 
c = a * b
d = 6 * 100
e = d / 100
f = c / e
g = f * 100
Problem: the length of a rectangle is twice its breadth . if its length is decreased by 10 cm and breadth is increased by 10 cm , the area of the rectangle is increased by 75 sq . cm . what is the length of the rectangle ?
Options: a ) 25 cm , b ) 35 cm , c ) 30 cm , d ) 45 cm , e ) 55 cm
Rationale: "let breadth = x cm then , length = 2 x cm area = x × 2 x = 2 x ^ 2 sq . cm . new length = ( 2 x − 10 ) cm new breadth = ( x + 10 ) cm new area = ( 2 x − 10 ) ( x + 10 ) sq . cm . given that , new area = initial area + 75 sq . cm . ⇒ ( 2 x − 10 ) ( x + 10 ) = 2 x ^ 2 + 75 ⇒ 2 x ^ 2 + 20 x − 10 x − 100 = 2 x ^ 2 + 75 ⇒ 10 x − 100 = 75 ⇒ 10 x = 75 + 100 = 175 ⇒ x = 175 / 10 = 17.5 cm length = 2 x = 2 × 17.5 = 35 cm answer : b"
Answer: b
Python program:
a = 100 / 3
Problem: factory x ' s bulbs work for over 5000 hours in 78 % of cases , whereas factory y ' s bulbs work for over 5000 hours in 65 % of cases . it is known that factory x supplies 90 % of the total bulbs available . what is the chance that a purchased bulb will work for longer than 5000 hours ?
Options: a ) 76.4 % , b ) 76.7 % , c ) 77.4 % , d ) 75 % , e ) 73.9 %
Rationale: "for x , 90 % of 78 % will work . for y , 10 % of 65 % will work . * 10 % is the rest of the bulb supply in the market . so , the probability that a purchased bulb will work is : 0.90 ( 0.78 ) = . 702 0.10 ( 0.65 ) = 0.065 the combined probability then is 70.2 + 6.5 = 76.7 % ans b"
Answer: b
Python program:
a = 78 + 65 
b = a / 2
Problem: 7 years ago , paula was 3 times as old as karl . in 2 years , paula will be twice as old as karl . what is the sum of their ages now ?
Options: a ) 26 , b ) 32 , c ) 38 , d ) 44 , e ) 50
Rationale: "p - 7 = 3 ( k - 7 ) and so p = 3 k - 14 p + 2 = 2 ( k + 2 ) ( 3 k - 14 ) + 2 = 2 k + 4 k = 16 p = 34 p + k = 50 the answer is e ."
Answer: e
Python program:
a = 2 * 2
b = 2 - a
c = negate + ( 
d = 7 * 3
e = d - 7
f = c * e
g = f - 3
h = 7 * 3
i = h - 7
j = g + i
Problem: a certain car dealership sells economy cars , luxury cars , and sport utility vehicles . the ratio of economy to luxury cars is 5 : 4 . the ratio of economy cars to sport utility vehicles is 3 : 2 . what is the ratio of luxury cars to sport utility vehicles ?
Options: a ) 9 : 8 , b ) 8 : 9 , c ) 6 : 5 , d ) 2 : 3 , e ) 1 : 2
Rationale: "the ratio of economy to luxury cars is 5 : 4 - - > e : l = 5 : 4 = 15 : 12 . the ratio of economy cars to sport utility vehicles is 3 : 2 - - > e : s = 3 : 2 = 15 : 10 . thus , l : s = 12 : 10 = 6 : 5 . answer : c ."
Answer: c
Python program:
a = 4 * 2
b = 2 * 2
c = a / b
d = 2 * 4
e = 4 * 4
f = d / e
g = c / f
Problem: a dress on sale in a shop is marked at $ d . during the discount sale its price is reduced by 65 % . staff are allowed a further 60 % reduction on the discounted price . if a staff member buys the dress what will she have to pay in terms of d ?
Options: a ) 0.15 d , b ) 0.16 d , c ) 0.65 d , d ) 0.14 d , e ) 0.05 d
Rationale: "effective discount = a + b + ab / 100 = - 65 - 60 + ( - 65 ) ( - 60 ) / 100 = - 86 sale price = d * ( 1 - 86 / 100 ) sale price = . 14 * d answer ( d )"
Answer: d
Python program:
a = 100 - 65
b = a / 100
c = 100 - 65
d = c / 100
e = 60 / 100
f = d * e
g = b - f
Problem: the difference of two numbers is 11 . one third of their sum is 7 . what are the two numbers ?
Options: a ) 21,10 , b ) 16,5 , c ) 3,14 , d ) 11,10 , e ) 7,14
Rationale: "let the two numbers be x and y . equation ( i ) : x - y = 11 equation ( ii ) : ( x + y ) / 3 = 7 solve system of equations : x + y = 21 x - y = 11 ( add equations together ) - - - 2 x = 32 - - - x = 16 16 - y = 11 - - - y = 5 since x = 16 and y = 5 , answer b ( 16,5 ) is correct ."
Answer: b
Python program:
a = 10 / 2
b = a * 7
c = 10 / 2
d = c * 7
e = 11 + d 
f = e / 2
g = b - f
h = 10 / 2
i = g + h
Problem: 75 % of 480 = ( ? ) x 15 ?
Options: a ) 32 , b ) 18 , c ) 360 , d ) none of these , e ) can not be determined
Rationale: "answer let 75 % of 480 = a x 15 . ⇒ ( 75 x 480 ) / 100 = 15 a ∴ a = ( 75 x 480 ) / ( 100 x 15 ) = 24 correct option : d"
Answer: d
Python program:
a = 15 * 480
b = a / 100
c = b * 75
d = c / 100
Problem: if a truck is traveling at a constant rate of 54 kilometers per hour , how many seconds will it take the truck to travel a distance of 600 meters ? ( 1 kilometer = 1000 meters )
Options: a ) 18 , b ) 24 , c ) 30 , d ) 36 , e ) 40
Rationale: "speed = 54 km / hr = > 54,000 m / hr in one minute = > 54000 / 60 = 900 meters in one sec = > 900 / 60 = 15 meters time = total distance need to be covered / avg . speed = > 600 / 15 = 40 and hence the answer : e"
Answer: e
Python program:
a = 600 / 1000
b = a / 54
c = b * 3600
Problem: what number times ( 1 ⁄ 7 ) ^ 2 will give the value of 7 ^ 3 ?
Options: a ) 7 , b ) 49 , c ) 343 , d ) 2401 , e ) 16,807
Rationale: "x * ( 1 / 7 ) ^ 2 = 7 ^ 3 x = 7 ^ 2 * 7 ^ 3 = 7 ^ 5 = 16,807 the answer is e ."
Answer: e
Python program:
a = 7 ** 7
b = 7 ** 3
c = a * b
Problem: the ratio 2 : 10 expressed as percent equals to
Options: a ) 50 % , b ) 30 % , c ) 25 % , d ) 20 % , e ) 90 %
Rationale: "explanation : actually it means 2 is what percent of 10 , which can be calculated as , ( 2 / 10 ) * 100 = 2 * 10 = 20 answer : option d"
Answer: d
Python program:
a = 2 / 10
b = a * 100
Problem: a watch was sold at a loss of 21 % . if it was sold for rs . 140 more , there would have been a gain of 4 % . what is the cost price ?
Options: a ) 560 , b ) 882 , c ) 799 , d ) 778 , e ) 901
Rationale: "79 % 104 % - - - - - - - - 25 % - - - - 140 100 % - - - - ? = > rs . 560 answer : a"
Answer: a
Python program:
a = 140 * 100
b = 100 + 4 
c = 100 - 21
d = b - c
e = a / d
Problem: at a certain restaurant , the ratio of the number of cooks to the number of waiters is 3 to 8 . when 12 more waiters are hired , the ratio of the number of cooks to the number of waiters changes to 1 to 4 . how many cooks does the restaurant have ?
Options: a ) 4 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: originally there were 3 k cooks and 8 k waiters . the new ratio is 1 : 4 which equals 3 : 12 . 12 k = 8 k + 12 k = 3 there are 9 cooks . the answer is c .
Answer: c
Python program:
a = 12 / 4
b = 12 / 4
c = a * b
Problem: a bag contains 5 green balls and 8 white balls . if two balls are drawn simultaneously , what is the probability that both balls are the same colour ?
Options: a ) 3 / 7 , b ) 6 / 11 , c ) 12 / 21 , d ) 19 / 39 , e ) 29 / 49
Rationale: "the total number of ways to draw two balls is 13 c 2 = 78 the number of ways to draw two green balls is 5 c 2 = 10 the number of ways to draw two white balls is 8 c 2 = 28 p ( two balls of the same colour ) = 38 / 78 = 19 / 39 the answer is d ."
Answer: d
Python program:
a = 5 + 8 
b = 8 / a
c = 8 - 1
d = 5 + 8 
e = d - 1
f = c / e
g = b * f
h = 5 - 1
i = 5 + 8 
j = i - 1
k = h / j
l = 5 + 8 
m = 5 / l
n = k * m
o = g + n
Problem: if 60 % of 3 / 5 of a number is 36 , then the number is ?
Options: a ) 80 , b ) 100 , c ) 75 , d ) 90 , e ) none of these
Rationale: "let the number be x . then 60 % of 3 / 5 of x = 36 60 / 100 * 3 / 5 * x = 36 x = ( 36 * 25 / 9 ) = 100 required number = 100 . correct option : b"
Answer: b
Python program:
a = 60 / 100
b = 3 / 5
c = a * b
d = 36 / c