euclaise/mathqa_programs huggingface dataset:
Problem: 1 / 0.08 is equal to
Options: a ) 25.5 , b ) 2.5 , c ) 12.5 , d ) . 25 , e ) none of these
Rationale: "explanation : 1 / 0.08 = ( 1 * 100 ) / 8 = 100 / 8 = 12.5 option c"
Answer: c
Python program:
a = 1 / 0
Problem: the simple form of the ratio 5 / 8 : 3 / 2 is ?
Options: a ) 5 : 8 , b ) 5 : 5 , c ) 5 : 9 , d ) 5 : 3 , e ) 5 : 1
Rationale: "5 / 8 : 3 / 2 = 5 : 8 answer : a"
Answer: a
Python program:
a = 3 / 2
Problem: a reduction of 40 % in the price of bananas would enable a man to obtain 50 more for rs . 40 , what is reduced price per dozen ?
Options: a ) 1.34 , b ) 2.84 , c ) 3.84 , d ) 4.34 , e ) 5
Rationale: "40 * ( 40 / 100 ) = 16 - - - 50 ? - - - 12 = > rs . 3.84 answer : c"
Answer: c
Python program:
a = 40 / 100
b = 40 * a
c = b / 50
d = 12 * c
Problem: a student traveled 30 percent of the distance of the trip alone , continued another 20 miles with a friend , and then finished the last half of the trip alone . how many miles long was the trip ?
Options: a ) 240 , b ) 200 , c ) 160 , d ) 100 , e ) 50
Rationale: "let x be the total length of the trip . 0.3 x + 20 miles + 0.5 x = x 20 miles = 0.2 x x = 100 miles the answer is d ."
Answer: d
Python program:
a = 1/(30)
b = 1 - a
c = 1 / 2
d = b - c
e = 20 / d
Problem: two pipes a and b can fill a tank in 12 and 24 minutes respectively . if both the pipes are used together , then how long will it take to fill the tank ?
Options: a ) 6 minutes , b ) 8 minutes , c ) 5 minutes , d ) 2 minutes , e ) 7 minutes
Rationale: "required time = 12 * 24 / 12 + 12 = 12 * 24 / 36 = 24 / 3 = 8 minutes answer : b"
Answer: b
Python program:
a = 12 * 100
b = 1 / 12
c = 1 / 24
d = b + c 
e = d * 2
f = 1 - e
g = f * 12
h = g * const_60
i = a + h
Problem: the price of a jacket is reduced by 25 % . during a special sale the price of the jacket is reduced another 10 % . by approximately what percent must the price of the jacket now be increased in order to restore it to its original amount ?
Options: a ) 32.5 , b ) 35 , c ) 48 , d ) 65 , e ) 67.5
Rationale: "1 ) let the price of jacket initially be $ 100 . 2 ) then it is decreased by 25 % , therefore bringing down the price to $ 75 . 3 ) again it is further discounted by 10 % , therefore bringing down the price to $ 67.5 . 4 ) now 67.5 has to be added by x % in order to equal the original price . 67.5 + ( x % ) 67.5 = 100 . solving this eq for x , we get x = 48.1 answer is c ."
Answer: c
Python program:
a = 100 - 25
b = 100 - 25
c = 10 / 100
d = b * c
e = a - d
f = 100 - e
g = 100 - 25
h = 100 - 25
i = 10 / 100
j = h * i
k = g - j
l = f / k
m = 100 * l
Problem: a man whose speed is 3.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph , find his average speed for the total journey ?
Options: a ) 2.0 , b ) 2.5 , c ) 3.0 , d ) 2.1 , e ) 4.0
Rationale: "m = 3.5 s = 1.5 ds = 5 us = 2 as = ( 2 * 5 * 2 ) / 5 = 4 answer : e"
Answer: e
Python program:
a = 3 - 5
b = 3 + 5 
c = b / 2
Problem: if a , b , c , and d are integers ; w , x , y , and z are prime numbers ; w < x < y < z ; and ( wa ) ( xb ) ( yc ) ( zd ) = 660 ( wa ) ( xb ) ( yc ) ( zd ) = 660 , what is the value of ( a + b ) – ( c + d ) ?
Options: a ) – 1 , b ) 0 , c ) 1 , d ) 2 , e ) 3
Rationale: 660660 = 2 ^ 2 x 3 ^ 1 x 5 ^ 1 x 11 ^ 1 w < x < y < z = 2 < 3 < 5 < 11 so , can can say - w = 2 x = 3 y = 5 z = 11 hence a = 2 , b = c = d = 1 ( a + b ) – ( c + d ) will be ( 2 + 1 ) – ( 1 + 1 ) = 1 answer will be ( c )
Answer: c
Python program:
a = 3 + 4 
b = a + 4 
c = 660 / b
d = c / 10
e = d / 2
f = e - 2
Problem: a man gains 50 % by selling an article for a certain price . if he sells it at double the price , the percentage of profit will be .
Options: a ) 130 % , b ) 300 % , c ) 150 % , d ) 160 % , e ) 170 %
Rationale: explanation : let the c . p . = x , then s . p . = ( 150 / 100 ) x = 3 x / 2 new s . p . = 2 ( 3 x / 2 ) = 3 x / 1 profit = 3 x / 1 - x = 3 x / 1 profit % = ( profit / c . p . ) * 100 = > ( 3 x / 1 ) * ( 1 / x ) * 100 = 300 % option b
Answer: b
Python program:
a = 50 / 100
b = 1 + a 
c = b * 2
d = c - 1
e = d * 100
f = e + 100
Problem: | 14 - 5 | - | 8 - 12 | = ?
Options: a ) 3 , b ) 2 , c ) 1 , d ) 5 , e ) 4
Rationale: | 14 - 5 | - | 8 - 12 | = | 9 | - | - 4 | = 9 - 4 = 5 correct answer d
Answer: d
Python program:
a = 14 - 5
b = 12 - 8
c = a - b
Problem: in kaya ' s teacher ' s desk there are 3 pink highlighters , 7 yellow highlighters , and 5 blue highlighters . how many highlighters are there in all ?
Options: a ) 11 , b ) 15 , c ) 77 , d ) 33 , e ) 88
Rationale: "add the numbers of highlighters . 3 + 7 + 5 = 15 . answer is b ."
Answer: b
Python program:
a = 3 + 7 
b = a + 5
Problem: the sum of all the digits of the integers from 18 to 21 inclusive is 24 ( 1 + 8 + 1 + 9 + 2 + 0 + 2 + 1 = 24 ) . what is the sum w of all the digits of the integers from 0 to 99 inclusive ?
Options: a ) 450 , b ) 810 , c ) 900 , d ) 1000 , e ) 1100
Rationale: "we want the sum of the digits from 0 to 99 , so i approximated : 0 - 9 - > 45 - > ( 9 + 0 ) * 10 / 2 40 - 49 - > 85 ( 13 + 4 ) * 10 / 2 90 - 99 - > 135 ( 18 + 9 ) * 10 / 2 we can see at a glance that theweightgoes up as the numbers go up ( meaning the difference between 85 and 45 is 40 , while 135 - 85 is 50 , this means that the second part of this sequence carries more weight for our result ) , so we know that the final answer has to be more than 850 ( 85 * 10 ) but close to it , and that ' s just w = 900 : the answer is c ."
Answer: c
Python program:
a = 9 + 1 
b = 9 * a
c = b / 2
d = 2 * 10
e = c * d
Problem: the difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4 % per annum is rs 1 . find the sum
Options: a ) rs 600 , b ) rs 625 , c ) rs 650 , d ) rs 675 , e ) none of these
Rationale: explanation : let the sum be p s . i . = p ∗ 4 ∗ 2 / 100 = 2 p / 25 c . i . = p ( 1 + 4 / 100 ) 2 − p = 676 p / 625 − p = 51 p / 625 as , c . i . - s . i = 1 = > 51 p / 625 − 2 p / 25 = 1 = > 51 p − 50 p / 625 = 1 p = 625 option b
Answer: b
Python program:
a = 4 / 100
b = a ** 2
c = b * 1
d = 1/(c)
Problem: the banker ' s gain on a bill due due 1 year hence at 12 % per annum is rs . 8.4 . the true discount is
Options: a ) rs . 70 , b ) rs . 36 , c ) rs . 54 , d ) rs . 50 , e ) none
Rationale: "solution t . d = [ b . g x 100 / r x t ] = rs . ( 8.4 x 100 / 12 x 1 ) = rs . 70 . answer a"
Answer: a
Python program:
a = 12 / 100
b = 8 / 4
Problem: in a basketball game , tim scored 20 points more than joe , but only half as many points as ken . if the 3 players scored a combined total of 100 points , how many points did tim score ?
Options: a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 45
Rationale: let joe scored point = x then tim scored = x + 20 ken scored = 2 * ( x + 20 ) = 2 x + 40 as given , x + x + 20 + 2 x + 40 = 100 points 4 x + 60 = 100 x = 100 - 60 / 4 = 10 so tim scored = x + 20 i . e ) 10 + 20 = 30 answer : d
Answer: d
Python program:
a = 20 * 3
b = a / 2
Problem: if taxi fares were $ 2.00 for the first 1 / 5 mile and $ 0.60 for each 1 / 5 mile there after , then the taxi fare for a 8 - mile ride was
Options: a ) $ 2.40 , b ) $ 25.20 , c ) $ 25.40 , d ) $ 25.60 , e ) $ 25.50
Rationale: "in 8 miles , initial 1 / 5 mile charge is $ 2 rest of the distance = 8 - ( 1 / 5 ) = 39 / 5 rest of the distance charge = 39 ( 0.6 ) = $ 23.4 ( as the charge is 0.6 for every 1 / 5 mile ) = > total charge for 4 miles = 2 + 23.4 = 25.4 answer is c"
Answer: c
Python program:
a = 1 / 5
b = 2 / 0
c = b - 1
d = c * 0
e = 2 + 0
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 670 then loss of pyarelal ?
Options: a ) 603 , b ) 703 , c ) 800 , d ) 903 , 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 670 , loss of pyarelal = 670 * 9 x / 10 x = 603 answer : a"
Answer: a
Python program:
a = 9 * 670
b = 1 + 9 
c = a / b
Problem: 40 % of the population of a village is 23040 . the total population of the village is ?
Options: a ) 57600 , b ) 44000 , c ) 34936 , d ) 25640 , e ) none
Rationale: "answer ∵ 40 % of p = 23040 ∴ p = ( 23040 x 100 ) / 40 = 57600 correct option : a"
Answer: a
Python program:
a = 100 / 40
b = a * 23040
Problem: what distance will be covered by a bus moving at 54 kmph in 30 seconds ?
Options: a ) 287 , b ) 900 , c ) 289 , d ) 276 , e ) 207
Rationale: "54 kmph = 54 * 5 / 18 = 30 mps d = speed * time = 30 * 30 = 900 m . answer : b"
Answer: b
Python program:
a = 54 * const_0_2778
b = a * 30
Problem: if ( 1 / 2 ) ^ 22 ( 1 / 81 ) ^ k = 1 / 18 ^ 22 , then k =
Options: a ) 8 , b ) 12 , c ) 16 , d ) 24 , e ) 11
Rationale: i ' m going to focus on denominator only . . ( 2 ^ 22 ) . ( ( 3 ^ 4 ) ^ k = 18 ^ 22 ( 2 ^ 22 ) . ( ( 3 ^ 4 k ) = ( 2 . 3 ^ 2 ) ^ 22 ( 2 ^ 22 ) . ( ( 3 ^ 4 k ) = ( 2 ^ 24 ) . ( 3 ^ 2 ) ^ 22 hence 4 k = 44 k = 11 answer e i hope it ' s quite clear
Answer: e
Python program:
a = 22 * 2
b = a / 4
Problem: two pipes a and b can separately fill a tank in 10 and 15 minutes respectively . a third pipe c can drain off 45 liters of water per minute . if all the pipes are opened , the tank can be filled in 15 minutes . what is the capacity of the tank ?
Options: a ) 450 , b ) 540 , c ) 542 , d ) 829 , e ) 279
Rationale: "1 / 10 + 1 / 15 - 1 / x = 1 / 15 x = 10 10 * 45 = 450 answer : a"
Answer: a
Python program:
a = 1 / 10
b = 1 / 15
c = a + b 
d = 1 / 45
e = c + d 
f = 1 / 15
g = e - f
h = 1/(g)
i = h * 3
j = i * 15
Problem: a cube of edge 17 cm is immersed completely in a rectangular vessel containing water . if the dimensions of the base of vessel are 20 cm * 15 cm , find the rise in water level ?
Options: a ) 6 cm , b ) 8.25 cm , c ) 11.25 cm , d ) 16.37 cm , e ) 20.62 cm
Rationale: "increase in volume = volume of the cube = 17 * 17 * 17 cm ^ 3 rise in water level = volume / area = 17 * 17 * 17 / 20 * 15 = 16.37 cm answer is d"
Answer: d
Python program:
a = volume_cube / (
Problem: find the simple interest on rs . 520 for 7 months at 8 paisa per month ?
Options: a ) 277 , b ) 270 , c ) 291 , d ) 266 , e ) 121
Rationale: "i = ( 520 * 7 * 8 ) / 100 = 291 answer : c"
Answer: c
Python program:
a = 7 / 100
b = 520 * a
Problem: a person incurs 10 % loss by selling a laptop for $ 900 . at what price should the watch be sold to earn 10 % profit ?
Options: a ) 1200 , b ) 1000 , c ) 1100 , d ) 1050 , e ) 1250
Rationale: "let the new s . p . = x then ( 100 - loss % ) : ( 1 st s . p . ) = ( 100 + gain % ) : ( 2 nd s . p . ) ( 100 - 10 ) / 900 = ( 100 + 10 ) / x x = 110 * 900 / 90 = 1100 new price = $ 1100 correct option is c"
Answer: c
Python program:
a = 10 / 100
b = 1 - a
c = 900 / b
Problem: product of two natural numbers is 11 . then , the sum of reciprocals of their squares is
Options: a ) 290 / 289 , b ) 122 / 121 , c ) 290 / 90 , d ) 290 / 19 , e ) none of these
Rationale: "explanation : if the numbers are a , b , then ab = 17 , as 17 is a prime number , so a = 1 , b = 17 . 1 / a 2 + 1 / b 2 = 1 / 1 ( 2 ) + 1 / 11 ( 2 ) = 122 / 121 option b"
Answer: b
Python program:
a = 1 / 1
b = a ** 2
c = 1 / 11
d = c ** 2
e = b + d
Problem: a survey of employers found that during 1993 employment costs rose 3.5 percent , where employment costs consist of salary costs and fringe - benefit costs . if salary costs rose 3 percent and fringe - benefit costs rose 4.5 percent during 1993 , then fringe - benefit costs represented what percent of employment costs at the beginning of 1993 ?
Options: a ) 16.5 % , b ) 20 % , c ) 33 % , d ) 55 % , e ) 65 %
Rationale: "the amount by which employment costs rose is equal to 0.035 ( salary costs + fringe benefit costs ) ; on the other hand the amount by which employment costs rose is equal to 0.03 * salary costs + 0.045 * fringe benefit costs ; so , 35 ( s + f ) = 30 s + 45 f - - > s = 2 f - - > f / s = 1 / 2 - - > f / ( s + f ) = 1 / ( 1 + 2 ) = 1 / 3 = 0.33 . answer : c ."
Answer: c
Python program:
a = 3 - 5
b = 4 - 5
c = a / b
d = c * 100
Problem: sandy gets 3 marks for each correct sum and loses 2 marks for each incorrect sum . sandy attempts 30 sums and obtains 45 marks . how many sums did sandy get correct ?
Options: a ) 18 , b ) 21 , c ) 24 , d ) 27 , e ) 28
Rationale: let x be the correct sums and ( 30 - x ) be the incorrect sums . 3 x - 2 ( 30 - x ) = 45 5 x = 105 x = 21 the answer is b .
Answer: b
Python program:
a = 2 * 30
b = a + 45 
c = 2 + 3 
d = b / c
Problem: bruce and anne can clean their house in 4 hours working together at their respective constant rates . if anne ’ s speed were doubled , they could clean their house in 3 hours working at their respective rates . how many q hours does it currently take anne to clean the house on her own ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 12 , e ) 14
Rationale: "lets suppose anne and bruce take a and b hrs working separately so in 1 hour they can together finish 1 / a + 1 / b portion of the work which equals 1 / 4 ( as the work is completed in 4 hours ) after anne doubles her rate of work the portion completed by the both is 1 / a + 2 / b which is equal to q = 1 / 3 ( as the work is completed in q = 3 hours ) solving these 2 equations we can find b as 12 so , d"
Answer: d
Python program:
a = 1 / 3
b = 1 / 4
c = a - b
d = 1/(c)
Problem: if the average ( arithmetic mean ) of a and b is 160 , and c – a = 200 , what is the average of b and c ?
Options: a ) 260 , b ) 250 , c ) 150 , d ) 225 , e ) 325
Rationale: "a + b / 2 = 160 = > a + b = 320 a = c - 200 . . . sub this value c - 200 + b = 320 = > c + b = 520 = > c + b / 2 = 260 answer : a"
Answer: a
Python program:
a = 200 * 2
b = 160 * 2
c = a - b
Problem: the sum of all the integers k such that – 24 < k < 24 is
Options: a ) 0 , b ) - 2 , c ) - 45 , d ) - 49 , e ) - 51
Rationale: "- 23 - - - - - - - - - - - - - - - - - - 0 - - - - - - - - - - - - - - - - - 23 values upto + 23 cancels outwe are left with only - 23 - 22 sum of which is - 45 . hence option d . c"
Answer: c
Python program:
a = negate + ( 
b = a + 1
Problem: a student is ranked 21 th from right and 11 th from left . how many students are there in totality ?
Options: a ) 18 , b ) 19 , c ) 20 , d ) 31 , e ) 22
Rationale: "from right 21 , from left 11 total = 21 + 11 - 1 = 31 answer : d"
Answer: d
Python program:
a = 21 + 11 
b = a - 1
Problem: the h . c . f . of two numbers is 23 and the other two factors of their l . c . m . are 13 and 19 . the larger of the two numbers is :
Options: a ) 437 , b ) 299 , c ) 322 , d ) 345 , e ) 355
Rationale: "clearly , the numbers are ( 23 x 13 ) and ( 23 x 19 ) . larger number = ( 23 x 19 ) = 437 . answer : option a"
Answer: a
Python program:
a = 23 * 19
Problem: linda spent 3 / 4 of her savings on furniture and the rest on a tv . if the tv cost her $ 240 , what were her original savings ?
Options: a ) $ 900 , b ) $ 800 , c ) $ 960 , d ) $ 700 , e ) $ 1500
Rationale: "if linda spent 3 / 4 of her savings on furnitute , the rest 4 / 4 - 3 / 4 = 1 / 4 on a tv but the tv cost her $ 240 . so 1 / 4 of her savings is $ 240 . so her original savings are 4 times $ 240 = $ 960 correct answer c"
Answer: c
Python program:
a = 3 / 4
b = 1 - a
c = 240 / b
Problem: how many seconds will a 800 m long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?
Options: a ) 11 , b ) 30 , c ) 99 , d ) 48 , e ) 61
Rationale: speed of train relative to man = 63 - 3 = 60 km / hr . = 60 * 5 / 18 = 50 / 3 m / sec . time taken to pass the man = 800 * 3 / 50 = 48 sec . answer : d
Answer: d
Python program:
a = 63 - 3
b = a * const_0_2778
c = 800 / b
Problem: a man cheats while buying as well as while selling . while buying he takes 10 % more than what he pays for and while selling he gives 20 % less than what he claims to . find the profit percent , if he sells at 13 % below the cost price of the claimed weight .
Options: a ) 19.63 % , b ) 20 % , c ) 37.5 % , d ) 25 % , e ) 37.5 %
Rationale: "there is a one step calculation method too . it requires more thought but is faster . the man takes 10 % more than what he pays for . so if he claims to take 100 pounds , he pays $ 100 but he actually takes 110 pounds for which he will take from the customer $ 110 . hence , in effect , there is a 10 % mark up . while selling , he sells 20 % less . this means , he claims to sell 100 pounds and gets $ 100 but actually sells only 80 pounds and should have got only $ 80 for it . so this is again a mark up of $ 20 on $ 80 which is 25 % . but he also sells at 13 % less ( 1 + m 1 % ) ( 1 + m 2 % ) ( 1 - d % ) = ( 1 + p % ) 11 / 10 * 5 / 4 * 87 / 100 = ( 1 + p % ) profit % = 19.63 % a"
Answer: a
Python program:
a = 100 + 10 
b = 100 - 20
c = 13 + b 
d = a - c
e = d * 2
Problem: if log 64 = 1.8061 , then the value of log 16 will be ( approx ) ?
Options: a ) 1.204 , b ) 1.9874 , c ) 1.3564 , d ) 1.2547 , e ) 1.6547
Rationale: "log 64 = 1.8061 log 4 ^ 3 = 1.8061 log 4 = 0.6020 2 log 4 = 1.2040 log 4 ^ 2 = 1.2040 log 16 = 1.2040 ( approx ) answer a"
Answer: a
Python program:
a = 4 * 1
b = math.log(100)
c = math.log(10)
d = b / c
e = a + d
Problem: the student manager of the university theater estimated that for every 6 movie tickets sold on valentine ' s weekend , the theater will sell 3 packs of grain crackers at $ 2.25 each , 4 bottles of a beverage at $ 1.50 each , and 4 chocolate bars at $ 1.00 each . find the approximate average ( arithmetic mean ) amount of estimated snack sales per movie ticket sold .
Options: a ) $ 1.40 , b ) $ 1.58 , c ) $ 2.00 , d ) $ 2.64 , e ) $ 2.79
Rationale: 3 * 2.25 + 4 * 1.50 + 4 * 1 = 6.75 + 6 + 4 = 16.75 . this is the sale for 6 tickets avg sale per ticket : 16.75 / 6 = $ 2 . 79 answer : e
Answer: e
Python program:
a = 3 * 2
b = 4 * 1
c = a + b 
d = 4 * 1
e = c + d 
f = e / 6
Problem: the sum of the ages of 5 children born at the intervals of 4 years each is 50 years . what is the age of the eldest child ?
Options: a ) 15 , b ) 8 , c ) 18 , d ) none of these , e ) can not be determined
Rationale: "explanation : let x = the youngest child . each of the other four children will then be x + 4 , x + 8 , x + 12 , x + 16 . we know that the sum of their ages is 50 . so , x + ( x + 4 ) + ( x + 8 ) + ( x + 12 ) + ( x + 16 ) = 50 x = 2 the youngest child is 2 years old . age of eldest child is = 2 + 16 = 18 answer : c"
Answer: c
Python program:
a = 5 / 4
b = 50 / a
c = 5 - 1
d = c * 4
e = b - d
f = e / 4
Problem: a 28 cm long wire is to be cut into two pieces so that one piece will be 2.00001 / 5 th of the other , how many centimeters will the shorter piece be ?
Options: a ) 12 , b ) 8 , c ) 88 , d ) 77 , e ) 14
Rationale: "1 : 2 / 5 = 5 : 2 2 / 7 * 28 = 8 answer : b"
Answer: b
Python program:
a = 2 / 1
b = a + 1 
c = 28 / b
d = 28 - c
Problem: eighteen years ago , a father was 3 times as old as his son . now the father is only twice as old as his son . then the sum of the present ages of the son and the father is :
Options: a ) 120 , b ) 76 , c ) 108 , d ) 105 , e ) 86
Rationale: let the present ages of the father and son be 2 x and x years respectively . then , ( 2 x - 18 ) = 3 ( x - 18 ) x = 36 . required sum = ( 2 x + x ) = 3 x = 108 years . answer is c
Answer: c
Python program:
a = 2 * 3
b = a * 3
c = b * 3
d = 2 * 3
e = d * 3
f = c - e
g = 2 * 3
h = g * 3
i = h * 3
j = 2 * 3
k = j * 3
l = i - k
m = l * 2
n = f + m
Problem: the banker ' s gain on a sum due 6 years hence at 12 % per annum is rs . 828 . what is the banker ' s discount ?
Options: a ) 1240 , b ) 1120 , c ) 1190 , d ) 1978 , e ) none of these
Rationale: "explanation : td = ( bg × 100 ) / tr = ( 828 × 100 ) / ( 6 × 12 ) = rs . 1150 bg = bd – td = > 828 = bd - 1150 = > bd = 1978 answer : option d"
Answer: d
Python program:
a = 828 * 100
b = 12 * 6
c = a / b
d = 828 + c
Problem: a runner runs the 40 miles from marathon to athens at a constant speed . halfway through the run she injures her foot , and continues to run at half her previous speed . if the second half takes her 12 hours longer than the first half , how many hours did it take the runner to run the second half ?
Options: a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 28
Rationale: "the runner runs the first 20 miles at speed v and the second 20 miles at speed v / 2 . the time t 2 to run the second half must be twice the time t 1 to run the first half . t 2 = 2 * t 1 = t 1 + 12 t 1 = 12 and so t 2 = 24 . the answer is c ."
Answer: c
Python program:
a = 40 / 2
b = a / 12
c = 40 / b
Problem: the racing magic takes 40 seconds to circle the racing track once . the charging bull makes 40 rounds of the track in an hour . if they left the starting point together , how many minutes will it take for them to meet at the starting point for the second time ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: "time taken by racing magic to make one circle = 40 seconds time taken bycharging bullto make one circle = 60 mins / 40 = 1.5 mins = 90 seconds lcm of 90 and 40 seconds = 360 seconds = 6 mins time taken for them to meet at the starting point for the second time = 6 mins * 2 = 12 mins answer d"
Answer: d
Python program:
a = 40 / 40
b = 40 * a
c = b * 2
d = c / 40
e = d * 2
Problem: every day daniel drives 96 miles back from work . on sunday , daniel drove all the way back from work at a constant speed of x miles per hour . on monday , daniel drove the first 32 miles back from work at ( 2 x ) miles per hour , and the rest of the way at ( x / 2 ) miles per hour . the time it took daniel to drive back from work on monday is longer than the time it took him to drive back from work on sunday by what percent ?
Options: a ) 10 % , b ) 20 % , c ) 30 % , d ) 40 % , e ) 50 %
Rationale: "let ' s test x = 4 . . . . on sunday , daniel drove 96 miles at 4 miles / hour . d = ( r ) ( t ) 96 = ( 4 ) ( t ) 96 / 4 = 24 = t it takes 24 hours to drive home on monday , daniel drove the first 32 miles at ( 2 ) ( 4 ) = 8 miles / hour and the rest of the way ( 64 miles ) at 4 / 2 = 2 miles / hour d = ( r ) ( t ) 32 = ( 8 ) ( t ) 32 / 8 = 4 = t it takes 4 hours for the first part d = ( r ) ( t ) 64 = ( 2 ) ( t ) 64 / 2 = 32 = t it takes 32 hours for the second part total time to drive home on monday = 4 + 32 = 36 hours we ' re asked by what percent 36 hours is greater than 32 hours . 36 / 32 = 1.5 , so it is 50 % greater . e"
Answer: e
Python program:
a = 32 / 2
b = 96 - 32
c = b * 2
d = a + c 
e = d - 96
f = e / 96
g = f * 100
Problem: a train running at the speed of 108 km / hr crosses a pole in 7 seconds . find the length of the train .
Options: a ) 150 meter , b ) 145 meter , c ) 140 meter , d ) 135 meter , e ) 210 meter
Rationale: "explanation : speed = 108 * ( 5 / 18 ) m / sec = 30 m / sec length of train ( distance ) = speed * time = 30 * 7 = 210 meter option e"
Answer: e
Python program:
a = 108 * 1000
b = a / 3600
c = b * 7
Problem: a train crosses a bridge of length 2500 m in 120 seconds and a lamp post on the bridge in 30 seconds . what is the length of the train in metres ?
Options: a ) 375 m , b ) 750 / 3 m , c ) 2500 / 3 m , d ) 800 m , e ) 300 m
Rationale: "let length of train = l case - 1 : distance = 2500 + l ( while crossing the bridge ) time = 120 seconds i . e . speed = distance / time = ( 2500 + l ) / 120 case - 2 : distance = l ( while passing the lamp post ) time = 30 seconds i . e . speed = distance / time = ( l ) / 30 but since speed has to be same in both cases so ( 2500 + l ) / 120 = ( l ) / 30 i . e . 4 l = 2500 + l i . e . 3 l = 2500 i . e . l = 2500 / 3 answer : option c"
Answer: c
Python program:
a = 120 - 30
b = 2500 / a
c = b * 30
Problem: find the sum of all odd number upto 250 .
Options: a ) 15345 , b ) 15645 , c ) 15625 , d ) 15342 , e ) 15683
Rationale: "explanation : number of odd numbers upto 250 = n / 2 = 250 / 2 = 125 sum of first 125 odd numbers = ( 125 ) 2 = 15625 answer : option c"
Answer: c
Python program:
a = 250 / 2
b = a / 2
c = b / 2
d = c / 2
e = d / 2
f = 250 / e
g = f / 2
h = 250 / 2
i = h / 2
j = i / 2
k = j / 2
l = k / 2
m = 250 / l
n = m / 2
o = math.sqrt(n)
p = 1 + o 
q = g + p