euclaise/mathqa_programs huggingface dataset:
Problem: if 2 / w + 2 / x = 2 / y and wx = y , then the average ( arithmetic mean ) of w and x is
Options: a ) 1 / 2 , b ) 1 , c ) 2 , d ) 4 , e ) 8
Rationale: "given : 2 / w + 2 / x = 2 / ywx = y find : ( w + x ) / 2 = ? 2 ( 1 / w + 1 / x ) = 2 ( 1 / y ) - divide both sides by 2 ( 1 / w + 1 / x ) = 1 / y ( x + w ) / wx = 1 / wx - sub ' d in y = wx x + w - 1 = 0 x + w = 1 therefore ( w + x ) / 2 = 1 / 2 ans : a"
Answer: a
Python program:
a = 2 + 2 
b = 2 / a
Problem: a rectangular field is to be fenced on three sides leaving a side of 30 feet uncovered . if the area of the field is 810 sq . feet , how many feet of fencing will be required ?
Options: a ) 34 , b ) 40 , c ) 68 , d ) 84 , e ) none
Rationale: "explanation we have : l = 30 ft and lb = 810 sq . ft . so , b = 27 ft . length of fencing = ( l + 2 b ) = ( 30 + 54 ) ft = 84 ft . answer d"
Answer: d
Python program:
a = 810 / 30
b = a * 2
c = b + 30
Problem: the food in a camp lasts for 40 men for 45 days . if fifteen more men join , how many days will the food last ?
Options: a ) 80 days , b ) 33 days , c ) 35 days , d ) 16 days , e ) 15 days
Rationale: one man can consume the same food in 40 * 45 = 1800 days . 15 more men join , the total number of men = 55 the number of days the food will last = 1800 / 55 = 33 days . answer : b
Answer: b
Python program:
a = 45 * 40
b = 12 + 3 
c = b + 40 
d = a / c
Problem: lionel left his house and walked towards walt ' s house , 48 miles away . four hours later , walt left his house and ran towards lionel ' s house . if lionel ' s speed was 3 miles per hour and walt ' s 6 miles per hour , how many miles had lionel walked when he met walt ?
Options: a ) 12 , b ) 16 , c ) 20 , d ) 24 , e ) 28
Rationale: "in the first 4 hours lionel at the rate of 3 miles per hour covered distance = rate * time = 4 * 3 = 12 miles . so , the distance between him and walt was 48 - 12 = 36 miles when walt left his house . now , their combined rate to cover this distance was 3 + 6 = 9 miles per hour , hence they will meet ( they will cover that distance ) in time = distance / rate = 36 / 9 = 4 hours . total time that lionel was walking is 4 + 4 = 8 hours , which means that he covered in that time interval distance = rate * time = 3 * 8 = 24 miles . answer : d ."
Answer: d
Python program:
a = 3 * 3
b = 48 - a
c = 6 + 3 
d = b / c
e = d + 3 
f = 2 * 0
Problem: a certain car can travel 72 kilometers on a liter of fuel . if the fuel tank ’ s contents decrease by 3.9 gallons over a period of 5.7 hours as the car moves at a constant speed , how fast is the car moving , in miles per hour ? ( 1 gallon = 3.8 liters ; 1 mile = 1.6 kilometers )
Options: a ) 52 , b ) 65 , c ) 117 , d ) 91 , e ) 104
Rationale: "fuel used 3.9 gallons ; convert to liters - - > 3.9 x 3.8 liters time = 5.7 hours 1 mile = 1.6 kilometers ; convert to miles - - > 1 km = 1 / 1.6 mile speed ( km / hour ) = d / t = 72 ( km * ) x 3.9 x 3.8 / 5.7 replace ( km * ) to miles ; multiply by 1 / 1.6 mile speed ( miles / hour ) = 72 x 3.9 x 3.8 / 5.7 x 1.6 = 78 miles / hour ans : c ps : i felt the factors were easy to cancel out , so did n ' t require much rounding off = 72 x 3.9 x 3.8 / 5.7 x 1.6 = 117 c"
Answer: c
Python program:
a = 72 * 3
b = a / 1
c = b * 3
d = c / 5
Problem: find the probability that a leap year selected at random will have 53 sundays
Options: a ) 6 / 7 , b ) 5 / 7 , c ) 4 / 7 , d ) 3 / 7 , e ) 2 / 7
Rationale: "there are 366 days in a leap year : 52 weeks and 2 more days . so , 52 sundays and 2 days . these 2 days can be : { mon , tue } , { tue , wed } , { wed , thu } , { thu , fri } , { fri , sat } , { sat , sun } and { sun , mon } ( 7 cases ) . in order to have 53 sundays we should have either { sat , sun } or { sun , mon } case . the probability of that is 2 / 7 . answer : e ."
Answer: e
Python program:
a = 3 + 4 
b = 2 / a
Problem: a tank is 25 m long , 12 m wide and 6 m deep . the cost of plastering its walls and bottom at 75 paise per sq . m , is :
Options: a ) rs . 456 , b ) rs . 458 , c ) rs . 558 , d ) rs . 568 , e ) none of these
Rationale: explanation : area to be plastered = [ 2 ( l + b ) x h ] + ( l x b ) = { [ 2 ( 25 + 12 ) x 6 ] + ( 25 x 12 ) } m 2 = ( 444 + 300 ) m 2 = 744 m 2 . cost of plastering = rs . 744 x 75 / 100 = rs . 558 answer : c
Answer: c
Python program:
a = 25 + 12 
b = a * 2
c = b * 6
d = 25 * 12
e = c + d 
f = 75 / 100
g = e * f
Problem: if p is the product of the integers from 1 to 38 , inclusive , what is the greatest integer k for which 3 ^ k is a factor of p ?
Options: a ) 13 , b ) 15 , c ) 17 , d ) 19 , e ) 21
Rationale: "38 ! has 3 , 6 , 9 , . . . . 30 , 33 , 36 as factors , which are 12 multiples of 3 . we need to add 5 more to these 12 because of 9 , 18 , 27 , and 36 . the greatest integer of k is 17 . the answer is c ."
Answer: c
Python program:
a = 3 * 4
b = a + 3
Problem: find the average increase rate , if increase in the population in the first year is 30 % and that in the second year is 40 % .
Options: a ) 41 , b ) 56 , c ) 40 , d ) 38 , e ) 39
Rationale: solution : let 100 be the original population . 1 st year ' s population increased = 30 % so , population after first year = ( 100 + 30 % of 100 ) = 130 . population in second year increases by 40 % , then population = ( 130 + 40 % of 130 ) = 182 . the final population become 182 which was originally at 100 . it means there is 82 % increment in the population in 2 years so , average increment = 82 / 2 = 41 % . mind calculation method : increase in population is given by , 100 = = 30 % ↑ = = > 130 = = 40 % ↑ = = > 182 . hence , average increase = 82 / 2 = 41 % answer : option a
Answer: a
Python program:
a = 40 - 30
b = a + 30
Problem: rs . 6000 is lent out in two parts . one part is lent at 4 % p . a simple interest and the other is lent at 10 % p . a simple interest . the total interest at the end of one year was rs . 450 . find the ratio of the amounts lent at the lower rate and higher rate of interest ?
Options: a ) 5 : 1 , b ) 5 : 7 , c ) 5 : 2 , d ) 5 : 8 , e ) 5 : 2
Rationale: "let the amount lent at 4 % be rs . x amount lent at 10 % is rs . ( 6000 - x ) total interest for one year on the two sums lent = 4 / 100 x + 10 / 100 ( 6000 - x ) = 600 - 3 x / 100 = > 600 - 3 / 100 x = 450 = > x = 2500 amount lent at 10 % = 3500 required ratio = 5 : 7 answer : b"
Answer: b
Python program:
a = 450 * 100
b = 6000 * 4
c = a - b
d = 10 - 4
e = c / d
f = 450 * 100
g = 6000 * 4
h = f - g
i = 10 - 4
j = h / i
k = e / j
Problem: the length of a room is 5.5 m and width is 3.75 m . what is the cost of paying the floor by slabs at the rate of $ 800 per sq . metre .
Options: a ) $ 12500 , b ) $ 13500 , c ) $ 16500 , d ) $ 14500 , e ) $ 18500
Rationale: "c $ 16500 area = 5.5 × 3.75 sq . metre . cost for 1 sq . metre . = $ 800 hence , total cost = 5.5 × 3.75 × 800 = 5.5 × 3000 = $ 16500"
Answer: c
Python program:
a = 5 * 5
b = 800 * a
Problem: ? % of 360 = 115.2
Options: a ) 277 , b ) 36 , c ) 64 , d ) 32 , e ) none of these
Rationale: ? % of 360 = 115.2 or , ? = 115.2 × 100 / 360 = 32 answer d
Answer: d
Python program:
a = 115 * 2
b = a / 360
Problem: walking 7 / 6 of his usual rate , a boy reaches his school 2 min early . find his usual time to reach the school ?
Options: a ) 14 , b ) 28 , c ) 99 , d ) 77 , e ) 66
Rationale: "speed ratio = 1 : 7 / 6 = 6 : 7 time ratio = 7 : 6 1 - - - - - - - - 7 2 - - - - - - - - - ? 14 m answer : a"
Answer: a
Python program:
a = 2 * 7
Problem: what least number must be subtracted from 427398 so that remaining no . is divisible by 11
Options: a ) 3 , b ) 4 , c ) 6 , d ) 7 , e ) 8
Rationale: "explanation : on dividing 427398 by 11 we get the remainder 4 , so 4 should be subtracted answer : option b"
Answer: b
Python program:
a = 427398 / 11
b = math.floor(a)
c = b * 11
d = 427398 - c
Problem: 4 milkmen rented a pasture . a grazed 24 cows for 3 months , b 10 cows for 5 months , c 35 cows for 4 months and d 21 cows for 3 months . if a ’ s share of rent is rs . 720 , find the total rent of the field .
Options: a ) rs . 3250 , b ) rs . 3350 , c ) rs . 3450 , d ) rs . 3550 , e ) rs . 3650
Rationale: ratio of shares of a , b , c , d = ( 24 * 3 ) : ( 10 * 5 ) : ( 35 * 4 ) : ( 21 * 3 ) = 72 : 50 : 140 : 63 let total rent be rs . x . then , a ’ s share = rs . 72 x / 325 . therefore , 72 x / 325 = 720 = > x = 720 * 325 / 72 = 3250 . hence , total rent of the field is rs . 3250 . answer : a
Answer: a
Python program:
a = 24 * 3
b = 10 * 5
c = a + b 
d = 35 * 4
e = 21 * 3
f = d + e 
g = c + f 
h = 720 * g
i = 24 * 3
j = h / i
Problem: 500 , 250 , 750 , 375 . . .
Options: a ) 875 , b ) 1050 , c ) 950 , d ) 1125 , e ) 925
Rationale: "500 / 2 = 250 x 3 = 750 / 2 = 375 x 3 = 1125 answer is d"
Answer: d
Python program:
a = negate - (
Problem: at present , the ratio between the ages of shekhar and shobha is 4 : 3 . after 6 years , shekhar ' s age will be 26 years . find out the age of shobha at present ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 15 , e ) 20
Rationale: after 6 years , shekhar ' s age will be 26 years therefore , present age of shekhar = 26 − 6 = 20 let present age of shobha = x then , 20 x = 43 x = 20 × 34 = 15 answer is d .
Answer: d
Python program:
a = 26 - 6
b = a / 4
c = b * 3
Problem: if ( a - b - c + d = 12 ) and ( a + b - c - d = 6 ) , what is the value of ( b - d ) ^ 2 ?
Options: a ) 4 . , b ) 9 . , c ) 12 . , d ) 16 . , e ) 64 .
Rationale: "eq 1 : a - b - c + d = 12 eq 2 : a + b - c - d = 6 ( 1 ) subtract eq 1 from eq 2 a - b - c + d = 12 - a + b - c - d = 6 - - - - - - - - - - - - - - - - - - - - - - - - - 2 b + 2 d = 6 ( 2 ) simplify - b + d = 3 b - d = - 3 ( b - d ) ^ 2 = ( - 3 ) ^ 2 = 9 my answer : b"
Answer: b
Python program:
a = 12 + 6 
b = a / 2
c = 6 - b
d = c ** 2
Problem: ashok and pyarelal invested money together in a business and share a capital of ashok is 1 / 9 of that of pyarelal . if the incur a loss of rs 1000 then loss of pyarelal ?
Options: a ) 600 , b ) 700 , c ) 800 , d ) 900 , e ) 1000
Rationale: "let the capital of pyarelal be x , then capital of ashok = x / 9 so ratio of investment of pyarelal and ashok = x : x / 9 = 9 x : x hence out of the total loss of 1000 , loss of pyarelal = 1000 * 9 x / 10 x = 900 answer : d"
Answer: d
Python program:
a = 9 * 1000
b = 1 + 9 
c = a / b
Problem: what will be the cost of building a fence around a square plot with area equal to 81 sq ft , if the price per foot of building the fence is rs . 58 ?
Options: a ) 3944 , b ) 2287 , c ) 2977 , d ) 2088 , e ) 1298
Rationale: "let the side of the square plot be a ft . a 2 = 81 = > a = 9 length of the fence = perimeter of the plot = 4 a = 36 ft . cost of building the fence = 36 * 58 = rs . 2088 . answer : d"
Answer: d
Python program:
a = math.sqrt(81)
b = square_perimeter * (
Problem: in 1998 the profits of company n were 10 percent of revenues . in 1999 , the revenues of company n fell by 30 percent , but profits were 16 percent of revenues . the profits in 1999 were what percent of the profits in 1998 ?
Options: a ) 80 % , b ) 105 % , c ) 120 % , d ) 112 % , e ) 138 %
Rationale: "0,112 r = x / 100 * 0.1 r answer d"
Answer: d
Python program:
a = 30 / 100
b = 1 - a
c = 16 / 100
d = b * c
e = 10 / 100
f = d / e
g = f * 100
Problem: while driving from a - ville to b - town , harriet drove at a constant speed of 105 kilometers per hour . upon arriving in b - town , harriet immediately turned and drove back to a - ville at a constant speed of 145 kilometers per hour . if the entire trip took 5 hours , how many minutes did it take harriet to drive from a - ville to b - town ?
Options: a ) 138 , b ) 148 , c ) 150 , d ) 162 , e ) 174
Rationale: "5 hr = 300 min . if harriet spend equal hrs on each leg she will spend 150 min on each . since speed a - b is less than speed b - a and distance on each leg is the same , time spent on a - b is more than 150 min , which mean we can eliminate ans . a , b and c . now let plug in ans . d or e and verify which one give same distance on each leg . e . t = 174 min * leg a - b - - - > d = 105.174 / 60 = 18270 / 60 * leg b - a - - - - > d = 145 * 126 / 60 = 18270 / 60 so the correct ans . ise"
Answer: e
Python program:
a = 105 * 5
b = 105 + 145 
c = a / b
d = 5 - c
e = d * const_60
Problem: in a competitive examination in a state a , 10 % candidates got selected from the total appeared candidates . state b had an equal number of candidates appeared and 12 % candidates got selected with 100 more candidates got selected than a . what was the number of candidates appeared from each state ?
Options: a ) 4000 , b ) 5000 , c ) 5500 , d ) 6500 , e ) 4200
Rationale: "let the number of candidates appeared be x then , 12 % of x - 10 % of x = 100 2 % of x = 100 x = 100 * 100 / 2 = 5000 answer is b"
Answer: b
Python program:
a = 12 - 10
b = a * 100
c = b * 100
Problem: if it is assumed that 80 percent of those who receive a questionnaire by mail will respond and 300 responses are needed , what is the minimum number of questionnaires that should be mailed ?
Options: a ) 375 , b ) 420 , c ) 480 , d ) 500 , e ) 600
Rationale: "minimum no of mail to be sent for getting 300 responses at 80 % = 300 / 0.8 = 375 option a"
Answer: a
Python program:
a = 80 / 100
b = 300 / a
Problem: when a number is divided by 6 & then multiply by 12 the answer is 13 what is the no . ?
Options: a ) 6.5 , b ) 5 , c ) 5.5 , d ) 5.8 , e ) 6
Rationale: "if $ x $ is the number , x / 6 * 12 = 13 = > 2 x = 13 = > x = 6.5 a"
Answer: a
Python program:
a = 13 / 12
b = a * 6
Problem: in arun ' s opinion , his weight is greater than 66 kg but leas than 72 kg . his brother does not agree with arun and he thinks that arun ' s weight is greater than 60 kg but less than 70 kg . his mother ' s view is that his weight can not be greater than 69 kg . if all of them are correct in their estimation , what is the average of diferent probable weights of arun ?
Options: a ) 86.5 kg , b ) 67.5 kg , c ) 46.5 kg , d ) 26.5 kg , e ) 16.5 kg
Rationale: "let arun ' s weight be x kg . according to arun , 66 < x < 72 . according to arun ' s brother , 60 < x < 70 . according to arun ' s mother , x < 69 . the values satisfying all the above conditions are 67 and 68 . required average = ( 67 + 68 ) / 2 = 67.5 kg answer : b"
Answer: b
Python program:
a = 66 + 1 
b = 69 + a 
c = b / 2
Problem: find large no . from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 6 as quotient and the 20 as remainder
Options: a ) 1235 , b ) 1456 , c ) 1634 , d ) 1678 , e ) 1635
Rationale: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 20 5 x = 1345 x = 269 large number = 269 + 1365 = 1634 c"
Answer: c
Python program:
a = 1365 - 20
b = 6 - 1
c = a / b
d = c * 6
e = d + 20
Problem: by selling 9 pencils for a rupee a man loses 20 % . how many for a rupee should he sell in order to gain 20 % ?
Options: a ) 8 , b ) 9 , c ) 7 , d ) 4 , e ) 6
Rationale: "80 % - - - 9 120 % - - - ? 80 / 120 * 9 = 6 answer : e"
Answer: e
Python program:
a = 100 + 20 
b = 100 - 20
c = 1 / b
d = a * c
e = 1 / d
f = e * 9
Problem: in a public show 62 % of the seats were filled . if there were 600 seats in the hall , how many seats were vacant ?
Options: a ) 100 , b ) 110 , c ) 120 , d ) 140 , e ) 228
Rationale: "75 % of 600 = 62 / 100 × 600 = 372 therefore , the number of vacant seats = 600 - 372 = 228 . answer : e"
Answer: e
Python program:
a = 100 - 62
b = 600 * a
c = b / 100
Problem: there is a 30 % increase in the price of an article in the first year , a 20 % decrease in the second year and a 10 % increase in the next year . if the final price of the article is rs . 4576 , then what was the price of the article initially ?
Options: a ) rs . 5000 , b ) rs . 3000 , c ) rs . 4000 , d ) rs . 2000 , e ) rs . 6000
Rationale: "let the price of the article , four years age be rs . 100 in the 1 st year , price of the article = 100 + 30 = rs . 130 . in the 2 nd year , price = 130 - 20 % of 130 = 130 - 26 = rs . 104 . in the 3 rd year , price = 104 + 10 % of 104 = 104 + 10.4 = rs . 114.40 . but present price of the article is rs . 4576 for 114.4 - - - > 100 ; 4576 - - - > ? required price = ( 4576 * 100 ) / 114.4 = 40 * 100 = rs . 4000 . answer : c"
Answer: c
Python program:
a = 30 - 20
b = a + 10 
c = b / 100
d = 1 + c 
e = 4576 / d
Problem: 50 boys and 100 girls are examined in a test ; 50 % of the boys and 40 % of the girls pass . the percentage of the total who failed is ?
Options: a ) 42.5 % , b ) 62.1 % , c ) 56.7 % , d ) 39.9 % , e ) 51.4 %
Rationale: "total number of students = 50 + 100 = 150 number of students passed = ( 50 % of 50 + 40 % of 100 ) = 25 + 40 = 65 number of failures = 85 * 100 / 150 = 56.7 % answer is c"
Answer: c
Python program:
a = 50 + 100 
b = 50 / 100
c = 50 * b
d = 40 / 100
e = 100 * d
f = c + e 
g = a - f
h = 50 + 100 
i = g / h
j = 100 * i
Problem: if ( 5 ^ 5 ) ( 9 ^ 3 ) = 3 ( 15 ^ x ) , what is the value of x ?
Options: a ) 5 , b ) 9 , c ) 11 , d ) 13 , e ) 15
Rationale: "( 5 ^ 5 ) ( 9 ^ 3 ) = 3 ( 15 ^ x ) = > 5 ^ 5 * 3 ^ 6 = 3 * 3 ^ x * 5 ^ x = > 5 ^ 5 * 3 ^ 6 = 3 ^ ( x + 1 ) * 5 ^ x value of x = 5 answer a"
Answer: a
Python program:
a = 5 ** 5
b = 9 ** 3
c = a * b
d = c / 3
e = math.log(d)
f = math.log(15)
g = e / f
Problem: 5356 x 51 = ?
Options: a ) 273156 , b ) 273243 , c ) 273247 , d ) 273250 , e ) 273258
Rationale: "5356 x 51 = 5356 x ( 50 + 1 ) = 5356 x 50 + 5356 x 1 = 267800 + 5356 = 273156 . a"
Answer: a
Python program:
a = 5356 / 51
b = a * 100
Problem: marts income is 60 percent more than tims income and tims income is 60 percent less than juans income . what percentage of juans income is marts income
Options: a ) 124 % , b ) b ) 64 % , c ) c ) 96 % , d ) d ) 80 % , e ) e ) 64 %
Rationale: "m = ( 160 / 100 ) t t = ( 40 / 100 ) j = > m = ( 64 / 100 ) j answer b ."
Answer: b
Python program:
a = 100 + 60 
b = 100 - 60
c = 100 / b
d = c * 100
e = a / d
f = e * 100
Problem: a man swims downstream 16 km and upstream 10 km taking 2 hours each time , what is the speed of the man in still water ?
Options: a ) 7.0 , b ) 8.2 , c ) 6.5 , d ) 7 , e ) 6
Rationale: "16 - - - 2 ds = 8 ? - - - - 1 10 - - - - 2 us = 5 ? - - - - 1 m = ? m = ( 8 + 5 ) / 2 = 6.5 answer : c"
Answer: c
Python program:
a = 10 / 2
b = 16 / 2
c = a + b 
d = c / 2
Problem: the manufacturing cost of a shoe is rs . 190 and the transportation lost is rs . 500 for 100 shoes . what will be the selling price if it is sold at 20 % gains
Options: a ) s 234 , b ) s 216 , c ) s 220 , d ) s 210 , e ) s 217
Rationale: "explanation : total cost of a watch = 190 + ( 500 / 100 ) = 195 . gain = 20 % = > sp = 1.2 cp = 1.2 x 195 = 234 answer : a"
Answer: a
Python program:
a = 500 / 100
b = 190 + a 
c = 20 / 100
d = 500 / 100
e = 190 + d 
f = c * e
g = b + f
Problem: what is the area of a circle having the same perimeter as that of a square whose area is 121 .
Options: a ) 306
b ) 307
c ) 308
d ) 309
e ) 310
Rationale: side of the square = sqrt ( 12 ) = 11 perimeter of the square = 44 2 * pie * r = 44 r = 44 / 2 * pie area of the circle = pie * r ^ 2 = 308 answer : c
Answer: c
Python program:
a = math.sqrt(121)
b = a * 4
c = b / math.pi
d = c / 2
e = math.sqrt(121)
f = e * 4
g = f / math.pi
h = g / 2
i = d * h
j = i * math.pi
k = j * 2
Problem: the manager of a produce market purchased a quantity of tomatoes for $ 0.80 per pound . due to improper handling , 20 percent of the tomatoes , by weight , were ruined and discarded . at what price per pound should the manager sell the remaining tomatoes if she wishes to make a profit on the sale of the tomatoes equal to 8 percent of the cost of the tomatoes .
Options: a ) $ 0.94 , b ) $ 0.96 , c ) $ 0.98 , d ) $ 1.00 , e ) $ 1.09
Rationale: "assume the manager bought 100 tomatoes . cost price = 80 given : 20 % are damaged - - > available tomatoes to sell = 80 80 * x - 80 = 0.08 * 80 80 x - 80 = 6.4 80 x = 86.64 x = 86.64 / 80 = 87 / 80 ( approx ) = 1.0875 x is slightly under 1.0875 = 1.09 answer : e"
Answer: e
Python program:
a = 8 / 100
b = 1 + a 
c = 100 - 20
d = c / 100
e = 0 / 80
f = b * e
Problem: a sum fetched a total simple interest of rs . 4016.25 at the rate of 3 % p . a . in 5 years . what is the sum ?
Options: a ) 26775 , b ) 28772 , c ) 28821 , d ) 89255 , e ) 28871
Rationale: "principal = ( 100 * 4016.25 ) / ( 3 * 5 ) = rs . 26775 . answer : a"
Answer: a
Python program:
a = 4016 * 25
b = a / 3
c = b / 5
Problem: what is the units digit of ( 498 ) ( 915 ) ( 381 ) ( 756 ) ( 29 )
Options: a ) 0 , b ) 1 , c ) 2 , d ) 5 , e ) 6
Rationale: "just multiply the digits in the units place for each term and you will get the answer . it should be 0 . you got a 5 as a unit digit and an even number term . so the multiplication of this will definitely yield a 0 . answer has to be 0 . i also tried it using the calculator and the answer is 2 . imo c ."
Answer: c
Python program:
a = math.factorial(498)
b = math.factorial(915)
c = a * b
d = math.factorial(498)
e = math.factorial(756)
f = d * e
g = c + f 
h = g / 498
Problem: angelo and isabella are both salespersons . in any given week , angelo makes $ 590 in base salary plus 8 percent of the portion of his sales above $ 1000 for that week . isabella makes 10 percent of her total sales for any given week . for what amount of weekly sales would angelo and isabella earn the same amount of money ?
Options: a ) 23,500 , b ) 24,500 , c ) 25,500 , d ) 26,500 , e ) 27,500
Rationale: let the weekly sales of both = x 590 + ( x − 1000 ) 8 / 100 = 10 / 100 x x = 25500 answer : c
Answer: c
Python program:
a = 8 / 100
b = a * 1000
c = 590 - b
d = 10 / 100
e = 8 / 100
f = d - e
g = c / f
h = g / 1000
i = h - 1
Problem: the least number which when divided by 2 , 3 , 5 and 6 leaves a remainder 3 , but when divided by 9 leaves no remainder , is
Options: a ) 16 , b ) 63 , c ) 73 , d ) 83 , e ) none of these
Rationale: "explanation : l . c . m of 2 , 3 , 5 , 6 = 30 therefore required number is of the form 30 k + 3 . least value of k for which ( 30 k + 3 ) is divisible by 9 is k = 2 therefore required number = ( 30 x 2 + 3 ) = 63 . answer : b"
Answer: b
Python program:
a = math.lcm(2, 3)
b = math.lcm(a, 5)
c = math.lcm(b, 6)
d = c * 2
Problem: how many 4 - digit numbers ( abcd ) can be formed such that | a – d | = 2 ?
Options: a ) 2000 , b ) 1900 , c ) 1800 , d ) 1600 , e ) 1,500
Rationale: digit a can be filled in 9 ways ( excluding 0 ) digit b can be filled in 10 ways digit c can be filled in 10 ways digit d can be filled in 2 ways ( because of modulus a - d ) the answer will be 9 * 10 * 10 * 2 = 1800 ans c
Answer: c
Python program:
a = 10 * 10
b = 10 - 1
c = a * b
d = c * 2
Problem: find the smallest number of 6 digits which is exactly divisible by 111 ?
Options: a ) 12000 , b ) 15550 , c ) 100011 , d ) 158993 , e ) 100010
Rationale: "smallest number of 6 digits is 100000 . on dividing 100000 by 111 , we get 100 as remainder . number to be added = ( 111 - 100 ) - 11 . hence , required number = 100011 answer b"
Answer: b
Python program:
a = 100 * 100
b = 10 * a
c = b - 100
d = c + 111
Problem: if the mean of numbers 28 , x , 42 , 78 and 104 is 90 , then what is the mean of 128 , 255 , 511 , 1023 and x ?
Options: a ) 395 , b ) 275 , c ) 355 , d ) 423 , e ) 365
Rationale: the mean of numbers 28 , x , 42 , 78 and 104 is 62 : 28 + x + 42 + 78 + 104 = 90 * 5 - - > x = 198 ; so , the mean of 128 , 255 , 511 , 1023 and x is ( 128 + 255 + 511 + 1023 + 198 ) / 5 = 423 . answer : d .
Answer: d
Python program:
a = 4 + 1 
b = 90 * a
c = 28 + 42 
d = c + 78 
e = d + 104 
f = b - e
g = f + 128 
h = g + 255 
i = h + 511 
j = i + 1023 
k = 4 + 1 
l = j / k
Problem: a boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 12 minutes . how long will it take to go 5 km in stationary water ?
Options: a ) 40 minutes , b ) 1 hour , c ) 1 hour 25 min , d ) 1 hour 30 min , e ) 1 hour 10 min
Rationale: "speed ( upstream ) = 2 / 1 = 2 kmhr speed ( downstream ) = 1 / ( 12 / 60 ) = 5 kmhr speed in still water = 1 / 2 ( 2 + 5 ) = 3.5 kmhr time taken in stationary = 5 / 3.5 = 1 hrs 25 min answer : c"
Answer: c
Python program:
a = 1 / 12
b = a * const_60
c = 2 / 2
d = b + c 
e = d / 2
f = 5 / e