euclaise/mathqa_programs huggingface dataset:
Problem: a store owner estimates that the average price of type a products will increase by 25 % next year and that the price of type b products will increase by 20 % next year . this year , the total amount paid for type a products was $ 4500 and the total price paid for type b products was $ 8300 . according to the store owner ' s estimate , and assuming the number of products purchased next year remains the same as that of this year , how much will be spent for both products next year ?
Options: a ) $ 14,755 , b ) $ 15,585 , c ) $ 16,000 , d ) $ 16,225 , e ) $ 17,155
Rationale: "cost of type a products next year = 1.25 * 4500 = 5625 cost of type b products next year = 1.2 * 8300 = 9960 total 5625 + 9960 = 15585 option b"
Answer: b
Python program:
a = 3 / 4
b = a * 1000
Problem: when n is divided by 20 , the remainder is 6 . what is the remainder when n + 16 is divided by 5 ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "assume n = 14 remainder ( n / 20 ) = 6 n + 16 = 36 remainder ( 36 / 5 ) = 1 option a"
Answer: a
Python program:
a = 6 - reminder
Problem: on a sum of money , the s . i . for 2 years is $ 660 , while the c . i . is $ 693 , the rate of interest being the same in both the cases . the rate of interest is ?
Options: a ) 10 % , b ) 32 % , c ) 72 % , d ) 14 % , e ) 82 %
Rationale: "difference in c . i . and s . i for 2 years = $ 693 - $ 660 = $ 33 s . i for one year = $ 330 s . i . on $ 330 for 1 year = $ 33 rate = ( 100 * 33 ) / ( 330 ) = 10 % the answer is a ."
Answer: a
Python program:
a = 693 - 660
b = 100 * a
c = 660 / 2
d = b / c
Problem: in a group of ducks and cows , the total number of legs are 32 more than twice the number of heads . find the total number of cows .
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: "let the number of ducks be d and number of cows be c then , total number of legs = 2 d + 4 c = 2 ( d + 2 c ) total number of heads = c + d given that total number of legs are 32 more than twice the number of heads = > 2 ( d + 2 c ) = 32 + 2 ( c + d ) = > d + 2 c = 16 + c + d = > 2 c = 16 + c = > c = 16 i . e . , total number of cows = 16 answer is c ."
Answer: c
Python program:
a = 32 / 2
Problem: a is half good a work man as b and together they finish a job in 12 days . in how many days working alone b finish the job ?
Options: a ) 23 , b ) 22 , c ) 18 , d ) 36 , e ) 48
Rationale: "c 18 wc = 1 : 2 2 x + x = 1 / 12 = > x = 1 / 36 2 x = 1 / 18 = > 18 days"
Answer: c
Python program:
a = 3 / 2
b = 12 * a
Problem: a cyclist traveled for two days . on the second day the cyclist traveled 4 hours longer and at an average speed 10 mile per hour slower than she traveled on the first day . if during the two days she traveled a total of 280 miles and spent a total of 10 hours traveling , what was her average speed on the second day ?
Options: a ) 5 mph , b ) 10 mph , c ) 20 mph , d ) 30 mph , e ) 40 mph
Rationale: "solution : d = 280 mi t = 12 hrs day 1 time = t 1 day 2 time = t 2 t 2 - t 1 = 4 hrs - - - - - ( i ) t 1 + t 2 = 12 hrs - - - - - ( ii ) adding i and ii , t 2 = 8 hrs and t 1 = 4 hrs day 1 rate = r 1 day 2 rate = r 2 r 1 - r 2 = 10 mph i . e . r 1 = 10 + r 2 280 = 8 r 2 + 4 r 1 i . e . 280 = 8 r 2 + 4 ( 10 + r 2 ) i . e . r 2 = 20 mph answer : e"
Answer: e
Python program:
a = 10 - 4
b = a / 2
c = b * 10
d = 280 - c
e = 10 - 4
f = e / 2
g = 10 - 4
h = g / 2
i = h + 4 
j = f + i 
k = d / j
Problem: a pair of articles was bought for $ 50 at a discount of 40 % . what must be the marked price of each of the article ?
Options: a ) $ 25 , b ) $ 15 , c ) $ 29.65 , d ) $ 35.95 , e ) $ 45.62
Rationale: s . p . of each of the article = 50 / 2 = $ 25 let m . p = $ x 60 % of x = 25 x = 25 * . 6 = $ 15 answer is b
Answer: b
Python program:
a = 100 - 40
b = 50 / 2
c = a * b
d = c / 100
Problem: by selling 16 pencils for a rupee a man loses 5 % . how many for a rupee should he sell in order to gain 15 % ?
Options: a ) 12.95 , b ) 19 , c ) 17.56 , d ) 16.56 , e ) 15
Rationale: "85 % - - - 16 105 % - - - ? 85 / 105 * 16 = 8 answer : a"
Answer: a
Python program:
a = 100 + 15 
b = 100 - 5
c = 1 / b
d = a * c
e = 1 / d
f = e * 16
Problem: if 7 : 13 : : 301 : x then the value of ‘ x ’ is :
Options: a ) 493 , b ) 537 , c ) 559 , d ) 587 , e ) 567
Rationale: "given the question ; 7 : 13 : : 301 : x 7 / 13 = 301 / x 7 x = 301 * 13 x = 301 * 13 / 7 x = 559 answer : c"
Answer: c
Python program:
a = 13 * 7
b = a + 13 
c = b / 301
Problem: two goods trains each 500 m long are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 45 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options: a ) 40 , b ) 93 , c ) 26 , d ) 23 , e ) 12
Rationale: "relative speed = 45 + 45 = 90 km / hr . 90 * 5 / 18 = 25 m / sec . distance covered = 500 + 500 = 1000 m . required time = 1000 / 25 = 40 sec . answer : a"
Answer: a
Python program:
a = 45 + 45
Problem: the difference between c . i . and s . i . on an amount of $ 10,000 for 2 years is $ 49 . what is the rate of interest per annum ?
Options: a ) 5 % , b ) 6 % , c ) 7 % , d ) 8 % , e ) 9 %
Rationale: $ 49 is the interest on the first year of interest . let x be the interest rate . the interest after the first year is 10000 * x . the interest on the first year ' s interest is 10000 * x * x 10000 * x ^ 2 = 49 x = 0.07 the answer is c .
Answer: c
Python program:
a = math.sqrt(49)
Problem: find the value of x . ( 47 % of 1442 - 36 % of 1412 ) + 66 = x ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 6 , e ) 5
Rationale: d ) 6
Answer: d
Python program:
a = 47 / 100
b = a * 1442
c = 36 / 100
d = c * 1412
e = b - d
f = e + 66 
g = reminder + ( 
h = math.floor(g, 1)
Problem: 9823 + x = 13200 , then x is ?
Options: a ) 3327 , b ) 3237 , c ) 3337 , d ) 3377 , e ) none of these
Rationale: "answer x = 13200 - 9823 = 3377 option : d"
Answer: d
Python program:
a = 13200 - 9823
Problem: a store ’ s selling price of $ 2500 for a certain printer would yield a profit of 40 percent of the store ’ s cost for the printer . what selling price would yield a profit of 50 percent of the printer ’ s cost ?
Options: a ) $ 2400 , b ) $ 2464 , c ) $ 2650 , d ) $ 2478 , e ) $ 2800
Rationale: 1.4 x = 2500 x = 2500 / 1.4 so , 1.5 x = 2500 * 1.5 / 1.4 = 2478 answer : - d
Answer: d
Python program:
a = 40 / 100
b = 1 + a 
c = b * original_price_before_gain
Problem: in a soccer bet , we play 4 teams . first team odd 1.28 , second 5.23 , third 3.25 , fourth 2.05 . we place the bet with 5.00 euros . how much money we expect to win ?
Options: a ) 219.5 , b ) 223.0 , c ) 235.01 , d ) 266.74 , e ) 669.0
Rationale: in the case we won the bet , we have : 1.28 * 5.23 * 3.25 * 2.0 * 5.00 = 219.50 we will win 223 so correct answer is b
Answer: b
Python program:
a = 5 * 2
b = a * 3
c = b * 5
d = c * 1
Problem: sum of two numbers prime to each other is 16 and their l . c . m . is 63 . what are the numbers ?
Options: a ) 9 and 10 , b ) 8 and 9 , c ) 11 and 5 , d ) 7 and 8 , e ) 7 and 9
Rationale: as two numbers are prime , only options satisfy all but option c will not make the product of numbers i . e 63 answer : e
Answer: e
Python program:
a = 63 + 16
Problem: 18 men can complete a piece of work in 20 days . in how many days can 12 men complete that piece of work ?
Options: a ) 23 days , b ) 30 days , c ) 22 days , d ) 29 days , e ) 20 days
Rationale: "b 30 days 18 * 20 = 12 * x = > x = 30 days"
Answer: b
Python program:
a = 20 * 18
b = a / 12
Problem: two trains each 150 m in length are running on the same parallel lines in opposite directions with the speed of 80 kmph and 70 kmph respectively . in what time will they cross each other completely ?
Options: a ) 7.8 sec , b ) 7.2 sec , c ) 8.2 sec , d ) 6.2 sec , e ) 9.2 sec
Rationale: "d = 150 m + 150 m = 300 m rs = 80 + 70 = 150 * 5 / 18 = 125 / 3 t = 300 * 3 / 125 = 7.2 sec answer : b"
Answer: b
Python program:
a = 80 * const_0_2778
b = 150 / a
Problem: two trains a and b starting from two points and travelling in opposite directions , reach their destinations 9 hours and 4 hours respectively after meeting each other . if the train a travels at 60 kmph , find the rate at which the train b runs .
Options: a ) 40 , b ) 60 , c ) 120 , d ) 90 , e ) 100
Rationale: "if two objects a and b start simultaneously from opposite points and , after meeting , reach their destinations in ‘ a ’ and ‘ b ’ hours respectively ( i . e . a takes ‘ a hrs ’ to travel from the meeting point to his destination and b takes ‘ b hrs ’ to travel from the meeting point to his destination ) , then the ratio of their speeds is given by : sa / sb = √ ( b / a ) i . e . ratio of speeds is given by the square root of the inverse ratio of time taken . sa / sb = √ ( 4 / 9 ) = 2 / 3 this gives us that the ratio of the speed of a : speed of b as 2 : 3 . since speed of a is 60 kmph , speed of b must be 80 * ( 3 / 2 ) = 90 kmph d"
Answer: d
Python program:
a = 9 / 4
b = math.sqrt(a)
c = 60 * b
Problem: an aeroplane covers a certain distance at a speed of 240 kmph in 5 hours . to cover the same distance in 123 hours , it must travel at a speed of :
Options: a ) 234 , b ) 377 , c ) 720 , d ) 378 , e ) 268
Rationale: speed and time are inversely proportional ⇒ speed ∝ 1 time ( when distance is constant ) here distance is constant and speed and time are inversely proportionalspeed ∝ 1 time ⇒ speed 1 speed 2 = time 2 time 1 ⇒ 240 speed 2 = ( 123 ) 5 ⇒ 240 speed 2 = ( 53 ) 5 ⇒ 240 speed 2 = 13 ⇒ speed 2 = 240 × 3 = 720 km / hr answer : d
Answer: d
Python program:
a = 240 * 5
b = 2 / 3
c = 1 + b 
d = a / c
e = d / 2
Problem: a certain car increased its average speed by 3 miles per hour in each successive 5 - minute interval after the first interval . if in the first 5 - minute interval its average speed was 20 miles per hour , how many miles did the car travel in the third 5 - minute interval ?
Options: a ) 1.0 , b ) 1.5 , c ) 2.0 , d ) 2.5 , e ) 3.0
Rationale: "in the third time interval the average speed of the car was 20 + 3 + 5 = 28 miles per hour ; in 5 minutes ( 1 / 12 hour ) at that speed car would travel 28 * 1 / 12 = 2 miles . answer : c ."
Answer: c
Python program:
a = 20 + 3 
b = a + 5 
c = 3 / const_60
d = b * c
Problem: 500 is increased by 30 % . find the final number .
Options: a ) 550 , b ) 500 , c ) 650 , d ) 600 , e ) 700
Rationale: explanation final number = initial number + 30 % ( original number ) = 500 + 30 % ( 500 ) = 500 + 150 = 650 . answer c
Answer: c
Python program:
a = 30 / 100
b = 500 * a
c = 500 + b
Problem: linda spent 4 / 5 of her savings on furniture and the rest on a tv . if the tv cost her $ 100 , what were her original savings ?
Options: a ) $ 900 , b ) $ 300 , c ) $ 500 , d ) $ 700 , e ) $ 800
Rationale: "if linda spent 4 / 5 of her savings on furniture , the rest 5 / 5 - 4 / 5 = 1 / 5 on a tv but the tv cost her $ 100 . so 1 / 5 of her savings is $ 100 . so her original savings are 5 times $ 100 = $ 500 correct answer c"
Answer: c
Python program:
a = 4 / 5
b = 1 - a
c = 100 / b
Problem: marla starts running around a circular track at the same time nick starts walking around the same circular track . marla completes 30 laps around the track per hour and nick completes 15 laps around the track per hour . how many minutes after marla and nick begin moving will marla have completed 4 more laps around the track than nick ?
Options: a ) 5 , b ) 16 , c ) 12 , d ) 15 , e ) 20
Rationale: "maria ' s rate - 30 laps per hour - - > 30 / 60 laps / min nick ' s rate - 15 laps per hour - - > 15 / 60 laps / min lets set equations : 30 / 60 * t = 4 ( since maria had to run 4 laps before nick would start ) 15 / 60 * t = 0 ( hick has just started and has n ' t run any lap yet ) ( 30 / 60 - 15 / 60 ) * t = 4 - 0 ( since nick was chasing maria ) t = 16 min needed maria to run 4 laps answer : b"
Answer: b
Python program:
a = 15 + 1 
b = a * 30
c = 30 / b
d = 15 + 1 
e = d * 30
f = 15 / e
g = c - f
h = 4 / g
Problem: solution x is 10 percent alcohol by volume , and solution y is 30 percent alcohol by volume . how many milliliters of solution y must be added to 300 milliliters of solution x to create a solution that is 25 percent alcohol by volume ?
Options: a ) 250 / 3 , b ) 500 / 3 , c ) 900 , d ) 480 , e ) 600
Rationale: "we know that x is 10 % , y is 30 % and w . avg = 25 % . what does this mean with respect to w . avg technique ? w . avg is 1 portion away from y and 3 portion away from x so for every 1 portion of x we will have to add 3 portions of y . if x = 300 then y = 900 answer : c"
Answer: c
Python program:
a = 25 - 10
b = 30 - 25
c = a / b
d = c * 300
Problem: a pet store regularly sells pet food at a discount of 10 percent to 30 percent from the manufacturer ’ s suggested retail price . if during a sale , the store discounts an additional 20 percent from the discount price , what would be the lowest possible price of a container of pet food that had a manufacturer ’ s suggested retail price o f $ 35.00 ?
Options: a ) $ 10.00 , b ) $ 11.20 , c ) $ 14.40 , d ) $ 16.00 , e ) $ 19.60
Rationale: for retail price = $ 35 first maximum discounted price = 35 - 30 % of 35 = 35 - 10.5 = 24.5 price after additional discount of 20 % = 24.5 - 20 % of 24.5 = 24.5 - 4.9 = 19.6 answer : option e
Answer: e
Python program:
a = 100 - 20
b = a / 100
c = 100 - 30
d = c / 100
e = d * 35
f = b * e
Problem: when 242 is divided by a certain divisor the remainder obtained is 8 . when 698 is divided by the same divisor the remainder obtained is 9 . when the sum of the two numbers 242 and 698 is divided by the divisor , the remainder obtained is 4 . what is the value of the divisor ?
Options: a ) 11 , b ) 17 , c ) 13 , d ) 23 , e ) none of these
Rationale: "explanatory answer when 242 is divided by a certain divisor the remainder obtained is 8 . let the divisor be d . when 242 is divided by d , let the quotient be ' x ' . the remainder is 8 . therefore , 242 = xd + 8 when 698 is divided by the same divisor the remainder obtained is 9 . let y be the quotient when 698 is divided by d . then , 698 = yd + 9 . when the sum of the two numbers , 242 and 698 , is divided by the divisor , the remainder obtained is 4 . 242 + 698 = 940 = xd + yd + 8 + 9 940 = xd + yd + 17 as xd and yd are divisible by d , the remainder when 940 is divided by d should have been 17 . however , because we know that the remainder is 4 , it would be possible only when 17 / d leaves a remainder of 4 . if the remainder obtained is 4 when 17 is divided by ' d ' , then ' d ' has to be 13 . choice c"
Answer: c
Python program:
a = 8 + 9 
b = a - 4
Problem: the lateral surface area of cube is 100 sq . units . find the volume of cube ?
Options: a ) 135
b ) 155
c ) 125
d ) 145
e ) 115
Rationale: lateral surface = 4 a ( power ) 2 = 100 sq . units a ( power ) 2 = 25 a = 5 . cube volume = a ( power ) 3 = > 125 m ( power ) 3 answer is c .
Answer: c
Python program:
a = 100 / 4
b = math.sqrt(a)
c = b ** 3
Problem: 10 men can complete a piece of work in 35 days . in how many days can 7 men complete that piece of work ?
Options: a ) 23 days , b ) 46 days , c ) 22 days , d ) 29 days , e ) 50 days
Rationale: e 50 days 10 * 35 = 7 * x = > x = 50 days
Answer: e
Python program:
a = 35 * 10
b = a / 7
Problem: mariah has decided to hire three workers . to determine whom she will hire , she has selected a group of 12 candidates . she plans to have one working interview with 3 of the 12 candidates every day to see how well they work together . how many days will it take her to have working interviews with all the different combinations of job candidates ?
Options: a ) 720 , b ) 120 , c ) 300 , d ) 30 , e ) 333
Rationale: "300 . answer c"
Answer: c
Python program:
a = math.factorial(12)
b = 12 - 3
c = math.factorial(b)
d = a / c
e = math.factorial(3)
f = d / e
g = f / 2
h = g - 12
i = h - 12
j = i - 10
Problem: the number of positive integer solutions for the equation x + y + z + t = 10 is
Options: a ) 60 , b ) 74 , c ) 84 , d ) 54 , e ) 104
Rationale: "the number of positive integer solutions for the equatio fx 1 + x 2 + ⋯ + xn = k ( k - 1 ) c ( n - 1 ) - where k is the number and n is number of variable in the equation . 10 - 1 c 4 - 1 = 9 c 3 = 84 answer : c"
Answer: c
Python program:
a = 10 - 1
b = math.factorial(a)
c = 4 - 1
d = math.factorial(c)
e = 10 - 1
f = 4 - 1
g = e - f
h = math.factorial(g)
i = d * h
j = b / i
Problem: two boys starts from the same place walking at the rate of 5.3 kmph and 5.6 kmph respectively in the same direction . what time will they take to be 10.5 km apart ?
Options: a ) 32 , b ) 36 , c ) 39 , d ) 38 , e ) 35
Rationale: "explanation : relative speed = 5.6 - 5.3 = 0.3 kmph ( because they walk in the same direction ) distance = 10.5 km time = distance / speed = 10.5 / 0.3 = 35 hr answer : e"
Answer: e
Python program:
a = 5 - 6
b = 10 / 5
Problem: a train 320 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 ) 72 kmph , e ) 88 kmph
Rationale: "s = 320 / 16 * 18 / 5 = 72 kmph answer : d"
Answer: d
Python program:
a = 320 / 16
b = const_3_6 * a
Problem: if x is a positive number and 1 / 2 the square root of x is the cube root of x , then x =
Options: a ) 64 , b ) 32 , c ) 16 , d ) 4 , e ) 1
Rationale: 1 / 2 the square root of x is cube root of x . if x = 64 . . then 1 / 2 the square root of x = 4 and cube of x is 64 . option a .
Answer: a
Python program:
a = 2 * 3
b = 2 ** a
Problem: if k is the greatest positive integer such that 4 ^ k is a divisor of 32 ! then k =
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 10
Rationale: "32 / 4 = 8 32 / 16 = 2 8 + 2 = 10 = k answer : e"
Answer: e
Python program:
a = 32 / 4
b = 1 + a
Problem: an engineer undertakes a project to build a road 10 km long in 300 days and employs 30 men for the purpose . after 100 days , he finds only 2 km of the road has been completed . find the ( approximate ) number of extra men he must employ to finish the work in time .
Options: a ) 20 , b ) 25 , c ) 30 , d ) 35 , e ) 40
Rationale: 30 workers working already let x be the total men required to finish the task in next 200 days 2 km done hence remaining is 8 km also , work has to be completed in next 200 days ( 300 - 100 = 200 ) we know that , proportion of men to distance is direct proportion and , proportion of men to days is inverse proportion hence , x = ( 30 * 8 * 100 ) / ( 2 * 200 ) thus , x = 60 thus , more men needed to finish the task = 60 - 30 = 30 answer : c
Answer: c
Python program:
a = 10 - 2
b = 30 * a
c = b * 100
d = 300 - 100
e = 2 * d
f = c / e
g = f - 30
Problem: the average of first four prime numbers greater than 50 is ?
Options: a ) 50 , b ) 57 , c ) 89 , d ) 56 , e ) 60
Rationale: "53 + 59 + 61 + 67 = 240 / 4 = 60 answer : e"
Answer: e
Python program:
a = 50 + 1
Problem: thirty percent of the women in a college class are science majors , and the non - science majors make up 80 % of the class . what percentage of the women are science majors if 40 % of the class are men ?
Options: a ) 2 % , b ) 5 % , c ) 28 % , d ) 30 % , e ) 45 %
Rationale: "3 / k + 2 / m = 6 / t assuming total # is 100 : [ science - women ] will have - 0.3 * 60 = 18 [ non - science - women ] will have - 42 [ science - men ] will have = 20 - 18 = 2 s 0 18 / 60 * 100 = 30 % answer - d"
Answer: d
Python program:
a = 100 - 80
b = 10 * 3
c = b / 100
d = 100 - 40
e = c * d
f = a - e
g = f / 40
h = g * 100
Problem: john and jane went out for a dinner and they ordered the same dish . both used a 10 % discount coupon . john paid a 15 % tip over the original price of the dish , while jane paid the tip over the discounted price for the coupon . if john paid $ 0.51 more than jane , what was the original price of the dish ?
Options: a ) 24 , b ) 34 , c ) 37.8 , d ) 42 , e ) 84
Rationale: "the difference between the amounts john paid and jane paid is the deference between 15 % of p and 15 % of 0.9 p : 0.15 p - 0.15 * 0.9 p = 0.51 - - > 15 p - 13.5 p = 51 - - > p = 34 . answer : b ."
Answer: b
Python program:
a = 15 / 100
b = 10 / 100
c = 1 - b
d = 15 / 100
e = c * d
f = a - e
g = 0 / 51
Problem: on dividing 122 by a number , the quotient is 6 and the remainder is 2 . find the divisor ?
Options: a ) 14 , b ) 16 , c ) 18 , d ) 20 , e ) 22
Rationale: "d = ( d - r ) / q = ( 122 - 2 ) / 6 = 122 / 6 = 20 d )"
Answer: d
Python program:
a = 122 / 6
b = math.floor(a)
Problem: evaluate : 434 - 12 * 3 * 2 = ?
Options: a ) 426 , b ) 526 , c ) 626 , d ) 726 , e ) 826
Rationale: "according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 434 - 12 * 3 * 2 = 434 - 8 = 426 correct answer a"
Answer: a
Python program:
a = 12 * 3
b = a * 2
c = 434 - b
Problem: at the wholesale store you can buy an 8 - pack of hot dogs for $ 1.55 , a 20 - pack for $ 3.05 , and a 250 - pack for $ 22.95 . what is the greatest number of hot dogs you can buy at this store with $ 250 ?
Options: a ) 1,108 , b ) 2,100 , c ) 2,628 , d ) 2,124 , e ) 2,256
Rationale: "to maximize number of hot dogs with 250 $ total number of hot dogs bought in 250 - pack = 22.95 * 10 = 229.5 $ amount remaining = 250 - 229.5 = 20.5 $ total number of hot dogs bought in 20 - pack = 3.05 * 6 = 18.3 $ amount remaining = 20.5 - 18.3 = 2.2 $ total number of hot dogs bought in 8 - pack = 1.55 * 1 = 1.55 $ amount remaining = 2.2 - 1.55 = 0.65 $ this amount is too less to buy any 8 - pack . greatest number of hot dogs one can buy with 250 $ = 250 * 10 + 20 * 6 + 8 * 1 = 2628 answer c"
Answer: c
Python program:
a = 250 / 22
b = a * 250
Problem: some of 60 % - intensity red paint is replaced with 30 % solution of red paint such that the new paint intensity is 40 % . what fraction of the original paint was replaced ?
Options: a ) 2 / 3 , b ) 1 / 3 , c ) 2 / 5 , d ) 1 / 2 , e ) 1 / 5
Rationale: "let total paint = 1 let amount replaced = x 60 ( 1 - x ) + 30 x = 40 x = 2 / 3 answer : a"
Answer: a
Python program:
a = 40 / 100
b = 60 / 100
c = a - b
d = 30 / 100
e = 60 / 100
f = d - e
g = c / f
Problem: a bucket full of nuts was discovered by the crow living in the basement . the crow eats a fifth of the total number of nuts in 4 hours . how many hours in total will it take the crow to finish a quarter of the nuts ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "in one hour , the crow eats 1 / 20 of the nuts . ( 1 / 4 ) / ( 1 / 20 ) = 5 hours the answer is b ."
Answer: b
Python program:
a = 1 / 4
b = 2 + 3 
c = 1 / b
d = c / 4
e = a / d
Problem: 2 , 3 , 4.5 , 6.75 , 10.12 , ( . . . )
Options: a ) 60 , b ) 60.75 , c ) 58.11 , d ) 15.18 , e ) 16.21
Rationale: "2 ( 2 ã — 3 ) ã · 2 = 3 ( 3 ã — 3 ) ã · 2 = 4.5 ( 4.5 ã — 3 ) ã · 2 = 6.75 ( 6.75 ã — 3 ) ã · 2 = 10.12 ( 10.12 ã — 3 ) ã · 2 = 15.78 answer is d"
Answer: d
Python program:
a = negate - (
Problem: there are 20 brown dogs , 10 white dogs , 15 black dogs . totally how many dogs are there in all ?
Options: a ) 45 , b ) 15 , c ) 25 , d ) 5 , e ) 30
Rationale: 20 + 10 + 15 = 45 . answer is a
Answer: a
Python program:
a = 20 + 10 
b = a + 15
Problem: in an examination , there were 2000 candidates , out of which 900 candidates were girls and rest were boys . if 28 % of the boys and 32 % of the girls passed , then the total percentage of failed candidates is ?
Options: a ) 35.67 % , b ) 64.75 % , c ) 68.57 % , d ) 70.20 % , e ) none of these
Rationale: girls = 900 , boys = 1100 passed = ( 28 % of 1100 ) + ( 32 % of 900 ) = 308 + 288 = 596 failed = 2000 - 596 = 1404 failed % = [ ( 1404 / 2000 ) x 100 ] % = 70.2 % . answer : d
Answer: d
Python program:
a = 900 * 32
b = a / 100
c = 2000 - 900
d = c * 28
e = d / 100
f = b + e 
g = 2000 - f
h = g / 2000
i = h * 100
Problem: if 3 ^ x * 4 ^ y = 1 , 594,323 and x – y = 13 , then x = ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "since 1 , 594,323 is an odd number , it is not a multiple of 4 . this means that y must equal zero . since x - y = 13 and y = 0 , then x = 13 . the answer is d ."
Answer: d
Python program:
a = 594 * 323