euclaise/mathqa_programs huggingface dataset:
Problem: in a simultaneous throw of a pair of dice , find the probability of getting a total more than 10
Options: a ) 5 / 13 , b ) 2 / 15 , c ) 1 / 12 , d ) 3 / 17 , e ) 6 / 19
Rationale: "total number of cases = 6 * 6 = 36 favourable cases = [ ( 5,6 ) ( 6,5 ) , ( 6,6 ) ] = 3 so probability = 3 / 36 = 1 / 12 answer is c"
Answer: c
Python program:
a = 2 * 3
b = 10 - a
c = b / 10
Problem: when a student joe , weighing 42 kg , joins a group of students whose average weight is 30 kg , the average weight goes up by 1 kg . subsequently , if two students , excluding joe , leave the group the average weight comes back to 30 kg . what is the difference between the average weight of the two students who left and the weight of joe ?
Options: a ) 5.5 kg , b ) 6 kg , c ) 30 kg , d ) 36.5 kg , e ) 71 kg
Rationale: after two persons leave the group the average remains the same . that means the weight of the two persons = 42 + 30 = 72 so , the average the two persons = 36 that gives the answer 42 - 36 = 6 answer b
Answer: b
Python program:
a = 30 + 1 
b = 42 - a
c = 30 * b
d = c + 42 
e = 30 + 1 
f = 42 - e
g = f - 1
h = g * 30
i = d - h
j = i / 2
k = 42 - j
Problem: the sum of two numbers is 44 . 5 times one number is equal to 6 times the other . the smaller of the two numbers is
Options: a ) 10 , b ) 12 , c ) 16 , d ) 22 , e ) 20
Rationale: sol . let the numbers be x and ( 44 - x ) . then , 5 x = 6 ( 44 - x ) ⇔ 11 x = 264 ⇔ x = 24 . so , the numbers are 24 and 20 . answer e
Answer: e
Python program:
a = 5 + 6 
b = 44 / a
c = b * 5
Problem: youseff lives x blocks from his office . it takes him 1 minute per block to walk to work and 20 seconds per block to ride his bike to work . it is takes him exactly 4 minutes more to walk to work than to ride his bike to work , then x equals ?
Options: a ) 4 , b ) 6 , c ) 10 , d ) 15 , e ) 20
Rationale: "please follow posting guidelines , link is in my signatures . as for your question , x / 60 = blocks / time / block = block ^ 2 / time . this is not what you want . you are given x blocks and 60 seconds per block . thus you need to put it as 60 * x to give you units of seconds as you are equating this to 240 ( which is time in seconds . ) . thus the correct equation is : 60 * x - 20 * x = 240 - - - - > 40 x = 240 - - > x = 6 option b"
Answer: b
Python program:
a = 4 * 3
b = a / 2
Problem: a take twice as much time as b or thrice as much time to finish a piece of work . working together , they can finish the work in 5 days . b can do the work alone in ?
Options: a ) 19 , b ) 12 , c ) 11 , d ) 30 , e ) 114
Rationale: suppose a , b and c take x , x / 2 and x / 3 respectively to finish the work . then , ( 1 / x + 2 / x + 3 / x ) = 1 / 5 6 / x = 1 / 5 = > x = 30 so , b takes 15 hours to finish the work . answer : d
Answer: d
Python program:
a = 1 + 2 
b = a + 3 
c = b * 5
Problem: the mass of 1 cubic meter of a substance is 200 kg under certain conditions . what is the volume in cubic centimeters of 1 gram of this substance under these conditions ? ( 1 kg = 1,000 grams and 1 cubic meter = 1 , 000,000 cubic centimeters )
Options: a ) 1
b ) 2
c ) 3
d ) 4
e ) 5
Rationale: 200 kg - 1 cubic meter ; 200,000 g - 1 cubic meter ; 200,000 g - 1 , 000,000 cubic centimeters ; 1 g - 1 , 000,000 / 200,000 = 10 / 2 = 5 cubic centimeters . answer : e .
Answer: e
Python program:
a = 1000 * 1000
b = 200 * 1000
c = a / b
Problem: a rectangular field is to be fenced on three sides leaving a side of 8 feet uncovered . if the area of the field is 680 sq . ft , how many feet of fencing will be required ?
Options: a ) 244 ft , b ) 88 ft , c ) 122 ft , d ) 178 ft , e ) 66 ft
Rationale: "given that length and area , so we can find the breadth . length x breadth = area 8 x breadth = 680 breadth = 85 feet area to be fenced = 2 b + l = 2 ( 85 ) + 8 = 178 feet answer : d ) 178 ft"
Answer: d
Python program:
a = 680 / 8
b = a * 2
c = b + 8
Problem: a train 400 m in length crosses a telegraph post in 16 seconds . the speed of the train is ?
Options: a ) 22 kmph , b ) 77 kmph , c ) 54 kmph , d ) 71 kmph , e ) 90 kmph
Rationale: "s = 400 / 16 * 18 / 5 = 90 kmph answer : e"
Answer: e
Python program:
a = 400 / 16
b = const_3_6 * a
Problem: ravi can do a piece of work in 50 days while prakash can do it in 75 days . in how many days will they finish it together ?
Options: a ) 30 days , b ) 35 days , c ) 25 days , d ) 27 days , e ) 29 days
Rationale: 1 / 50 + 1 / 75 = 5 / 150 30 / 1 = 30 days answer : a
Answer: a
Python program:
a = 1/(50)
b = 1/(75)
c = a + b 
d = 1 / c
Problem: the marks obtained by polly and sandy are in the ratio 3 : 5 and those obtained by sandy and willy are in the ratio of 5 : 2 . the marks obtained by polly and willy are in the ratio of . . . ?
Options: a ) 2 : 1 , b ) 3 : 2 , c ) 4 : 3 , d ) 5 : 4 , e ) 6 : 5
Rationale: "polly : sandy = 3 : 5 sandy : willy = 5 : 2 polly : sandy : willy = 3 : 5 : 2 polly : willy = 3 : 2 the answer is b ."
Answer: b
Python program:
a = 3 * 5
b = 5 * 2
c = a / b
Problem: add 10 % of 30 and 15 % of 50 .
Options: a ) 9.5 , b ) 10.5 , c ) 11.5 , d ) 12 , e ) 15
Rationale: "10 % of 30 + 15 % of 50 30 * 10 / 100 + 50 * 15 / 100 3 + 7.5 = 10.5 answer b"
Answer: b
Python program:
a = 10 * 30
b = a / 100
c = 15 * 50
d = c / 100
e = b + d
Problem: smita was making a cube with dimensions 5 * 5 * 5 using 1 * 1 * 1 cubes . what is the number of cubes needed to make a hollow cube looking of the same shape ?
Options: a ) 98
b ) 104
c ) 100
d ) 61
e ) 51
Rationale: cube use to make perfect 5 * 5 * 5 = 125 no need of cube to make hollow = ( 5 - 2 ) * ( 5 - 2 ) * ( 5 - 2 ) = 27 so total cube need to make hollow cube is = 125 - 27 = 98 answer : a
Answer: a
Python program:
a = volume_cube - (
Problem: the average of temperatures at noontime from monday to friday is 50 ; the lowest one is 40 , what is the possible maximum range of the temperatures ?
Options: a ) 20 , b ) 25 , c ) 40 , d ) 50 , e ) 75
Rationale: "there are 5 days so the sum of temperature can be 50 * 5 = 250 lowest is 40 . to find the maximum range we can say the temperature was the lowest for 4 of the 5 days so 4 * 40 = 160 . on the fifth day it is 250 - 160 = 90 range is therefore 90 - 40 = 50 answer d"
Answer: d
Python program:
a = 2 + 3 
b = 50 * a
c = 40 * 4
d = b - c
e = d - 40
Problem: a sun is divided among x , y and z in such a way that for each rupee x gets , y gets 45 paisa and z gets 30 paisa . if the share of y is rs . 36 , what is the total amount ?
Options: a ) 166 , b ) 140 , c ) 178 , d ) 177 , e ) 169
Rationale: "x : y : z = 100 : 45 : 30 20 : 9 : 6 9 - - - 36 35 - - - ? = > 140 answer : b"
Answer: b
Python program:
a = 100 / 45
b = a * 36
c = 30 / 45
d = c * 36
e = b + d 
f = e + 36
Problem: a retailer sold 2 houses at each $ 10000 . on 1 st house he got 30 % profit and on 2 nd house he loss 10 % then find his net profit or loss ?
Options: a ) 15 % , b ) 17 % , c ) 21 % , d ) 19 % , e ) 25 %
Rationale: a = 30 % b = - 10 % profit % = 30 - 10 + ( - 300 / 100 ) = 17 % answer is b
Answer: b
Python program:
a = 10 / 100
b = 1 - a
c = b * 2
d = 10 / 100
e = c - d
f = e * 10
Problem: the remainder when e = 1 + 3 + 3 ^ 2 + 3 ^ 3 + . . . . . . . . . . + 3 ^ 200 is divided 13 .
Options: a ) 12 , b ) 7 , c ) 0 , d ) 5 , e ) 3
Rationale: e = 1 + 3 + 3 ^ 2 + 3 ^ 3 + . . . . . . . . . . . . . . . . . . + 3 ^ 200 is a geometric progression having common ratio as ' 3 ' and number of terms as ' 201 ' . since sum to n terms in gp = a ( r ^ n - 1 ) / ( r - 1 ) where a = first term and r = common ration hence , 1 * ( 3 ^ 201 - 1 ) / ( 3 - 1 ) rem of ( 3 ^ 201 - 1 ) / 2 divided by 13 3 ^ 201 - 1 / 26 wkt , 3 ^ 3 = 27 = 26 + 1 { ( 26 + 1 ) ^ 67 - 1 } / 26 { 1 - 1 } / 26 = > 0 . c
Answer: c
Python program:
a = 200 + 1 
b = a / 3
c = reminder + ( 
d = c + reminder 
e = b * d
Problem: today joelle opened an interest - bearing savings account and deposited $ 6000 . if the annual interest rate is 5 percent compounded interest , and she neither deposits nor withdraws money for exactly 2 years , how much money will she have in the account ?
Options: a ) $ 6715 , b ) $ 5615 , c ) $ 6415 , d ) $ 6615 , e ) $ 6315
Rationale: interest for 1 st year = 6000 * 5 / 100 = 300 interest for 2 nd year = 6300 * 5 / 100 = 315 total = 6000 + 300 + 315 = 6615 answer : d
Answer: d
Python program:
a = 5 / 100
b = 1 + a 
c = b ** 2
d = 6000 * c
Problem: a boat can travel with a speed of 24 km / hr in still water . if the speed of the stream is 4 km / hr , find the time taken by the boat to go 196 km downstream
Options: a ) 3 hours , b ) 4 hours , c ) 5 hours , d ) 6 hours , e ) 7 hours
Rationale: "explanation : speed of the boat in still water = 24 km / hr speed of the stream = 4 km / hr speed downstream = ( 22 + 5 ) = 28 km / hr distance travelled downstream = 196 km time taken = distance / speed = 196 / 28 = 7 hours answer : option e"
Answer: e
Python program:
a = 24 + 4 
b = 196 / a
Problem: a train 900 m long is running at a speed of 78 km / hr . if it crosses a tunnel in 1 min , then the length of the tunnel is ?
Options: a ) 200 m , b ) 379 m , c ) 400 m , d ) 589 m , e ) 600 m
Rationale: "speed = 78 * 5 / 18 = 65 / 3 m / sec . time = 1 min = 60 sec . let the length of the train be x meters . then , ( 900 + x ) / 60 = 65 / 3 x = 400 m . answer : c"
Answer: c
Python program:
a = 78 - 1
b = a * const_0_2778
c = 900 / b
Problem: jayant opened a shop investing rs . 30,000 . madhu joined him 2 months later , investing rs . 45,000 . they earned a profit of rs . 54,000 after completion of one year . what will be madhu ' s share of profit ?
Options: a ) rs . 27,000 , b ) rs . 24,000 , c ) rs . 30,000 , d ) rs . 36,000 , e ) none of these
Rationale: "30,000 * 12 = 45,000 * 8 1 : 1 madhu ' s share = 1 / 2 * 54,000 i . e . rs . 27,000 answer : a"
Answer: a
Python program:
a = 4 * 2
b = 2 + 3 
c = b * 2
d = a * c
e = d * 100
f = 2 + 3 
g = f * 100
h = g * 100
i = e + h 
j = 2 + 3 
k = j * 2
l = k / 2
m = 4 * 3
n = l / m
o = i * n
Problem: 600 men have provisions for 20 days . if 200 more men join them , for how many days will the provisions last now ?
Options: a ) 15 , b ) 11 , c ) 10 , d ) 8 , e ) 7
Rationale: "600 * 20 = 800 * x x = 15 . answer : a"
Answer: a
Python program:
a = 20 * 600
b = 600 + 200 
c = a / b
Problem: the hcf of two numbers is 52 and the other two factors of their lcm are 11 and 12 . what is the largest number .
Options: a ) 624 , b ) 450 , c ) 480 , d ) 504 , e ) 555
Rationale: "explanation : hcf of the two numbers = 52 hcf will be always a factor of lcm 52 is factor of lcm other two factors are 11 & 12 then the numbers are ( 52 * 11 ) and ( 52 x 12 ) = 572 and 624 answer : option a"
Answer: a
Python program:
a = 52 * 12
Problem: a whale goes on a feeding frenzy that lasts for 9 hours . for the first hour he catches and eats x kilos of plankton . in every hour after the first , it consumes 3 kilos of plankton more than it consumed in the previous hour . if by the end of the frenzy the whale will have consumed a whopping accumulated total 270 kilos of plankton , how many kilos did he consume on the sixth hour ?
Options: a ) 33 , b ) 47 , c ) 50 , d ) 53 , e ) 62
Rationale: "if you list the amount eaten each hour , you ' ll get an equally spaced list , increasing by 3 each hour . in any equally spaced list , the median equals the mean . here , the mean is 270 / 9 = 30 , so the median is also 30 , and that is the amount eaten in the 5 th hour . we need to add 3 to find the total eaten in the next hour , so the answer is 33 . option a"
Answer: a
Python program:
a = 270 / 9
b = a + 3
Problem: in a garment industry , 12 men working 8 hours per day complete a piece of work in 10 days . to complete the same work in 8 days , working 5 hours a day , the number of men required is :
Options: a ) 24 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: "explanation : let the required number of men be x . less days , more men ( indirect proportion ) more working hrs per day , less men ( indirect proportion ) days 8 : 10 working hrs 5 : 8 : : 12 : x = > 8 x 5 x x = 10 x 8 x 12 = > x = 10 x 8 x 12 / ( 8 x 5 ) = > x = 24 answer : a"
Answer: a
Python program:
a = 12 * 8
b = a * 10
c = b / 5
d = c / 8
Problem: if the radii of umbra and penumbra cast by an object on a wall are of the ratio 2 : 6 , what is the area of the penumbra ring around the umbra of the latter ’ s radius is 40 cms ?
Options: a ) 40288.57 cm ^ 2
b ) 40388.57 cm ^ 2
c ) 40488.57 cm ^ 2
d ) 40588.57 cm ^ 2
e ) 40688.57 cm ^ 2
Rationale: et the radius of umbra and penumbra are 2 k and 6 k . then as given radius of umbra = 40 cm so 2 k = 40 k = 20 radius of penumbra = 20 * 6 = 120 area of penumbra ring around the umbra = area of penumbra - area of umbra 22 / 7 * [ ( 120 ) ^ 2 - ( 40 ) ^ 2 ] = 40288.57 cm ^ 2 answer : a
Answer: a
Python program:
a = 6 * 40
b = 6 * 40
c = a * b
d = math.pi * c
e = 40 * 2
f = 40 * 2
g = e * f
h = math.pi * g
i = d - h
j = i / 2
k = j / 2
Problem: if in a box of dimensions 6 m * 5 m * 4 m smaller boxes of dimensions 60 cm * 50 cm * 40 cm are kept in it , then what will be the maximum number of the small boxes that can be kept in it ?
Options: a ) 1098 , b ) 1000 , c ) 1628 , d ) 1098 , e ) 1094
Rationale: 6 * 5 * 4 = 60 / 100 * 50 / 100 * 40 / 100 * x 1 = 1 / 10 * 1 / 10 * 1 / 10 * x = > x = 1000 answer : b
Answer: b
Python program:
a = 6 * 5
b = a * 4
c = 60 / 100
d = 50 / 100
e = c * d
f = 40 / 100
g = e * f
h = b / g
Problem: the area of a square field is 64816 sq m . how long will a lady take to cross the field diagonally at the rate of 7.2 km / hr ?
Options: a ) 2 min , b ) 4 min , c ) 5 min , d ) 3 min , e ) 3.5 min
Rationale: "area of a square field = 64816 sq m let the side of square = a a ^ 2 = 64816 = > a = 254.59 diagonal = ( 2 ) ^ ( 1 / 2 ) * a = 1.414 * 254.59 = 360 speed of lady = 7.2 km / hour = 7200 m / hour = 120 m / min time taken by lady to cross the field diagonally = 360 / 120 = 3 min answer d"
Answer: d
Python program:
a = 7 * 2
b = 64816 / a
Problem: the ratio 15 : 25 expressed as percent equals to
Options: a ) 70 % , b ) 60 % , c ) 30 % , d ) 75 % , e ) none of above
Rationale: "explanation : actually it means 15 is what percent of 25 , which can be calculated as , ( 15 / 25 ) * 100 = 15 * 4 = 60 answer : option b"
Answer: b
Python program:
a = 15 / 25
b = a * 100
Problem: the ratio between the number of sheep and the number of horses at the stewar farm is 2 to 7 . if each of horse is fed 230 ounces of horse food per day and the farm needs a total 12880 ounces of horse food per day . what is number sheep in the form ? ?
Options: a ) 18 , b ) 16 , c ) 32 , d ) 56 , e ) 58
Rationale: "et no of sheep and horses are 2 k and 7 k no of horses = 12880 / 230 = 56 now 7 k = 56 and k = 8 no of sheep = ( 2 * 8 ) = 16 answer : b"
Answer: b
Python program:
a = 12880 / 230
b = a / 7
c = b * 2
Problem: the ratio of the arithmetic mean of two numbers to one of the numbers is 4 : 6 . what is the ratio of the smaller number to the larger number ?
Options: a ) 1 : 5 , b ) 1 : 4 , c ) 1 : 3 , d ) 1 : 2 , e ) 2 : 3
Rationale: for two numbers , the arithmetic mean is the middle of the two numbers . the ratio of the mean to the larger number is 4 : 6 , thus the smaller number must have a ratio of 2 . the ratio of the smaller number to the larger number is 2 : 6 = 1 : 3 . the answer is c .
Answer: c
Python program:
a = 4 / 6
b = 1 / 2
c = a - b
d = c * 2
Problem: the speed of a boat in still water in 22 km / hr and the rate of current is 4 km / hr . the distance travelled downstream in 24 minutes is :
Options: a ) 10.6 , b ) 10.2 , c ) 10.8 , d ) 10.4 , e ) 10.0
Rationale: "speed downstream = ( 22 + 4 ) = 26 kmph time = 24 minutes = 24 / 60 hour = 2 / 5 hour distance travelled = time × speed = 2 / 5 × 26 = 10.4 km answer is d ."
Answer: d
Python program:
a = 22 + 4 
b = 24 / const_60
c = a * b
Problem: the present ratio of students to teachers at a certain school is 45 to 1 . if the student enrollment were to increase by 50 students and the number of teachers were to increase by 5 , the ratio of students to teachers would then be 25 to 1 . what is the present number of teachers ?
Options: a ) 4 , b ) 8 , c ) 10 , d ) 12 , e ) 15
Rationale: "we are given that the ratio of students to teacher is 45 to 1 . we can rewrite this using variable multipliers . students : teachers = 45 x : x we are next given that student enrollment increases by 50 and the number of teachers increases by 5 . with this change the new ratio becomes 25 to 1 . we can put all this into an equation : students / teachers  25 / 1 = ( 45 x + 50 ) / ( x + 5 ) if we cross multiply we have : 25 ( x + 5 ) = 45 x + 50 25 x + 125 = 45 x + 50 3.75 = x x ~ 4 since x is the present number of teachers , currently there are 4 teachers . answer a ."
Answer: a
Python program:
a = 45 + 25 
b = a / 25
Problem: the number of stamps that kaye and alberto had were in the ration of 5 : 3 respectively . after kaye gave alberto 10 of her stamps , the ration of the number of kaye had to the number of alberto had was 3 : 2 . as a result of the gift , kaye had how many more stamps than alberto ?
Options: a ) 20 , b ) 30 , c ) 40 , d ) 60 , e ) 80
Rationale: "c k 1 = 5 x a 1 = 3 x k 2 = 5 x - 10 a 2 = 3 x + 10 k 2 / a 2 = 3 / 2 ( 5 x - 10 ) / ( 3 x + 10 ) = 3 / 2 2 * ( 5 x - 10 ) = 3 * ( 3 x + 10 ) 10 x - 20 = 9 x + 30 x = 50 k 2 = 5 * 50 - 10 = 240 a 2 = 3 * 50 + 10 = 160 k 2 - a 2 = 80 answer : e"
Answer: e
Python program:
a = 5 + 3 
b = 3 + 2 
c = math.lcm(a, b)
d = 3 + 2 
e = c / d
f = 3 * e
Problem: a certain bacteria colony doubles in size every day for 16 days , at which point it reaches the limit of its habitat and can no longer grow . if two bacteria colonies start growing simultaneously , how many days will it take them to reach the habitat ’ s limit ?
Options: a ) 6.33 , b ) 7.5 , c ) 10 , d ) 15 , e ) 19
Rationale: if there is one bacteria colony , then it will reach the limit of its habitat in 16 days . if there are two bacteria colonies , then in order to reach the limit of habitat they would need to double one time less than in case with one colony . thus colonies need to double 15 times . answer : d . similar questions to practice : hope it helps .
Answer: d
Python program:
a = 16 / 16
b = 16 - a
Problem: find the area of the quadrilateral of one of its diagonals is 15 cm and its off sets 6 cm and 4 cm ?
Options: a ) 50 cm 2 , b ) 60 cm 2 , c ) 75 cm 2 , d ) 90 cm 2 , e ) 150 cm 2
Rationale: "1 / 2 * 15 ( 6 + 4 ) = 75 cm 2 answer : c"
Answer: c
Python program:
a = 1 / 2
b = 4 + 6 
c = a * b
d = c * 15
Problem: the average of 10 numbers is 23 . if each number is increased by 1 , what will the new average be ?
Options: a ) 36 , b ) 24 , c ) 72 , d ) 29 , e ) 22
Rationale: "sum of the 10 numbers = 230 if each number is increased by 1 , the total increase = 1 * 10 = 10 the new sum = 230 + 10 = 240 the new average = 240 / 10 = 24 . answer : b"
Answer: b
Python program:
a = 23 * 1
Problem: sakshi can do a piece of work in 15 days . tanya is 25 % more efficient than sakshi . the number of days taken by tanya to do the same piece of work :
Options: a ) 15 , b ) 16 , c ) 18 , d ) 12 , e ) 10
Rationale: "solution ratio of times taken by sakshi and tanya = 125 : 100 = 5 : 4 . suppose tanya taken x days to do the work . 5 : 4 : : 15 : x ⇒ x = ( 15 x 4 / 5 ) ⇒ x = 12 days . hence , tanya takes 16 days is complete the work . answer d"
Answer: d
Python program:
a = 25 / 100
b = 1 + a 
c = 15 / b
Problem: an electric pump can fill a tank in 5 hours . because of a leak in the tank , it took 10 hours to fill the tank . if the tank is full , how much time will the leak take to empty it ?
Options: a ) 10 hours , b ) 12 hours , c ) 8 hours , d ) 5 hours , e ) 15 hours
Rationale: "work done by the leak in 1 hour = 1 / 5 - 1 / 10 = 1 / 10 the leak will empty the tank in 10 hours answer is a"
Answer: a
Python program:
a = 10 / 1
Problem: 4 , 6 , 12 , 14 , 28 , 30 , . . ?
Options: a ) 20 , b ) 40 , c ) no = 60 , d ) 80 , e ) 100
Rationale: "c 60 the given sequence is a combination of two series 4 , 12 , 28 , . . . . and 6 , 14 , 30 , . . . . the pattern is + 8 , + 16 , + 32 . so , the missing number = ( 28 + 32 ) = 60"
Answer: c
Python program:
a = negate - (
Problem: a cubical block of metal weighs 6 pounds . how much will another cube of the same metal weigh if its sides are twice as long ?
Options: a ) 48 , b ) 99 , c ) 266 , d ) 28 , e ) 17
Rationale: "explanation : if you double the sides of a cube , the ratio of the surface areas of the old and new cubes will be 1 : 4 . the ratio of the volumes of the old and new cubes will be 1 : 8 . weight is proportional to volume . so , if the first weighs 6 pounds , the second weighs 6 x 8 pounds = 48 . answer : a ) 48"
Answer: a
Python program:
a = 2 * 4
b = 6 * a
Problem: working together at their respective constant rates , machine a and machine b can produce 1,600 units in 8 hours . working alone , machine b would complete that same output in 50 % more time . if machine a were to work on its own for an 8 - hour shift , what percent of the 1,600 unit total would it produce ?
Options: a ) 25 , b ) 33 , c ) 50 , d ) 67 , e ) 75
Rationale: 1 / a + 1 / b = 1 / t 1 / a + 1 / 12 = 1 / 8 ( 50 % more of 8 is 12 ) 1 / a = 1 / 24 machine a can produce 1600 units in 24 hrs , so it can produce 1600 * 8 / 24 = 533.33 units is 8 hrs . 533.33 is 33.33 % of 1600 . b is the answer
Answer: b
Python program:
a = 4 * 4
b = a * 100
c = b / 8
d = 4 * 4
e = d * 100
f = 8 * 50
g = f / 100
h = 8 + g 
i = e / h
j = c - i
k = j * 8
l = 4 * 4
m = l * 100
n = k / m
o = n * 100
Problem: find the value for x from below equation : x / 3 = - 4 ?
Options: a ) - 12 , b ) 1 , c ) - 2 , d ) - 3 , e ) 4
Rationale: "1 . multiply both sides by 3 : x * 3 / 3 = - 4 / 3 . simplify both sides : x = - 12 a"
Answer: a
Python program:
a = 4 - 4
b = a * 3
Problem: a sum of money is sufficient to pay x ' s wages for 36 days and y ' s wages for 45 days . the same money is sufficient to pay the wages of both for ?
Options: a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 20
Rationale: let the total money be $ x x ' s 1 day work = $ x / 36 y ' s 1 day work = $ x / 45 x + y 1 day work = $ x / 20 money is sufficient to pay the wages of both for 20 days answer is e
Answer: e
Python program:
a = 1 / 36
b = 1 / 45
c = a + b 
d = 1/(c)
Problem: length of a rectangular plot is 16 mtr more than its breadth . if the cost of fencing the plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ?
Options: a ) 58 m , b ) 60 m , c ) 80 m , d ) 82 m , e ) 84 m
Rationale: "let breadth = x metres . then , length = ( x + 16 ) metres . perimeter = 5300 m = 200 m . 26.50 2 [ ( x + 16 ) + x ] = 200 2 x + 16 = 100 2 x = 84 x = 42 . hence , length = x + 16 = 58 m a"
Answer: a
Python program:
a = 5300 / 26
b = 2 * 16
c = a + b 
d = c / 4
Problem: at what price must an article costing rs . 75 be marked in order that after deducting 5 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 62.5 , b ) 62.0 , c ) 62.6 , d ) 62.1 , e ) 98.68
Rationale: "cp = 75 sp = 75 * ( 125 / 100 ) = 93.75 mp * ( 95 / 100 ) = 93.75 mp = 98.68 answer : e"
Answer: e
Python program:
a = 75 * 25
b = a / 100
c = 75 + b 
d = c * 100
e = 100 - 5
f = d / e
Problem: two stations a and b are 155 km apart on a straight line . one train starts from a at 7 a . m . and travels towards b at 20 kmph . another train starts from b at 8 a . m . and travels towards a at a speed of 25 kmph . at what time will they meet ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 8
Rationale: "suppose they meet x hours after 7 a . m . distance covered by a in x hours = 20 x km . distance covered by b in ( x - 1 ) hours = 25 ( x - 1 ) km . therefore 20 x + 25 ( x - 1 ) = 155 45 x = 180 x = 4 . so , they meet at 11 a . m . answer : option c"
Answer: c
Python program:
a = 155 - 20
b = 25 + 20 
c = a / b
d = 8 + c