euclaise/mathqa_programs huggingface dataset:
Problem: 1 / 2 + [ ( 2 / 3 * 3 / 8 ) + 4 ] - 8 / 16 =
Options: a ) 29 / 16 , b ) 19 / 16 , c ) 15 / 16 , d ) 17 / 4 , e ) 0
Rationale: 1 / 2 + [ ( 2 / 3 * 3 / 8 ) + 4 ] - 8 / 16 = 1 / 2 + [ ( 1 / 4 ) + 4 ] - 8 / 16 = 1 / 2 + [ 17 / 4 ] - 9 / 16 = 8 / 16 + 68 / 16 - 8 / 16 = 68 / 16 = 17 / 4 d
Answer: d
Python program:
a = 2 / 3
b = 3 / 8
c = a * b
d = c + 4 
e = 1 / 2
f = d + e 
g = 8 / 16
h = f - g
Problem: michelle deposited a certain sum of money in a savings account on july 1 st , 2007 . she earns an 6 % interest compounded semiannually . the sum of money in the account on december 31 st , 2009 is approximately what percent of the initial deposit ?
Options: a ) 117 % , b ) 120 % , c ) 121 % , d ) 135 % , e ) 140 %
Rationale: "since michelle earns 6 % interest compounded semiannually , then she earns 3 % interest every 6 months . now , the simple interest earned in 5 periods ( 30 months = 5 * 6 months ) would be 3 % * 5 = 15 % . but , since the interest iscompoundedevery 6 months , then there would be interest earned on interest ( very small amount ) thus the actual interest earned would be a little bit more than 15 % , only answer choice a fits . answer : a"
Answer: a
Python program:
a = 6 / 100
b = a / 2
c = 1 + b 
d = 2 + 3 
e = c ** d
f = e * 100
Problem: a company producing fruit juice changed its packaging from boxes measuring 5 x 10 x 20 centimeters to boxes measuring 6 x 10 x 20 centimeters . if the price of a box did not change and all boxes are full of juice , by approximately what percent did the price of the juice decrease ?
Options: a ) 12.00 % , b ) 16.67 % , c ) 18.33 % , d ) 20.00 % , e ) 21.50 %
Rationale: suppose when v = 5 x 10 x 20 = 1000 cm , the price is $ 1200 per cm price = $ 1.2 the price is $ 1200 if v = 6 x 10 x 20 = 1000 cm . per cm price = $ 1.0 so the price is decreased by $ 0.2 so the % price decreased by $ 0.2 / 1.20 = 16.67 % answer : b
Answer: b
Python program:
a = 5 * 10
b = a * 20
c = 6 * 10
d = c * 20
e = b / d
f = 1 - e
g = f * 100
Problem: if $ 5,000 is invested in an account at a simple annual rate of r percent , the interest is $ 250 . when $ 19,000 is invested at the same interest rate , what is the interest from the investment ?
Options: a ) $ 700 , b ) $ 750 , c ) $ 800 , d ) $ 950 , e ) $ 900
Rationale: "- > 250 / 5,000 = 5 % and 19,000 * 5 % = 950 . thus , d is the answer ."
Answer: d
Python program:
a = 2 * 100
b = a * 100
c = 250 * b
d = 2 * 100
e = d * 100
f = e / 4
g = c / f
Problem: a man can row 4.2 km / hr in still water . it takes him twice as long to row upstream as to row downstream . what is the rate of the current ?
Options: a ) 1.9 , b ) 1.7 , c ) 1.4 , d ) 1.5 , e ) 1.1
Rationale: "speed of boat in still water ( b ) = 4.2 km / hr . speed of boat with stream ( down stream ) , d = b + u speed of boat against stream ( up stream ) , u = b – u it is given upstream time is twice to that of down stream . ⇒ downstream speed is twice to that of upstream . so b + u = 2 ( b – u ) ⇒ u = b / 3 = 1.4 km / hr . answer : c"
Answer: c
Python program:
a = 4 * 2
b = a - 4
c = b / 3
Problem: divide rs . 116000 among 3 persons a , b and c such that the ratio of the shares of a and b is 3 : 4 and that of b : c is 5 : 6 . find the share of a ?
Options: a ) 29491 , b ) 28491 , c ) 39491 , d ) 49491 , e ) 59491
Rationale: compound ratio of a : b : c a : b = 3 : 4 b : c = 5 : 6 - - - - - - - - - - a : b : c = 15 : 20 : 24 we can divide rs . 116000 in this ratio . share of a = 15 / 59 * 116000 = 29491 answer : a
Answer: a
Python program:
a = 3 * 5
b = 3 * 5
c = 4 * 5
d = b + c 
e = 4 * 6
f = d + e 
g = a / f
h = 116000 * g
Problem: in a certain corporation , there are 300 male employees and 150 female employees . it is known that 40 % of the male employees have advanced degrees and 40 % of the females have advanced degrees . if one of the 450 employees is chosen at random , what is the probability this employee has an advanced degree or is female ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 5 , d ) 7 / 10 , e ) 11 / 15
Rationale: "p ( female ) = 150 / 450 = 1 / 3 p ( male with advanced degree ) = 0.4 * 300 / 450 = 120 / 450 = 4 / 15 the sum of the probabilities is 9 / 15 = 3 / 5 the answer is c ."
Answer: c
Python program:
a = 40 * 40
b = 40 / a
c = 1 - b
d = c * 150
e = d / 450
f = 40 * 40
g = 40 / f
h = g * 300
i = 40 * 40
j = 40 / i
k = j * 150
l = h + k 
m = l / 450
n = e + m
Problem: in a park there are two ponds with both brown ducks and green ducks . in the smaller pond there are 20 ducks and in the larger pond there are 80 ducks . if 20 % of the ducks in the smaller pond are green and 15 % of the ducks in the larger pond are green , then what percentage of ducks are green ?
Options: a ) 13 % , b ) 14 % , c ) 15 % , d ) 16 % , e ) 17 %
Rationale: "number of ducks in small pond = 20 green ducks in small pond = 20 % of 20 = 4 ducks number of ducks in large pond = 80 green ducks in large pond = 15 % of 80 = 12 ducks total number of ducks = 20 + 80 = 100 total number of green ducks = 4 + 12 = 16 ducks percentage of green ducks = 16 / 100 * 100 = 16 % answer : d"
Answer: d
Python program:
a = 20 / 100
b = 20 * a
c = 15 / 100
d = 80 * c
e = b + d 
f = 20 + 80 
g = e / f
h = g * 100
Problem: the current of a stream runs at the rate of 5 kmph . a boat goes 6 km and back to the starting point in 2 hours , then find the speed of the boat in still water ?
Options: a ) a ) 7.63 , b ) b ) 2.6 , c ) c ) 8.83 , d ) d ) 6.69 , e ) e ) 3
Rationale: "s = 5 m = x ds = x + 5 us = x - 5 6 / ( x + 5 ) + 6 / ( x - 5 ) = 2 x = 8.83 answer : c"
Answer: c
Python program:
a = 5 ** 2
b = a / 2
Problem: if two projectiles are launched at the same moment from 1386 km apart and travel directly towards each other at 445 km per hour and 545 km per hour respectively , how many minutes will it take for them to meet ?
Options: a ) 80 , b ) 82 , c ) 84 , d ) 86 , e ) 88
Rationale: "the projectiles travel a total of 990 km per hour . the time to meet is 1386 / 990 = 1.4 hours = 84 minutes the answer is c ."
Answer: c
Python program:
a = 445 + 545 
b = 1386 / a
c = b * const_60
Problem: find the average of all the numbers between 11 and 21 which are divisible by 2 .
Options: a ) 15 , b ) 18 , c ) 16 , d ) 22 , e ) none
Rationale: "sol . average = ( 12 + 14 + 16 + 18 + 20 / 5 ) = 80 / 5 = 16 . answer c"
Answer: c
Python program:
a = 11 + 4 
b = 21 - 4
c = a + b 
d = c / 2
Problem: a train speeds past a pole in 15 sec and a platform 140 m long in 25 sec , its length is ?
Options: a ) 238 , b ) 150 , c ) 988 , d ) 210 , e ) 171
Rationale: "let the length of the train be x m and its speed be y m / sec . then , x / y = 15 = > y = x / 15 ( x + 140 ) / 25 = x / 15 = > x = 210 m . answer : d"
Answer: d
Python program:
a = 2 - 1
b = 140 * a
Problem: a shopkeeper sells 20 % of his stock at 10 % profit ans sells the remaining at a loss of 5 % . he incurred an overall loss of rs . 400 . find the total worth of the stock ?
Options: a ) rs . 25000 , b ) rs . 20000 , c ) rs . 15000 , d ) rs . 22000 , e ) none of these
Rationale: let the total worth of the stock be rs . x . the sp of 20 % of the stock = 1 / 5 * x * 1.1 = 11 x / 50 the sp of 80 % of the stock = 4 / 5 * x * 0.95 = 19 x / 25 = 38 x / 50 total sp = 11 x / 50 + 38 x / 50 = 49 x / 50 overall loss = x - 49 x / 50 = x / 50 x / 50 = 400 = > x = 20000 answer : b
Answer: b
Python program:
a = 5 / 100
b = 100 - 20
c = b / 100
d = a * c
e = 10 / 100
f = 20 / 100
g = e * f
h = d - g
i = 400 / h
Problem: the events a and b are independent , the probability that event a occurs is greater than 0 , and the probability that event a occurs is twice the probability that event b occurs . the probability that at least one of events a and b occurs is 12 times the probability that both events a and b occur . what is the probability that event a occurs ?
Options: a ) 21 / 26 , b ) 25 / 26 , c ) 11 / 26 , d ) 6 / 26 , e ) 22 / 33
Rationale: "let us say probability of a occuring is a . let us say probability of b occuring is b . a = 2 b probability ( either a or b or both ) = 12 times probability ( a and b ) a * ( 1 - b ) + b * ( 1 - a ) + ab = 12 * ab substituting a = 2 b in the second equation : 2 b * ( 1 - b ) + b * ( 1 - 2 b ) + 2 b * b = 12 * 2 b * b 3 b - 2 b ^ 2 = 24 b ^ 2 3 b = 26 b ^ 2 b = 3 / 26 = 3 / 26 so , a = 2 b = 6 / 26 the correct answer is d ."
Answer: d
Python program:
a = 2 + 1 
b = 12 * 2
c = b + 2 
d = a / c
e = d * 2
Problem: a snooker tournament charges $ 40.00 for vip seats and $ 15.00 for general admission ( “ regular ” seats ) . on a certain night , a total of 320 tickets were sold , for a total cost of $ 7,500 . how many fewer tickets were sold that night for vip seats than for general admission seats ?
Options: a ) 212 , b ) 200 , c ) 220 , d ) 230 , e ) 240
Rationale: "let no of sits in vip enclosure is x then x * 40 + 15 ( 320 - x ) = 7500 or 25 x = 7500 - 4800 , x = 2700 / 25 = 108 vip = 108 general 212 a"
Answer: a
Python program:
a = 3 + 4 
b = a * 1000
c = 2 + 3 
d = c * 100
e = b + d 
f = 320 * 15
g = e - f
h = 2 + 3 
i = 2 + 3 
j = h * i
k = g / j
l = 320 - k
Problem: a sum of money is to be divided among ann , bob and chloe . first , ann receives $ 4 plus one - half of what remains . next , bob receives $ 4 plus one - third of what remains . finally , chloe receives the remaining $ 32 . how much money r did bob receive ?
Options: a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 52
Rationale: "notice that we need not consider ann ' s portion in the solution . we can just let k = the money remaining after ann has received her portion and go from there . our equation will use the fact that , once we remove bob ' s portion , we have $ 32 for chloe . so , we getk - bob ' s $ = 32 bob received 4 dollars plus one - third of what remained once bob receives $ 4 , the amount remaining is k - 4 dollars . so , bob gets a 1 / 3 of that as well . 1 / 3 of k - 4 is ( k - 4 ) / 3 so altogether , bob receives 4 + ( k - 4 ) / 3 so , our equation becomes : k - [ 4 + ( k - 4 ) / 3 ] = 32 simplify to get : k - 4 - ( k - 4 ) / 3 = 32 multiply both sides by 3 to get : 3 k - 12 - k + 4 = 96 simplify : 2 k - 8 = 96 solve : k = 52 plug this k - value intok - bob ' s $ = 32 to get : 52 - bob ' s $ = 32 so , bob ' s $ r = 20 answer : b"
Answer: b
Python program:
a = 32 * 2
b = a / 3
Problem: a ’ s speed is 20 / 12 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 / 17 , b ) 3 / 17 , c ) 1 / 10 , d ) 6 / 20 , e ) 3 / 10
Rationale: "we have the ratio of a ’ s speed and b ’ s speed . this means , we know how much distance a covers compared with b in the same time . this is what the beginning of the race will look like : ( start ) a _________ b ______________________________ if a covers 20 meters , b covers 12 meters in that time . so if the race is 20 meters long , when a reaches the finish line , b would be 8 meters behind him . if we want the race to end in a dead heat , we want b to be at the finish line too at the same time . this means b should get a head start of 8 meters so that he doesn ’ t need to cover that . in that case , the time required by a ( to cover 20 meters ) would be the same as the time required by b ( to cover 12 meters ) to reach the finish line . so b should get a head start of 8 / 20 th of the race . answer ( d )"
Answer: d
Python program:
a = 20 - 12
b = a / 20
Problem: a train speeds past a pole in 15 seconds and a platform 130 meters long in 25 seconds . what is the length of the train ( in meters ) ?
Options: a ) 175 , b ) 185 , c ) 195 , d ) 205 , e ) 215
Rationale: "let the length of the train be x meters . the speed of the train is x / 15 . then , x + 130 = 25 * ( x / 15 ) 10 x = 1950 x = 195 meters the answer is c ."
Answer: c
Python program:
a = 2 - 1
b = 130 * a
Problem: calculate the time it will take for a full tank to become completely empty due to a leak given that the tank could be filled in 7 hours , but due to the leak in its bottom it takes 8 hours to be filled ?
Options: a ) 59 hours , b ) 54 hours , c ) 59 hours , d ) 56 hours , e ) 26 hours
Rationale: part filled without leak in 1 hour = 1 / 7 part filled with leak in 1 hour = 1 / 8 work done by leak in 1 hour = 1 / 7 â ˆ ’ 1 / 8 = 56 hours answer : d
Answer: d
Python program:
a = 1 / 7
b = 1 / 8
c = a - b
d = 1/(c)
Problem: a is 2 times as fast as b . a alone can do the work in 20 days . if a and b working together in how many days will the work be completed ?
Options: a ) 23 , b ) 13 , c ) 21 , d ) 24 , e ) 25
Rationale: "a can finish 1 work in 20 days b can finish 1 / 2 work in 20 days - since a is 2 faster than b this means b can finish 1 work in 20 * 2 days = 40 days now using the awesome gmat formula when two machines work together they can finish the job in = ab / ( a + b ) = 20 * 40 / ( 20 + 40 ) = 13 days so answer is b"
Answer: b
Python program:
a = 1 / 20
b = 1 / 20
c = b / 2
d = a + c 
e = 1 / d
Problem: company s produces two kinds of stereos : basic and deluxe . of the stereos produced by company s last month , 2 / 3 were basic and the rest were deluxe . if it takes 1.2 as many hours to produce a deluxe stereo as it does to produce a basic stereo , then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos ?
Options: a ) 3 / 8 , b ) 14 / 31 , c ) 7 / 15 , d ) 17 / 35 , e ) 1 / 2
Rationale: "the easiest way for me is to plug in numbers . let the number of basic stereos produced be 40 , and number of delux stereos produced be 20 . total of 60 stereos . if it takes an hour to produce a basic stereo then it will take 1.2 hours to produce a deluxe stereo . 40 basic stereos = 40 hours . 20 delux stereos = 24 hours . total hours = 64 . then the fraction would be 24 / 64 = 3 / 8 . therefore answer a ."
Answer: a
Python program:
a = 3 + 2 
b = a / 10
Problem: a train leaves mumabai at 9 am at a speed of 30 kmph . after one hour , another train leaves mumbai in the same direction as that of the first train at a speed of 60 kmph . when and at what distance from mumbai do the two trains meet ?
Options: a ) 27 , b ) 279 , c ) 60 , d ) 278 , e ) 379
Rationale: when the second train leaves mumbai the first train covers 30 * 1 = 30 km so , the distance between first train and second train is 30 km at 10.00 am time taken by the trains to meet = distance / relative speed = 30 / ( 60 - 30 ) = 1 hours so , the two trains meet at 11 a . m . the two trains meet 1 * 60 = 60 km away from mumbai . answer : c
Answer: c
Python program:
a = 30 * 1
b = 60 - 30
c = a / b
d = c * 60
Problem: a = 4 ^ 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 2 different values and answer is c . . . ."
Answer: c
Python program:
a = 3 * 4
b = 15 - a
Problem: a envelop weight 8.5 gm , if 800 of these envelop are sent with an advertisement mail . how much wieght ?
Options: a ) 6.6 kg , b ) 6.8 kg , c ) 6.7 kg , d ) 6.9 kg , e ) 7.8 kg
Rationale: "800 * 8.5 6800.0 gm 6.8 kg answer : b"
Answer: b
Python program:
a = 8 * 5
b = a / 1000
Problem: in a city , 35 % of the population is composed of migrants , 20 % of whom are from rural areas . of the local population , 48 % is female while this figure for rural and urban migrants is 30 % and 40 % respectively . if the total population of the city is 728400 , what is its female population ?
Options: a ) 324138 , b ) 248888 , c ) 378908 , d ) 277880 , e ) 379010
Rationale: explanation : total population = 728400 migrants = 35 % of 728400 = 254940 local population = ( 728400 - 254940 ) = 473460 . rural migrants = 20 % of 254940 = 50988 urban migrants = ( 254940 - 50988 ) = 203952 female population = 48 % of 473460 + 30 % of 50988 + 40 % of 203952 = 324138 answer : a
Answer: a
Python program:
a = 728400 * 35
b = a / 100
c = 728400 - b
d = 48 * c
e = d / 100
f = 728400 * 35
g = f / 100
h = g * 20
i = h / 100
j = 30 * i
k = j / 100
l = e + k 
m = 728400 * 35
n = m / 100
o = 728400 * 35
p = o / 100
q = p * 20
r = q / 100
s = n - r
t = 40 * s
u = t / 100
v = l + u
Problem: a batsman scored 120 runs whichincluded 3 boundaries and 8 sixes . what % of his total score did he make by running between the wickets ?
Options: a ) 40 % , b ) 50 % , c ) 65 % , d ) 68 % , e ) 70 %
Rationale: "number of runs made by running = 110 - ( 3 x 4 + 8 x 6 ) = 120 - ( 60 ) = 60 now , we need to calculate 60 is what percent of 120 . = > 60 / 120 * 100 = 50 % b"
Answer: b
Python program:
a = 3 * 4
b = 3 + 3 
c = b * 8
d = a + c 
e = d / 120
f = e * 100
Problem: 397 x 397 + 104 x 104 + 2 x 400 x 104 = x ?
Options: a ) 234341 , b ) 235633 , c ) 234677 , d ) 315656 , e ) 251501
Rationale: "given exp . = ( 397 ) 2 + ( 104 ) 2 + 2 x 397 x 104 = ( 397 + 104 ) 2 = ( 501 ) 2 = ( 500 + 1 ) 2 = ( 5002 ) + ( 1 ) 2 + ( 3 x 500 x 1 ) = 250000 + 1 + 1500 = 251501 e"
Answer: e
Python program:
a = 397 * 397
b = 104 * 104
c = a + b 
d = 2 * 397
e = d * 104
f = c - e
Problem: the events a and b are independent , the probability that event a occurs is greater than 0 , and the probability that event a occurs is twice the probability that event b occurs . the probability that at least one of events a and b occurs is 3 times the probability that both events a and b occur . what is the probability that event a occurs ?
Options: a ) 44 / 7 , b ) 9 / 8 , c ) 25 / 8 , d ) 3 / 4 , e ) 7 / 8
Rationale: "let us say probability of a occuring is a . let us say probability of b occuring is b . a = 2 b probability ( either a or b or both ) = 3 times probability ( a and b ) a * ( 1 - b ) + b * ( 1 - a ) + ab = 3 * ab substituting a = 2 b in the second equation : 2 b * ( 1 - b ) + b * ( 1 - 2 b ) + 2 b * b = 3 * 2 b * b 3 b - 2 b ^ 2 = 6 b ^ 2 3 b = 8 b ^ 2 b = 3 / 8 = 3 / 8 so , a = 2 b = 3 / 4 the correct answer is d ."
Answer: d
Python program:
a = 2 + 1 
b = 3 * 2
c = b + 2 
d = a / c
e = d * 2
Problem: john goes to his office by car at a speed of 40 kmph and reaches 8 minutes earlier . if he goes at a speed of 30 kmph , he reaches 4 mins late . what is the distance from his house to office ?
Options: a ) 18 km , b ) 20 km , c ) 22 km , d ) 24 km , e ) 30 km
Rationale: let his office time be 10 a . m . he reaches office at 8 minutes earlier when he travels at 40 kmph = > he reaches at 9 : 52 a . m he reaches his office 4 minutes late when travels at 30 kmph speed = > he reaches at 10.04 a . m the time difference is ( 10.04 – 9.52 ) = 12 minutes let the distance be d and time = distance speed t 1 – t 2 = 12 minutes = 12 / 60 hours = 1 / 5 hours d / 30 – d / 40 = 1 / 5 ( 4 d - 3 d ) / 120 = 1 / 5 d = 24 km
Answer: d
Python program:
a = 8 + 4 
b = a / const_60
c = 30 * b
d = 40 - 30
e = c / d
f = 40 * e
Problem: a certain list consists of 11 different numbers . if n is in the list and n is 5 times the average ( arithmetic mean ) of the other 10 numbers in the list , then n is what fraction of the sum of the 11 numbers in the list ?
Options: a ) 1 / 3 , b ) 2 / 5 , c ) 1 / 4 , d ) 3 / 5 , e ) 1 / 6
Rationale: "series : a 1 , a 2 . . . . a 10 , n sum of a 1 + a 2 + . . . + a 10 = 10 * x ( x = average ) so , n = 5 * x hence , a 1 + a 2 + . . + a 10 + n = 15 x so , the fraction asked = 5 x / 15 x = 1 / 3 answer is a"
Answer: a
Python program:
a = 1 * 1
b = 10 / 5
c = b + 11 
d = c / 5
e = d * 2
f = e - 5
g = f - 3
h = a / g
Problem: compound interest of rs . 4000 at 10 % per annum for 1 1 / 2 years will be ( interest compounded half yearly ) .
Options: a ) rs . 473 , b ) rs . 374 , c ) rs . 495 , d ) rs . 630 , e ) none of the above
Rationale: 10 % interest per annum will be 5 % interest half yearly for 3 terms ( 1 1 / 2 years ) so compound interest = 4000 [ 1 + ( 5 / 100 ) ] ^ 3 - 4000 = 4000 [ ( 21 / 20 ) ^ 3 - 1 ] = 4000 ( 9261 - 8000 ) / 8000 = 4 * 1261 / 8 = 630 answer : d
Answer: d
Python program:
a = 10 / 2
b = a / 100
c = 1 + b 
d = 1 / 2
e = 1 + d 
f = e * 2
g = c ** f
h = 4000 * g
i = h - 4000
Problem: find the length of the longest pole that can be placed in an indoor stadium 24 m long , 18 m wide and 16 m high
Options: a ) 31 , b ) 32 , c ) 33 , d ) 34 , e ) 35
Rationale: "sqrt ( 1156 ) = 34 becoz max length is cuboid diagonal d = sqrt ( l ^ 2 + b ^ 2 + h ^ 2 ) where l lenght b breadth & h height answer : d"
Answer: d
Python program:
a = 16 ** 2
b = 24 ** 2
c = 18 ** 2
d = b + c 
e = a + d 
f = math.sqrt(e)
Problem: one hour before john started walking from p to q , a distance of 13 miles , ann had started walking along the same road from q to p . ann walked at a constant speed of 3 miles per hour and john at 2 miles per hour . how many miles had ann walked when they met ?
Options: a ) 6 miles , b ) 8,4 miles , c ) 9 miles , d ) 9,6 miles , e ) 12 miles
Rationale: "ann walks from q to p at a speed of 3 miles / hr for one hour . she covers 3 miles in 1 hour and now distance between john and ann is 13 - 3 = 10 miles . ann walks at 3 mph and john at 2 mph so their relative speed is 3 + 2 = 5 mph . they have to cover 10 miles so it will take them 10 / 5 = 2 hours to meet . in 2 hrs , ann would have covered 2 hrs * 3 miles per hour = 6 miles . adding this to the 3 miles she covered before john , ann covered a total of 3 + 6 = 9 miles . answer ( c )"
Answer: c
Python program:
a = 3 + 2 
b = 13 / a
c = b * 2
Problem: sheela deposits rs . 3800 in bank savings account . if this is 22 % of her monthly income . what is her monthly income in ?
Options: a ) 22000 , b ) 20000 , c ) 25123 , d ) 17272 , e ) none of these
Rationale: "explanation : 22 % of income = rs . 3800 100 % of income = 3800 x 100 / 22 = rs . 17272 answer : d"
Answer: d
Python program:
a = 3800 * 100
b = a / 22
Problem: one pipe can fill a pool 1.5 times faster than a second pipe . when both pipes are opened , they fill the pool in four hours . how long would it take to fill the pool if only the slower pipe is used ?
Options: a ) 11.25 , b ) 11.52 , c ) 1.25 , d ) 9 , e ) 10
Rationale: "say the rate of the slower pipe is r pool / hour , then the rate of the faster pipe would be 1.5 r = 3 r / 2 . since when both pipes are opened , they fill the pool in four hours , then their combined rate is 1 / 4 pool / hour . thus we have that r + 3 r / 2 = 1 / 4 - - > r = 1 / 10 pool / hour - - > time is reciprocal of rate thus it ' s 10 / 1 = 10 hours . answer : e ."
Answer: e
Python program:
a = 3 + 2 
b = 1/(a)
c = 1 + 1 
d = b / c
e = 1/(d)
f = e / 1
Problem: 3 photographers , lisa , mike and norm , take photos of a wedding . the total of lisa and mikes photos is 60 less than the sum of mike ' s and norms . if norms photos number 10 more than twice the number of lisa ' s photos , then how many photos did norm take ?
Options: a ) 40 , b ) 50 , c ) 60 , d ) 110 , e ) 80
Rationale: l + m = m + n - 60 / n = 2 l + 10 60 = m + n - l - m 60 = n - l 60 = 2 l + 10 - l 50 = l 2 ( 50 ) + 10 = 110 d
Answer: d
Python program:
a = 60 * 2
b = a - 10
Problem: the time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream . if the speed of the boat in still water is 39 kmph , find the speed of the stream ?
Options: a ) 12 kmph , b ) 13 kmph , c ) 14 kmph , d ) 15 kmph , e ) 16 kmph
Rationale: "the ratio of the times taken is 2 : 1 . the ratio of the speed of the boat in still water to the speed of the stream = ( 2 + 1 ) / ( 2 - 1 ) = 3 / 1 = 3 : 1 speed of the stream = 39 / 3 = 13 kmph answer : b"
Answer: b
Python program:
a = 39 * 2
b = a / 3
c = 39 - b