euclaise/mathqa_programs huggingface dataset:
Problem: a store owner estimates that the average price of type a products will increase by 40 % next year and that the price of type b products will increase by 10 % 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 ) $ 15,430 , c ) $ 16,000 , d ) $ 16,225 , e ) $ 17,155
Rationale: "cost of type a products next year = 1.40 * 4500 = 6300 cost of type b products next year = 1.1 * 8300 = 9130 total 6300 + 9130 = 15430 option b"
Answer: b
Python program:
a = 3 / 4
b = a * 1000
Problem: the school soccer team looks at their record and finds that they win , lose , and tie games in a ratio of 4 : 3 : 1 . how many games did they play if they lost 9 games ?
Options: a ) 3 , b ) 9 , c ) 12 , d ) 18 , e ) 24
Rationale: the ratio is 4 wins : 3 losses : 1 tie . think of ratio as ` ` parts . ' ' divide 9 ( total losses ) by 3 ( ratio losses ) to find 1 ` ` part ' ' of the ratio . 9 / 3 = 3 this means the team tied 3 games . multiply 3 ( 1 ` ` part ' ' of ratio ) by 4 ( ratio wins ) to find total wins . 3 * 4 = 12 . this mean the team won 12 games . add up wins , losses , and ties . 12 + 9 + 3 = 24 the answer is e
Answer: e
Python program:
a = 9 / 3
b = 4 + 3 
c = b + 1 
d = a * c
Problem: if 9 gallons of gasoline are added to a tank that is already filled to 3 / 4 of its capacity , the tank is then filled to 9 / 10 of its capacity . how many gallons does the tank hold ?
Options: a ) 20 , b ) 24 , c ) 36 , d ) 40 , e ) 54
Rationale: "let the capacity of the tank = c ( 3 / 4 ) c + 9 = ( 9 / 10 ) c = > ( 9 / 10 ) c - ( 3 / 4 ) c = 9 = > ( 3 / 20 ) c = 9 = > c = ( 9 * 20 ) / 3 = 60 number of gallons of gasoline that the tank currently holds = 3 / 4 * c + 9 = 45 + 9 = 54 answer e"
Answer: e
Python program:
a = 9 / 10
b = 3 / 4
c = a - b
d = 9 / c
e = 3 / 4
f = d * e
g = f + 9
Problem: what is the remainder when 121212 . . . . . . . ( 300 ) digits is divided by 99 .
Options: a ) 18 , b ) 36 , c ) 72 , d ) 0 , e ) 1
Rationale: 12 / 99 = 12 1212 / 99 = 24 121212 / 99 = 36 . . . 121212 . . . ( 300 ) / 99 = ( 12 * 300 ) % 99 = 36 if they say 300 digits then ( 12 * 150 ) % 99 = 18 answer : a
Answer: a
Python program:
a = 10 + 1 
b = 99 / a
c = b * 2
Problem: walking 9 / 8 of his usual rate , a boy reaches his school 4 min early . find his usual time to reach the school ?
Options: a ) 22 , b ) 99 , c ) 27 , d ) 36 , e ) 20
Rationale: "speed ratio = 1 : 9 / 8 = 8 : 9 time ratio = 9 : 8 1 - - - - - - - - 9 4 - - - - - - - - - ? 36 m . answer : d"
Answer: d
Python program:
a = 4 * 9
Problem: the average of 30 numbers is 48 . if three numbers namely 45 , 55 and 43 are discarded , the average of remaining numbers is ?
Options: a ) 47 , b ) 47.03 , c ) 48.03 , d ) 48 , e ) 49
Rationale: "explanation : total of 30 numbers = 30 * 48 = 1440 average o 27 numbers = 1440 - ( 45 + 55 + 43 ) / 27 = 48.03 answer : option c"
Answer: c
Python program:
a = 55 * 30
b = 48 * 30
c = a - b
Problem: a man rows his boat 95 km downstream and 45 km upstream , taking 2 1 / 2 hours each time . find the speed of the stream ?
Options: a ) 5 kmph , b ) 7 kmph , c ) 9 kmph , d ) 8 kmph , e ) 10 kmph
Rationale: "speed downstream = d / t = 95 / ( 2 1 / 2 ) = 38 kmph speed upstream = d / t = 45 / ( 2 1 / 2 ) = 18 kmph the speed of the stream = ( 38 - 18 ) / 2 = 10 kmph answer : e"
Answer: e
Python program:
a = 95 / 2
b = 45 / 2
c = a - b
d = c / 2
Problem: a company has 15 managers and 75 associates . the 15 managers have an average salary of $ 210,000 . the 75 associates have an average salary of $ 30,000 . what is the average salary for the company ?
Options: a ) $ 35,000 , b ) $ 45,000 , c ) $ 55,000 , d ) $ 60,000 , e ) $ 75,000
Rationale: "another method is to get ratios say 30000 = a and we know the # of people are in 1 : 5 ratio average = ( 7 a * 1 + a * 5 ) / 6 = 12 a / 6 = 2 a = 60000 answer is d . $ 60,000"
Answer: d
Python program:
a = 3 * 3
b = a * 10
c = 100 * 10
d = b * c
e = 3 * 10
f = 100 * 10
g = e * f
h = d + g 
i = 75 + 15 
j = h / i
Problem: a batsman scored 1 runs in his 18 th innings and that makes his average 18 . find his average upto the 17 th innings ?
Options: a ) 19 , b ) 20 , c ) 21 , d ) 22 , e ) 23
Rationale: avg = sum of the value / no . of the value 18 = ( sum of the first 17 innings score + 1 ) / 18 ( 18 * 18 - 1 ) = sum of the first 17 innings score sum of the first 17 innings score = 323 ave upto 17 innings = 323 / 17 = 19 answer : a
Answer: a
Python program:
a = 18 * 18
b = a - 1
c = b / 17
Problem: if jack walked 9 miles in 1 hour and 15 minutes , what was his rate of walking in miles per hour ?
Options: a ) 4 , b ) 4.5 , c ) 6 , d ) 6.25 , e ) 7.2
Rationale: "distance walked in 1 hour and 15 mins = 9 miles speed per hour = distance / time = 9 / ( 5 / 4 ) = 7.2 miles per hour answer e"
Answer: e
Python program:
a = 9 * const_60
b = 15 + const_60 
c = a / b
Problem: a student chose a number , multiplied it by 2 , then subtracted 148 from the result and got 110 . what was the number he chose ?
Options: a ) 90 , b ) 129 , c ) 120 , d ) 160 , e ) 200
Rationale: "solution : let x be the number he chose , then 2 * x * 148 = 110 2 x = 258 x = 129 correct answer b"
Answer: b
Python program:
a = 110 + 148 
b = a / 2
Problem: a crate measures 3 feet by 8 feet by 12 feet on the inside . a stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides . what is the radius , in feet , of the pillar with the largest volume that could still fit in the crate ?
Options: a ) 27 , b ) 3 , c ) 6 , d ) 8 , e ) 12
Rationale: "we can find the radius of all the three cases of cylinders . the only crux to find the answer faster is that : voulme is pi * r ^ 2 * h . the volume is a function of r ^ 2 . so r has to be the highest to find the largest volume . so r = 3 for the surface 8 * 12 face . volume = 27 pi answer b"
Answer: b
Python program:
a = 8 * 12
b = a * 3
c = b / 12
d = c / 8
Problem: if [ x ] is the greatest integer less than or equal to x , what is the value of [ 1.6 ] + [ - 3.4 ] + [ 10.7 ] ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "you are asked what the closest lesser integer value to [ x ] is . [ 1.6 ] = 1.0 [ - 3.4 ] = - 4.0 [ 10.7 ] = 10.0 therefore , answer is : 1.0 - 4.0 + 10.0 = 7.0 option e ."
Answer: e
Python program:
a = 3 + 4 
b = a - 1
Problem: a firm is comprised of partners and associates in a ratio of 2 : 61 . if 75 more associates were hired , the ratio of partners to associates would be 4 : 137 . how many partners are currently in the firm ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: "the ratio 2 : 61 = 4 : 122 so the ratio changed from 4 : 122 to 4 : 137 . 137 - 122 = 15 which is 1 / 5 of the increase in 75 associates . the ratio changed from 20 : 610 to 20 : 685 . thus the number of partners is 20 . the answer is e ."
Answer: e
Python program:
a = 137 * 2
b = a - 61
c = 75 / b
d = c * 2
Problem: evaluate : 37 - 18 ÷ 3 × 2 =
Options: a ) 20 , b ) 25 , c ) 27 , d ) 22 , e ) 17
Rationale: "according to order of operations , 18 ÷ 3 × 2 ( division and multiplication ) is done first from left to right 18 ÷ 3 × 2 = 6 × 2 = 12 hence 37 - 18 ÷ 3 × 2 = 37 - 12 = 25 correct answer b ) 25"
Answer: b
Python program:
a = 18 * 3
b = a * 2
c = 37 - b
Problem: a train 225 m long running at 90 kmph crosses a platform in 25 sec . what is the length of the platform ?
Options: a ) 271 , b ) 266 , c ) 400 , d ) 277 , e ) 232
Rationale: "length of the platform = 90 * 5 / 18 * 25 = 625 – 225 = 400 answer : c"
Answer: c
Python program:
a = 90 * const_0_2778
b = 25 * a
c = b - 225
Problem: in an election only two candidates contested 20 % of the voters did not vote and 120 votes were declared as invalid . the winner got 200 votes more than his opponent thus he secured 41 % votes of the total voters on the voter list . percentage votes of the defeated candidate out of the total votes casted is :
Options: a ) 22 , b ) 389 , c ) 38 , d ) 45 , e ) 01
Rationale: let there be x voters and k votes goes to loser then 0.8 x - 120 = k + ( k + 200 ) k + 200 = 0.41 x \ inline \ rightarrow k = 1440 and ( k + 200 ) = 1640 therefore \ inline \ frac { 1440 } { 3200 } \ times 100 = 45 % answer : d ) 45 %
Answer: d
Python program:
a = 10 + 20 
b = 41 / 100
c = b * 1000
d = a + c 
e = d + 1000 
f = 200 + 120 
g = f * 10
h = e / g
i = h * 100
Problem: a 600 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec . what is the length of the platform ?
Options: a ) 800 , b ) 700 , c ) 360 , d ) 370 , e ) 380
Rationale: "speed = 600 / 18 = 100 / 3 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 39 = 100 / 3 = > x = 1300 m . l = 1300 - 600 = 700 m answer : option b"
Answer: b
Python program:
a = speed * (
b = a - 39
Problem: 17 times a number gives 187 . the number is
Options: a ) 11 , b ) 12 , c ) 13.2 , d ) none , e ) can not be determined
Rationale: "explanation : let the number be ' n ' 17 × n = 187 ⇒ n = 11 correct option : a"
Answer: a
Python program:
a = 187 / 17
b = 187 / a
Problem: 0.0008154 / 0.00205 x 16.5 = ?
Options: a ) 8.5 , b ) 6.6 , c ) 7.6 , d ) 6.4 , e ) 5.7
Rationale: "explanation : ? = 0.0008154 / 0.00205 x 16.5 = 6.6 answer : option b"
Answer: b
Python program:
a = 0 / 8154
Problem: tammy climbed a mountain in two days . she spent a total of 14 hours climbing the mountain . on the second day , she walked at an average speed that was half a kilometer per hour faster , but 2 hours less than what she walked on the first day . if the total distance she climbed during the two days is 52 kilometers , how many r kilometers per hour did tammy walk on the second day ?
Options: a ) 3 , b ) 3.5 , c ) 4 , d ) 4.5 , e ) 6
Rationale: "ans : c total time = 14 hrs let time traveled during 1 st day = x let time traveled during 2 nd day = x - 2 total time = 14 x + x - 2 = 14 x = 8 speed * time = distance s * 8 + ( s + 0.5 ) ( 8 - 2 ) = 52 solving s = 4.5 now speed for 2 nd day is 0.5 less than the 1 st day which is 4.5 thus speed for 2 nd day = 4 its simple algebra for s * 8 + ( s + 0.5 ) ( 8 - 2 ) = 52 but for some reason im getting 3.5 and not 4.5 . 8 s + 6 s + 3 = 52 14 s = 49 s = 3.5"
Answer: c
Python program:
a = 14 + 2 
b = a / 2
c = b - 2
d = c / 2
e = 52 - d
f = 14 + 2 
g = f / 2
h = g - 2
i = 14 + 2 
j = i / 2
k = h + j 
l = e / k
m = 1 / 2
n = l + m
Problem: a man sitting in a train which is traveling at 80 kmph observes that a goods train , traveling in opposite direction , takes 9 seconds to pass him . if the goods train is 280 m long , find its speed . ?
Options: a ) 32 kmph , b ) 58 kmph , c ) 62 kmph , d ) 65 kmph , e ) 75 kmph
Rationale: "relative speed = 280 / 9 m / sec = ( ( 280 / 9 ) * ( 18 / 5 ) ) kmph = 112 kmph . speed of goods train = ( 112 - 80 ) kmph = 32 kmph . answer : a"
Answer: a
Python program:
a = 280 / 9
b = a * const_3_6
c = b - 80
Problem: howmany 3 digit numbers are there tens digit place is more than hundreds digit place and units place less than hundreds digit place ?
Options: a ) 80 , b ) 100 , c ) 110 , d ) 120 , e ) 140
Rationale: we have numbers { 01 , 23 , 45 , 67 , 89 } now we would decide the cases on behalf of value of hundred place digit . and accordingly choose unit ' s digit and ten ' s digit . value of hundred place digit must be choosen in such a manner that there should exist a greater digit for ten ' s place and a smaller digit for unit place . thus we can have values of hundred ' s digit from 12 , 34 , 56 , 78 only now starting from hundred ' s digit = 8 : hundred ' s digit possible values for ten ' s digit possible values for unit digit total ways 8 9 01 , 23 , 45 , 67 1 * 1 * 8 = 8 7 89 0 , 12 , 34 , 56 1 * 2 * 7 = 14 6 7 , 89 01 , 23 , 45 1 * 3 * 6 = 18 5 67 , 89 0 , 12 , 34 1 * 4 * 5 = 20 4 5 , 67 , 89 01 , 23 1 * 5 * 4 = 20 3 45 , 67 , 89 0 . 1.2 1 * 6 * 3 = 18 2 3 , 45 , 67 , 89 01 1 * 7 * 2 = 14 1 23 , 45 , 67 , 89 0 1 * 8 * 1 = 8 so , total no of cases = 8 + 14 + 18 + 20 + 20 + 18 + 14 + 8 = 120 hence total no of possible 3 digit numbers = 120 answer : d
Answer: d
Python program:
a = 3 * 10
b = a * 4
Problem: a = 7 ^ 15 - 625 ^ 3 and a / x is an integer , where x is a positive integer greater than 1 , such that it does not have a factor p such that 1 < p < x , then how many different values for x are possible ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: "this is a tricky worded question and i think the answer is should be d not c . . . here is my reason : the stem says that x is a positive integer such that has no factor grater than 2 and less than x itself . the stem wants to say that x is a prime number . because any prime number has no factor grater than 1 and itself . on the other hand the stem says that x could get how many different number not must get different number ( this is very important issue ) as our friends say , if we simplify numerator more we can obtain : 5 ^ 12 ( 5 ^ 3 - 1 ) = 5 ^ 12 ( 124 ) = 5 ^ 12 ( 31 * 2 * 2 ) divided by x and we are told that this fraction is an integer . so , x could be ( not must be ) 5 , 31 , or 2 ! ! ! so , x could get 4 different values and answer is e . . . ."
Answer: e
Python program:
a = 3 * 4
b = 15 - a
Problem: average of 10 matches is 32 , how many runs one should should score to increase his average by 4 runs .
Options: a ) 70 , b ) 76 , c ) 78 , d ) 80 , e ) 88
Rationale: "explanation : average after 11 innings should be 36 so , required score = ( 11 * 36 ) - ( 10 * 32 ) = 396 - 320 = 76 answer : option b"
Answer: b
Python program:
a = 32 + 4 
b = 10 + 1 
c = a * b
d = 10 * 32
e = c - d
Problem: a particular library has 300 books in a special collection , all of which were in the library at the beginning of the month . these book are occasionally loaned out through an inter - library program . if , by the end of the month , 65 percent of books that were loaned out are returned and there are 244 books in the special collection at that time , how many books of the special collection were loaned out during that month ?
Options: a ) 120 , b ) 140 , c ) 160 , d ) 180 , e ) 200
Rationale: "the total number of books is 300 . let x be the number of books which were loaned out . 65 % of books that were loaned out are returned . 35 % of books that were loaned out are not returned . now , there are 244 books , thus the number of un - returned books is 300 - 244 = 56 books . 0.35 x = 56 x = 160 the answer is c ."
Answer: c
Python program:
a = 300 - 244
b = 65 / 100
c = 1 - b
d = a / c
Problem: in a lake , there is a patch of lily pads . every day , the patch doubles in size . it takes 58 days for the patch to cover the entire lake , how many days would it take the patch to cover half of the lake ?
Options: a ) 57 , b ) 2 ^ 4 * 3 , c ) 24 , d ) 38 , e ) 47
Rationale: "so 57 days answer a = 57"
Answer: a
Python program:
a = 58 - 1
Problem: joshua and jose work at an auto repair center with 1 other workers . for a survey on health care insurance , 2 of the 6 workers will be randomly chosen to be interviewed . what is the probability that joshua and jose will both be chosen ?
Options: a ) 1 / 15 , b ) 1 / 12 , c ) 1 / 9 , d ) 1 / 6 , e ) 1 / 3
Rationale: "two methods 1 ) probability of chosing josh first = 1 / 3 probability of chosing jose second = 1 / 2 total = 1 / 6 probability of chosing jose first = 1 / 3 probability of chosing josh second = 1 / 2 total = 1 / 6 final = 1 / 6 + 1 / 6 = 1 / 3 e"
Answer: e
Python program:
a = math.factorial(6)
b = math.factorial(2)
c = math.factorial(1)
d = b * c
e = a / d
f = math.factorial(6)
g = e / f
Problem: what is the value of n if the sum of the consecutive odd intergers e from 1 to n equals 169 ?
Options: a ) 47 , b ) 25 , c ) 37 , d ) 33 , e ) 29
Rationale: "before you tackle this question you must first understand that the question is comprised of two key parts , 1 st is finding out how manytermsis in that sequence and 2 nd whatactual number valuethat term is . in an arithmetic progression , in this case consecutive odd integers 1 , 3 , 5 , . . . . , there are two set of rules . rule # 1 ( arithmetic sequence ) : xn = a + d ( n - 1 ) identifies what the actual # in the sequence would be . each number in the sequence has a term such as 1 ( is the first term ) , 3 ( is the second term ) and so on . so if i were to ask you to find out what the 10 th term is of that sequence you would use that formula to find that value . a = 1 ( first term ) d = 2 ( the common difference ) remember in the sequence 1 , 3 , 5 , 7 the common difference is always 2 * on a side note we use n - 1 because we do n ' t have d in the first term , therefore if we were solving for the first term we would get 0 as n - 1 and 0 times d would give us 0 , leaving only the first term . this works regardless what your first term is in any sequence . but remember the question askswhat is thevalueof n if the sum of the consecutive odd integers from 1 to n equals 169 ? which means we first need a consecutive sequence that sums up to 169 and than find what the value of the n is , in this case it would be the last number in that sequence . in order to find that we first need to knowhow many terms ( how many of the n there is ) in order to be able to plug n in this formula given we know what the sum is . for that to happen we need to use rule # 2 . rule # 2 ( summing an arithmetic series ) : 169 = n / 2 ( 2 a + ( n - 1 ) d ) . given the question gives us what the sum is ( 169 in this case ) we would simply use this formula to solve for n . once we solve for n ( 13 in this case ) we can simply plug n into the first formula ( rule 1 ) and find the value . it feels very confusing and difficult at first , but once you identify the steps all you need to do is plug and play . we have the sum ( 169 ) of a sequence , the number of terms in that sequence is ( unknown ) . rule # 2 tells us how many numbers there are in that sequence and rule # 1 gives us what that last term is ."
Answer: b
Python program:
a = math.sqrt(169)
b = a * 2
c = 2 * 1
d = b - c
e = d + 1
Problem: joseph completes work worth $ 3.25 in hour and his cost to company per hour is $ 2.85 . ray completes worth worth of $ 2.80 in an hour and his cost to company is $ 2.65 per hour . if joseph works for 55000 hours , how many must ray work so that company makes at least as much in total gross profit as in case of joseph ?
Options: a ) 7858 , b ) 8301 , c ) 14667 , d ) 63840 , e ) 146,667
Rationale: joseph : profit / hour = 3.25 - 2.85 = 0.4 : no of hours = 55,000 : gross profit = 55,000 * 0.4 = 22,000 ray : profit / hour = 0.15 : gross profit = 22,000 : no of hours = 22,000 / 0.15 = 220,000 / 1.5 ( only closes is 146,667 ) answer e
Answer: e
Python program:
a = 3 - 25
b = 10 * 100
c = 55000 / b
d = a * c
e = 2 - 8
f = d / e
Problem: a train 250 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is :
Options: a ) 95 , b ) 50 , c ) 12 , d ) 13 , e ) 67
Rationale: "speed of the train relative to man = ( 250 / 10 ) m / sec = ( 25 ) m / sec . [ ( 25 ) * ( 18 / 5 ) ] km / hr = 90 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 90 = = > x = 95 km / hr . answer : option a"
Answer: a
Python program:
a = 5 * const_0_2778
b = a * 5
c = 250 - b
d = c / 5
e = d / const_0_2778
Problem: of the 200 employees at company x , 50 are full - time , and 150 have worked at company x for at least a year . there are 10 employees at company x who aren ’ t full - time and haven ’ t worked at company x for at least a year . how many full - time employees of company x have worked at the company for at least a year ?
Options: a ) 20 , b ) 30 , c ) 10 , d ) 80 , e ) 100
Rationale: "200 employees 50 are full - time 150 have worked at company x for at least a year 10 employees at company x who aren ’ t full - time and haven ’ t worked at company x for at least a year . how many full - time employees of company x have worked at the company for at least a year ? 200 - 50 = 150 employees not full time 150 - 10 = 140 employees not full time who worked over a year 150 employees have worked at company x for at least a year - 140 employees not full time who worked over a year = 10 full - time employees of company x have worked at the company for at least a year ans c"
Answer: c
Python program:
a = 200 - 50
b = a - 10
Problem: population is 24000 . population increases by 10 % every year , then the population after 3 years is ?
Options: a ) 26630 , b ) 26640 , c ) 36644 , d ) 31944 , e ) 26844
Rationale: "population after 1 st year = 24000 * 10 / 100 = 2400 = = = > 24000 + 2400 = 26400 population after 2 nd year = 26400 * 10 / 100 = 2640 = = = > 26400 + 2640 = 29040 population after 3 rd year = 29040 * 10 / 100 = 2904 = = = > 29040 + 2904 = 31944 answer : d"
Answer: d
Python program:
a = 3 * 10
b = a / 100
c = 1 + b 
d = 24000 * c
Problem: a man purchased 3 blankets @ rs . 100 each , 2 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 150 . find the unknown rate of two blankets ?
Options: a ) 278 , b ) 900 , c ) 278 , d ) 450 , e ) 772
Rationale: "10 * 150 = 1500 3 * 100 + 2 * 150 = 600 1500 – 600 = 900 answer : b"
Answer: b
Python program:
a = 10 * 150
b = 3 * 100
c = 2 * 150
d = b + c 
e = a - d
Problem: find the least number which when divided by 34 and 5 leaves a remainder of 4 in each case .
Options: a ) 170 , b ) 172 , c ) 174 , d ) 176 , e ) 178
Rationale: "the least number which when divided by different divisors leaving the same remainder in each case = lcm ( different divisors ) + remainder left in each case . hence the required least number = lcm ( 31 , 5 ) + 4 = 174 . answer : c"
Answer: c
Python program:
a = math.lcm(34, 5)
b = 4 + a
Problem: an artist wishes to paint a circular region on a square poster that is 3 feet on a side . if the area of the circular region is to be 1 / 2 the area of the poster , what must be the radius of the circular region in feet ?
Options: a ) 1 / pi , b ) sqrt ( 2 / pi ) , c ) sqrt ( 4.5 / pi ) , d ) 2 / sqrt ( pi ) , e ) pi / 2
Rationale: "area of the poster is 3 x 3 = 9 1 / 2 the area = 4.5 pi * r ^ 2 = 4.5 r ^ 2 = 4.5 / pi r = sqrt ( 4.5 / pi ) answer ( c )"
Answer: c
Python program:
a = square_area / (
b = a / 2
c = math.sqrt(b)
Problem: two trains 120 m and 150 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?
Options: a ) 10.9 sec , b ) 14.8 sec , c ) 10.6 sec , d ) 10.8 sec , e ) 9.27 sec
Rationale: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 120 + 150 = 270 m . required time = 270 * 9 / 250 = 9.27 = 9.27 sec . answer : e"
Answer: e
Python program:
a = 120 + 150 
b = 60 + 40 
c = b * const_0_2778
d = a / c
Problem: a 160 meter long train crosses a man standing on the platform in 8 sec . what is the speed of the train ?
Options: a ) 96 kmph , b ) 94 kmph , c ) 92 kmph , d ) 86 kmph , e ) 72 kmph
Rationale: "s = 160 / 8 * 18 / 5 = 72 kmph answer : e"
Answer: e
Python program:
a = 160 / 8
b = a * const_3_6
Problem: 18 beavers , working together in a constant pace , can build a dam in 12 hours . how many hours will it take 12 beavers that work at the same pace , to build the same dam ?
Options: a ) 2 . , b ) 4 . , c ) 5 . , d ) 6 , e ) 18 .
Rationale: "total work = 18 * 12 = 216 beaver hours 12 beaver * x = 216 beaver hours x = 216 / 12 = 18 answer : e"
Answer: e
Python program:
a = 12 * 18
b = a / 12
Problem: a batsman makes a score of 87 runs in the 17 th inning and thus increases his avg by 3 . find his average after 17 th inning .
Options: a ) 12 , b ) 39 , c ) 43 , d ) 52 , e ) 34
Rationale: "let the average after 17 th inning = x . then , average after 16 th inning = ( x - 3 ) . : . 16 ( x - 3 ) + 87 = 17 x or x = ( 87 - 48 ) = 39 . ans : b"
Answer: b
Python program:
a = 17 * 3
b = 87 - a
c = b + 3