euclaise/mathqa_programs huggingface dataset:
Problem: the length of a rectangular field is 7 / 5 its width . if the perimeter of the field is 240 meters , what is the width of the field ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "let l be the length and w be the width . l = ( 7 / 5 ) w perimeter : 2 l + 2 w = 240 , 2 ( 7 / 5 ) w + 2 w = 240 solve the above equation to find : w = 50 m and l = 70 m . correct answer a ) 50"
Answer: a
Python program:
a = 7 / 5
b = 7 / 5
c = a + b 
d = c + 2 
e = 240 / d
Problem: the sum of the present ages of two persons a and b is 60 . if the age of a is twice that of b , find the sum of their ages 10 years hence ?
Options: a ) 58 , b ) 59 , c ) 62 , d ) 70 , e ) 80
Rationale: "explanation : a + b = 60 , a = 2 b 2 b + b = 60 = > b = 20 then a = 40 . 10 years , their ages will be 50 and 30 . sum of their ages = 50 + 30 = 80 . e )"
Answer: e
Python program:
a = 60 / 10
b = a * 2
c = b + 10 
d = 60 / 10
e = d + 10 
f = c + e
Problem: at a certain committee meeting only associate professors and assistant professors are present . each associate professor has brought 2 pencils and 1 chart to the meeting , while each assistant professor has brought 1 pencil and 2 charts . if a total of 10 pencils and 8 charts have been brought to the meeting , how many people are present ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "say there are ' a ' associate professors . so we have 2 a pencils and a charts . say there are ' b ' assistant professors . so we have b pencils and 2 b charts . total pencils are 10 so 2 a + b = 10 total charts are 11 so a + 2 b = 8 add both : 3 a + 3 b = 18 so a + b = 6 total number of people = 6 a"
Answer: a
Python program:
a = 8 + 10 
b = 2 + 1 
c = a / b
Problem: it is the new year and mandy has made a resolution to lose weight this year . she plans to exercise and do yoga . for exercise she plans to workout at the gym and ride her bicycle in the ratio of 2 : 3 everyday . she will also do yoga in the ratio , yoga : exercise = 2 : 3 . if she rides her bike for 14 minutes , how much time will she spend doing yoga ? ( rounded to minutes )
Options: a ) 10 min . , b ) 41 min . , c ) 17 min . , d ) 23 min . , e ) 25 min .
Rationale: "the ratio is 2 : 3 = gym : ride , so ( 14 ) ( 3 / 2 ) = 21 minutes at the gym , and 21 + 14 = 35 minutes exercise , so ( 2 / 3 ) ( 35 ) = 23 minutes yoga . answer : d"
Answer: d
Python program:
a = 2 + 3 
b = 3 / a
c = 14 * b
d = 2 + 3 
e = 3 / d
f = 2 + 3 
g = 3 / f
h = e * g
i = c / h
Problem: jim â € ™ s taxi service charges an initial fee of $ 2.25 at the beginning of a trip and an additional charge of $ 0.4 for each 2 / 5 of a mile traveled . what is the total charge for a trip of 3.6 miles ?
Options: a ) $ 3.15 , b ) $ 4.45 , c ) $ 4.80 , d ) $ 5.05 , e ) $ 5.85
Rationale: "let the fixed charge of jim â € ™ s taxi service = 2.25 $ and charge per 2 / 5 mile ( . 4 mile ) = . 4 $ total charge for a trip of 3.6 miles = 2.25 + ( 3.6 / . 4 ) * . 4 = 2.25 + 9 * . 4 = 5.85 $ answer e"
Answer: e
Python program:
a = 2 / 5
b = 3 / 6
c = b * 0
d = c + 2
Problem: in a market , a dozen eggs cost as much as a pound of rice , and a half - liter of kerosene costs as much as 8 eggs . if the cost of each pound of rice is $ 0.33 , then how many w cents does a liter of kerosene cost ? [ one dollar has 100 cents . ]
Options: a ) 0.33 , b ) 0.44 , c ) 0.55 , d ) 44 , e ) 55
Rationale: "main thing to remember is answer is asked in cents , however when we calculate , it comes up as 0.44 $ just multiply by 100 , answer w = 44 . d"
Answer: d
Python program:
a = 1 / 2
b = 8 / a
c = b / 12
d = 0 * 33
e = c * d
Problem: a train requires 5 seconds to pass a pole while it requires 25 seconds to cross a stationary train which is 360 mtrs long . find the speed of the train .
Options: a ) 66.8 kmph , b ) 65.8 kmph , c ) 54.8 kmph , d ) 64.8 kmph , e ) 44.8 kmph
Rationale: "in 5 s the train crosses the pole and in 25 sec the train crosses one more stationary train in 20 sec the train travels a distance of 360 mtrs speed = 360 / 20 = 18 m / s = 18 ( 3600 / 1000 ) = 18 * 18 / 5 = 64.8 kmph answer : d"
Answer: d
Python program:
a = 25 - 5
b = 360 / a
c = b * const_3_6
Problem: a two digit number is 18 less than the square of the sum of its digits . how many such numbers are there ?
Options: a ) 2233 , b ) 2222 , c ) 2211 , d ) 6382 , e ) 23,17
Rationale: option 2 take n = 10 a + b . given that , ( 10 a + b ) + 18 = k 2 = ( a + b ) 2 given number = k 2 - 18 = ( 10 a + b ) that means , when we add 18 to the given number it should be a perfect square . so k 2 takes the following values . 1 , 4 , 9 , 16 , 25 , 36 , 49 , 64 , 81 , 100 , 121 , . . . . 1 to 16 are ruled out as if we subtract 18 from them , the resulting number is a single digit number . now 25 - 18 = 7 36 - 18 = 18 49 - 18 = 31 64 - 18 = 46 81 - 18 = 63 100 - 18 = 82 121 - 18 = 103 now 63 , 82 satisfies . answer : d
Answer: d
Python program:
a = 100 / 2
b = a * 10
c = 18 ** 3
d = b + c
Problem: what is the average ( arithmetic mean ) of 10 , 20,30 , 40,50 , 60,70 , 80,90 ?
Options: a ) 90 , b ) 95 , c ) 70 , d ) 85 , e ) 50
Rationale: "so addition of all term - 10 , 20 , 30 , . . . . . . . 90 so average = ( 10 + 20 + 30 + 40 + 50 + 60 + 70 + 80 + 90 ) / 9 = ( 450 ) / 9 = 50 hence , the correct answer is e ."
Answer: e
Python program:
a = 10 + 40 
b = 40 - 50
c = b / 20
d = c + 1 
e = a * d
f = e / 2
g = 40 - 50
h = g / 10
i = h + 1 
j = f / i
Problem: if the average of 6 x and 8 y is greater than 100 , and x is twice y , what is the least integer value of x ?
Options: a ) 22 , b ) 20 , c ) 21 , d ) 23 , e ) 24
Rationale: "substitution can be used in the following way : always start with the equation : x = 2 y . it is more straight forward to manage as compared to the inequality . substitute y = x / 2 , not the other way because you need to find the minimum value of x . so you can get rid of y . now go on to the inequality . so 8 y = 8 x / 2 = 4 x now average of 6 x and 4 x is greater than 100 . average of 6 x and 4 x is 5 x . so , 5 x > 100 x > 20 answer : b"
Answer: b
Python program:
a = 6 * 2
Problem: two cubes of their volumes in the ratio 343 : 729 . the ratio of their surface area is :
Options: a ) 7 : 9 , b ) 2 : 5 , c ) 3 : 5 , d ) 1 : 5 , e ) 4 : 5
Rationale: "the ratio of their surface area is 343 : 729 7 : 9 answer is a ."
Answer: a
Python program:
a = 343 ** const_0_33
b = 729 ** const_0_33
c = a / b
Problem: two pipes p and q can fill a cistern in 12 and 14 minutes respectively . both are opened together , but at the end of 3 minutes the first is turned off . how much longer will the cistern take to fill ?
Options: a ) 11 1 / 2 min , b ) 11 1 / 4 min , c ) 11 2 / 4 min , d ) 11 1 / 5 min , e ) 10 1 / 2 min
Rationale: "3 / 12 + x / 14 = 1 x = 10 1 / 2 answer : e"
Answer: e
Python program:
a = 1 / 12
b = 1 / 14
c = a + b 
d = c * 3
e = 1 - d
f = e * 14
Problem: a can complete a project in 20 days and b can complete the same project in 20 days . if a and b start working on the project together and a quits 10 days before the project is completed , in how many days will the project be completed ?
Options: a ) 18 days , b ) 27 days , c ) 26.67 days , d ) 16 days , e ) 15 days
Rationale: "let x = the number of days taken to complete the project . the amount of work done by a is ( x - 10 ) * ( 1 / 20 ) . the amount of work done by b is ( x ) * ( 1 / 30 ) . ( 1 / 20 ) * ( x - 10 ) + ( 1 / 20 ) * ( x ) = 1 ( x / 20 ) + ( x / 20 ) - ( 10 / 20 ) = 1 x / 10 = 3 / 2 x = 15 therefore , the answer is e : 15 ."
Answer: e
Python program:
a = 1 / 20
b = a * 10
c = 1 - b
d = 1 / 20
e = 1 / 20
f = d + e 
g = c / f
h = g + 10
Problem: a work crew of 4 men takes 5 days to complete one - half of a job . if 11 men are then added to the crew and the men continue to work at the same rate , how many days will it take the enlarged crew to do the rest of the job ?
Options: a ) 2 , b ) 3 , c ) 1 1 / 3 , d ) 4 , e ) 4 4 / 5
Rationale: "suppose 1 man can do work in x days . . so 4 men will do in . . 4 / x = 1 / 5 * 1 / 2 as half job is done x = 40 now 11 more are added then 15 / 40 = 1 / 2 * 1 / d for remaining half job d = 1 1 / 3 number of days c"
Answer: c
Python program:
a = 4 * 5
b = 4 + 11 
c = a / b
d = 5 + c
Problem: a train 120 meters long takes 6 seconds to cross a man walking at 5 kmph in the direction opposite to that of the train . find the speed of the train .
Options: a ) 67 kmph , b ) 50 kmph , c ) 55 kmph , d ) 60 kmph , e ) 70 kmph
Rationale: "explanation : let the speed of the train be x kmph . speed of the train relative to man = ( x + 5 ) kmph = ( x + 5 ) × 5 / 18 m / sec . therefore 120 / ( ( x + 5 ) × 5 / 18 ) = 6 < = > 30 ( x + 5 ) = 2160 < = > x = 67 speed of the train is 67 kmph . answer : option a"
Answer: a
Python program:
a = 6 * const_0_2778
b = 120 / a
c = b - 5
Problem: a small company reduced its faculty by approximately 13 percent to 195 employees . what was the original number of employees ?
Options: a ) 182 , b ) 208 , c ) 220 , d ) 224 , e ) 302
Rationale: "if x is the original number of employees , then after 13 % reduction in employees number is . 87 x but we are given . 87 x = 195 x = 224 so the original number of employees is 224 correct answer - d"
Answer: d
Python program:
a = 100 - 13
b = a / 100
c = 195 / b
Problem: population is 22000 . population increases by 10 % every year , then the population after 3 years is ?
Options: a ) 26630 , b ) 29282 , c ) 36620 , d ) 26620 , e ) 26820
Rationale: "population after 1 st year = 22000 * 10 / 100 = 2200 = = = > 22000 + 2200 = 24000 population after 2 nd year = 24000 * 10 / 100 = 2400 = = = > 24000 + 2400 = 26620 population after 3 rd year = 26620 * 10 / 100 = 2662 = = = > 26620 + 2662 = 29282 answer : b"
Answer: b
Python program:
a = 3 * 10
b = a / 100
c = 1 + b 
d = 22000 * c
Problem: a 180 meter long train crosses a man standing on the platform in 12 sec . what is the speed of the train ?
Options: a ) 54 kmph , b ) 108 kmph , c ) 176 kmph , d ) 134 kmph , e ) 161 kmph
Rationale: "s = 180 / 12 * 18 / 5 = 54 kmph answer : a"
Answer: a
Python program:
a = 180 / 12
b = a * const_3_6
Problem: ( 26.3 * 12 * 20 ) / 3 + 125 = ?
Options: a ) 2339 , b ) 2229 , c ) 4429 , d ) 5529 , e ) 2669
Rationale: b 2229 ? = [ ( 26.3 * 12 * 20 ) / 3 ] + 125 ? = 2104 + 125 = 2229
Answer: b
Python program:
a = 26 * 3
b = a * 20
c = b / 3
d = c + 125
Problem: rectangular tile each of size 45 cm by 50 cm must be laid horizontally on a rectangular floor of size 250 cm by 180 cm , such that the tiles do not overlap and they are placed with edges jutting against each other on all edges . a tile can be placed in any orientation so long as its edges are parallel to the edges of floor . no tile should overshoot any edge of the floor . the maximum number of tiles that can be accommodated on the floor is :
Options: a ) 35 , b ) 40 , c ) 25 , d ) 18 , e ) 20
Rationale: "area of tile = 45 * 50 = 2250 area of floor = 250 * 180 = 45000 no of tiles = 45000 / 2250 = 20 so , the no of tile = 20 answer : e"
Answer: e
Python program:
a = 250 * 180
b = 45 * 50
c = a / b
Problem: if 15 people contributed a total of $ 30.00 toward a gift and each of them contributed at least $ 1.00 , then the maximum possible amount any one person could have contributed is
Options: a ) $ 1.00 , b ) $ 16 , c ) $ 5.00 , d ) $ 6.00 , e ) $ 20.00
Rationale: "b for me 14 people with 1 $ each - > maximum = 16"
Answer: b
Python program:
a = 15 - 1
b = a * 1
c = 30 - 0
Problem: a water tank , having the shape of a rectangular prism of base 100 square centimeters , is being filled at the rate of 1 liter per minute . find the rate at which the height of the water in the water tank increases . express your answer in centimeters per minute .
Options: a ) 30 cm
b ) 10 cm
c ) 50 cm
d ) 90 cm
e ) 70 cm
Rationale: the volume of a rectangular prism is given by area of base ? height the rate at which the tank is being filled is 1 liter per minute which we need to convert 1 liter = 1 dm 3 but 1 dm = 10 cm . hence 1 liter = ( 10 cm ) 3 = 1000 cm 3 the height h of the water is related to the volume by volume = area of base * h in one minute the volume increases by 1 liter or 1000 cm 3 and the height increases by h = volume / area of base = 1000 cm 3 / 100 cm 2 = 10 cm correct answer b
Answer: b
Python program:
a = 1000 / 100
Problem: the difference between a two - digit number and the number obtained by interchanging the positions of its digits is 72 . what is the difference between the two digits of that number ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: "sol . let the ten ’ s digit be x and unit ’ s digit be y , then , ( 10 x + y ) - ( 10 y + x ) = 72 ⇔ 9 ( x - y ) = 72 ⇔ x - y = 8 answer d"
Answer: d
Python program:
a = 10 - 1
b = 72 / a
Problem: machine a can put caps on a set of bottles in 8 hours at a constant rate . if machine a does the job for 6 hours and machine b does the rest of the job , which works at 1 / 4 constant rate of machine a . how long will it take for machine b alone to do the rest of the job ?
Options: a ) 4 hrs , b ) 6 hrs , c ) 8 hrs , d ) 10 hrs , e ) 16 hrs
Rationale: machine a will do 6 / 8 in 6 hrs , so a does 3 / 4 of the work . . therefore , b will do the remaining 1 / 4 th work alone . . as the speed of b is 1 / 4 rate of a , b will do the 1 / 4 th work in same time that a takes to complete full job . . . ans 8 c
Answer: c
Python program:
a = 6 / 8
b = 1 - a
c = 1/(8)
d = 1/(4)
e = c * d
f = 1/(e)
g = b * f
Problem: a ’ s speed is 16 / 15 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that the race ends in a dead heat ?
Options: a ) 1 / 8 , b ) 1 / 16 , c ) 1 / 15 , d ) 1 / 32 , e ) 1 / 31
Rationale: "let x be the fraction of the distance that b runs . let v be the speed at which b runs . the time should be the same for both runners . time = d / ( 16 v / 15 ) = xd / v ( 15 / 16 ) * d / v = x * d / v x = 15 / 16 b should have a head start of 1 / 16 of the full distance . the answer is b ."
Answer: b
Python program:
a = 16 - 15
b = a / 16
Problem: 6 women can do 75 unit of work in 8 days by working 5 hr / day in how many days 4 women do 30 units of work by working 8 hr / day
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: ( 6 x 8 x 5 ) / 75 = ( ax 4 x 8 ) / 30 a = 3 answer : a
Answer: a
Python program:
a = 75 / 6
b = a / 8
c = b / 5
d = c * 8
e = d * 4
f = 30 / e
Problem: 50 % of a number is more than 20 % of 650 by 190 . find the number ?
Options: a ) 640 , b ) 278 , c ) 800 , d ) 267 , e ) 121
Rationale: "( 50 / 100 ) * x â € “ ( 20 / 100 ) * 650 = 190 1 / 2 x = 320 x = 640 answer : a"
Answer: a
Python program:
a = 650 * 20
b = a / 100
c = b + 190 
d = c * 100
e = d / 50
Problem: what is the units digit of the expression 14 ^ 7 − 16 ^ 4 ?
Options: a ) 0 , b ) 3 , c ) 8 , d ) 6 , e ) 4
Rationale: i think answer on this one should be c too . since we know that 14 ^ 7 > 16 ^ 4 , as will said one should always check if the number is positive .
Answer: c
Python program:
a = 4 + 3 
b = a + 2
Problem: when xyz co discontinued an agency arrangement with john , management held his commission of rs . 25000 / - for one month . earlier john had availed an advance agency fees of 8280 / - from company . but robert forgot that . after one month john asked his fees and accountant gives rs . 18500 / - to him . what is the incentive amount given to john ?
Options: a ) a ) 1780 , b ) b ) 1250 , c ) c ) 10780 , d ) d ) 10500 , e ) e ) 8600
Rationale: total fees = rs . 25000 / - advance fees = 8280 / - balance fees = 25000 - 8280 = 16720 paid amount = 18500 / - incentive amount = 18500 - 16720 = 1780 / - answer is a
Answer: a
Python program:
a = 8280 + 18500 
b = a - 25000
Problem: if | 5 x - 5 | = 150 , what is the sum of all the possible values of x ?
Options: a ) 2 , b ) - 2 , c ) 6 , d ) - 3 , e ) 5
Rationale: "there will be two cases 5 x - 5 = 150 or 5 x - 5 = - 150 = > x = 31 or x = - 29 sum of both the values will be - 29 + 31 = 2 answer is a"
Answer: a
Python program:
a = 150 - 5
b = 150 + 5 
c = a - b
d = c - 5
Problem: x is the product of each integer from 1 to 100 , inclusive and y = 100 ^ k , where k is an integer . what is the greatest value of k for which y is a factor of x ?
Options: a ) 5 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: "the number of trailing zeros in the decimal representation of n ! , the factorial of a non - negative integer n , can be determined with this formula : n 5 + n 52 + n 53 + . . . + n 5 k , where k must be chosen such that 5 k ≤ n x = 1 * 2 * 3 . . . . * 100 = 100 ! no . of trailing zeros in 100 ! = 100 / 5 + 100 / 5 ^ 2 = 20 + 4 = 24 100 ^ k = 10 ^ 2 k → k = 24 / 2 = 12 e"
Answer: e
Python program:
a = 100 / 10
b = a + 1
Problem: jean drew a gumball at random from a jar of pink and blue gumballs . since the gumball she selected was blue and she wanted a pink one , she replaced it and drew another . the second gumball also happened to be blue and she replaced it as well . if the probability of her drawing the two blue gumballs was 9 / 49 , what is the probability that the next one she draws will be pink ?
Options: a ) 1 / 49 , b ) 4 / 7 , c ) 3 / 7 , d ) 16 / 49 , e ) 40 / 49
Rationale: the probability of drawing a pink gumball both times is the same . the probability that she drew two blue gumballs = 9 / 49 = ( 3 / 7 ) * ( 3 / 7 ) therefore probability that the next one she draws is pink = 4 / 7 option ( b )
Answer: b
Python program:
a = 9 / 49
b = math.sqrt(a)
c = 1 - b
Problem: a sum was put a simple interest at a certain rate for 2 years . had it been put at 4 % higher rate , it would have fetched rs . 60 more . the sum is :
Options: a ) rs . 750 , b ) rs . 700 , c ) rs . 820 , d ) rs . 940 , e ) rs . 900
Rationale: "explanation : let the sub be rs . x and the initial rate be r % . then x × ( r + 4 ) × 2 / 100 − x × r × 2 / 100 = 60 ⇒ x × 4 × 2 / 100 = 60 ⇒ x × 2 / 100 = 15 ⇒ 2 x = 1500 ⇒ x = 750 answer : option a"
Answer: a
Python program:
a = 60 / 2
b = a / 4
c = b * 100
Problem: three coins are tossed . find the probability of at least 2 tails ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 1 / 4 , d ) 1 / 8 , e ) 3 / 8
Rationale: "n ( s ) = 2 ^ 3 = 8 let e is the event of getting at least 2 tails n ( e ) = ttt , tth , htt , tht = 4 p ( e ) = n ( e ) / n ( s ) = 4 / 8 = 1 / 2 ans - a"
Answer: a
Python program:
a = 2 ** 2
b = 2 / a
Problem: a train can travel 50 % faster than a car . both start from point a at the same time and reach point b at 75 kms away from a at the same time . on the way , however , the train lost about 12.5 minutes while stopping at the stations . the speed of the car is ?
Options: a ) 2387 , b ) 267 , c ) 120 , d ) 277 , e ) 271
Rationale: "let speed of the car be x km / hr . then , speed of the train = 150 / 100 x = 3 / 2 x km / hr . 75 / x - 75 / ( 3 / 2 x ) = 125 / ( 10 * 60 ) 75 / x - 50 / x = 5 / 24 = 120 km / hr . answer : c"
Answer: c
Python program:
a = 12 * 5
b = a - 1
c = 12 * 5
d = b * c
e = 4 + 1 
f = d / e
Problem: tom traveled the entire 60 miles trip . if he did the first 12 miles of at a constant rate 24 miles per hour and the remaining trip of at a constant rate 48 miles per hour , what is the his average speed , in miles per hour ?
Options: a ) 20 mph , b ) 24 mph , c ) 30 mph , d ) 40 mph , e ) 42 mph
Rationale: "avg speed = total distance / total time = ( d 1 + d 2 ) / ( t 1 + t 2 ) = ( 12 + 48 ) / ( ( 12 / 24 ) + ( 48 / 48 ) ) = 60 * 2 / 3 = 40 mph d"
Answer: d
Python program:
a = 60 - 12
b = 48 / a
c = 12 / 24
d = b + c 
e = 60 / d
Problem: a grocer has a sale of rs . 2435 , rs . 2920 , rs . 2855 , rs . 3230 and rs . 2560 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 2500 ?
Options: a ) 5000 , b ) 4000 , c ) 1000 , d ) 6000 , e ) 8000
Rationale: "total sale for 5 months = rs . ( 2435 + 2920 + 2855 + 3230 + 2560 ) = rs . 14000 . required sale = rs . [ ( 2500 x 6 ) - 14000 ] = rs . ( 15000 - 14000 ) = rs . 1000 answer : option c"
Answer: c
Python program:
a = 5 + 1 
b = a * 2500
c = 2435 + 2920 
d = c + 2855 
e = d + 3230 
f = e + 2560 
g = b - f
Problem: a mixture contains alcohol and water in the ratio 4 : 3 . if 5 litres of water is added to the mixture , the ratio becomes 4 : 5 . find the quantity of alcohol in the given mixture
Options: a ) 10 litres , b ) 20 litres , c ) 30 litres , d ) 5 litres , e ) 14 litres
Rationale: "let the quantity of alcohol and water be 4 x litres and 3 x litres respectively 4 x / ( 3 x + 5 ) = 4 / 5  20 x = 4 ( 3 x + 5 )  8 x = 20  x = 2.5 quantity of alcohol = ( 4 x 2.5 ) litres = 10 litres . answer a 10 litres"
Answer: a
Python program:
a = 5 * 1
Problem: evaluate 28 % of 550 + 45 % of 280
Options: a ) 232 , b ) 242 , c ) 252 , d ) 262 , e ) 280
Rationale: "explanation : = ( 28 / 100 ) * 550 + ( 45 / 100 ) * 280 = 154 + 126 = 280 answer : option e"
Answer: e
Python program:
a = 550 / 28
b = 28 / a
Problem: what sum of money put at c . i amounts in 2 years to rs . 8840 and in 3 years to rs . 9261 ?
Options: a ) 8054 , b ) 8877 , c ) 2877 , d ) 2678 , e ) 1011
Rationale: "8840 - - - - 421 100 - - - - ? = > 4.76 % x * 104.76 / 100 * 104.76 / 100 = 8840 x * 1.0975 = 8840 x = 8840 / 1.0975 = > 8054.54 answer : a"
Answer: a
Python program:
a = 9261 / 8840
b = a - 1
c = b + 1 
d = c ** 2
e = 8840 / d
Problem: if square - root of 15 is 3.87 . then find the value of square - root of ( 5 / 3 )
Options: a ) 1.29 , b ) 1.39 , c ) 1.49 , d ) 1.59 , e ) 1.69
Rationale: = > root 5 / root 3 = ( root 5 / root 3 ) * ( root 3 / root 3 ) = root 15 / root 9 = 3.87 / 3 = 1.29 answer : a
Answer: a
Python program:
a = 5 / 3
b = math.sqrt(a)
Problem: a salesman sold twice as much pears in the afternoon than in the morning . if he sold $ 480 kilograms of pears that day , how many kilograms did he sell in the afternoon ?
Options: a ) 120 , b ) 180 , c ) 240 , d ) 280 , e ) 320
Rationale: "3 x = 480 x = 160 therefore , the salesman sold 160 kg in the morning and 2 ⋅ 160 = 320 kg in the afternoon . so answer is e ."
Answer: e
Python program:
a = 480 / 3
b = a * 2
Problem: 0.004 × 0.5 = ?
Options: a ) none of these , b ) 0.02 , c ) 0.002 , d ) 0.0002 , e ) 2
Rationale: "explanation : 0.004 × 0.5 = 0.002 . answer : option c"
Answer: c
Python program:
a = 0 / 4
b = a * 100
Problem: on rainy mornings , mo drinks exactly n cups of hot chocolate ( assume that n is an integer ) . on mornings that are not rainy , mo drinks exactly 3 cups of tea . last week mo drank a total of 20 cups of tea and hot chocolate together . if during that week mo drank 10 more tea cups than hot chocolate cups , then how many rainy days were there last week ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: t = the number of cups of tea c = the number of cups of hot chocolate t + c = 20 t - c = 10 - > t = 15 . c = 5 . mo drinks 3 cups of tea a day then number of days that are not rainy = 15 / 3 = 5 so number of rainy days = 7 - 5 = 2 a is the answer .
Answer: a
Python program:
a = 4 + 3 
b = 20 + 10 
c = b / 2
d = c / 3
e = a - d
Problem: how long will a boy take to run round a square field of side 50 meters , if he runs at the rate of 10 km / hr ?
Options: a ) 52 sec , b ) 45 sec , c ) 72 sec , d ) 25 sec , e ) 39 sec
Rationale: "speed = 10 km / hr = 10 * 5 / 18 = 25 / 9 m / sec distance = 50 * 4 = 200 m time taken = 200 * 9 / 25 = 72 sec answer is c"
Answer: c
Python program:
a = 50 * 4
b = 1000 / 3600
c = 10 * b
d = a / c
Problem: the roof of an apartment building is rectangular and its length is 3 times longer than its width . if the area of the roof is 675 feet squared , what is the difference between the length and the width of the roof ?
Options: a ) 38 . , b ) 30 . , c ) 42 . , d ) 44 . , e ) 46 .
Rationale: "let the width = x x * 3 x = 675 x ^ 2 = 225 x = 15 length = 3 * 15 = 45 difference = 45 - 15 = 30 b is the answer"
Answer: b
Python program:
a = 675 / 3
b = math.sqrt(a)
c = b * 3
d = 675 / 3
e = math.sqrt(d)
f = c - e